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_ZGVsMxv_tan; } + GLIBC_2.40 { + _ZGVnN2v_erf; + _ZGVnN2v_erff; + _ZGVnN4v_erff; + _ZGVsMxv_erf; + _ZGVsMxv_erff; + } } diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index 8fec7a4b44..d8d88de218 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -21,6 +21,7 @@ libmvec_hidden_proto (V_NAME_F1(acos)); libmvec_hidden_proto (V_NAME_F1(asin)); libmvec_hidden_proto (V_NAME_F1(atan)); libmvec_hidden_proto (V_NAME_F1(cos)); +libmvec_hidden_proto (V_NAME_F1(erf)); libmvec_hidden_proto (V_NAME_F1(exp10)); libmvec_hidden_proto (V_NAME_F1(exp2)); libmvec_hidden_proto (V_NAME_F1(exp)); diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 04837bdcd7..71f53363a0 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -49,6 +49,10 @@ # define __DECL_SIMD_cos __DECL_SIMD_aarch64 # undef __DECL_SIMD_cosf # define __DECL_SIMD_cosf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_erf +# define __DECL_SIMD_erf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_erff +# define __DECL_SIMD_erff __DECL_SIMD_aarch64 # undef __DECL_SIMD_exp # define __DECL_SIMD_exp __DECL_SIMD_aarch64 # undef __DECL_SIMD_expf @@ -120,6 +124,7 @@ __vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_erff (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_exp2f (__f32x4_t); @@ -136,6 +141,7 @@ __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_erf (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp2 (__f64x2_t); @@ -157,6 +163,7 @@ __sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_erff (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_exp2f (__sv_f32_t, __sv_bool_t); @@ -173,6 +180,7 @@ __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_erf (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp2 (__sv_f64_t, __sv_bool_t); diff --git a/sysdeps/aarch64/fpu/erf_advsimd.c b/sysdeps/aarch64/fpu/erf_advsimd.c new file mode 100644 index 0000000000..3e70cbc025 --- /dev/null +++ b/sysdeps/aarch64/fpu/erf_advsimd.c @@ -0,0 +1,161 @@ +/* Double-precision vector (Advanced SIMD) erf function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" + +static const struct data +{ + float64x2_t third; + float64x2_t tenth, two_over_five, two_over_fifteen; + float64x2_t two_over_nine, two_over_fortyfive; + float64x2_t max, shift; +#if WANT_SIMD_EXCEPT + float64x2_t tiny_bound, huge_bound, scale_minus_one; +#endif +} data = { + .third = V2 (0x1.5555555555556p-2), /* used to compute 2/3 and 1/6 too. */ + .two_over_fifteen = V2 (0x1.1111111111111p-3), + .tenth = V2 (-0x1.999999999999ap-4), + .two_over_five = V2 (-0x1.999999999999ap-2), + .two_over_nine = V2 (-0x1.c71c71c71c71cp-3), + .two_over_fortyfive = V2 (0x1.6c16c16c16c17p-5), + .max = V2 (5.9921875), /* 6 - 1/128. */ + .shift = V2 (0x1p45), +#if WANT_SIMD_EXCEPT + .huge_bound = V2 (0x1p205), + .tiny_bound = V2 (0x1p-226), + .scale_minus_one = V2 (0x1.06eba8214db69p-3), /* 2/sqrt(pi) - 1.0. */ +#endif +}; + +#define AbsMask 0x7fffffffffffffff + +struct entry +{ + float64x2_t erf; + float64x2_t scale; +}; + +static inline struct entry +lookup (uint64x2_t i) +{ + struct entry e; + float64x2_t e1 = vld1q_f64 ((float64_t *) (__erf_data.tab + i[0])), + e2 = vld1q_f64 ((float64_t *) (__erf_data.tab + i[1])); + e.erf = vuzp1q_f64 (e1, e2); + e.scale = vuzp2q_f64 (e1, e2); + return e; +} + +/* Double-precision implementation of vector erf(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/128. + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + + erf(x) ~ erf(r) + scale * d * [ + + 1 + - r d + + 1/3 (2 r^2 - 1) d^2 + - 1/6 (r (2 r^2 - 3)) d^3 + + 1/30 (4 r^4 - 12 r^2 + 3) d^4 + - 1/90 (4 r^4 - 20 r^2 + 15) d^5 + ] + + Maximum measure error: 2.29 ULP + V_NAME_D1 (erf)(-0x1.00003c924e5d1p-8) got -0x1.20dd59132ebadp-8 + want -0x1.20dd59132ebafp-8. */ +float64x2_t VPCS_ATTR V_NAME_D1 (erf) (float64x2_t x) +{ + const struct data *dat = ptr_barrier (&data); + + float64x2_t a = vabsq_f64 (x); + /* Reciprocal conditions that do not catch NaNs so they can be used in BSLs + to return expected results. */ + uint64x2_t a_le_max = vcleq_f64 (a, dat->max); + uint64x2_t a_gt_max = vcgtq_f64 (a, dat->max); + +#if WANT_SIMD_EXCEPT + /* |x| huge or tiny. */ + uint64x2_t cmp1 = vcgtq_f64 (a, dat->huge_bound); + uint64x2_t cmp2 = vcltq_f64 (a, dat->tiny_bound); + uint64x2_t cmp = vorrq_u64 (cmp1, cmp2); + /* If any lanes are special, mask them with 1 for small x or 8 for large + values and retain a copy of a to allow special case handler to fix special + lanes later. This is only necessary if fenv exceptions are to be triggered + correctly. */ + if (__glibc_unlikely (v_any_u64 (cmp))) + { + a = vbslq_f64 (cmp1, v_f64 (8.0), a); + a = vbslq_f64 (cmp2, v_f64 (1.0), a); + } +#endif + + /* Set r to multiple of 1/128 nearest to |x|. */ + float64x2_t shift = dat->shift; + float64x2_t z = vaddq_f64 (a, shift); + + /* Lookup erf(r) and scale(r) in table, without shortcut for small values, + but with saturated indices for large values and NaNs in order to avoid + segfault. */ + uint64x2_t i + = vsubq_u64 (vreinterpretq_u64_f64 (z), vreinterpretq_u64_f64 (shift)); + i = vbslq_u64 (a_le_max, i, v_u64 (768)); + struct entry e = lookup (i); + + float64x2_t r = vsubq_f64 (z, shift); + + /* erf(x) ~ erf(r) + scale * d * poly (r, d). */ + float64x2_t d = vsubq_f64 (a, r); + float64x2_t d2 = vmulq_f64 (d, d); + float64x2_t r2 = vmulq_f64 (r, r); + + /* poly (d, r) = 1 + p1(r) * d + p2(r) * d^2 + ... + p5(r) * d^5. */ + float64x2_t p1 = r; + float64x2_t p2 + = vfmsq_f64 (dat->third, r2, vaddq_f64 (dat->third, dat->third)); + float64x2_t p3 = vmulq_f64 (r, vfmaq_f64 (v_f64 (-0.5), r2, dat->third)); + float64x2_t p4 = vfmaq_f64 (dat->two_over_five, r2, dat->two_over_fifteen); + p4 = vfmsq_f64 (dat->tenth, r2, p4); + float64x2_t p5 = vfmaq_f64 (dat->two_over_nine, r2, dat->two_over_fortyfive); + p5 = vmulq_f64 (r, vfmaq_f64 (vmulq_f64 (v_f64 (0.5), dat->third), r2, p5)); + + float64x2_t p34 = vfmaq_f64 (p3, d, p4); + float64x2_t p12 = vfmaq_f64 (p1, d, p2); + float64x2_t y = vfmaq_f64 (p34, d2, p5); + y = vfmaq_f64 (p12, d2, y); + + y = vfmaq_f64 (e.erf, e.scale, vfmsq_f64 (d, d2, y)); + + /* Solves the |x| = inf and NaN cases. */ + y = vbslq_f64 (a_gt_max, v_f64 (1.0), y); + + /* Copy sign. */ + y = vbslq_f64 (v_u64 (AbsMask), y, x); + +#if WANT_SIMD_EXCEPT + if (__glibc_unlikely (v_any_u64 (cmp2))) + { + /* Neutralise huge values of x before fixing small values. */ + x = vbslq_f64 (cmp1, v_f64 (1.0), x); + /* Fix tiny values that trigger spurious underflow. */ + return vbslq_f64 (cmp2, vfmaq_f64 (x, dat->scale_minus_one, x), y); + } +#endif + return y; +} diff --git a/sysdeps/aarch64/fpu/erf_data.c b/sysdeps/aarch64/fpu/erf_data.c new file mode 100644 index 0000000000..6d2dcd235c --- /dev/null +++ b/sysdeps/aarch64/fpu/erf_data.c @@ -0,0 +1,800 @@ +/* Table for Advanced SIMD erf approximation + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "vecmath_config.h" + +/* Lookup table used in erf. + For each possible rounded input r (multiples of 1/128), between + r = 0.0 and r = 6.0 (769 values): + - the first entry __erff_data.tab.erf contains the values of erf(r), + - the second entry __erff_data.tab.scale contains the values of + 2/sqrt(pi)*exp(-r^2). Note that indices 0 and 1 are never hit by the + algorithm, since lookup is performed only for x >= 1/64-1/512. */ +const struct erf_data __erf_data = { + .tab = { { 0x0.0000000000000p+0, 0x1.20dd750429b6dp+0 }, + { 0x1.20dbf3deb1340p-7, 0x1.20d8f1975c85dp+0 }, + { 0x1.20d77083f17a0p-6, 0x1.20cb67bd452c7p+0 }, + { 0x1.b137e0cf584dcp-6, 0x1.20b4d8bac36c1p+0 }, + { 0x1.20c5645dd2538p-5, 0x1.209546ad13ccfp+0 }, + { 0x1.68e5d3bbc9526p-5, 0x1.206cb4897b148p+0 }, + { 0x1.b0fafef135745p-5, 0x1.203b261cd0052p+0 }, + { 0x1.f902a77bd3821p-5, 0x1.2000a00ae3804p+0 }, + { 0x1.207d480e90658p-4, 0x1.1fbd27cdc72d3p+0 }, + { 0x1.44703e87e8593p-4, 0x1.1f70c3b4f2cc7p+0 }, + { 0x1.68591a1e83b5dp-4, 0x1.1f1b7ae44867fp+0 }, + { 0x1.8c36beb8a8d23p-4, 0x1.1ebd5552f795bp+0 }, + { 0x1.b0081148a873ap-4, 0x1.1e565bca400d4p+0 }, + { 0x1.d3cbf7e70a4b3p-4, 0x1.1de697e413d28p+0 }, + { 0x1.f78159ec8bb50p-4, 0x1.1d6e14099944ap+0 }, + { 0x1.0d939005f65e5p-3, 0x1.1cecdb718d61cp+0 }, + { 0x1.1f5e1a35c3b89p-3, 0x1.1c62fa1e869b6p+0 }, + { 0x1.311fc15f56d14p-3, 0x1.1bd07cdd189acp+0 }, + { 0x1.42d7fc2f64959p-3, 0x1.1b357141d95d5p+0 }, + { 0x1.548642321d7c6p-3, 0x1.1a91e5a748165p+0 }, + { 0x1.662a0bdf7a89fp-3, 0x1.19e5e92b964abp+0 }, + { 0x1.77c2d2a765f9ep-3, 0x1.19318bae53a04p+0 }, + { 0x1.895010fdbdbfdp-3, 0x1.1874ddcdfce24p+0 }, + { 0x1.9ad142662e14dp-3, 0x1.17aff0e56ec10p+0 }, + { 0x1.ac45e37fe2526p-3, 0x1.16e2d7093cd8cp+0 }, + { 0x1.bdad72110a648p-3, 0x1.160da304ed92fp+0 }, + { 0x1.cf076d1233237p-3, 0x1.153068581b781p+0 }, + { 0x1.e05354b96ff36p-3, 0x1.144b3b337c90cp+0 }, + { 0x1.f190aa85540e2p-3, 0x1.135e3075d076bp+0 }, + { 0x1.015f78a3dcf3dp-2, 0x1.12695da8b5bdep+0 }, + { 0x1.09eed6982b948p-2, 0x1.116cd8fd67618p+0 }, + { 0x1.127631eb8de32p-2, 0x1.1068b94962e5ep+0 }, + { 0x1.1af54e232d609p-2, 0x1.0f5d1602f7e41p+0 }, + { 0x1.236bef825d9a2p-2, 0x1.0e4a073dc1b91p+0 }, + { 0x1.2bd9db0f7827fp-2, 0x1.0d2fa5a70c168p+0 }, + { 0x1.343ed6989b7d9p-2, 0x1.0c0e0a8223359p+0 }, + { 0x1.3c9aa8b84bedap-2, 0x1.0ae54fa490722p+0 }, + { 0x1.44ed18d9f6462p-2, 0x1.09b58f724416bp+0 }, + { 0x1.4d35ef3e5372ep-2, 0x1.087ee4d9ad247p+0 }, + { 0x1.5574f4ffac98ep-2, 0x1.07416b4fbfe7cp+0 }, + { 0x1.5da9f415ff23fp-2, 0x1.05fd3ecbec297p+0 }, + { 0x1.65d4b75b00471p-2, 0x1.04b27bc403d30p+0 }, + { 0x1.6df50a8dff772p-2, 0x1.03613f2812dafp+0 }, + { 0x1.760aba57a76bfp-2, 0x1.0209a65e29545p+0 }, + { 0x1.7e15944d9d3e4p-2, 0x1.00abcf3e187a9p+0 }, + { 0x1.861566f5fd3c0p-2, 0x1.fe8fb01a47307p-1 }, + { 0x1.8e0a01cab516bp-2, 0x1.fbbbbef34b4b2p-1 }, + { 0x1.95f3353cbb146p-2, 0x1.f8dc092d58ff8p-1 }, + { 0x1.9dd0d2b721f39p-2, 0x1.f5f0cdaf15313p-1 }, + { 0x1.a5a2aca209394p-2, 0x1.f2fa4c16c0019p-1 }, + { 0x1.ad68966569a87p-2, 0x1.eff8c4b1375dbp-1 }, + { 0x1.b522646bbda68p-2, 0x1.ecec7870ebca7p-1 }, + { 0x1.bccfec24855b8p-2, 0x1.e9d5a8e4c934ep-1 }, + { 0x1.c4710406a65fcp-2, 0x1.e6b4982f158b9p-1 }, + { 0x1.cc058392a6d2dp-2, 0x1.e38988fc46e72p-1 }, + { 0x1.d38d4354c3bd0p-2, 0x1.e054be79d3042p-1 }, + { 0x1.db081ce6e2a48p-2, 0x1.dd167c4cf9d2ap-1 }, + { 0x1.e275eaf25e458p-2, 0x1.d9cf06898cdafp-1 }, + { 0x1.e9d68931ae650p-2, 0x1.d67ea1a8b5368p-1 }, + { 0x1.f129d471eabb1p-2, 0x1.d325927fb9d89p-1 }, + { 0x1.f86faa9428f9dp-2, 0x1.cfc41e36c7df9p-1 }, + { 0x1.ffa7ea8eb5fd0p-2, 0x1.cc5a8a3fbea40p-1 }, + { 0x1.03693a371519cp-1, 0x1.c8e91c4d01368p-1 }, + { 0x1.06f794ab2cae7p-1, 0x1.c5701a484ef9dp-1 }, + { 0x1.0a7ef5c18edd2p-1, 0x1.c1efca49a5011p-1 }, + { 0x1.0dff4f247f6c6p-1, 0x1.be68728e29d5dp-1 }, + { 0x1.1178930ada115p-1, 0x1.bada596f25436p-1 }, + { 0x1.14eab43841b55p-1, 0x1.b745c55905bf8p-1 }, + { 0x1.1855a5fd3dd50p-1, 0x1.b3aafcc27502ep-1 }, + { 0x1.1bb95c3746199p-1, 0x1.b00a46237d5bep-1 }, + { 0x1.1f15cb50bc4dep-1, 0x1.ac63e7ecc1411p-1 }, + { 0x1.226ae840d4d70p-1, 0x1.a8b8287ec6a09p-1 }, + { 0x1.25b8a88b6dd7fp-1, 0x1.a5074e2157620p-1 }, + { 0x1.28ff0240d52cdp-1, 0x1.a1519efaf889ep-1 }, + { 0x1.2c3debfd7d6c1p-1, 0x1.9d97610879642p-1 }, + { 0x1.2f755ce9a21f4p-1, 0x1.99d8da149c13fp-1 }, + { 0x1.32a54cb8db67bp-1, 0x1.96164fafd8de3p-1 }, + { 0x1.35cdb3a9a144dp-1, 0x1.925007283d7aap-1 }, + { 0x1.38ee8a84beb71p-1, 0x1.8e86458169af8p-1 }, + { 0x1.3c07ca9cb4f9ep-1, 0x1.8ab94f6caa71dp-1 }, + { 0x1.3f196dcd0f135p-1, 0x1.86e9694134b9ep-1 }, + { 0x1.42236e79a5fa6p-1, 0x1.8316d6f48133dp-1 }, + { 0x1.4525c78dd5966p-1, 0x1.7f41dc12c9e89p-1 }, + { 0x1.4820747ba2dc2p-1, 0x1.7b6abbb7aaf19p-1 }, + { 0x1.4b13713ad3513p-1, 0x1.7791b886e7403p-1 }, + { 0x1.4dfeba47f63ccp-1, 0x1.73b714a552763p-1 }, + { 0x1.50e24ca35fd2cp-1, 0x1.6fdb11b1e0c34p-1 }, + { 0x1.53be25d016a4fp-1, 0x1.6bfdf0beddaf5p-1 }, + { 0x1.569243d2b3a9bp-1, 0x1.681ff24b4ab04p-1 }, + { 0x1.595ea53035283p-1, 0x1.6441563c665d4p-1 }, + { 0x1.5c2348ecc4dc3p-1, 0x1.60625bd75d07bp-1 }, + { 0x1.5ee02e8a71a53p-1, 0x1.5c8341bb23767p-1 }, + { 0x1.61955607dd15dp-1, 0x1.58a445da7c74cp-1 }, + { 0x1.6442bfdedd397p-1, 0x1.54c5a57629db0p-1 }, + { 0x1.66e86d0312e82p-1, 0x1.50e79d1749ac9p-1 }, + { 0x1.69865ee075011p-1, 0x1.4d0a6889dfd9fp-1 }, + { 0x1.6c1c9759d0e5fp-1, 0x1.492e42d78d2c5p-1 }, + { 0x1.6eab18c74091bp-1, 0x1.4553664273d24p-1 }, + { 0x1.7131e5f496a5ap-1, 0x1.417a0c4049fd0p-1 }, + { 0x1.73b1021fc0cb8p-1, 0x1.3da26d759aef5p-1 }, + { 0x1.762870f720c6fp-1, 0x1.39ccc1b136d5ap-1 }, + { 0x1.78983697dc96fp-1, 0x1.35f93fe7d1b3dp-1 }, + { 0x1.7b00578c26037p-1, 0x1.32281e2fd1a92p-1 }, + { 0x1.7d60d8c979f7bp-1, 0x1.2e5991bd4cbfcp-1 }, + { 0x1.7fb9bfaed8078p-1, 0x1.2a8dcede3673bp-1 }, + { 0x1.820b1202f27fbp-1, 0x1.26c508f6bd0ffp-1 }, + { 0x1.8454d5f25760dp-1, 0x1.22ff727dd6f7bp-1 }, + { 0x1.8697120d92a4ap-1, 0x1.1f3d3cf9ffe5ap-1 }, + { 0x1.88d1cd474a2e0p-1, 0x1.1b7e98fe26217p-1 }, + { 0x1.8b050ef253c37p-1, 0x1.17c3b626c7a11p-1 }, + { 0x1.8d30debfc572ep-1, 0x1.140cc3173f007p-1 }, + { 0x1.8f5544bd00c04p-1, 0x1.1059ed7740313p-1 }, + { 0x1.91724951b8fc6p-1, 0x1.0cab61f084b93p-1 }, + { 0x1.9387f53df5238p-1, 0x1.09014c2ca74dap-1 }, + { 0x1.959651980da31p-1, 0x1.055bd6d32e8d7p-1 }, + { 0x1.979d67caa6631p-1, 0x1.01bb2b87c6968p-1 }, + { 0x1.999d4192a5715p-1, 0x1.fc3ee5d1524b0p-2 }, + { 0x1.9b95e8fd26abap-1, 0x1.f511a91a67d2ap-2 }, + { 0x1.9d8768656cc42p-1, 0x1.edeeee0959518p-2 }, + { 0x1.9f71ca72cffb6p-1, 0x1.e6d6ffaa65a25p-2 }, + { 0x1.a1551a16aaeafp-1, 0x1.dfca26f5bbf88p-2 }, + { 0x1.a331628a45b92p-1, 0x1.d8c8aace11e63p-2 }, + { 0x1.a506af4cc00f4p-1, 0x1.d1d2cfff91594p-2 }, + { 0x1.a6d50c20fa293p-1, 0x1.cae8d93f1d7b6p-2 }, + { 0x1.a89c850b7d54dp-1, 0x1.c40b0729ed547p-2 }, + { 0x1.aa5d265064366p-1, 0x1.bd3998457afdap-2 }, + { 0x1.ac16fc7143263p-1, 0x1.b674c8ffc6283p-2 }, + { 0x1.adca142b10f98p-1, 0x1.afbcd3afe8ab6p-2 }, + { 0x1.af767a741088bp-1, 0x1.a911f096fbc26p-2 }, + { 0x1.b11c3c79bb424p-1, 0x1.a27455e14c93cp-2 }, + { 0x1.b2bb679ead19cp-1, 0x1.9be437a7de946p-2 }, + { 0x1.b4540978921eep-1, 0x1.9561c7f23a47bp-2 }, + { 0x1.b5e62fce16095p-1, 0x1.8eed36b886d93p-2 }, + { 0x1.b771e894d602ep-1, 0x1.8886b1e5ecfd1p-2 }, + { 0x1.b8f741ef54f83p-1, 0x1.822e655b417e6p-2 }, + { 0x1.ba764a2af2b78p-1, 0x1.7be47af1f5d89p-2 }, + { 0x1.bbef0fbde6221p-1, 0x1.75a91a7f4d2edp-2 }, + { 0x1.bd61a1453ab44p-1, 0x1.6f7c69d7d3ef8p-2 }, + { 0x1.bece0d82d1a5cp-1, 0x1.695e8cd31867ep-2 }, + { 0x1.c034635b66e23p-1, 0x1.634fa54fa285fp-2 }, + { 0x1.c194b1d49a184p-1, 0x1.5d4fd33729015p-2 }, + { 0x1.c2ef0812fc1bdp-1, 0x1.575f3483021c3p-2 }, + { 0x1.c443755820d64p-1, 0x1.517de540ce2a3p-2 }, + { 0x1.c5920900b5fd1p-1, 0x1.4babff975a04cp-2 }, + { 0x1.c6dad2829ec62p-1, 0x1.45e99bcbb7915p-2 }, + { 0x1.c81de16b14cefp-1, 0x1.4036d0468a7a2p-2 }, + { 0x1.c95b455cce69dp-1, 0x1.3a93b1998736cp-2 }, + { 0x1.ca930e0e2a825p-1, 0x1.35005285227f1p-2 }, + { 0x1.cbc54b476248dp-1, 0x1.2f7cc3fe6f423p-2 }, + { 0x1.ccf20ce0c0d27p-1, 0x1.2a09153529381p-2 }, + { 0x1.ce1962c0e0d8bp-1, 0x1.24a55399ea239p-2 }, + { 0x1.cf3b5cdaf0c39p-1, 0x1.1f518ae487dc8p-2 }, + { 0x1.d0580b2cfd249p-1, 0x1.1a0dc51a9934dp-2 }, + { 0x1.d16f7dbe41ca0p-1, 0x1.14da0a961fd14p-2 }, + { 0x1.d281c49d818d0p-1, 0x1.0fb6620c550afp-2 }, + { 0x1.d38eefdf64fddp-1, 0x1.0aa2d09497f2bp-2 }, + { 0x1.d4970f9ce00d9p-1, 0x1.059f59af7a906p-2 }, + { 0x1.d59a33f19ed42p-1, 0x1.00abff4dec7a3p-2 }, + { 0x1.d6986cfa798e7p-1, 0x1.f79183b101c5bp-3 }, + { 0x1.d791cad3eff01p-1, 0x1.edeb406d9c824p-3 }, + { 0x1.d8865d98abe01p-1, 0x1.e4652fadcb6b2p-3 }, + { 0x1.d97635600bb89p-1, 0x1.daff4969c0b04p-3 }, + { 0x1.da61623cb41e0p-1, 0x1.d1b982c501370p-3 }, + { 0x1.db47f43b2980dp-1, 0x1.c893ce1dcbef7p-3 }, + { 0x1.dc29fb60715afp-1, 0x1.bf8e1b1ca2279p-3 }, + { 0x1.dd0787a8bb39dp-1, 0x1.b6a856c3ed54fp-3 }, + { 0x1.dde0a90611a0dp-1, 0x1.ade26b7fbed95p-3 }, + { 0x1.deb56f5f12d28p-1, 0x1.a53c4135a6526p-3 }, + { 0x1.df85ea8db188ep-1, 0x1.9cb5bd549b111p-3 }, + { 0x1.e0522a5dfda73p-1, 0x1.944ec2e4f5630p-3 }, + { 0x1.e11a3e8cf4eb8p-1, 0x1.8c07329874652p-3 }, + { 0x1.e1de36c75ba58p-1, 0x1.83deeada4d25ap-3 }, + { 0x1.e29e22a89d766p-1, 0x1.7bd5c7df3fe9cp-3 }, + { 0x1.e35a11b9b61cep-1, 0x1.73eba3b5b07b7p-3 }, + { 0x1.e4121370224ccp-1, 0x1.6c205655be71fp-3 }, + { 0x1.e4c6372cd8927p-1, 0x1.6473b5b15a7a1p-3 }, + { 0x1.e5768c3b4a3fcp-1, 0x1.5ce595c455b0ap-3 }, + { 0x1.e62321d06c5e0p-1, 0x1.5575c8a468361p-3 }, + { 0x1.e6cc0709c8a0dp-1, 0x1.4e241e912c305p-3 }, + { 0x1.e7714aec96534p-1, 0x1.46f066040a832p-3 }, + { 0x1.e812fc64db369p-1, 0x1.3fda6bc016994p-3 }, + { 0x1.e8b12a44944a8p-1, 0x1.38e1fae1d6a9dp-3 }, + { 0x1.e94be342e6743p-1, 0x1.3206dceef5f87p-3 }, + { 0x1.e9e335fb56f87p-1, 0x1.2b48d9e5dea1cp-3 }, + { 0x1.ea7730ed0bbb9p-1, 0x1.24a7b84d38971p-3 }, + { 0x1.eb07e27a133aap-1, 0x1.1e233d434b813p-3 }, + { 0x1.eb9558e6b42cep-1, 0x1.17bb2c8d41535p-3 }, + { 0x1.ec1fa258c4beap-1, 0x1.116f48a6476ccp-3 }, + { 0x1.eca6ccd709544p-1, 0x1.0b3f52ce8c383p-3 }, + { 0x1.ed2ae6489ac1ep-1, 0x1.052b0b1a174eap-3 }, + { 0x1.edabfc7453e63p-1, 0x1.fe6460fef4680p-4 }, + { 0x1.ee2a1d004692cp-1, 0x1.f2a901ccafb37p-4 }, + { 0x1.eea5557137ae0p-1, 0x1.e723726b824a9p-4 }, + { 0x1.ef1db32a2277cp-1, 0x1.dbd32ac4c99b0p-4 }, + { 0x1.ef93436bc2daap-1, 0x1.d0b7a0f921e7cp-4 }, + { 0x1.f006135426b26p-1, 0x1.c5d0497c09e74p-4 }, + { 0x1.f0762fde45ee6p-1, 0x1.bb1c972f23e50p-4 }, + { 0x1.f0e3a5e1a1788p-1, 0x1.b09bfb7d11a83p-4 }, + { 0x1.f14e8211e8c55p-1, 0x1.a64de673e8837p-4 }, + { 0x1.f1b6d0fea5f4dp-1, 0x1.9c31c6df3b1b8p-4 }, + { 0x1.f21c9f12f0677p-1, 0x1.92470a61b6965p-4 }, + { 0x1.f27ff89525acfp-1, 0x1.888d1d8e510a3p-4 }, + { 0x1.f2e0e9a6a8b09p-1, 0x1.7f036c0107294p-4 }, + { 0x1.f33f7e43a706bp-1, 0x1.75a96077274bap-4 }, + { 0x1.f39bc242e43e6p-1, 0x1.6c7e64e7281cbp-4 }, + { 0x1.f3f5c1558b19ep-1, 0x1.6381e2980956bp-4 }, + { 0x1.f44d870704911p-1, 0x1.5ab342383d177p-4 }, + { 0x1.f4a31ebcd47dfp-1, 0x1.5211ebf41880bp-4 }, + { 0x1.f4f693b67bd77p-1, 0x1.499d478bca735p-4 }, + { 0x1.f547f10d60597p-1, 0x1.4154bc68d75c3p-4 }, + { 0x1.f59741b4b97cfp-1, 0x1.3937b1b319259p-4 }, + { 0x1.f5e4907982a07p-1, 0x1.31458e6542847p-4 }, + { 0x1.f62fe80272419p-1, 0x1.297db960e4f63p-4 }, + { 0x1.f67952cff6282p-1, 0x1.21df9981f8e53p-4 }, + { 0x1.f6c0db3c34641p-1, 0x1.1a6a95b1e786fp-4 }, + { 0x1.f7068b7b10fd9p-1, 0x1.131e14fa1625dp-4 }, + { 0x1.f74a6d9a38383p-1, 0x1.0bf97e95f2a64p-4 }, + { 0x1.f78c8b812d498p-1, 0x1.04fc3a0481321p-4 }, + { 0x1.f7cceef15d631p-1, 0x1.fc4b5e32d6259p-5 }, + { 0x1.f80ba18636f07p-1, 0x1.eeea8c1b1db93p-5 }, + { 0x1.f848acb544e95p-1, 0x1.e1d4cf1e2450ap-5 }, + { 0x1.f88419ce4e184p-1, 0x1.d508f9a1ea64ep-5 }, + { 0x1.f8bdf1fb78370p-1, 0x1.c885df3451a07p-5 }, + { 0x1.f8f63e416ebffp-1, 0x1.bc4a54a84e834p-5 }, + { 0x1.f92d077f8d56dp-1, 0x1.b055303221015p-5 }, + { 0x1.f96256700da8ep-1, 0x1.a4a549829587ep-5 }, + { 0x1.f99633a838a57p-1, 0x1.993979e14fffdp-5 }, + { 0x1.f9c8a7989af0dp-1, 0x1.8e109c4622913p-5 }, + { 0x1.f9f9ba8d3c733p-1, 0x1.83298d717210ep-5 }, + { 0x1.fa2974addae45p-1, 0x1.78832c03aa2b1p-5 }, + { 0x1.fa57ddfe27376p-1, 0x1.6e1c5893c380bp-5 }, + { 0x1.fa84fe5e05c8dp-1, 0x1.63f3f5c4de13bp-5 }, + { 0x1.fab0dd89d1309p-1, 0x1.5a08e85af27e0p-5 }, + { 0x1.fadb831a9f9c3p-1, 0x1.505a174e9c929p-5 }, + { 0x1.fb04f6868a944p-1, 0x1.46e66be002240p-5 }, + { 0x1.fb2d3f20f9101p-1, 0x1.3dacd1a8d8ccdp-5 }, + { 0x1.fb54641aebbc9p-1, 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0x1.fffffffffe380p-1, 0x1.25f9ee0b923dcp-37 }, + { 0x1.fffffffffe5b6p-1, 0x1.0f9a0686531ffp-37 }, + { 0x1.fffffffffe7c0p-1, 0x1.f5cc7718082afp-38 }, + { 0x1.fffffffffe9a2p-1, 0x1.cf7e53d6a2ca5p-38 }, + { 0x1.fffffffffeb60p-1, 0x1.ac0f5f3229372p-38 }, + { 0x1.fffffffffecfbp-1, 0x1.8b498644847eap-38 }, + { 0x1.fffffffffee77p-1, 0x1.6cfa9bcca59dcp-38 }, + { 0x1.fffffffffefd6p-1, 0x1.50f411d4fd2cdp-38 }, + { 0x1.ffffffffff11ap-1, 0x1.370ab8327af5ep-38 }, + { 0x1.ffffffffff245p-1, 0x1.1f167f88c6b6ep-38 }, + { 0x1.ffffffffff359p-1, 0x1.08f24085d4597p-38 }, + { 0x1.ffffffffff457p-1, 0x1.e8f70e181d619p-39 }, + { 0x1.ffffffffff542p-1, 0x1.c324c20e337dcp-39 }, + { 0x1.ffffffffff61bp-1, 0x1.a03261574b54ep-39 }, + { 0x1.ffffffffff6e3p-1, 0x1.7fe903cdf5855p-39 }, + { 0x1.ffffffffff79bp-1, 0x1.6215c58da3450p-39 }, + { 0x1.ffffffffff845p-1, 0x1.46897d4b69fc6p-39 }, + { 0x1.ffffffffff8e2p-1, 0x1.2d1877d731b7bp-39 }, + { 0x1.ffffffffff973p-1, 0x1.159a386b11517p-39 }, + { 0x1.ffffffffff9f8p-1, 0x1.ffd27ae9393cep-40 }, + { 0x1.ffffffffffa73p-1, 0x1.d7c593130dd0bp-40 }, + { 0x1.ffffffffffae4p-1, 0x1.b2cd607c79bcfp-40 }, + { 0x1.ffffffffffb4cp-1, 0x1.90ae4d3405651p-40 }, + { 0x1.ffffffffffbadp-1, 0x1.71312dd1759e2p-40 }, + { 0x1.ffffffffffc05p-1, 0x1.5422ef5d8949dp-40 }, + { 0x1.ffffffffffc57p-1, 0x1.39544b0ecc957p-40 }, + { 0x1.ffffffffffca2p-1, 0x1.20997f73e73ddp-40 }, + { 0x1.ffffffffffce7p-1, 0x1.09ca0eaacd277p-40 }, + { 0x1.ffffffffffd27p-1, 0x1.e9810295890ecp-41 }, + { 0x1.ffffffffffd62p-1, 0x1.c2b45b5aa4a1dp-41 }, + { 0x1.ffffffffffd98p-1, 0x1.9eee068fa7596p-41 }, + { 0x1.ffffffffffdcap-1, 0x1.7df2b399c10a8p-41 }, + { 0x1.ffffffffffdf8p-1, 0x1.5f8b87a31bd85p-41 }, + { 0x1.ffffffffffe22p-1, 0x1.4385c96e9a2d9p-41 }, + { 0x1.ffffffffffe49p-1, 0x1.29b2933ef4cbcp-41 }, + { 0x1.ffffffffffe6cp-1, 0x1.11e68a6378f8ap-41 }, + { 0x1.ffffffffffe8dp-1, 0x1.f7f338086a86bp-42 }, + { 0x1.ffffffffffeabp-1, 0x1.cf8d7d9ce040ap-42 }, + { 0x1.ffffffffffec7p-1, 0x1.aa577251ae484p-42 }, + { 0x1.ffffffffffee1p-1, 0x1.8811d739efb5ep-42 }, + { 0x1.ffffffffffef8p-1, 0x1.68823e52970bep-42 }, + { 0x1.fffffffffff0ep-1, 0x1.4b72ae68e8b4cp-42 }, + { 0x1.fffffffffff22p-1, 0x1.30b14dbe876bcp-42 }, + { 0x1.fffffffffff34p-1, 0x1.181012ef86610p-42 }, + { 0x1.fffffffffff45p-1, 0x1.01647ba798744p-42 }, + { 0x1.fffffffffff54p-1, 0x1.d90e917701675p-43 }, + { 0x1.fffffffffff62p-1, 0x1.b2a87e86d0c8ap-43 }, + { 0x1.fffffffffff6fp-1, 0x1.8f53dcb377293p-43 }, + { 0x1.fffffffffff7bp-1, 0x1.6ed2f2515e933p-43 }, + { 0x1.fffffffffff86p-1, 0x1.50ecc9ed47f19p-43 }, + { 0x1.fffffffffff90p-1, 0x1.356cd5ce7799ep-43 }, + { 0x1.fffffffffff9ap-1, 0x1.1c229a587ab78p-43 }, + { 0x1.fffffffffffa2p-1, 0x1.04e15ecc7f3f6p-43 }, + { 0x1.fffffffffffaap-1, 0x1.deffc7e6a6017p-44 }, + { 0x1.fffffffffffb1p-1, 0x1.b7b040832f310p-44 }, + { 0x1.fffffffffffb8p-1, 0x1.938e021f36d76p-44 }, + { 0x1.fffffffffffbep-1, 0x1.7258610b3b233p-44 }, + { 0x1.fffffffffffc3p-1, 0x1.53d3bfc82a909p-44 }, + { 0x1.fffffffffffc8p-1, 0x1.37c92babdc2fdp-44 }, + { 0x1.fffffffffffcdp-1, 0x1.1e06010120f6ap-44 }, + { 0x1.fffffffffffd1p-1, 0x1.065b9616170d4p-44 }, + { 0x1.fffffffffffd5p-1, 0x1.e13dd96b3753ap-45 }, + { 0x1.fffffffffffd9p-1, 0x1.b950d32467392p-45 }, + { 0x1.fffffffffffdcp-1, 0x1.94a72263259a5p-45 }, + { 0x1.fffffffffffdfp-1, 0x1.72fd93e036cdcp-45 }, + { 0x1.fffffffffffe2p-1, 0x1.54164576929abp-45 }, + { 0x1.fffffffffffe4p-1, 0x1.37b83c521fe96p-45 }, + { 0x1.fffffffffffe7p-1, 0x1.1daf033182e96p-45 }, + { 0x1.fffffffffffe9p-1, 0x1.05ca50205d26ap-45 }, + { 0x1.fffffffffffebp-1, 0x1.dfbb6235639fap-46 }, + { 0x1.fffffffffffedp-1, 0x1.b7807e294781fp-46 }, + { 0x1.fffffffffffeep-1, 0x1.9298add70a734p-46 }, + { 0x1.ffffffffffff0p-1, 0x1.70beaf9c7ffb6p-46 }, + { 0x1.ffffffffffff1p-1, 0x1.51b2cd6709222p-46 }, + { 0x1.ffffffffffff3p-1, 0x1.353a6cf7f7fffp-46 }, + { 0x1.ffffffffffff4p-1, 0x1.1b1fa8cbe84a7p-46 }, + { 0x1.ffffffffffff5p-1, 0x1.0330f0fd69921p-46 }, + { 0x1.ffffffffffff6p-1, 0x1.da81670f96f9bp-47 }, + { 0x1.ffffffffffff7p-1, 0x1.b24a16b4d09aap-47 }, + { 0x1.ffffffffffff7p-1, 0x1.8d6eeb6efdbd6p-47 }, + { 0x1.ffffffffffff8p-1, 0x1.6ba91ac734785p-47 }, + { 0x1.ffffffffffff9p-1, 0x1.4cb7966770ab5p-47 }, + { 0x1.ffffffffffff9p-1, 0x1.305e9721d0981p-47 }, + { 0x1.ffffffffffffap-1, 0x1.1667311fff70ap-47 }, + { 0x1.ffffffffffffbp-1, 0x1.fd3de10d62855p-48 }, + { 0x1.ffffffffffffbp-1, 0x1.d1aefbcd48d0cp-48 }, + { 0x1.ffffffffffffbp-1, 0x1.a9cc93c25aca9p-48 }, + { 0x1.ffffffffffffcp-1, 0x1.85487ee3ea735p-48 }, + { 0x1.ffffffffffffcp-1, 0x1.63daf8b4b1e0cp-48 }, + { 0x1.ffffffffffffdp-1, 0x1.45421e69a6ca1p-48 }, + { 0x1.ffffffffffffdp-1, 0x1.294175802d99ap-48 }, + { 0x1.ffffffffffffdp-1, 0x1.0fa17bf41068fp-48 }, + { 0x1.ffffffffffffdp-1, 0x1.f05e82aae2bb9p-49 }, + { 0x1.ffffffffffffep-1, 0x1.c578101b29058p-49 }, + { 0x1.ffffffffffffep-1, 0x1.9e39dc5dd2f7cp-49 }, + { 0x1.ffffffffffffep-1, 0x1.7a553a728bbf2p-49 }, + { 0x1.ffffffffffffep-1, 0x1.5982008db1304p-49 }, + { 0x1.ffffffffffffep-1, 0x1.3b7e00422e51bp-49 }, + { 0x1.ffffffffffffep-1, 0x1.200c898d9ee3ep-49 }, + { 0x1.fffffffffffffp-1, 0x1.06f5f7eb65a56p-49 }, + { 0x1.fffffffffffffp-1, 0x1.e00e9148a1d25p-50 }, + { 0x1.fffffffffffffp-1, 0x1.b623734024e92p-50 }, + { 0x1.fffffffffffffp-1, 0x1.8fd4e01891bf8p-50 }, + { 0x1.fffffffffffffp-1, 0x1.6cd44c7470d89p-50 }, + { 0x1.fffffffffffffp-1, 0x1.4cd9c04158cd7p-50 }, + { 0x1.fffffffffffffp-1, 0x1.2fa34bf5c8344p-50 }, + { 0x1.fffffffffffffp-1, 0x1.14f4890ff2461p-50 }, + { 0x1.fffffffffffffp-1, 0x1.f92c49dfa4df5p-51 }, + { 0x1.fffffffffffffp-1, 0x1.ccaaea71ab0dfp-51 }, + { 0x1.fffffffffffffp-1, 0x1.a40829f001197p-51 }, + { 0x1.0000000000000p+0, 0x1.7eef13b59e96cp-51 }, + { 0x1.0000000000000p+0, 0x1.5d11e1a252bf5p-51 }, + { 0x1.0000000000000p+0, 0x1.3e296303b2297p-51 }, + { 0x1.0000000000000p+0, 0x1.21f47009f43cep-51 }, + { 0x1.0000000000000p+0, 0x1.083768c5e4541p-51 }, + { 0x1.0000000000000p+0, 0x1.e1777d831265ep-52 }, + { 0x1.0000000000000p+0, 0x1.b69f10b0191b5p-52 }, + { 0x1.0000000000000p+0, 0x1.8f8a3a05b5b52p-52 }, + { 0x1.0000000000000p+0, 0x1.6be573c40c8e7p-52 }, + { 0x1.0000000000000p+0, 0x1.4b645ba991fdbp-52 }, + { 0x1.0000000000000p+0, 0x1.2dc119095729fp-52 }, + }, +}; diff --git a/sysdeps/aarch64/fpu/erf_sve.c b/sysdeps/aarch64/fpu/erf_sve.c new file mode 100644 index 0000000000..7d51417406 --- /dev/null +++ b/sysdeps/aarch64/fpu/erf_sve.c @@ -0,0 +1,115 @@ +/* Double-precision vector (SVE) erf function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" + +static const struct data +{ + double third; + double tenth, two_over_five, two_over_fifteen; + double two_over_nine, two_over_fortyfive; + double max, shift; +} data = { + .third = 0x1.5555555555556p-2, /* used to compute 2/3 and 1/6 too. */ + .two_over_fifteen = 0x1.1111111111111p-3, + .tenth = -0x1.999999999999ap-4, + .two_over_five = -0x1.999999999999ap-2, + .two_over_nine = -0x1.c71c71c71c71cp-3, + .two_over_fortyfive = 0x1.6c16c16c16c17p-5, + .max = 5.9921875, /* 6 - 1/128. */ + .shift = 0x1p45, +}; + +#define SignMask (0x8000000000000000) + +/* Double-precision implementation of vector erf(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/128. + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + erf(x) ~ erf(r) + scale * d * [ + + 1 + - r d + + 1/3 (2 r^2 - 1) d^2 + - 1/6 (r (2 r^2 - 3)) d^3 + + 1/30 (4 r^4 - 12 r^2 + 3) d^4 + - 1/90 (4 r^4 - 20 r^2 + 15) d^5 + ] + + Maximum measure error: 2.29 ULP + _ZGVsMxv_erf(-0x1.00003c924e5d1p-8) got -0x1.20dd59132ebadp-8 + want -0x1.20dd59132ebafp-8. */ +svfloat64_t SV_NAME_D1 (erf) (svfloat64_t x, const svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + + /* |x| >= 6.0 - 1/128. Opposite conditions except none of them catch NaNs so + they can be used in lookup and BSLs to yield the expected results. */ + svbool_t a_ge_max = svacge (pg, x, dat->max); + svbool_t a_lt_max = svaclt (pg, x, dat->max); + + /* Set r to multiple of 1/128 nearest to |x|. */ + svfloat64_t a = svabs_x (pg, x); + svfloat64_t shift = sv_f64 (dat->shift); + svfloat64_t z = svadd_x (pg, a, shift); + svuint64_t i + = svsub_x (pg, svreinterpret_u64 (z), svreinterpret_u64 (shift)); + + /* Lookup without shortcut for small values but with predicate to avoid + segfault for large values and NaNs. */ + svfloat64_t r = svsub_x (pg, z, shift); + svfloat64_t erfr = svld1_gather_index (a_lt_max, __sv_erf_data.erf, i); + svfloat64_t scale = svld1_gather_index (a_lt_max, __sv_erf_data.scale, i); + + /* erf(x) ~ erf(r) + scale * d * poly (r, d). */ + svfloat64_t d = svsub_x (pg, a, r); + svfloat64_t d2 = svmul_x (pg, d, d); + svfloat64_t r2 = svmul_x (pg, r, r); + + /* poly (d, r) = 1 + p1(r) * d + p2(r) * d^2 + ... + p5(r) * d^5. */ + svfloat64_t p1 = r; + svfloat64_t third = sv_f64 (dat->third); + svfloat64_t twothird = svmul_x (pg, third, 2.0); + svfloat64_t sixth = svmul_x (pg, third, 0.5); + svfloat64_t p2 = svmls_x (pg, third, r2, twothird); + svfloat64_t p3 = svmad_x (pg, r2, third, -0.5); + p3 = svmul_x (pg, r, p3); + svfloat64_t p4 + = svmla_x (pg, sv_f64 (dat->two_over_five), r2, dat->two_over_fifteen); + p4 = svmls_x (pg, sv_f64 (dat->tenth), r2, p4); + svfloat64_t p5 + = svmla_x (pg, sv_f64 (dat->two_over_nine), r2, dat->two_over_fortyfive); + p5 = svmla_x (pg, sixth, r2, p5); + p5 = svmul_x (pg, r, p5); + + svfloat64_t p34 = svmla_x (pg, p3, d, p4); + svfloat64_t p12 = svmla_x (pg, p1, d, p2); + svfloat64_t y = svmla_x (pg, p34, d2, p5); + y = svmla_x (pg, p12, d2, y); + + y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y)); + + /* Solves the |x| = inf and NaN cases. */ + y = svsel (a_ge_max, sv_f64 (1.0), y); + + /* Copy sign. */ + svuint64_t ix = svreinterpret_u64 (x); + svuint64_t iy = svreinterpret_u64 (y); + svuint64_t sign = svand_x (pg, ix, SignMask); + return svreinterpret_f64 (svorr_x (pg, sign, iy)); +} diff --git a/sysdeps/aarch64/fpu/erff_advsimd.c b/sysdeps/aarch64/fpu/erff_advsimd.c new file mode 100644 index 0000000000..c44644a71c --- /dev/null +++ b/sysdeps/aarch64/fpu/erff_advsimd.c @@ -0,0 +1,123 @@ +/* Single-precision vector (Advanced SIMD) erf function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" + +static const struct data +{ + float32x4_t max, shift, third; +#if WANT_SIMD_EXCEPT + float32x4_t tiny_bound, scale_minus_one; +#endif +} data = { + .max = V4 (3.9375), /* 4 - 8/128. */ + .shift = V4 (0x1p16f), + .third = V4 (0x1.555556p-2f), /* 1/3. */ +#if WANT_SIMD_EXCEPT + .tiny_bound = V4 (0x1p-62f), + .scale_minus_one = V4 (0x1.06eba8p-3f), /* scale - 1.0. */ +#endif +}; + +#define AbsMask 0x7fffffff + +struct entry +{ + float32x4_t erf; + float32x4_t scale; +}; + +static inline struct entry +lookup (uint32x4_t i) +{ + struct entry e; + float64_t t0 = *((float64_t *) (__erff_data.tab + i[0])); + float64_t t1 = *((float64_t *) (__erff_data.tab + i[1])); + float64_t t2 = *((float64_t *) (__erff_data.tab + i[2])); + float64_t t3 = *((float64_t *) (__erff_data.tab + i[3])); + float32x4_t e1 = vreinterpretq_f32_f64 ((float64x2_t){ t0, t1 }); + float32x4_t e2 = vreinterpretq_f32_f64 ((float64x2_t){ t2, t3 }); + e.erf = vuzp1q_f32 (e1, e2); + e.scale = vuzp2q_f32 (e1, e2); + return e; +} + +/* Single-precision implementation of vector erf(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/128. + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + + erf(x) ~ erf(r) + scale * d * [1 - r * d - 1/3 * d^2] + + Values of erf(r) and scale are read from lookup tables. + For |x| > 3.9375, erf(|x|) rounds to 1.0f. + + Maximum error: 1.93 ULP + _ZGVnN4v_erff(0x1.c373e6p-9) got 0x1.fd686cp-9 + want 0x1.fd6868p-9. */ +float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (erf) (float32x4_t x) +{ + const struct data *dat = ptr_barrier (&data); + +#if WANT_SIMD_EXCEPT + /* |x| < 2^-62. */ + uint32x4_t cmp = vcaltq_f32 (x, dat->tiny_bound); + float32x4_t xm = x; + /* If any lanes are special, mask them with 1 and retain a copy of x to allow + special case handler to fix special lanes later. This is only necessary if + fenv exceptions are to be triggered correctly. */ + if (__glibc_unlikely (v_any_u32 (cmp))) + x = vbslq_f32 (cmp, v_f32 (1), x); +#endif + + float32x4_t a = vabsq_f32 (x); + uint32x4_t a_gt_max = vcgtq_f32 (a, dat->max); + + /* Lookup erf(r) and scale(r) in tables, e.g. set erf(r) to 0 and scale to + 2/sqrt(pi), when x reduced to r = 0. */ + float32x4_t shift = dat->shift; + float32x4_t z = vaddq_f32 (a, shift); + + uint32x4_t i + = vsubq_u32 (vreinterpretq_u32_f32 (z), vreinterpretq_u32_f32 (shift)); + i = vminq_u32 (i, v_u32 (512)); + struct entry e = lookup (i); + + float32x4_t r = vsubq_f32 (z, shift); + + /* erf(x) ~ erf(r) + scale * d * (1 - r * d - 1/3 * d^2). */ + float32x4_t d = vsubq_f32 (a, r); + float32x4_t d2 = vmulq_f32 (d, d); + float32x4_t y = vfmaq_f32 (r, dat->third, d); + y = vfmaq_f32 (e.erf, e.scale, vfmsq_f32 (d, d2, y)); + + /* Solves the |x| = inf case. */ + y = vbslq_f32 (a_gt_max, v_f32 (1.0f), y); + + /* Copy sign. */ + y = vbslq_f32 (v_u32 (AbsMask), y, x); + +#if WANT_SIMD_EXCEPT + if (__glibc_unlikely (v_any_u32 (cmp))) + return vbslq_f32 (cmp, vfmaq_f32 (xm, dat->scale_minus_one, xm), y); +#endif + return y; +} +libmvec_hidden_def (V_NAME_F1 (erf)) +HALF_WIDTH_ALIAS_F1 (erf) diff --git a/sysdeps/aarch64/fpu/erff_data.c b/sysdeps/aarch64/fpu/erff_data.c new file mode 100644 index 0000000000..9a32940915 --- /dev/null +++ b/sysdeps/aarch64/fpu/erff_data.c @@ -0,0 +1,544 @@ +/* Table for Advanced SIMD erff approximation + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "vecmath_config.h" + +/* Lookup table used in erff. + For each possible rounded input r (multiples of 1/128), between + r = 0.0 and r = 4.0 (513 values): + - the first entry __erff_data.tab.erf contains the values of erf(r), + - the second entry __erff_data.tab.scale contains the values of + 2/sqrt(pi)*exp(-r^2). Note that indices 0 and 1 are never hit by the + algorithm, since lookup is performed only for x >= 1/64-1/512. */ +const struct erff_data __erff_data = { + .tab = { { 0x0.000000p+0, 0x1.20dd76p+0 }, + { 0x1.20dbf4p-7, 0x1.20d8f2p+0 }, + { 0x1.20d770p-6, 0x1.20cb68p+0 }, + { 0x1.b137e0p-6, 0x1.20b4d8p+0 }, + { 0x1.20c564p-5, 0x1.209546p+0 }, + { 0x1.68e5d4p-5, 0x1.206cb4p+0 }, + { 0x1.b0fafep-5, 0x1.203b26p+0 }, + { 0x1.f902a8p-5, 0x1.2000a0p+0 }, + { 0x1.207d48p-4, 0x1.1fbd28p+0 }, + { 0x1.44703ep-4, 0x1.1f70c4p+0 }, + { 0x1.68591ap-4, 0x1.1f1b7ap+0 }, + { 0x1.8c36bep-4, 0x1.1ebd56p+0 }, + { 0x1.b00812p-4, 0x1.1e565cp+0 }, + { 0x1.d3cbf8p-4, 0x1.1de698p+0 }, + { 0x1.f7815ap-4, 0x1.1d6e14p+0 }, + { 0x1.0d9390p-3, 0x1.1cecdcp+0 }, + { 0x1.1f5e1ap-3, 0x1.1c62fap+0 }, + { 0x1.311fc2p-3, 0x1.1bd07cp+0 }, + { 0x1.42d7fcp-3, 0x1.1b3572p+0 }, + { 0x1.548642p-3, 0x1.1a91e6p+0 }, + { 0x1.662a0cp-3, 0x1.19e5eap+0 }, + { 0x1.77c2d2p-3, 0x1.19318cp+0 }, + { 0x1.895010p-3, 0x1.1874dep+0 }, + { 0x1.9ad142p-3, 0x1.17aff0p+0 }, + { 0x1.ac45e4p-3, 0x1.16e2d8p+0 }, + { 0x1.bdad72p-3, 0x1.160da4p+0 }, + { 0x1.cf076ep-3, 0x1.153068p+0 }, + { 0x1.e05354p-3, 0x1.144b3cp+0 }, + { 0x1.f190aap-3, 0x1.135e30p+0 }, + { 0x1.015f78p-2, 0x1.12695ep+0 }, + { 0x1.09eed6p-2, 0x1.116cd8p+0 }, + { 0x1.127632p-2, 0x1.1068bap+0 }, + { 0x1.1af54ep-2, 0x1.0f5d16p+0 }, + { 0x1.236bf0p-2, 0x1.0e4a08p+0 }, + { 0x1.2bd9dcp-2, 0x1.0d2fa6p+0 }, + { 0x1.343ed6p-2, 0x1.0c0e0ap+0 }, + { 0x1.3c9aa8p-2, 0x1.0ae550p+0 }, + { 0x1.44ed18p-2, 0x1.09b590p+0 }, + { 0x1.4d35f0p-2, 0x1.087ee4p+0 }, + { 0x1.5574f4p-2, 0x1.07416cp+0 }, + { 0x1.5da9f4p-2, 0x1.05fd3ep+0 }, + { 0x1.65d4b8p-2, 0x1.04b27cp+0 }, + { 0x1.6df50ap-2, 0x1.036140p+0 }, + { 0x1.760abap-2, 0x1.0209a6p+0 }, + { 0x1.7e1594p-2, 0x1.00abd0p+0 }, + { 0x1.861566p-2, 0x1.fe8fb0p-1 }, + { 0x1.8e0a02p-2, 0x1.fbbbbep-1 }, + { 0x1.95f336p-2, 0x1.f8dc0ap-1 }, + { 0x1.9dd0d2p-2, 0x1.f5f0cep-1 }, + { 0x1.a5a2acp-2, 0x1.f2fa4cp-1 }, + { 0x1.ad6896p-2, 0x1.eff8c4p-1 }, + { 0x1.b52264p-2, 0x1.ecec78p-1 }, + { 0x1.bccfecp-2, 0x1.e9d5a8p-1 }, + { 0x1.c47104p-2, 0x1.e6b498p-1 }, + { 0x1.cc0584p-2, 0x1.e38988p-1 }, + { 0x1.d38d44p-2, 0x1.e054bep-1 }, + { 0x1.db081cp-2, 0x1.dd167cp-1 }, + { 0x1.e275eap-2, 0x1.d9cf06p-1 }, + { 0x1.e9d68ap-2, 0x1.d67ea2p-1 }, + { 0x1.f129d4p-2, 0x1.d32592p-1 }, + { 0x1.f86faap-2, 0x1.cfc41ep-1 }, + { 0x1.ffa7eap-2, 0x1.cc5a8ap-1 }, + { 0x1.03693ap-1, 0x1.c8e91cp-1 }, + { 0x1.06f794p-1, 0x1.c5701ap-1 }, + { 0x1.0a7ef6p-1, 0x1.c1efcap-1 }, + { 0x1.0dff50p-1, 0x1.be6872p-1 }, + { 0x1.117894p-1, 0x1.bada5ap-1 }, + { 0x1.14eab4p-1, 0x1.b745c6p-1 }, + { 0x1.1855a6p-1, 0x1.b3aafcp-1 }, + { 0x1.1bb95cp-1, 0x1.b00a46p-1 }, + { 0x1.1f15ccp-1, 0x1.ac63e8p-1 }, + { 0x1.226ae8p-1, 0x1.a8b828p-1 }, + { 0x1.25b8a8p-1, 0x1.a5074ep-1 }, + { 0x1.28ff02p-1, 0x1.a1519ep-1 }, + { 0x1.2c3decp-1, 0x1.9d9762p-1 }, + { 0x1.2f755cp-1, 0x1.99d8dap-1 }, + { 0x1.32a54cp-1, 0x1.961650p-1 }, + { 0x1.35cdb4p-1, 0x1.925008p-1 }, + { 0x1.38ee8ap-1, 0x1.8e8646p-1 }, + { 0x1.3c07cap-1, 0x1.8ab950p-1 }, + { 0x1.3f196ep-1, 0x1.86e96ap-1 }, + { 0x1.42236ep-1, 0x1.8316d6p-1 }, + { 0x1.4525c8p-1, 0x1.7f41dcp-1 }, + { 0x1.482074p-1, 0x1.7b6abcp-1 }, + { 0x1.4b1372p-1, 0x1.7791b8p-1 }, + { 0x1.4dfebap-1, 0x1.73b714p-1 }, + { 0x1.50e24cp-1, 0x1.6fdb12p-1 }, + { 0x1.53be26p-1, 0x1.6bfdf0p-1 }, + { 0x1.569244p-1, 0x1.681ff2p-1 }, + { 0x1.595ea6p-1, 0x1.644156p-1 }, + { 0x1.5c2348p-1, 0x1.60625cp-1 }, + { 0x1.5ee02ep-1, 0x1.5c8342p-1 }, + { 0x1.619556p-1, 0x1.58a446p-1 }, + { 0x1.6442c0p-1, 0x1.54c5a6p-1 }, + { 0x1.66e86ep-1, 0x1.50e79ep-1 }, + { 0x1.69865ep-1, 0x1.4d0a68p-1 }, + { 0x1.6c1c98p-1, 0x1.492e42p-1 }, + { 0x1.6eab18p-1, 0x1.455366p-1 }, + { 0x1.7131e6p-1, 0x1.417a0cp-1 }, + { 0x1.73b102p-1, 0x1.3da26ep-1 }, + { 0x1.762870p-1, 0x1.39ccc2p-1 }, + { 0x1.789836p-1, 0x1.35f940p-1 }, + { 0x1.7b0058p-1, 0x1.32281ep-1 }, + { 0x1.7d60d8p-1, 0x1.2e5992p-1 }, + { 0x1.7fb9c0p-1, 0x1.2a8dcep-1 }, + { 0x1.820b12p-1, 0x1.26c508p-1 }, + { 0x1.8454d6p-1, 0x1.22ff72p-1 }, + { 0x1.869712p-1, 0x1.1f3d3cp-1 }, + { 0x1.88d1cep-1, 0x1.1b7e98p-1 }, + { 0x1.8b050ep-1, 0x1.17c3b6p-1 }, + { 0x1.8d30dep-1, 0x1.140cc4p-1 }, + { 0x1.8f5544p-1, 0x1.1059eep-1 }, + { 0x1.91724ap-1, 0x1.0cab62p-1 }, + { 0x1.9387f6p-1, 0x1.09014cp-1 }, + { 0x1.959652p-1, 0x1.055bd6p-1 }, + { 0x1.979d68p-1, 0x1.01bb2cp-1 }, + { 0x1.999d42p-1, 0x1.fc3ee6p-2 }, + { 0x1.9b95e8p-1, 0x1.f511aap-2 }, + { 0x1.9d8768p-1, 0x1.edeeeep-2 }, + { 0x1.9f71cap-1, 0x1.e6d700p-2 }, + { 0x1.a1551ap-1, 0x1.dfca26p-2 }, + { 0x1.a33162p-1, 0x1.d8c8aap-2 }, + { 0x1.a506b0p-1, 0x1.d1d2d0p-2 }, + { 0x1.a6d50cp-1, 0x1.cae8dap-2 }, + { 0x1.a89c86p-1, 0x1.c40b08p-2 }, + { 0x1.aa5d26p-1, 0x1.bd3998p-2 }, + { 0x1.ac16fcp-1, 0x1.b674c8p-2 }, + { 0x1.adca14p-1, 0x1.afbcd4p-2 }, + { 0x1.af767ap-1, 0x1.a911f0p-2 }, + { 0x1.b11c3cp-1, 0x1.a27456p-2 }, + { 0x1.b2bb68p-1, 0x1.9be438p-2 }, + { 0x1.b4540ap-1, 0x1.9561c8p-2 }, + { 0x1.b5e630p-1, 0x1.8eed36p-2 }, + { 0x1.b771e8p-1, 0x1.8886b2p-2 }, + { 0x1.b8f742p-1, 0x1.822e66p-2 }, + { 0x1.ba764ap-1, 0x1.7be47ap-2 }, + { 0x1.bbef10p-1, 0x1.75a91ap-2 }, + { 0x1.bd61a2p-1, 0x1.6f7c6ap-2 }, + { 0x1.bece0ep-1, 0x1.695e8cp-2 }, + { 0x1.c03464p-1, 0x1.634fa6p-2 }, + { 0x1.c194b2p-1, 0x1.5d4fd4p-2 }, + { 0x1.c2ef08p-1, 0x1.575f34p-2 }, + { 0x1.c44376p-1, 0x1.517de6p-2 }, + { 0x1.c5920ap-1, 0x1.4bac00p-2 }, + { 0x1.c6dad2p-1, 0x1.45e99cp-2 }, + { 0x1.c81de2p-1, 0x1.4036d0p-2 }, + { 0x1.c95b46p-1, 0x1.3a93b2p-2 }, + { 0x1.ca930ep-1, 0x1.350052p-2 }, + { 0x1.cbc54cp-1, 0x1.2f7cc4p-2 }, + { 0x1.ccf20cp-1, 0x1.2a0916p-2 }, + { 0x1.ce1962p-1, 0x1.24a554p-2 }, + { 0x1.cf3b5cp-1, 0x1.1f518ap-2 }, + { 0x1.d0580cp-1, 0x1.1a0dc6p-2 }, + { 0x1.d16f7ep-1, 0x1.14da0ap-2 }, + { 0x1.d281c4p-1, 0x1.0fb662p-2 }, + { 0x1.d38ef0p-1, 0x1.0aa2d0p-2 }, + { 0x1.d49710p-1, 0x1.059f5ap-2 }, + { 0x1.d59a34p-1, 0x1.00ac00p-2 }, + { 0x1.d6986cp-1, 0x1.f79184p-3 }, + { 0x1.d791cap-1, 0x1.edeb40p-3 }, + { 0x1.d8865ep-1, 0x1.e46530p-3 }, + { 0x1.d97636p-1, 0x1.daff4ap-3 }, + { 0x1.da6162p-1, 0x1.d1b982p-3 }, + { 0x1.db47f4p-1, 0x1.c893cep-3 }, + { 0x1.dc29fcp-1, 0x1.bf8e1cp-3 }, + { 0x1.dd0788p-1, 0x1.b6a856p-3 }, + { 0x1.dde0aap-1, 0x1.ade26cp-3 }, + { 0x1.deb570p-1, 0x1.a53c42p-3 }, + { 0x1.df85eap-1, 0x1.9cb5bep-3 }, + { 0x1.e0522ap-1, 0x1.944ec2p-3 }, + { 0x1.e11a3ep-1, 0x1.8c0732p-3 }, + { 0x1.e1de36p-1, 0x1.83deeap-3 }, + { 0x1.e29e22p-1, 0x1.7bd5c8p-3 }, + { 0x1.e35a12p-1, 0x1.73eba4p-3 }, + { 0x1.e41214p-1, 0x1.6c2056p-3 }, + { 0x1.e4c638p-1, 0x1.6473b6p-3 }, + { 0x1.e5768cp-1, 0x1.5ce596p-3 }, + { 0x1.e62322p-1, 0x1.5575c8p-3 }, + { 0x1.e6cc08p-1, 0x1.4e241ep-3 }, + { 0x1.e7714ap-1, 0x1.46f066p-3 }, + { 0x1.e812fcp-1, 0x1.3fda6cp-3 }, + { 0x1.e8b12ap-1, 0x1.38e1fap-3 }, + { 0x1.e94be4p-1, 0x1.3206dcp-3 }, + { 0x1.e9e336p-1, 0x1.2b48dap-3 }, + { 0x1.ea7730p-1, 0x1.24a7b8p-3 }, + { 0x1.eb07e2p-1, 0x1.1e233ep-3 }, + { 0x1.eb9558p-1, 0x1.17bb2cp-3 }, + { 0x1.ec1fa2p-1, 0x1.116f48p-3 }, + { 0x1.eca6ccp-1, 0x1.0b3f52p-3 }, + { 0x1.ed2ae6p-1, 0x1.052b0cp-3 }, + { 0x1.edabfcp-1, 0x1.fe6460p-4 }, + { 0x1.ee2a1ep-1, 0x1.f2a902p-4 }, + { 0x1.eea556p-1, 0x1.e72372p-4 }, + { 0x1.ef1db4p-1, 0x1.dbd32ap-4 }, + { 0x1.ef9344p-1, 0x1.d0b7a0p-4 }, + { 0x1.f00614p-1, 0x1.c5d04ap-4 }, + { 0x1.f07630p-1, 0x1.bb1c98p-4 }, + { 0x1.f0e3a6p-1, 0x1.b09bfcp-4 }, + { 0x1.f14e82p-1, 0x1.a64de6p-4 }, + { 0x1.f1b6d0p-1, 0x1.9c31c6p-4 }, + { 0x1.f21ca0p-1, 0x1.92470ap-4 }, + { 0x1.f27ff8p-1, 0x1.888d1ep-4 }, + { 0x1.f2e0eap-1, 0x1.7f036cp-4 }, + { 0x1.f33f7ep-1, 0x1.75a960p-4 }, + { 0x1.f39bc2p-1, 0x1.6c7e64p-4 }, + { 0x1.f3f5c2p-1, 0x1.6381e2p-4 }, + { 0x1.f44d88p-1, 0x1.5ab342p-4 }, + { 0x1.f4a31ep-1, 0x1.5211ecp-4 }, + { 0x1.f4f694p-1, 0x1.499d48p-4 }, + { 0x1.f547f2p-1, 0x1.4154bcp-4 }, + { 0x1.f59742p-1, 0x1.3937b2p-4 }, + { 0x1.f5e490p-1, 0x1.31458ep-4 }, + { 0x1.f62fe8p-1, 0x1.297dbap-4 }, + { 0x1.f67952p-1, 0x1.21df9ap-4 }, + { 0x1.f6c0dcp-1, 0x1.1a6a96p-4 }, + { 0x1.f7068cp-1, 0x1.131e14p-4 }, + { 0x1.f74a6ep-1, 0x1.0bf97ep-4 }, + { 0x1.f78c8cp-1, 0x1.04fc3ap-4 }, + { 0x1.f7cceep-1, 0x1.fc4b5ep-5 }, + { 0x1.f80ba2p-1, 0x1.eeea8cp-5 }, + { 0x1.f848acp-1, 0x1.e1d4d0p-5 }, + { 0x1.f8841ap-1, 0x1.d508fap-5 }, + { 0x1.f8bdf2p-1, 0x1.c885e0p-5 }, + { 0x1.f8f63ep-1, 0x1.bc4a54p-5 }, + { 0x1.f92d08p-1, 0x1.b05530p-5 }, + { 0x1.f96256p-1, 0x1.a4a54ap-5 }, + { 0x1.f99634p-1, 0x1.99397ap-5 }, + { 0x1.f9c8a8p-1, 0x1.8e109cp-5 }, + { 0x1.f9f9bap-1, 0x1.83298ep-5 }, + { 0x1.fa2974p-1, 0x1.78832cp-5 }, + { 0x1.fa57dep-1, 0x1.6e1c58p-5 }, + { 0x1.fa84fep-1, 0x1.63f3f6p-5 }, + { 0x1.fab0dep-1, 0x1.5a08e8p-5 }, + { 0x1.fadb84p-1, 0x1.505a18p-5 }, + { 0x1.fb04f6p-1, 0x1.46e66cp-5 }, + { 0x1.fb2d40p-1, 0x1.3dacd2p-5 }, + { 0x1.fb5464p-1, 0x1.34ac36p-5 }, + { 0x1.fb7a6cp-1, 0x1.2be38cp-5 }, + { 0x1.fb9f60p-1, 0x1.2351c2p-5 }, + { 0x1.fbc344p-1, 0x1.1af5d2p-5 }, + { 0x1.fbe61ep-1, 0x1.12ceb4p-5 }, + { 0x1.fc07fap-1, 0x1.0adb60p-5 }, + { 0x1.fc28d8p-1, 0x1.031ad6p-5 }, + { 0x1.fc48c2p-1, 0x1.f7182ap-6 }, + { 0x1.fc67bcp-1, 0x1.e85c44p-6 }, + { 0x1.fc85d0p-1, 0x1.da0006p-6 }, + { 0x1.fca2fep-1, 0x1.cc0180p-6 }, + { 0x1.fcbf52p-1, 0x1.be5ecep-6 }, + { 0x1.fcdaccp-1, 0x1.b1160ap-6 }, + { 0x1.fcf576p-1, 0x1.a4255ap-6 }, + { 0x1.fd0f54p-1, 0x1.978ae8p-6 }, + { 0x1.fd286ap-1, 0x1.8b44e6p-6 }, + { 0x1.fd40bep-1, 0x1.7f5188p-6 }, + { 0x1.fd5856p-1, 0x1.73af0cp-6 }, + { 0x1.fd6f34p-1, 0x1.685bb6p-6 }, + { 0x1.fd8562p-1, 0x1.5d55ccp-6 }, + { 0x1.fd9ae2p-1, 0x1.529b9ep-6 }, + { 0x1.fdafb8p-1, 0x1.482b84p-6 }, + { 0x1.fdc3e8p-1, 0x1.3e03d8p-6 }, + { 0x1.fdd77ap-1, 0x1.3422fep-6 }, + { 0x1.fdea6ep-1, 0x1.2a875cp-6 }, + { 0x1.fdfcccp-1, 0x1.212f62p-6 }, + { 0x1.fe0e96p-1, 0x1.181984p-6 }, + { 0x1.fe1fd0p-1, 0x1.0f443ep-6 }, + { 0x1.fe3080p-1, 0x1.06ae14p-6 }, + { 0x1.fe40a6p-1, 0x1.fcab14p-7 }, + { 0x1.fe504cp-1, 0x1.ec7262p-7 }, + { 0x1.fe5f70p-1, 0x1.dcaf36p-7 }, + { 0x1.fe6e18p-1, 0x1.cd5ecap-7 }, + { 0x1.fe7c46p-1, 0x1.be7e5ap-7 }, + { 0x1.fe8a00p-1, 0x1.b00b38p-7 }, + { 0x1.fe9748p-1, 0x1.a202bep-7 }, + { 0x1.fea422p-1, 0x1.94624ep-7 }, + { 0x1.feb090p-1, 0x1.87275ep-7 }, + { 0x1.febc96p-1, 0x1.7a4f6ap-7 }, + { 0x1.fec836p-1, 0x1.6dd7fep-7 }, + { 0x1.fed374p-1, 0x1.61beaep-7 }, + { 0x1.fede52p-1, 0x1.56011cp-7 }, + { 0x1.fee8d4p-1, 0x1.4a9cf6p-7 }, + { 0x1.fef2fep-1, 0x1.3f8ff6p-7 }, + { 0x1.fefccep-1, 0x1.34d7dcp-7 }, + { 0x1.ff064cp-1, 0x1.2a727ap-7 }, + { 0x1.ff0f76p-1, 0x1.205dacp-7 }, + { 0x1.ff1852p-1, 0x1.169756p-7 }, + { 0x1.ff20e0p-1, 0x1.0d1d6ap-7 }, + { 0x1.ff2924p-1, 0x1.03ede2p-7 }, + { 0x1.ff3120p-1, 0x1.f60d8ap-8 }, + { 0x1.ff38d6p-1, 0x1.e4cc4ap-8 }, + { 0x1.ff4048p-1, 0x1.d4143ap-8 }, + { 0x1.ff4778p-1, 0x1.c3e1a6p-8 }, + { 0x1.ff4e68p-1, 0x1.b430ecp-8 }, + { 0x1.ff551ap-1, 0x1.a4fe84p-8 }, + { 0x1.ff5b90p-1, 0x1.9646f4p-8 }, + { 0x1.ff61ccp-1, 0x1.8806d8p-8 }, + { 0x1.ff67d0p-1, 0x1.7a3adep-8 }, + { 0x1.ff6d9ep-1, 0x1.6cdfccp-8 }, + { 0x1.ff7338p-1, 0x1.5ff276p-8 }, + { 0x1.ff789ep-1, 0x1.536fc2p-8 }, + { 0x1.ff7dd4p-1, 0x1.4754acp-8 }, + { 0x1.ff82dap-1, 0x1.3b9e40p-8 }, + { 0x1.ff87b2p-1, 0x1.30499cp-8 }, + { 0x1.ff8c5cp-1, 0x1.2553eep-8 }, + { 0x1.ff90dcp-1, 0x1.1aba78p-8 }, + { 0x1.ff9532p-1, 0x1.107a8cp-8 }, + { 0x1.ff9960p-1, 0x1.06918cp-8 }, + { 0x1.ff9d68p-1, 0x1.f9f9d0p-9 }, + { 0x1.ffa14ap-1, 0x1.e77448p-9 }, + { 0x1.ffa506p-1, 0x1.d58da6p-9 }, + { 0x1.ffa8a0p-1, 0x1.c4412cp-9 }, + { 0x1.ffac18p-1, 0x1.b38a3ap-9 }, + { 0x1.ffaf6ep-1, 0x1.a36454p-9 }, + { 0x1.ffb2a6p-1, 0x1.93cb12p-9 }, + { 0x1.ffb5bep-1, 0x1.84ba30p-9 }, + { 0x1.ffb8b8p-1, 0x1.762d84p-9 }, + { 0x1.ffbb98p-1, 0x1.682100p-9 }, + { 0x1.ffbe5ap-1, 0x1.5a90b0p-9 }, + { 0x1.ffc102p-1, 0x1.4d78bcp-9 }, + { 0x1.ffc390p-1, 0x1.40d564p-9 }, + { 0x1.ffc606p-1, 0x1.34a306p-9 }, + { 0x1.ffc862p-1, 0x1.28de12p-9 }, + { 0x1.ffcaa8p-1, 0x1.1d8318p-9 }, + { 0x1.ffccd8p-1, 0x1.128ebap-9 }, + { 0x1.ffcef4p-1, 0x1.07fdb4p-9 }, + { 0x1.ffd0fap-1, 0x1.fb99b8p-10 }, + { 0x1.ffd2eap-1, 0x1.e7f232p-10 }, + { 0x1.ffd4cap-1, 0x1.d4fed8p-10 }, + { 0x1.ffd696p-1, 0x1.c2b9d0p-10 }, + { 0x1.ffd84ep-1, 0x1.b11d70p-10 }, + { 0x1.ffd9f8p-1, 0x1.a02436p-10 }, + { 0x1.ffdb90p-1, 0x1.8fc8c8p-10 }, + { 0x1.ffdd18p-1, 0x1.8005f0p-10 }, + { 0x1.ffde90p-1, 0x1.70d6a4p-10 }, + { 0x1.ffdffap-1, 0x1.6235fcp-10 }, + { 0x1.ffe154p-1, 0x1.541f34p-10 }, + { 0x1.ffe2a2p-1, 0x1.468daep-10 }, + { 0x1.ffe3e2p-1, 0x1.397ceep-10 }, + { 0x1.ffe514p-1, 0x1.2ce898p-10 }, + { 0x1.ffe63cp-1, 0x1.20cc76p-10 }, + { 0x1.ffe756p-1, 0x1.15246ep-10 }, + { 0x1.ffe866p-1, 0x1.09ec86p-10 }, + { 0x1.ffe96ap-1, 0x1.fe41cep-11 }, + { 0x1.ffea64p-1, 0x1.e97ba4p-11 }, + { 0x1.ffeb54p-1, 0x1.d57f52p-11 }, + { 0x1.ffec3ap-1, 0x1.c245d4p-11 }, + { 0x1.ffed16p-1, 0x1.afc85ep-11 }, + { 0x1.ffedeap-1, 0x1.9e0058p-11 }, + { 0x1.ffeeb4p-1, 0x1.8ce75ep-11 }, + { 0x1.ffef76p-1, 0x1.7c7744p-11 }, + { 0x1.fff032p-1, 0x1.6caa0ep-11 }, + { 0x1.fff0e4p-1, 0x1.5d79ecp-11 }, + { 0x1.fff18ep-1, 0x1.4ee142p-11 }, + { 0x1.fff232p-1, 0x1.40daa4p-11 }, + { 0x1.fff2d0p-1, 0x1.3360ccp-11 }, + { 0x1.fff366p-1, 0x1.266ea8p-11 }, + { 0x1.fff3f6p-1, 0x1.19ff46p-11 }, + { 0x1.fff480p-1, 0x1.0e0de8p-11 }, + { 0x1.fff504p-1, 0x1.0295f0p-11 }, + { 0x1.fff582p-1, 0x1.ef25d4p-12 }, + { 0x1.fff5fcp-1, 0x1.da0110p-12 }, + { 0x1.fff670p-1, 0x1.c5b542p-12 }, + { 0x1.fff6dep-1, 0x1.b23a5ap-12 }, + { 0x1.fff74ap-1, 0x1.9f8894p-12 }, + { 0x1.fff7aep-1, 0x1.8d986ap-12 }, + { 0x1.fff810p-1, 0x1.7c629ap-12 }, + { 0x1.fff86cp-1, 0x1.6be022p-12 }, + { 0x1.fff8c6p-1, 0x1.5c0a38p-12 }, + { 0x1.fff91cp-1, 0x1.4cda54p-12 }, + { 0x1.fff96cp-1, 0x1.3e4a24p-12 }, + { 0x1.fff9bap-1, 0x1.305390p-12 }, + { 0x1.fffa04p-1, 0x1.22f0b4p-12 }, + { 0x1.fffa4cp-1, 0x1.161be4p-12 }, + { 0x1.fffa90p-1, 0x1.09cfa4p-12 }, + { 0x1.fffad0p-1, 0x1.fc0d56p-13 }, + { 0x1.fffb0ep-1, 0x1.e577bcp-13 }, + { 0x1.fffb4ap-1, 0x1.cfd4a6p-13 }, + { 0x1.fffb82p-1, 0x1.bb1a96p-13 }, + { 0x1.fffbb8p-1, 0x1.a74068p-13 }, + { 0x1.fffbecp-1, 0x1.943d4ap-13 }, + { 0x1.fffc1ep-1, 0x1.8208bcp-13 }, + { 0x1.fffc4ep-1, 0x1.709a8ep-13 }, + { 0x1.fffc7ap-1, 0x1.5feadap-13 }, + { 0x1.fffca6p-1, 0x1.4ff208p-13 }, + { 0x1.fffccep-1, 0x1.40a8c2p-13 }, + { 0x1.fffcf6p-1, 0x1.3207fcp-13 }, + { 0x1.fffd1ap-1, 0x1.2408eap-13 }, + { 0x1.fffd3ep-1, 0x1.16a502p-13 }, + { 0x1.fffd60p-1, 0x1.09d5f8p-13 }, + { 0x1.fffd80p-1, 0x1.fb2b7ap-14 }, + { 0x1.fffda0p-1, 0x1.e3bcf4p-14 }, + { 0x1.fffdbep-1, 0x1.cd5528p-14 }, + { 0x1.fffddap-1, 0x1.b7e946p-14 }, + { 0x1.fffdf4p-1, 0x1.a36eecp-14 }, + { 0x1.fffe0ep-1, 0x1.8fdc1cp-14 }, + { 0x1.fffe26p-1, 0x1.7d2738p-14 }, + { 0x1.fffe3ep-1, 0x1.6b4702p-14 }, + { 0x1.fffe54p-1, 0x1.5a329cp-14 }, + { 0x1.fffe68p-1, 0x1.49e178p-14 }, + { 0x1.fffe7ep-1, 0x1.3a4b60p-14 }, + { 0x1.fffe90p-1, 0x1.2b6876p-14 }, + { 0x1.fffea2p-1, 0x1.1d3120p-14 }, + { 0x1.fffeb4p-1, 0x1.0f9e1cp-14 }, + { 0x1.fffec4p-1, 0x1.02a868p-14 }, + { 0x1.fffed4p-1, 0x1.ec929ap-15 }, + { 0x1.fffee4p-1, 0x1.d4f4b4p-15 }, + { 0x1.fffef2p-1, 0x1.be6abcp-15 }, + { 0x1.ffff00p-1, 0x1.a8e8ccp-15 }, + { 0x1.ffff0cp-1, 0x1.94637ep-15 }, + { 0x1.ffff18p-1, 0x1.80cfdcp-15 }, + { 0x1.ffff24p-1, 0x1.6e2368p-15 }, + { 0x1.ffff30p-1, 0x1.5c540cp-15 }, + { 0x1.ffff3ap-1, 0x1.4b581cp-15 }, + { 0x1.ffff44p-1, 0x1.3b2652p-15 }, + { 0x1.ffff4ep-1, 0x1.2bb5ccp-15 }, + { 0x1.ffff56p-1, 0x1.1cfe02p-15 }, + { 0x1.ffff60p-1, 0x1.0ef6c4p-15 }, + { 0x1.ffff68p-1, 0x1.019842p-15 }, + { 0x1.ffff70p-1, 0x1.e9b5e8p-16 }, + { 0x1.ffff78p-1, 0x1.d16f58p-16 }, + { 0x1.ffff7ep-1, 0x1.ba4f04p-16 }, + { 0x1.ffff84p-1, 0x1.a447b8p-16 }, + { 0x1.ffff8cp-1, 0x1.8f4cccp-16 }, + { 0x1.ffff92p-1, 0x1.7b5224p-16 }, + { 0x1.ffff98p-1, 0x1.684c22p-16 }, + { 0x1.ffff9cp-1, 0x1.562facp-16 }, + { 0x1.ffffa2p-1, 0x1.44f21ep-16 }, + { 0x1.ffffa6p-1, 0x1.34894ap-16 }, + { 0x1.ffffacp-1, 0x1.24eb72p-16 }, + { 0x1.ffffb0p-1, 0x1.160f44p-16 }, + { 0x1.ffffb4p-1, 0x1.07ebd2p-16 }, + { 0x1.ffffb8p-1, 0x1.f4f12ep-17 }, + { 0x1.ffffbcp-1, 0x1.db5ad0p-17 }, + { 0x1.ffffc0p-1, 0x1.c304f0p-17 }, + { 0x1.ffffc4p-1, 0x1.abe09ep-17 }, + { 0x1.ffffc6p-1, 0x1.95df98p-17 }, + { 0x1.ffffcap-1, 0x1.80f43ap-17 }, + { 0x1.ffffccp-1, 0x1.6d1178p-17 }, + { 0x1.ffffd0p-1, 0x1.5a2ae0p-17 }, + { 0x1.ffffd2p-1, 0x1.483488p-17 }, + { 0x1.ffffd4p-1, 0x1.372310p-17 }, + { 0x1.ffffd6p-1, 0x1.26eb9ep-17 }, + { 0x1.ffffd8p-1, 0x1.1783cep-17 }, + { 0x1.ffffdcp-1, 0x1.08e1bap-17 }, + { 0x1.ffffdep-1, 0x1.f5f7d8p-18 }, + { 0x1.ffffdep-1, 0x1.db92b6p-18 }, + { 0x1.ffffe0p-1, 0x1.c282cep-18 }, + { 0x1.ffffe2p-1, 0x1.aab7acp-18 }, + { 0x1.ffffe4p-1, 0x1.94219cp-18 }, + { 0x1.ffffe6p-1, 0x1.7eb1a2p-18 }, + { 0x1.ffffe8p-1, 0x1.6a5972p-18 }, + { 0x1.ffffe8p-1, 0x1.570b6ap-18 }, + { 0x1.ffffeap-1, 0x1.44ba86p-18 }, + { 0x1.ffffeap-1, 0x1.335a62p-18 }, + { 0x1.ffffecp-1, 0x1.22df2ap-18 }, + { 0x1.ffffeep-1, 0x1.133d96p-18 }, + { 0x1.ffffeep-1, 0x1.046aeap-18 }, + { 0x1.fffff0p-1, 0x1.ecb9d0p-19 }, + { 0x1.fffff0p-1, 0x1.d21398p-19 }, + { 0x1.fffff2p-1, 0x1.b8d094p-19 }, + { 0x1.fffff2p-1, 0x1.a0df10p-19 }, + { 0x1.fffff2p-1, 0x1.8a2e26p-19 }, + { 0x1.fffff4p-1, 0x1.74adc8p-19 }, + { 0x1.fffff4p-1, 0x1.604ea8p-19 }, + { 0x1.fffff4p-1, 0x1.4d0232p-19 }, + { 0x1.fffff6p-1, 0x1.3aba86p-19 }, + { 0x1.fffff6p-1, 0x1.296a70p-19 }, + { 0x1.fffff6p-1, 0x1.190562p-19 }, + { 0x1.fffff8p-1, 0x1.097f62p-19 }, + { 0x1.fffff8p-1, 0x1.f59a20p-20 }, + { 0x1.fffff8p-1, 0x1.d9c736p-20 }, + { 0x1.fffff8p-1, 0x1.bf716cp-20 }, + { 0x1.fffffap-1, 0x1.a6852cp-20 }, + { 0x1.fffffap-1, 0x1.8eefd8p-20 }, + { 0x1.fffffap-1, 0x1.789fb8p-20 }, + { 0x1.fffffap-1, 0x1.6383f8p-20 }, + { 0x1.fffffap-1, 0x1.4f8c96p-20 }, + { 0x1.fffffap-1, 0x1.3caa62p-20 }, + { 0x1.fffffcp-1, 0x1.2acee2p-20 }, + { 0x1.fffffcp-1, 0x1.19ec60p-20 }, + { 0x1.fffffcp-1, 0x1.09f5d0p-20 }, + { 0x1.fffffcp-1, 0x1.f5bd96p-21 }, + { 0x1.fffffcp-1, 0x1.d9371ep-21 }, + { 0x1.fffffcp-1, 0x1.be41dep-21 }, + { 0x1.fffffcp-1, 0x1.a4c89ep-21 }, + { 0x1.fffffcp-1, 0x1.8cb738p-21 }, + { 0x1.fffffep-1, 0x1.75fa8ep-21 }, + { 0x1.fffffep-1, 0x1.608078p-21 }, + { 0x1.fffffep-1, 0x1.4c37c0p-21 }, + { 0x1.fffffep-1, 0x1.39100ep-21 }, + { 0x1.fffffep-1, 0x1.26f9e0p-21 }, + { 0x1.fffffep-1, 0x1.15e682p-21 }, + { 0x1.fffffep-1, 0x1.05c804p-21 }, + { 0x1.fffffep-1, 0x1.ed2254p-22 }, + { 0x1.fffffep-1, 0x1.d06ad6p-22 }, + { 0x1.fffffep-1, 0x1.b551c8p-22 }, + { 0x1.fffffep-1, 0x1.9bc0a0p-22 }, + { 0x1.fffffep-1, 0x1.83a200p-22 }, + { 0x1.fffffep-1, 0x1.6ce1aap-22 }, + { 0x1.fffffep-1, 0x1.576c72p-22 }, + { 0x1.fffffep-1, 0x1.43302cp-22 }, + { 0x1.fffffep-1, 0x1.301ba2p-22 }, + { 0x1.fffffep-1, 0x1.1e1e86p-22 }, + { 0x1.fffffep-1, 0x1.0d2966p-22 }, + { 0x1.000000p+0, 0x1.fa5b50p-23 }, + { 0x1.000000p+0, 0x1.dc3ae4p-23 }, + { 0x1.000000p+0, 0x1.bfd756p-23 }, + { 0x1.000000p+0, 0x1.a517dap-23 }, + { 0x1.000000p+0, 0x1.8be4f8p-23 }, + { 0x1.000000p+0, 0x1.74287ep-23 }, + { 0x1.000000p+0, 0x1.5dcd66p-23 }, + { 0x1.000000p+0, 0x1.48bfd4p-23 }, + { 0x1.000000p+0, 0x1.34ecf8p-23 }, + { 0x1.000000p+0, 0x1.224310p-23 }, + { 0x1.000000p+0, 0x1.10b148p-23 }, + }, +}; diff --git a/sysdeps/aarch64/fpu/erff_sve.c b/sysdeps/aarch64/fpu/erff_sve.c new file mode 100644 index 0000000000..38f00db9be --- /dev/null +++ b/sysdeps/aarch64/fpu/erff_sve.c @@ -0,0 +1,93 @@ +/* Single-precision vector (SVE) erf function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" + +static const struct data +{ + float min, max, scale, shift, third; +} data = { + .min = 0x1.cp-7f, /* 1/64 - 1/512. */ + .max = 3.9375, /* 4 - 8/128. */ + .scale = 0x1.20dd76p+0f, /* 2/sqrt(pi). */ + .shift = 0x1p16f, + .third = 0x1.555556p-2f, /* 1/3. */ +}; + +#define SignMask (0x80000000) + +/* Single-precision implementation of vector erf(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/128. + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + + erf(x) ~ erf(r) + scale * d * [1 - r * d - 1/3 * d^2] + + Values of erf(r) and scale are read from lookup tables. + For |x| < 0x1.cp-7, the algorithm sets r = 0, erf(r) = 0, and scale = 2 / + sqrt(pi), so it simply boils down to a Taylor series expansion near 0. For + |x| > 3.9375, erf(|x|) rounds to 1.0f. + + Maximum error on each interval: + - [0, 0x1.cp-7]: 1.93 ULP + _ZGVsMxv_erff(0x1.c373e6p-9) got 0x1.fd686cp-9 want 0x1.fd6868p-9 + - [0x1.cp-7, 4.0]: 1.26 ULP + _ZGVsMxv_erff(0x1.1d002ep+0) got 0x1.c4eb9ap-1 want 0x1.c4eb98p-1. */ +svfloat32_t SV_NAME_F1 (erf) (svfloat32_t x, const svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + + /* |x| > 1/64 - 1/512. */ + svbool_t a_gt_min = svacgt (pg, x, dat->min); + + /* |x| >= 4.0 - 8/128. */ + svbool_t a_ge_max = svacge (pg, x, dat->max); + svfloat32_t a = svabs_x (pg, x); + + svfloat32_t shift = sv_f32 (dat->shift); + svfloat32_t z = svadd_x (pg, a, shift); + svuint32_t i + = svsub_x (pg, svreinterpret_u32 (z), svreinterpret_u32 (shift)); + + /* Saturate lookup index. */ + i = svsel (a_ge_max, sv_u32 (512), i); + + /* r and erf(r) set to 0 for |x| below min. */ + svfloat32_t r = svsub_z (a_gt_min, z, shift); + svfloat32_t erfr = svld1_gather_index (a_gt_min, __sv_erff_data.erf, i); + + /* scale set to 2/sqrt(pi) for |x| below min. */ + svfloat32_t scale = svld1_gather_index (a_gt_min, __sv_erff_data.scale, i); + scale = svsel (a_gt_min, scale, sv_f32 (dat->scale)); + + /* erf(x) ~ erf(r) + scale * d * (1 - r * d + 1/3 * d^2). */ + svfloat32_t d = svsub_x (pg, a, r); + svfloat32_t d2 = svmul_x (pg, d, d); + svfloat32_t y = svmla_x (pg, r, d, dat->third); + y = svmla_x (pg, erfr, scale, svmls_x (pg, d, d2, y)); + + /* Solves the |x| = inf case. */ + y = svsel (a_ge_max, sv_f32 (1.0f), y); + + /* Copy sign. */ + svuint32_t ix = svreinterpret_u32 (x); + svuint32_t iy = svreinterpret_u32 (y); + svuint32_t sign = svand_x (pg, ix, SignMask); + return svreinterpret_f32 (svorr_x (pg, sign, iy)); +} diff --git a/sysdeps/aarch64/fpu/sv_erf_data.c b/sysdeps/aarch64/fpu/sv_erf_data.c new file mode 100644 index 0000000000..a53878f893 --- /dev/null +++ b/sysdeps/aarch64/fpu/sv_erf_data.c @@ -0,0 +1,1570 @@ +/* Table for SVE erf approximation + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "vecmath_config.h" + +/* Lookup table used in vector erf. + For each possible rounded input r (multiples of 1/128), between + r = 0.0 and r = 6.0 (769 values): + - the first entry __erf_data.tab.erf contains the values of erf(r), + - the second entry __erf_data.tab.scale contains the values of + 2/sqrt(pi)*exp(-r^2). Note that indices 0 and 1 are never hit by the + algorithm, since lookup is performed only for x >= 1/64-1/512. */ +const struct sv_erf_data __sv_erf_data = { + .erf = { 0x0.0000000000000p+0, + 0x1.20dbf3deb1340p-7, + 0x1.20d77083f17a0p-6, + 0x1.b137e0cf584dcp-6, + 0x1.20c5645dd2538p-5, + 0x1.68e5d3bbc9526p-5, + 0x1.b0fafef135745p-5, + 0x1.f902a77bd3821p-5, + 0x1.207d480e90658p-4, + 0x1.44703e87e8593p-4, + 0x1.68591a1e83b5dp-4, + 0x1.8c36beb8a8d23p-4, + 0x1.b0081148a873ap-4, + 0x1.d3cbf7e70a4b3p-4, + 0x1.f78159ec8bb50p-4, + 0x1.0d939005f65e5p-3, + 0x1.1f5e1a35c3b89p-3, + 0x1.311fc15f56d14p-3, + 0x1.42d7fc2f64959p-3, + 0x1.548642321d7c6p-3, + 0x1.662a0bdf7a89fp-3, + 0x1.77c2d2a765f9ep-3, + 0x1.895010fdbdbfdp-3, + 0x1.9ad142662e14dp-3, + 0x1.ac45e37fe2526p-3, + 0x1.bdad72110a648p-3, + 0x1.cf076d1233237p-3, + 0x1.e05354b96ff36p-3, + 0x1.f190aa85540e2p-3, + 0x1.015f78a3dcf3dp-2, + 0x1.09eed6982b948p-2, + 0x1.127631eb8de32p-2, + 0x1.1af54e232d609p-2, + 0x1.236bef825d9a2p-2, + 0x1.2bd9db0f7827fp-2, + 0x1.343ed6989b7d9p-2, + 0x1.3c9aa8b84bedap-2, + 0x1.44ed18d9f6462p-2, + 0x1.4d35ef3e5372ep-2, + 0x1.5574f4ffac98ep-2, + 0x1.5da9f415ff23fp-2, + 0x1.65d4b75b00471p-2, + 0x1.6df50a8dff772p-2, + 0x1.760aba57a76bfp-2, + 0x1.7e15944d9d3e4p-2, + 0x1.861566f5fd3c0p-2, + 0x1.8e0a01cab516bp-2, + 0x1.95f3353cbb146p-2, + 0x1.9dd0d2b721f39p-2, + 0x1.a5a2aca209394p-2, + 0x1.ad68966569a87p-2, + 0x1.b522646bbda68p-2, + 0x1.bccfec24855b8p-2, + 0x1.c4710406a65fcp-2, + 0x1.cc058392a6d2dp-2, + 0x1.d38d4354c3bd0p-2, + 0x1.db081ce6e2a48p-2, + 0x1.e275eaf25e458p-2, + 0x1.e9d68931ae650p-2, + 0x1.f129d471eabb1p-2, + 0x1.f86faa9428f9dp-2, + 0x1.ffa7ea8eb5fd0p-2, + 0x1.03693a371519cp-1, + 0x1.06f794ab2cae7p-1, + 0x1.0a7ef5c18edd2p-1, + 0x1.0dff4f247f6c6p-1, + 0x1.1178930ada115p-1, + 0x1.14eab43841b55p-1, + 0x1.1855a5fd3dd50p-1, + 0x1.1bb95c3746199p-1, + 0x1.1f15cb50bc4dep-1, + 0x1.226ae840d4d70p-1, + 0x1.25b8a88b6dd7fp-1, + 0x1.28ff0240d52cdp-1, + 0x1.2c3debfd7d6c1p-1, + 0x1.2f755ce9a21f4p-1, + 0x1.32a54cb8db67bp-1, + 0x1.35cdb3a9a144dp-1, + 0x1.38ee8a84beb71p-1, + 0x1.3c07ca9cb4f9ep-1, + 0x1.3f196dcd0f135p-1, + 0x1.42236e79a5fa6p-1, + 0x1.4525c78dd5966p-1, + 0x1.4820747ba2dc2p-1, + 0x1.4b13713ad3513p-1, + 0x1.4dfeba47f63ccp-1, + 0x1.50e24ca35fd2cp-1, + 0x1.53be25d016a4fp-1, + 0x1.569243d2b3a9bp-1, + 0x1.595ea53035283p-1, + 0x1.5c2348ecc4dc3p-1, + 0x1.5ee02e8a71a53p-1, + 0x1.61955607dd15dp-1, + 0x1.6442bfdedd397p-1, + 0x1.66e86d0312e82p-1, + 0x1.69865ee075011p-1, + 0x1.6c1c9759d0e5fp-1, + 0x1.6eab18c74091bp-1, + 0x1.7131e5f496a5ap-1, + 0x1.73b1021fc0cb8p-1, + 0x1.762870f720c6fp-1, + 0x1.78983697dc96fp-1, + 0x1.7b00578c26037p-1, + 0x1.7d60d8c979f7bp-1, + 0x1.7fb9bfaed8078p-1, + 0x1.820b1202f27fbp-1, + 0x1.8454d5f25760dp-1, + 0x1.8697120d92a4ap-1, + 0x1.88d1cd474a2e0p-1, + 0x1.8b050ef253c37p-1, + 0x1.8d30debfc572ep-1, + 0x1.8f5544bd00c04p-1, + 0x1.91724951b8fc6p-1, + 0x1.9387f53df5238p-1, + 0x1.959651980da31p-1, + 0x1.979d67caa6631p-1, + 0x1.999d4192a5715p-1, + 0x1.9b95e8fd26abap-1, + 0x1.9d8768656cc42p-1, + 0x1.9f71ca72cffb6p-1, + 0x1.a1551a16aaeafp-1, + 0x1.a331628a45b92p-1, + 0x1.a506af4cc00f4p-1, + 0x1.a6d50c20fa293p-1, + 0x1.a89c850b7d54dp-1, + 0x1.aa5d265064366p-1, + 0x1.ac16fc7143263p-1, + 0x1.adca142b10f98p-1, + 0x1.af767a741088bp-1, + 0x1.b11c3c79bb424p-1, + 0x1.b2bb679ead19cp-1, + 0x1.b4540978921eep-1, + 0x1.b5e62fce16095p-1, + 0x1.b771e894d602ep-1, + 0x1.b8f741ef54f83p-1, + 0x1.ba764a2af2b78p-1, + 0x1.bbef0fbde6221p-1, + 0x1.bd61a1453ab44p-1, + 0x1.bece0d82d1a5cp-1, + 0x1.c034635b66e23p-1, + 0x1.c194b1d49a184p-1, + 0x1.c2ef0812fc1bdp-1, + 0x1.c443755820d64p-1, + 0x1.c5920900b5fd1p-1, + 0x1.c6dad2829ec62p-1, + 0x1.c81de16b14cefp-1, + 0x1.c95b455cce69dp-1, + 0x1.ca930e0e2a825p-1, + 0x1.cbc54b476248dp-1, + 0x1.ccf20ce0c0d27p-1, + 0x1.ce1962c0e0d8bp-1, + 0x1.cf3b5cdaf0c39p-1, + 0x1.d0580b2cfd249p-1, + 0x1.d16f7dbe41ca0p-1, + 0x1.d281c49d818d0p-1, + 0x1.d38eefdf64fddp-1, + 0x1.d4970f9ce00d9p-1, + 0x1.d59a33f19ed42p-1, + 0x1.d6986cfa798e7p-1, + 0x1.d791cad3eff01p-1, + 0x1.d8865d98abe01p-1, + 0x1.d97635600bb89p-1, + 0x1.da61623cb41e0p-1, + 0x1.db47f43b2980dp-1, + 0x1.dc29fb60715afp-1, + 0x1.dd0787a8bb39dp-1, + 0x1.dde0a90611a0dp-1, + 0x1.deb56f5f12d28p-1, + 0x1.df85ea8db188ep-1, + 0x1.e0522a5dfda73p-1, + 0x1.e11a3e8cf4eb8p-1, + 0x1.e1de36c75ba58p-1, + 0x1.e29e22a89d766p-1, + 0x1.e35a11b9b61cep-1, + 0x1.e4121370224ccp-1, + 0x1.e4c6372cd8927p-1, + 0x1.e5768c3b4a3fcp-1, + 0x1.e62321d06c5e0p-1, + 0x1.e6cc0709c8a0dp-1, + 0x1.e7714aec96534p-1, + 0x1.e812fc64db369p-1, + 0x1.e8b12a44944a8p-1, + 0x1.e94be342e6743p-1, + 0x1.e9e335fb56f87p-1, + 0x1.ea7730ed0bbb9p-1, + 0x1.eb07e27a133aap-1, + 0x1.eb9558e6b42cep-1, + 0x1.ec1fa258c4beap-1, + 0x1.eca6ccd709544p-1, + 0x1.ed2ae6489ac1ep-1, + 0x1.edabfc7453e63p-1, + 0x1.ee2a1d004692cp-1, + 0x1.eea5557137ae0p-1, + 0x1.ef1db32a2277cp-1, + 0x1.ef93436bc2daap-1, + 0x1.f006135426b26p-1, + 0x1.f0762fde45ee6p-1, + 0x1.f0e3a5e1a1788p-1, + 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a/sysdeps/aarch64/fpu/sv_erff_data.c b/sysdeps/aarch64/fpu/sv_erff_data.c new file mode 100644 index 0000000000..6dcd72af69 --- /dev/null +++ b/sysdeps/aarch64/fpu/sv_erff_data.c @@ -0,0 +1,1058 @@ +/* Table for SVE erff approximation + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "vecmath_config.h" + +/* Lookup table used in SVE erff. + For each possible rounded input r (multiples of 1/128), between + r = 0.0 and r = 4.0 (513 values): + - __erff_data.erf contains the values of erf(r), + - __erff_data.scale contains the values of 2/sqrt(pi)*exp(-r^2). + Note that indices 0 and 1 are never hit by the algorithm, since lookup is + performed only for x >= 1/64-1/512. */ +const struct sv_erff_data __sv_erff_data = { + .erf = { 0x0.000000p+0, + 0x1.20dbf4p-7, + 0x1.20d770p-6, + 0x1.b137e0p-6, + 0x1.20c564p-5, + 0x1.68e5d4p-5, + 0x1.b0fafep-5, + 0x1.f902a8p-5, + 0x1.207d48p-4, + 0x1.44703ep-4, + 0x1.68591ap-4, + 0x1.8c36bep-4, + 0x1.b00812p-4, + 0x1.d3cbf8p-4, + 0x1.f7815ap-4, + 0x1.0d9390p-3, + 0x1.1f5e1ap-3, + 0x1.311fc2p-3, + 0x1.42d7fcp-3, + 0x1.548642p-3, + 0x1.662a0cp-3, + 0x1.77c2d2p-3, + 0x1.895010p-3, + 0x1.9ad142p-3, + 0x1.ac45e4p-3, + 0x1.bdad72p-3, + 0x1.cf076ep-3, + 0x1.e05354p-3, + 0x1.f190aap-3, + 0x1.015f78p-2, + 0x1.09eed6p-2, + 0x1.127632p-2, + 0x1.1af54ep-2, + 0x1.236bf0p-2, + 0x1.2bd9dcp-2, + 0x1.343ed6p-2, + 0x1.3c9aa8p-2, + 0x1.44ed18p-2, + 0x1.4d35f0p-2, + 0x1.5574f4p-2, + 0x1.5da9f4p-2, + 0x1.65d4b8p-2, + 0x1.6df50ap-2, + 0x1.760abap-2, + 0x1.7e1594p-2, + 0x1.861566p-2, + 0x1.8e0a02p-2, + 0x1.95f336p-2, + 0x1.9dd0d2p-2, + 0x1.a5a2acp-2, + 0x1.ad6896p-2, + 0x1.b52264p-2, + 0x1.bccfecp-2, + 0x1.c47104p-2, + 0x1.cc0584p-2, + 0x1.d38d44p-2, + 0x1.db081cp-2, + 0x1.e275eap-2, + 0x1.e9d68ap-2, + 0x1.f129d4p-2, + 0x1.f86faap-2, + 0x1.ffa7eap-2, + 0x1.03693ap-1, + 0x1.06f794p-1, + 0x1.0a7ef6p-1, + 0x1.0dff50p-1, + 0x1.117894p-1, + 0x1.14eab4p-1, + 0x1.1855a6p-1, + 0x1.1bb95cp-1, + 0x1.1f15ccp-1, + 0x1.226ae8p-1, + 0x1.25b8a8p-1, + 0x1.28ff02p-1, + 0x1.2c3decp-1, + 0x1.2f755cp-1, + 0x1.32a54cp-1, + 0x1.35cdb4p-1, + 0x1.38ee8ap-1, + 0x1.3c07cap-1, + 0x1.3f196ep-1, + 0x1.42236ep-1, + 0x1.4525c8p-1, + 0x1.482074p-1, + 0x1.4b1372p-1, + 0x1.4dfebap-1, + 0x1.50e24cp-1, + 0x1.53be26p-1, + 0x1.569244p-1, + 0x1.595ea6p-1, + 0x1.5c2348p-1, + 0x1.5ee02ep-1, + 0x1.619556p-1, + 0x1.6442c0p-1, + 0x1.66e86ep-1, + 0x1.69865ep-1, + 0x1.6c1c98p-1, + 0x1.6eab18p-1, + 0x1.7131e6p-1, + 0x1.73b102p-1, + 0x1.762870p-1, + 0x1.789836p-1, + 0x1.7b0058p-1, + 0x1.7d60d8p-1, + 0x1.7fb9c0p-1, + 0x1.820b12p-1, + 0x1.8454d6p-1, + 0x1.869712p-1, + 0x1.88d1cep-1, + 0x1.8b050ep-1, + 0x1.8d30dep-1, + 0x1.8f5544p-1, + 0x1.91724ap-1, + 0x1.9387f6p-1, + 0x1.959652p-1, + 0x1.979d68p-1, + 0x1.999d42p-1, + 0x1.9b95e8p-1, + 0x1.9d8768p-1, + 0x1.9f71cap-1, + 0x1.a1551ap-1, + 0x1.a33162p-1, + 0x1.a506b0p-1, + 0x1.a6d50cp-1, + 0x1.a89c86p-1, + 0x1.aa5d26p-1, + 0x1.ac16fcp-1, + 0x1.adca14p-1, + 0x1.af767ap-1, + 0x1.b11c3cp-1, + 0x1.b2bb68p-1, + 0x1.b4540ap-1, + 0x1.b5e630p-1, + 0x1.b771e8p-1, + 0x1.b8f742p-1, + 0x1.ba764ap-1, + 0x1.bbef10p-1, + 0x1.bd61a2p-1, + 0x1.bece0ep-1, + 0x1.c03464p-1, + 0x1.c194b2p-1, + 0x1.c2ef08p-1, + 0x1.c44376p-1, + 0x1.c5920ap-1, + 0x1.c6dad2p-1, + 0x1.c81de2p-1, + 0x1.c95b46p-1, + 0x1.ca930ep-1, + 0x1.cbc54cp-1, + 0x1.ccf20cp-1, + 0x1.ce1962p-1, + 0x1.cf3b5cp-1, + 0x1.d0580cp-1, + 0x1.d16f7ep-1, + 0x1.d281c4p-1, + 0x1.d38ef0p-1, + 0x1.d49710p-1, + 0x1.d59a34p-1, + 0x1.d6986cp-1, + 0x1.d791cap-1, + 0x1.d8865ep-1, + 0x1.d97636p-1, + 0x1.da6162p-1, + 0x1.db47f4p-1, + 0x1.dc29fcp-1, + 0x1.dd0788p-1, + 0x1.dde0aap-1, + 0x1.deb570p-1, + 0x1.df85eap-1, + 0x1.e0522ap-1, + 0x1.e11a3ep-1, + 0x1.e1de36p-1, + 0x1.e29e22p-1, + 0x1.e35a12p-1, + 0x1.e41214p-1, + 0x1.e4c638p-1, + 0x1.e5768cp-1, + 0x1.e62322p-1, + 0x1.e6cc08p-1, + 0x1.e7714ap-1, + 0x1.e812fcp-1, + 0x1.e8b12ap-1, + 0x1.e94be4p-1, + 0x1.e9e336p-1, + 0x1.ea7730p-1, + 0x1.eb07e2p-1, + 0x1.eb9558p-1, + 0x1.ec1fa2p-1, + 0x1.eca6ccp-1, + 0x1.ed2ae6p-1, + 0x1.edabfcp-1, + 0x1.ee2a1ep-1, + 0x1.eea556p-1, + 0x1.ef1db4p-1, + 0x1.ef9344p-1, + 0x1.f00614p-1, + 0x1.f07630p-1, + 0x1.f0e3a6p-1, + 0x1.f14e82p-1, + 0x1.f1b6d0p-1, + 0x1.f21ca0p-1, + 0x1.f27ff8p-1, + 0x1.f2e0eap-1, + 0x1.f33f7ep-1, + 0x1.f39bc2p-1, + 0x1.f3f5c2p-1, + 0x1.f44d88p-1, + 0x1.f4a31ep-1, + 0x1.f4f694p-1, + 0x1.f547f2p-1, + 0x1.f59742p-1, + 0x1.f5e490p-1, + 0x1.f62fe8p-1, + 0x1.f67952p-1, + 0x1.f6c0dcp-1, + 0x1.f7068cp-1, + 0x1.f74a6ep-1, + 0x1.f78c8cp-1, + 0x1.f7cceep-1, + 0x1.f80ba2p-1, + 0x1.f848acp-1, + 0x1.f8841ap-1, + 0x1.f8bdf2p-1, + 0x1.f8f63ep-1, + 0x1.f92d08p-1, + 0x1.f96256p-1, + 0x1.f99634p-1, + 0x1.f9c8a8p-1, + 0x1.f9f9bap-1, + 0x1.fa2974p-1, + 0x1.fa57dep-1, + 0x1.fa84fep-1, + 0x1.fab0dep-1, + 0x1.fadb84p-1, + 0x1.fb04f6p-1, + 0x1.fb2d40p-1, + 0x1.fb5464p-1, + 0x1.fb7a6cp-1, + 0x1.fb9f60p-1, + 0x1.fbc344p-1, + 0x1.fbe61ep-1, + 0x1.fc07fap-1, + 0x1.fc28d8p-1, + 0x1.fc48c2p-1, + 0x1.fc67bcp-1, + 0x1.fc85d0p-1, + 0x1.fca2fep-1, + 0x1.fcbf52p-1, + 0x1.fcdaccp-1, + 0x1.fcf576p-1, + 0x1.fd0f54p-1, + 0x1.fd286ap-1, + 0x1.fd40bep-1, + 0x1.fd5856p-1, + 0x1.fd6f34p-1, + 0x1.fd8562p-1, + 0x1.fd9ae2p-1, + 0x1.fdafb8p-1, + 0x1.fdc3e8p-1, + 0x1.fdd77ap-1, + 0x1.fdea6ep-1, + 0x1.fdfcccp-1, + 0x1.fe0e96p-1, + 0x1.fe1fd0p-1, + 0x1.fe3080p-1, + 0x1.fe40a6p-1, + 0x1.fe504cp-1, + 0x1.fe5f70p-1, + 0x1.fe6e18p-1, + 0x1.fe7c46p-1, + 0x1.fe8a00p-1, + 0x1.fe9748p-1, + 0x1.fea422p-1, + 0x1.feb090p-1, + 0x1.febc96p-1, + 0x1.fec836p-1, + 0x1.fed374p-1, + 0x1.fede52p-1, + 0x1.fee8d4p-1, + 0x1.fef2fep-1, + 0x1.fefccep-1, + 0x1.ff064cp-1, + 0x1.ff0f76p-1, + 0x1.ff1852p-1, + 0x1.ff20e0p-1, + 0x1.ff2924p-1, + 0x1.ff3120p-1, + 0x1.ff38d6p-1, + 0x1.ff4048p-1, + 0x1.ff4778p-1, + 0x1.ff4e68p-1, + 0x1.ff551ap-1, + 0x1.ff5b90p-1, + 0x1.ff61ccp-1, + 0x1.ff67d0p-1, + 0x1.ff6d9ep-1, + 0x1.ff7338p-1, + 0x1.ff789ep-1, + 0x1.ff7dd4p-1, + 0x1.ff82dap-1, + 0x1.ff87b2p-1, + 0x1.ff8c5cp-1, + 0x1.ff90dcp-1, + 0x1.ff9532p-1, + 0x1.ff9960p-1, + 0x1.ff9d68p-1, + 0x1.ffa14ap-1, + 0x1.ffa506p-1, + 0x1.ffa8a0p-1, + 0x1.ffac18p-1, + 0x1.ffaf6ep-1, + 0x1.ffb2a6p-1, + 0x1.ffb5bep-1, + 0x1.ffb8b8p-1, + 0x1.ffbb98p-1, + 0x1.ffbe5ap-1, + 0x1.ffc102p-1, + 0x1.ffc390p-1, + 0x1.ffc606p-1, + 0x1.ffc862p-1, + 0x1.ffcaa8p-1, + 0x1.ffccd8p-1, + 0x1.ffcef4p-1, + 0x1.ffd0fap-1, + 0x1.ffd2eap-1, + 0x1.ffd4cap-1, + 0x1.ffd696p-1, + 0x1.ffd84ep-1, + 0x1.ffd9f8p-1, + 0x1.ffdb90p-1, + 0x1.ffdd18p-1, + 0x1.ffde90p-1, + 0x1.ffdffap-1, + 0x1.ffe154p-1, + 0x1.ffe2a2p-1, + 0x1.ffe3e2p-1, + 0x1.ffe514p-1, + 0x1.ffe63cp-1, + 0x1.ffe756p-1, + 0x1.ffe866p-1, + 0x1.ffe96ap-1, + 0x1.ffea64p-1, + 0x1.ffeb54p-1, + 0x1.ffec3ap-1, + 0x1.ffed16p-1, + 0x1.ffedeap-1, + 0x1.ffeeb4p-1, + 0x1.ffef76p-1, + 0x1.fff032p-1, + 0x1.fff0e4p-1, + 0x1.fff18ep-1, + 0x1.fff232p-1, + 0x1.fff2d0p-1, + 0x1.fff366p-1, + 0x1.fff3f6p-1, + 0x1.fff480p-1, + 0x1.fff504p-1, + 0x1.fff582p-1, + 0x1.fff5fcp-1, + 0x1.fff670p-1, + 0x1.fff6dep-1, + 0x1.fff74ap-1, + 0x1.fff7aep-1, + 0x1.fff810p-1, + 0x1.fff86cp-1, + 0x1.fff8c6p-1, + 0x1.fff91cp-1, + 0x1.fff96cp-1, + 0x1.fff9bap-1, + 0x1.fffa04p-1, + 0x1.fffa4cp-1, + 0x1.fffa90p-1, + 0x1.fffad0p-1, + 0x1.fffb0ep-1, + 0x1.fffb4ap-1, + 0x1.fffb82p-1, + 0x1.fffbb8p-1, + 0x1.fffbecp-1, + 0x1.fffc1ep-1, + 0x1.fffc4ep-1, + 0x1.fffc7ap-1, + 0x1.fffca6p-1, + 0x1.fffccep-1, + 0x1.fffcf6p-1, + 0x1.fffd1ap-1, + 0x1.fffd3ep-1, + 0x1.fffd60p-1, + 0x1.fffd80p-1, + 0x1.fffda0p-1, + 0x1.fffdbep-1, + 0x1.fffddap-1, + 0x1.fffdf4p-1, + 0x1.fffe0ep-1, + 0x1.fffe26p-1, + 0x1.fffe3ep-1, + 0x1.fffe54p-1, + 0x1.fffe68p-1, + 0x1.fffe7ep-1, + 0x1.fffe90p-1, + 0x1.fffea2p-1, + 0x1.fffeb4p-1, + 0x1.fffec4p-1, + 0x1.fffed4p-1, + 0x1.fffee4p-1, + 0x1.fffef2p-1, + 0x1.ffff00p-1, + 0x1.ffff0cp-1, + 0x1.ffff18p-1, + 0x1.ffff24p-1, + 0x1.ffff30p-1, + 0x1.ffff3ap-1, + 0x1.ffff44p-1, + 0x1.ffff4ep-1, + 0x1.ffff56p-1, + 0x1.ffff60p-1, + 0x1.ffff68p-1, + 0x1.ffff70p-1, + 0x1.ffff78p-1, + 0x1.ffff7ep-1, + 0x1.ffff84p-1, + 0x1.ffff8cp-1, + 0x1.ffff92p-1, + 0x1.ffff98p-1, + 0x1.ffff9cp-1, + 0x1.ffffa2p-1, + 0x1.ffffa6p-1, + 0x1.ffffacp-1, + 0x1.ffffb0p-1, + 0x1.ffffb4p-1, + 0x1.ffffb8p-1, 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0x1.05c804p-21, + 0x1.ed2254p-22, + 0x1.d06ad6p-22, + 0x1.b551c8p-22, + 0x1.9bc0a0p-22, + 0x1.83a200p-22, + 0x1.6ce1aap-22, + 0x1.576c72p-22, + 0x1.43302cp-22, + 0x1.301ba2p-22, + 0x1.1e1e86p-22, + 0x1.0d2966p-22, + 0x1.fa5b50p-23, + 0x1.dc3ae4p-23, + 0x1.bfd756p-23, + 0x1.a517dap-23, + 0x1.8be4f8p-23, + 0x1.74287ep-23, + 0x1.5dcd66p-23, + 0x1.48bfd4p-23, + 0x1.34ecf8p-23, + 0x1.224310p-23, + 0x1.10b148p-23, + }, +}; diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index caac3f7ce4..41fdb92d7e 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -28,6 +28,7 @@ VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan) VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2) VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos) +VPCS_VECTOR_WRAPPER (erf_advsimd, _ZGVnN2v_erf) VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp) VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10) VPCS_VECTOR_WRAPPER (exp2_advsimd, _ZGVnN2v_exp2) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 2e29cbe739..8e3d64da42 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -47,6 +47,7 @@ SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan) SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2) SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos) +SVE_VECTOR_WRAPPER (erf_sve, _ZGVsMxv_erf) SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp) SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10) SVE_VECTOR_WRAPPER (exp2_sve, _ZGVsMxv_exp2) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index c8a3df4bcd..33ae92878f 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -28,6 +28,7 @@ VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf) VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f) VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf) +VPCS_VECTOR_WRAPPER (erff_advsimd, _ZGVnN4v_erff) VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf) VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f) VPCS_VECTOR_WRAPPER (exp2f_advsimd, _ZGVnN4v_exp2f) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index 0bc247b90b..ac0464f196 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -47,6 +47,7 @@ SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf) SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f) SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf) +SVE_VECTOR_WRAPPER (erff_sve, _ZGVsMxv_erff) SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf) SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f) SVE_VECTOR_WRAPPER (exp2f_sve, _ZGVsMxv_exp2f) diff --git a/sysdeps/aarch64/fpu/vecmath_config.h b/sysdeps/aarch64/fpu/vecmath_config.h index 62f71f57f3..409c0c9bd9 100644 --- a/sysdeps/aarch64/fpu/vecmath_config.h +++ b/sysdeps/aarch64/fpu/vecmath_config.h @@ -84,4 +84,32 @@ extern const struct v_log10_data } table[1 << V_LOG10_TABLE_BITS]; } __v_log10_data attribute_hidden; +extern const struct erff_data +{ + struct + { + float erf, scale; + } tab[513]; +} __erff_data attribute_hidden; + +extern const struct sv_erff_data +{ + float erf[513]; + float scale[513]; +} __sv_erff_data attribute_hidden; + +extern const struct erf_data +{ + struct + { + double erf, scale; + } tab[769]; +} __erf_data attribute_hidden; + +extern const struct sv_erf_data +{ + double erf[769]; + double scale[769]; +} __sv_erf_data attribute_hidden; + #endif diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index 1d52bf9ebf..ed4791e26a 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -957,11 +957,19 @@ double: 1 float: 1 ldouble: 1 +Function: "erf_advsimd": +double: 1 +float: 2 + Function: "erf_downward": double: 1 float: 1 ldouble: 2 +Function: "erf_sve": +double: 1 +float: 2 + Function: "erf_towardzero": double: 1 float: 1 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index 580952b4de..6193518fb0 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -73,3 +73,8 @@ GLIBC_2.39 _ZGVsMxv_tan F GLIBC_2.39 _ZGVsMxv_tanf F GLIBC_2.39 _ZGVsMxvv_atan2 F GLIBC_2.39 _ZGVsMxvv_atan2f F +GLIBC_2.40 _ZGVnN2v_erf F +GLIBC_2.40 _ZGVnN2v_erff F +GLIBC_2.40 _ZGVnN4v_erff F +GLIBC_2.40 _ZGVsMxv_erf F +GLIBC_2.40 _ZGVsMxv_erff F From patchwork Tue Feb 20 16:59:39 2024 Content-Type: text/plain; charset="utf-8" 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KAM_DMARC_NONE, KAM_SHORT, RCVD_IN_DNSWL_NONE, RCVD_IN_MSPIKE_H2, SPF_HELO_PASS, SPF_NONE, TXREP, T_SCC_BODY_TEXT_LINE, UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org --- Thanks, Joe sysdeps/aarch64/fpu/Makefile | 4 +- sysdeps/aarch64/fpu/Versions | 5 + sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/bits/math-vector.h | 8 ++ sysdeps/aarch64/fpu/cosh_advsimd.c | 108 +++++++++++++++++ sysdeps/aarch64/fpu/cosh_sve.c | 105 +++++++++++++++++ sysdeps/aarch64/fpu/coshf_advsimd.c | 84 +++++++++++++ sysdeps/aarch64/fpu/coshf_sve.c | 59 ++++++++++ sysdeps/aarch64/fpu/sv_expf_inline.h | 75 ++++++++++++ .../fpu/test-double-advsimd-wrappers.c | 1 + .../aarch64/fpu/test-double-sve-wrappers.c | 1 + .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + sysdeps/aarch64/fpu/v_exp_tail_data.c | 110 ++++++++++++++++++ sysdeps/aarch64/fpu/v_expf_inline.h | 71 +++++++++++ sysdeps/aarch64/fpu/vecmath_config.h | 2 + sysdeps/aarch64/libm-test-ulps | 8 ++ .../unix/sysv/linux/aarch64/libmvec.abilist | 5 + 18 files changed, 648 insertions(+), 1 deletion(-) create mode 100644 sysdeps/aarch64/fpu/cosh_advsimd.c create mode 100644 sysdeps/aarch64/fpu/cosh_sve.c create mode 100644 sysdeps/aarch64/fpu/coshf_advsimd.c create mode 100644 sysdeps/aarch64/fpu/coshf_sve.c create mode 100644 sysdeps/aarch64/fpu/sv_expf_inline.h create mode 100644 sysdeps/aarch64/fpu/v_exp_tail_data.c create mode 100644 sysdeps/aarch64/fpu/v_expf_inline.h Reviewed-by: Szabolcs Nagy diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index 320b6ed43a..019c3a5188 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -3,6 +3,7 @@ libmvec-supported-funcs = acos \ atan \ atan2 \ cos \ + cosh \ erf \ exp \ exp10 \ @@ -32,7 +33,8 @@ libmvec-support = $(addsuffix f_advsimd,$(float-advsimd-funcs)) \ erf_data \ erff_data \ sv_erf_data \ - sv_erff_data + sv_erff_data \ + v_exp_tail_data endif sve-cflags = -march=armv8-a+sve diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index d7b1e87191..884b4b57f0 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -79,6 +79,11 @@ libmvec { _ZGVsMxv_tan; } GLIBC_2.40 { + _ZGVnN2v_cosh; + _ZGVnN2v_coshf; + _ZGVnN4v_coshf; + _ZGVsMxv_cosh; + _ZGVsMxv_coshf; _ZGVnN2v_erf; _ZGVnN2v_erff; _ZGVnN4v_erff; diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index d8d88de218..c63b2948d4 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -21,6 +21,7 @@ libmvec_hidden_proto (V_NAME_F1(acos)); libmvec_hidden_proto (V_NAME_F1(asin)); libmvec_hidden_proto (V_NAME_F1(atan)); libmvec_hidden_proto (V_NAME_F1(cos)); +libmvec_hidden_proto (V_NAME_F1(cosh)); libmvec_hidden_proto (V_NAME_F1(erf)); libmvec_hidden_proto (V_NAME_F1(exp10)); libmvec_hidden_proto (V_NAME_F1(exp2)); diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 71f53363a0..8ca5509870 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -49,6 +49,10 @@ # define __DECL_SIMD_cos __DECL_SIMD_aarch64 # undef __DECL_SIMD_cosf # define __DECL_SIMD_cosf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_cosh +# define __DECL_SIMD_cosh __DECL_SIMD_aarch64 +# undef __DECL_SIMD_coshf +# define __DECL_SIMD_coshf __DECL_SIMD_aarch64 # undef __DECL_SIMD_erf # define __DECL_SIMD_erf __DECL_SIMD_aarch64 # undef __DECL_SIMD_erff @@ -124,6 +128,7 @@ __vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_coshf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_erff (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t); @@ -141,6 +146,7 @@ __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_cosh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_erf (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t); @@ -163,6 +169,7 @@ __sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_coshf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_erff (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t); @@ -180,6 +187,7 @@ __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_cosh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_erf (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t); diff --git a/sysdeps/aarch64/fpu/cosh_advsimd.c b/sysdeps/aarch64/fpu/cosh_advsimd.c new file mode 100644 index 0000000000..ec7b59637e --- /dev/null +++ b/sysdeps/aarch64/fpu/cosh_advsimd.c @@ -0,0 +1,108 @@ +/* Double-precision vector (AdvSIMD) cosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" + +static const struct data +{ + float64x2_t poly[3]; + float64x2_t inv_ln2, ln2, shift, thres; + uint64x2_t index_mask, special_bound; +} data = { + .poly = { V2 (0x1.fffffffffffd4p-2), V2 (0x1.5555571d6b68cp-3), + V2 (0x1.5555576a59599p-5), }, + + .inv_ln2 = V2 (0x1.71547652b82fep8), /* N/ln2. */ + /* -ln2/N. */ + .ln2 = {-0x1.62e42fefa39efp-9, -0x1.abc9e3b39803f3p-64}, + .shift = V2 (0x1.8p+52), + .thres = V2 (704.0), + + .index_mask = V2 (0xff), + /* 0x1.6p9, above which exp overflows. */ + .special_bound = V2 (0x4086000000000000), +}; + +static float64x2_t NOINLINE VPCS_ATTR +special_case (float64x2_t x, float64x2_t y, uint64x2_t special) +{ + return v_call_f64 (cosh, x, y, special); +} + +/* Helper for approximating exp(x). Copied from v_exp_tail, with no + special-case handling or tail. */ +static inline float64x2_t +exp_inline (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + /* n = round(x/(ln2/N)). */ + float64x2_t z = vfmaq_f64 (d->shift, x, d->inv_ln2); + uint64x2_t u = vreinterpretq_u64_f64 (z); + float64x2_t n = vsubq_f64 (z, d->shift); + + /* r = x - n*ln2/N. */ + float64x2_t r = vfmaq_laneq_f64 (x, n, d->ln2, 0); + r = vfmaq_laneq_f64 (r, n, d->ln2, 1); + + uint64x2_t e = vshlq_n_u64 (u, 52 - V_EXP_TAIL_TABLE_BITS); + uint64x2_t i = vandq_u64 (u, d->index_mask); + + /* y = tail + exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */ + float64x2_t y = vfmaq_f64 (d->poly[1], d->poly[2], r); + y = vfmaq_f64 (d->poly[0], y, r); + y = vmulq_f64 (vfmaq_f64 (v_f64 (1), y, r), r); + + /* s = 2^(n/N). */ + u = v_lookup_u64 (__v_exp_tail_data, i); + float64x2_t s = vreinterpretq_f64_u64 (vaddq_u64 (u, e)); + + return vfmaq_f64 (s, y, s); +} + +/* Approximation for vector double-precision cosh(x) using exp_inline. + cosh(x) = (exp(x) + exp(-x)) / 2. + The greatest observed error is in the scalar fall-back region, so is the + same as the scalar routine, 1.93 ULP: + _ZGVnN2v_cosh (0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021 + want 0x1.fdf28623ef923p+1021. + + The greatest observed error in the non-special region is 1.54 ULP: + _ZGVnN2v_cosh (0x1.8e205b6ecacf7p+2) got 0x1.f711dcb0c77afp+7 + want 0x1.f711dcb0c77b1p+7. */ +float64x2_t VPCS_ATTR V_NAME_D1 (cosh) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + float64x2_t ax = vabsq_f64 (x); + uint64x2_t special + = vcgtq_u64 (vreinterpretq_u64_f64 (ax), d->special_bound); + + /* Up to the point that exp overflows, we can use it to calculate cosh by + exp(|x|) / 2 + 1 / (2 * exp(|x|)). */ + float64x2_t t = exp_inline (ax); + float64x2_t half_t = vmulq_n_f64 (t, 0.5); + float64x2_t half_over_t = vdivq_f64 (v_f64 (0.5), t); + + /* Fall back to scalar for any special cases. */ + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (x, vaddq_f64 (half_t, half_over_t), special); + + return vaddq_f64 (half_t, half_over_t); +} diff --git a/sysdeps/aarch64/fpu/cosh_sve.c b/sysdeps/aarch64/fpu/cosh_sve.c new file mode 100644 index 0000000000..919f34604a --- /dev/null +++ b/sysdeps/aarch64/fpu/cosh_sve.c @@ -0,0 +1,105 @@ +/* Double-precision vector (SVE) cosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" + +static const struct data +{ + float64_t poly[3]; + float64_t inv_ln2, ln2_hi, ln2_lo, shift, thres; + uint64_t index_mask, special_bound; +} data = { + .poly = { 0x1.fffffffffffd4p-2, 0x1.5555571d6b68cp-3, + 0x1.5555576a59599p-5, }, + + .inv_ln2 = 0x1.71547652b82fep8, /* N/ln2. */ + /* -ln2/N. */ + .ln2_hi = -0x1.62e42fefa39efp-9, + .ln2_lo = -0x1.abc9e3b39803f3p-64, + .shift = 0x1.8p+52, + .thres = 704.0, + + .index_mask = 0xff, + /* 0x1.6p9, above which exp overflows. */ + .special_bound = 0x4086000000000000, +}; + +static svfloat64_t NOINLINE +special_case (svfloat64_t x, svfloat64_t y, svbool_t special) +{ + return sv_call_f64 (cosh, x, y, special); +} + +/* Helper for approximating exp(x). Copied from sv_exp_tail, with no + special-case handling or tail. */ +static inline svfloat64_t +exp_inline (svfloat64_t x, const svbool_t pg, const struct data *d) +{ + /* Calculate exp(x). */ + svfloat64_t z = svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2); + svfloat64_t n = svsub_x (pg, z, d->shift); + + svfloat64_t r = svmla_x (pg, x, n, d->ln2_hi); + r = svmla_x (pg, r, n, d->ln2_lo); + + svuint64_t u = svreinterpret_u64 (z); + svuint64_t e = svlsl_x (pg, u, 52 - V_EXP_TAIL_TABLE_BITS); + svuint64_t i = svand_x (pg, u, d->index_mask); + + svfloat64_t y = svmla_x (pg, sv_f64 (d->poly[1]), r, d->poly[2]); + y = svmla_x (pg, sv_f64 (d->poly[0]), r, y); + y = svmla_x (pg, sv_f64 (1.0), r, y); + y = svmul_x (pg, r, y); + + /* s = 2^(n/N). */ + u = svld1_gather_index (pg, __v_exp_tail_data, i); + svfloat64_t s = svreinterpret_f64 (svadd_x (pg, u, e)); + + return svmla_x (pg, s, s, y); +} + +/* Approximation for SVE double-precision cosh(x) using exp_inline. + cosh(x) = (exp(x) + exp(-x)) / 2. + The greatest observed error is in the scalar fall-back region, so is the + same as the scalar routine, 1.93 ULP: + _ZGVsMxv_cosh (0x1.628ad45039d2fp+9) got 0x1.fd774e958236dp+1021 + want 0x1.fd774e958236fp+1021. + + The greatest observed error in the non-special region is 1.54 ULP: + _ZGVsMxv_cosh (0x1.ba5651dd4486bp+2) got 0x1.f5e2bb8d5c98fp+8 + want 0x1.f5e2bb8d5c991p+8. */ +svfloat64_t SV_NAME_D1 (cosh) (svfloat64_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svfloat64_t ax = svabs_x (pg, x); + svbool_t special = svcmpgt (pg, svreinterpret_u64 (ax), d->special_bound); + + /* Up to the point that exp overflows, we can use it to calculate cosh by + exp(|x|) / 2 + 1 / (2 * exp(|x|)). */ + svfloat64_t t = exp_inline (ax, pg, d); + svfloat64_t half_t = svmul_x (pg, t, 0.5); + svfloat64_t half_over_t = svdivr_x (pg, t, 0.5); + + /* Fall back to scalar for any special cases. */ + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, svadd_x (pg, half_t, half_over_t), special); + + return svadd_x (pg, half_t, half_over_t); +} diff --git a/sysdeps/aarch64/fpu/coshf_advsimd.c b/sysdeps/aarch64/fpu/coshf_advsimd.c new file mode 100644 index 0000000000..c1ab4923b8 --- /dev/null +++ b/sysdeps/aarch64/fpu/coshf_advsimd.c @@ -0,0 +1,84 @@ +/* Single-precision vector (AdvSIMD) cosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_expf_inline.h" +#include "v_math.h" + +static const struct data +{ + struct v_expf_data expf_consts; + uint32x4_t tiny_bound, special_bound; +} data = { + .expf_consts = V_EXPF_DATA, + .tiny_bound = V4 (0x20000000), /* 0x1p-63: Round to 1 below this. */ + /* 0x1.5a92d8p+6: expf overflows above this, so have to use special case. */ + .special_bound = V4 (0x42ad496c), +}; + +#if !WANT_SIMD_EXCEPT +static float32x4_t NOINLINE VPCS_ATTR +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +{ + return v_call_f32 (coshf, x, y, special); +} +#endif + +/* Single-precision vector cosh, using vector expf. + Maximum error is 2.38 ULP: + _ZGVnN4v_coshf (0x1.e8001ep+1) got 0x1.6a491ep+4 + want 0x1.6a4922p+4. */ +float32x4_t VPCS_ATTR V_NAME_F1 (cosh) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + + float32x4_t ax = vabsq_f32 (x); + uint32x4_t iax = vreinterpretq_u32_f32 (ax); + uint32x4_t special = vcgeq_u32 (iax, d->special_bound); + +#if WANT_SIMD_EXCEPT + /* If fp exceptions are to be triggered correctly, fall back to the scalar + variant for all inputs if any input is a special value or above the bound + at which expf overflows. */ + if (__glibc_unlikely (v_any_u32 (special))) + return v_call_f32 (coshf, x, x, v_u32 (-1)); + + uint32x4_t tiny = vcleq_u32 (iax, d->tiny_bound); + /* If any input is tiny, avoid underflow exception by fixing tiny lanes of + input to 0, which will generate no exceptions. */ + if (__glibc_unlikely (v_any_u32 (tiny))) + ax = v_zerofy_f32 (ax, tiny); +#endif + + /* Calculate cosh by exp(x) / 2 + exp(-x) / 2. */ + float32x4_t t = v_expf_inline (ax, &d->expf_consts); + float32x4_t half_t = vmulq_n_f32 (t, 0.5); + float32x4_t half_over_t = vdivq_f32 (v_f32 (0.5), t); + +#if WANT_SIMD_EXCEPT + if (__glibc_unlikely (v_any_u32 (tiny))) + return vbslq_f32 (tiny, v_f32 (1), vaddq_f32 (half_t, half_over_t)); +#else + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (x, vaddq_f32 (half_t, half_over_t), special); +#endif + + return vaddq_f32 (half_t, half_over_t); +} +libmvec_hidden_def (V_NAME_F1 (cosh)) +HALF_WIDTH_ALIAS_F1 (cosh) diff --git a/sysdeps/aarch64/fpu/coshf_sve.c b/sysdeps/aarch64/fpu/coshf_sve.c new file mode 100644 index 0000000000..e5d8a299c6 --- /dev/null +++ b/sysdeps/aarch64/fpu/coshf_sve.c @@ -0,0 +1,59 @@ +/* Single-precision vector (SVE) cosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" +#include "sv_expf_inline.h" + +static const struct data +{ + struct sv_expf_data expf_consts; + uint32_t special_bound; +} data = { + .expf_consts = SV_EXPF_DATA, + /* 0x1.5a92d8p+6: expf overflows above this, so have to use special case. */ + .special_bound = 0x42ad496c, +}; + +static svfloat32_t NOINLINE +special_case (svfloat32_t x, svfloat32_t y, svbool_t pg) +{ + return sv_call_f32 (coshf, x, y, pg); +} + +/* Single-precision vector cosh, using vector expf. + Maximum error is 1.89 ULP: + _ZGVsMxv_coshf (-0x1.65898cp+6) got 0x1.f00aep+127 + want 0x1.f00adcp+127. */ +svfloat32_t SV_NAME_F1 (cosh) (svfloat32_t x, svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svfloat32_t ax = svabs_x (pg, x); + svbool_t special = svcmpge (pg, svreinterpret_u32 (ax), d->special_bound); + + /* Calculate cosh by exp(x) / 2 + exp(-x) / 2. */ + svfloat32_t t = expf_inline (ax, pg, &d->expf_consts); + svfloat32_t half_t = svmul_x (pg, t, 0.5); + svfloat32_t half_over_t = svdivr_x (pg, t, 0.5); + + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, svadd_x (pg, half_t, half_over_t), special); + + return svadd_x (pg, half_t, half_over_t); +} diff --git a/sysdeps/aarch64/fpu/sv_expf_inline.h b/sysdeps/aarch64/fpu/sv_expf_inline.h new file mode 100644 index 0000000000..23963b5f8e --- /dev/null +++ b/sysdeps/aarch64/fpu/sv_expf_inline.h @@ -0,0 +1,75 @@ +/* SVE helper for single-precision routines which depend on exp + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_SV_EXPF_INLINE_H +#define AARCH64_FPU_SV_EXPF_INLINE_H + +#include "sv_math.h" + +struct sv_expf_data +{ + float poly[5]; + float inv_ln2, ln2_hi, ln2_lo, shift; +}; + +/* Coefficients copied from the polynomial in AdvSIMD variant, reversed for + compatibility with polynomial helpers. Shift is 1.5*2^17 + 127. */ +#define SV_EXPF_DATA \ + { \ + .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f, \ + 0x1.0e4020p-7f }, \ + \ + .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \ + .ln2_lo = 0x1.7f7d1cp-20f, .shift = 0x1.803f8p17f, \ + } + +#define C(i) sv_f32 (d->poly[i]) + +static inline svfloat32_t +expf_inline (svfloat32_t x, const svbool_t pg, const struct sv_expf_data *d) +{ + /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] + x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ + + /* Load some constants in quad-word chunks to minimise memory access. */ + svfloat32_t c4_invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->poly[4]); + + /* n = round(x/(ln2/N)). */ + svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, c4_invln2_and_ln2, 1); + svfloat32_t n = svsub_x (pg, z, d->shift); + + /* r = x - n*ln2/N. */ + svfloat32_t r = svmls_lane (x, n, c4_invln2_and_ln2, 2); + r = svmls_lane (r, n, c4_invln2_and_ln2, 3); + + /* scale = 2^(n/N). */ + svfloat32_t scale = svexpa (svreinterpret_u32_f32 (z)); + + /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */ + svfloat32_t p12 = svmla_x (pg, C (1), C (2), r); + svfloat32_t p34 = svmla_lane (C (3), r, c4_invln2_and_ln2, 0); + svfloat32_t r2 = svmul_f32_x (pg, r, r); + svfloat32_t p14 = svmla_x (pg, p12, p34, r2); + svfloat32_t p0 = svmul_f32_x (pg, r, C (0)); + svfloat32_t poly = svmla_x (pg, p0, r2, p14); + + return svmla_x (pg, scale, scale, poly); +} + +#endif diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index 41fdb92d7e..b37cb7d5e9 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -28,6 +28,7 @@ VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan) VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2) VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos) +VPCS_VECTOR_WRAPPER (cosh_advsimd, _ZGVnN2v_cosh) VPCS_VECTOR_WRAPPER (erf_advsimd, _ZGVnN2v_erf) VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp) VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 8e3d64da42..011f07d2c1 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -47,6 +47,7 @@ SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan) SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2) SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos) +SVE_VECTOR_WRAPPER (cosh_sve, _ZGVsMxv_cosh) SVE_VECTOR_WRAPPER (erf_sve, _ZGVsMxv_erf) SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp) SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 33ae92878f..3545299143 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -28,6 +28,7 @@ VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf) VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f) VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf) +VPCS_VECTOR_WRAPPER (coshf_advsimd, _ZGVnN4v_coshf) VPCS_VECTOR_WRAPPER (erff_advsimd, _ZGVnN4v_erff) VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf) VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index ac0464f196..bbc74ede88 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -47,6 +47,7 @@ SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf) SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f) SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf) +SVE_VECTOR_WRAPPER (coshf_sve, _ZGVsMxv_coshf) SVE_VECTOR_WRAPPER (erff_sve, _ZGVsMxv_erff) SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf) SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f) diff --git a/sysdeps/aarch64/fpu/v_exp_tail_data.c b/sysdeps/aarch64/fpu/v_exp_tail_data.c new file mode 100644 index 0000000000..151e97c21b --- /dev/null +++ b/sysdeps/aarch64/fpu/v_exp_tail_data.c @@ -0,0 +1,110 @@ +/* Lookup table for high-precision exp(x, tail) function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "vecmath_config.h" + +/* 2^(j/N), j=0..N, N=2^8=256. */ +const uint64_t __v_exp_tail_data[] = { + 0x3ff0000000000000, 0x3feffb1afa5abcbf, 0x3feff63da9fb3335, + 0x3feff168143b0281, 0x3fefec9a3e778061, 0x3fefe7d42e11bbcc, + 0x3fefe315e86e7f85, 0x3fefde5f72f654b1, 0x3fefd9b0d3158574, + 0x3fefd50a0e3c1f89, 0x3fefd06b29ddf6de, 0x3fefcbd42b72a836, + 0x3fefc74518759bc8, 0x3fefc2bdf66607e0, 0x3fefbe3ecac6f383, + 0x3fefb9c79b1f3919, 0x3fefb5586cf9890f, 0x3fefb0f145e46c85, + 0x3fefac922b7247f7, 0x3fefa83b23395dec, 0x3fefa3ec32d3d1a2, + 0x3fef9fa55fdfa9c5, 0x3fef9b66affed31b, 0x3fef973028d7233e, + 0x3fef9301d0125b51, 0x3fef8edbab5e2ab6, 0x3fef8abdc06c31cc, + 0x3fef86a814f204ab, 0x3fef829aaea92de0, 0x3fef7e95934f312e, + 0x3fef7a98c8a58e51, 0x3fef76a45471c3c2, 0x3fef72b83c7d517b, + 0x3fef6ed48695bbc0, 0x3fef6af9388c8dea, 0x3fef672658375d2f, + 0x3fef635beb6fcb75, 0x3fef5f99f8138a1c, 0x3fef5be084045cd4, + 0x3fef582f95281c6b, 0x3fef54873168b9aa, 0x3fef50e75eb44027, + 0x3fef4d5022fcd91d, 0x3fef49c18438ce4d, 0x3fef463b88628cd6, + 0x3fef42be3578a819, 0x3fef3f49917ddc96, 0x3fef3bdda27912d1, + 0x3fef387a6e756238, 0x3fef351ffb82140a, 0x3fef31ce4fb2a63f, + 0x3fef2e85711ece75, 0x3fef2b4565e27cdd, 0x3fef280e341ddf29, + 0x3fef24dfe1f56381, 0x3fef21ba7591bb70, 0x3fef1e9df51fdee1, + 0x3fef1b8a66d10f13, 0x3fef187fd0dad990, 0x3fef157e39771b2f, + 0x3fef1285a6e4030b, 0x3fef0f961f641589, 0x3fef0cafa93e2f56, + 0x3fef09d24abd886b, 0x3fef06fe0a31b715, 0x3fef0432edeeb2fd, + 0x3fef0170fc4cd831, 0x3feefeb83ba8ea32, 0x3feefc08b26416ff, + 0x3feef96266e3fa2d, 0x3feef6c55f929ff1, 0x3feef431a2de883b, + 0x3feef1a7373aa9cb, 0x3feeef26231e754a, 0x3feeecae6d05d866, + 0x3feeea401b7140ef, 0x3feee7db34e59ff7, 0x3feee57fbfec6cf4, + 0x3feee32dc313a8e5, 0x3feee0e544ede173, 0x3feedea64c123422, + 0x3feedc70df1c5175, 0x3feeda4504ac801c, 0x3feed822c367a024, + 0x3feed60a21f72e2a, 0x3feed3fb2709468a, 0x3feed1f5d950a897, + 0x3feecffa3f84b9d4, 0x3feece086061892d, 0x3feecc2042a7d232, + 0x3feeca41ed1d0057, 0x3feec86d668b3237, 0x3feec6a2b5c13cd0, + 0x3feec4e1e192aed2, 0x3feec32af0d7d3de, 0x3feec17dea6db7d7, + 0x3feebfdad5362a27, 0x3feebe41b817c114, 0x3feebcb299fddd0d, + 0x3feebb2d81d8abff, 0x3feeb9b2769d2ca7, 0x3feeb8417f4531ee, + 0x3feeb6daa2cf6642, 0x3feeb57de83f4eef, 0x3feeb42b569d4f82, + 0x3feeb2e2f4f6ad27, 0x3feeb1a4ca5d920f, 0x3feeb070dde910d2, + 0x3feeaf4736b527da, 0x3feeae27dbe2c4cf, 0x3feead12d497c7fd, + 0x3feeac0827ff07cc, 0x3feeab07dd485429, 0x3feeaa11fba87a03, + 0x3feea9268a5946b7, 0x3feea84590998b93, 0x3feea76f15ad2148, + 0x3feea6a320dceb71, 0x3feea5e1b976dc09, 0x3feea52ae6cdf6f4, + 0x3feea47eb03a5585, 0x3feea3dd1d1929fd, 0x3feea34634ccc320, + 0x3feea2b9febc8fb7, 0x3feea23882552225, 0x3feea1c1c70833f6, + 0x3feea155d44ca973, 0x3feea0f4b19e9538, 0x3feea09e667f3bcd, + 0x3feea052fa75173e, 0x3feea012750bdabf, 0x3fee9fdcddd47645, + 0x3fee9fb23c651a2f, 0x3fee9f9298593ae5, 0x3fee9f7df9519484, + 0x3fee9f7466f42e87, 0x3fee9f75e8ec5f74, 0x3fee9f8286ead08a, + 0x3fee9f9a48a58174, 0x3fee9fbd35d7cbfd, 0x3fee9feb564267c9, + 0x3feea024b1ab6e09, 0x3feea0694fde5d3f, 0x3feea0b938ac1cf6, + 0x3feea11473eb0187, 0x3feea17b0976cfdb, 0x3feea1ed0130c132, + 0x3feea26a62ff86f0, 0x3feea2f336cf4e62, 0x3feea3878491c491, + 0x3feea427543e1a12, 0x3feea4d2add106d9, 0x3feea589994cce13, + 0x3feea64c1eb941f7, 0x3feea71a4623c7ad, 0x3feea7f4179f5b21, + 0x3feea8d99b4492ed, 0x3feea9cad931a436, 0x3feeaac7d98a6699, + 0x3feeabd0a478580f, 0x3feeace5422aa0db, 0x3feeae05bad61778, + 0x3feeaf3216b5448c, 0x3feeb06a5e0866d9, 0x3feeb1ae99157736, + 0x3feeb2fed0282c8a, 0x3feeb45b0b91ffc6, 0x3feeb5c353aa2fe2, + 0x3feeb737b0cdc5e5, 0x3feeb8b82b5f98e5, 0x3feeba44cbc8520f, + 0x3feebbdd9a7670b3, 0x3feebd829fde4e50, 0x3feebf33e47a22a2, + 0x3feec0f170ca07ba, 0x3feec2bb4d53fe0d, 0x3feec49182a3f090, + 0x3feec674194bb8d5, 0x3feec86319e32323, 0x3feeca5e8d07f29e, + 0x3feecc667b5de565, 0x3feece7aed8eb8bb, 0x3feed09bec4a2d33, + 0x3feed2c980460ad8, 0x3feed503b23e255d, 0x3feed74a8af46052, + 0x3feed99e1330b358, 0x3feedbfe53c12e59, 0x3feede6b5579fdbf, + 0x3feee0e521356eba, 0x3feee36bbfd3f37a, 0x3feee5ff3a3c2774, + 0x3feee89f995ad3ad, 0x3feeeb4ce622f2ff, 0x3feeee07298db666, + 0x3feef0ce6c9a8952, 0x3feef3a2b84f15fb, 0x3feef68415b749b1, + 0x3feef9728de5593a, 0x3feefc6e29f1c52a, 0x3feeff76f2fb5e47, + 0x3fef028cf22749e4, 0x3fef05b030a1064a, 0x3fef08e0b79a6f1f, + 0x3fef0c1e904bc1d2, 0x3fef0f69c3f3a207, 0x3fef12c25bd71e09, + 0x3fef16286141b33d, 0x3fef199bdd85529c, 0x3fef1d1cd9fa652c, + 0x3fef20ab5fffd07a, 0x3fef244778fafb22, 0x3fef27f12e57d14b, + 0x3fef2ba88988c933, 0x3fef2f6d9406e7b5, 0x3fef33405751c4db, + 0x3fef3720dcef9069, 0x3fef3b0f2e6d1675, 0x3fef3f0b555dc3fa, + 0x3fef43155b5bab74, 0x3fef472d4a07897c, 0x3fef4b532b08c968, + 0x3fef4f87080d89f2, 0x3fef53c8eacaa1d6, 0x3fef5818dcfba487, + 0x3fef5c76e862e6d3, 0x3fef60e316c98398, 0x3fef655d71ff6075, + 0x3fef69e603db3285, 0x3fef6e7cd63a8315, 0x3fef7321f301b460, + 0x3fef77d5641c0658, 0x3fef7c97337b9b5f, 0x3fef81676b197d17, + 0x3fef864614f5a129, 0x3fef8b333b16ee12, 0x3fef902ee78b3ff6, + 0x3fef953924676d76, 0x3fef9a51fbc74c83, 0x3fef9f7977cdb740, + 0x3fefa4afa2a490da, 0x3fefa9f4867cca6e, 0x3fefaf482d8e67f1, + 0x3fefb4aaa2188510, 0x3fefba1bee615a27, 0x3fefbf9c1cb6412a, + 0x3fefc52b376bba97, 0x3fefcac948dd7274, 0x3fefd0765b6e4540, + 0x3fefd632798844f8, 0x3fefdbfdad9cbe14, 0x3fefe1d802243c89, + 0x3fefe7c1819e90d8, 0x3fefedba3692d514, 0x3feff3c22b8f71f1, + 0x3feff9d96b2a23d9, +}; diff --git a/sysdeps/aarch64/fpu/v_expf_inline.h b/sysdeps/aarch64/fpu/v_expf_inline.h new file mode 100644 index 0000000000..a3b0e32f9e --- /dev/null +++ b/sysdeps/aarch64/fpu/v_expf_inline.h @@ -0,0 +1,71 @@ +/* Helper for single-precision AdvSIMD routines which depend on exp + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_V_EXPF_INLINE_H +#define AARCH64_FPU_V_EXPF_INLINE_H + +#include "v_math.h" + +struct v_expf_data +{ + float32x4_t poly[5]; + float32x4_t shift, invln2_and_ln2; +}; + +/* maxerr: 1.45358 +0.5 ulp. */ +#define V_EXPF_DATA \ + { \ + .poly = { V4 (0x1.0e4020p-7f), V4 (0x1.573e2ep-5f), V4 (0x1.555e66p-3f), \ + V4 (0x1.fffdb6p-2f), V4 (0x1.ffffecp-1f) }, \ + .shift = V4 (0x1.8p23f), \ + .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, \ + } + +#define ExponentBias v_u32 (0x3f800000) /* asuint(1.0f). */ +#define C(i) d->poly[i] + +static inline float32x4_t +v_expf_inline (float32x4_t x, const struct v_expf_data *d) +{ + /* Helper routine for calculating exp(x). + Copied from v_expf.c, with all special-case handling removed - the + calling routine should handle special values if required. */ + + /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] + x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ + float32x4_t n, r, z; + z = vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0); + n = vsubq_f32 (z, d->shift); + r = vfmsq_laneq_f32 (x, n, d->invln2_and_ln2, 1); + r = vfmsq_laneq_f32 (r, n, d->invln2_and_ln2, 2); + uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_f32 (z), 23); + float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, ExponentBias)); + + /* Custom order-4 Estrin avoids building high order monomial. */ + float32x4_t r2 = vmulq_f32 (r, r); + float32x4_t p, q, poly; + p = vfmaq_f32 (C (1), C (0), r); + q = vfmaq_f32 (C (3), C (2), r); + q = vfmaq_f32 (q, p, r2); + p = vmulq_f32 (C (4), r); + poly = vfmaq_f32 (p, q, r2); + return vfmaq_f32 (scale, poly, scale); +} + +#endif diff --git a/sysdeps/aarch64/fpu/vecmath_config.h b/sysdeps/aarch64/fpu/vecmath_config.h index 409c0c9bd9..3f0b5f4764 100644 --- a/sysdeps/aarch64/fpu/vecmath_config.h +++ b/sysdeps/aarch64/fpu/vecmath_config.h @@ -59,6 +59,8 @@ extern const struct v_log_data } table[1 << V_LOG_TABLE_BITS]; } __v_log_data attribute_hidden; +#define V_EXP_TAIL_TABLE_BITS 8 +extern const uint64_t __v_exp_tail_data[1 << V_EXP_TAIL_TABLE_BITS] attribute_hidden; #define V_EXP_TABLE_BITS 7 extern const uint64_t __v_exp_data[1 << V_EXP_TABLE_BITS] attribute_hidden; diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index ed4791e26a..97f45236dd 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -701,11 +701,19 @@ double: 2 float: 2 ldouble: 2 +Function: "cosh_advsimd": +double: 2 +float: 2 + Function: "cosh_downward": double: 3 float: 1 ldouble: 3 +Function: "cosh_sve": +double: 2 +float: 2 + Function: "cosh_towardzero": double: 3 float: 1 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index 6193518fb0..f66da42c36 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -73,8 +73,13 @@ GLIBC_2.39 _ZGVsMxv_tan F GLIBC_2.39 _ZGVsMxv_tanf F GLIBC_2.39 _ZGVsMxvv_atan2 F GLIBC_2.39 _ZGVsMxvv_atan2f F +GLIBC_2.40 _ZGVnN2v_cosh F +GLIBC_2.40 _ZGVnN2v_coshf F GLIBC_2.40 _ZGVnN2v_erf F GLIBC_2.40 _ZGVnN2v_erff F +GLIBC_2.40 _ZGVnN4v_coshf F GLIBC_2.40 _ZGVnN4v_erff F +GLIBC_2.40 _ZGVsMxv_cosh F +GLIBC_2.40 _ZGVsMxv_coshf F GLIBC_2.40 _ZGVsMxv_erf F GLIBC_2.40 _ZGVsMxv_erff F From patchwork Tue Feb 20 16:59:40 2024 Content-Type: text/plain; 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CTRY:IE; LANG:en; SCL:1; SRV:; IPV:CAL; SFV:NSPM; H:64aa7808-outbound-1.mta.getcheckrecipient.com; PTR:ec2-63-35-35-123.eu-west-1.compute.amazonaws.com; CAT:NONE; SFS:(13230031)(36860700004)(46966006)(40470700004); DIR:OUT; SFP:1101; X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-OriginalArrivalTime: 20 Feb 2024 16:59:59.2319 (UTC) X-MS-Exchange-CrossTenant-Network-Message-Id: 866bf43a-119c-4743-f5df-08dc32355f3d X-MS-Exchange-CrossTenant-Id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-CrossTenant-OriginalAttributedTenantConnectingIp: TenantId=f34e5979-57d9-4aaa-ad4d-b122a662184d; Ip=[63.35.35.123]; Helo=[64aa7808-outbound-1.mta.getcheckrecipient.com] X-MS-Exchange-CrossTenant-AuthSource: DB1PEPF000509EE.eurprd03.prod.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: HybridOnPrem X-MS-Exchange-Transport-CrossTenantHeadersStamped: DU0PR08MB8346 X-Spam-Status: No, score=-12.6 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, FORGED_SPF_HELO, GIT_PATCH_0, KAM_DMARC_NONE, KAM_SHORT, RCVD_IN_DNSWL_NONE, RCVD_IN_MSPIKE_H2, SPF_HELO_PASS, SPF_NONE, TXREP, T_SCC_BODY_TEXT_LINE, UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org --- Thanks, Joe sysdeps/aarch64/fpu/Makefile | 1 + sysdeps/aarch64/fpu/Versions | 5 + sysdeps/aarch64/fpu/acosh_advsimd.c | 67 +++++++++++ sysdeps/aarch64/fpu/acosh_sve.c | 51 ++++++++ sysdeps/aarch64/fpu/acoshf_advsimd.c | 78 +++++++++++++ sysdeps/aarch64/fpu/acoshf_sve.c | 49 ++++++++ sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/bits/math-vector.h | 8 ++ sysdeps/aarch64/fpu/sv_log1p_inline.h | 109 ++++++++++++++++++ sysdeps/aarch64/fpu/sv_log1pf_inline.h | 76 ++++++++++++ .../fpu/test-double-advsimd-wrappers.c | 1 + .../aarch64/fpu/test-double-sve-wrappers.c | 1 + .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + sysdeps/aarch64/fpu/v_log1p_inline.h | 103 +++++++++++++++++ sysdeps/aarch64/fpu/v_log1pf_inline.h | 78 +++++++++++++ sysdeps/aarch64/fpu/v_math.h | 10 ++ sysdeps/aarch64/libm-test-ulps | 8 ++ .../unix/sysv/linux/aarch64/libmvec.abilist | 5 + 19 files changed, 653 insertions(+) create mode 100644 sysdeps/aarch64/fpu/acosh_advsimd.c create mode 100644 sysdeps/aarch64/fpu/acosh_sve.c create mode 100644 sysdeps/aarch64/fpu/acoshf_advsimd.c create mode 100644 sysdeps/aarch64/fpu/acoshf_sve.c create mode 100644 sysdeps/aarch64/fpu/sv_log1p_inline.h create mode 100644 sysdeps/aarch64/fpu/sv_log1pf_inline.h create mode 100644 sysdeps/aarch64/fpu/v_log1p_inline.h create mode 100644 sysdeps/aarch64/fpu/v_log1pf_inline.h Reviewed-by: Szabolcs Nagy diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index 019c3a5188..2e5bbb5a07 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -1,4 +1,5 @@ libmvec-supported-funcs = acos \ + acosh \ asin \ atan \ atan2 \ diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index 884b4b57f0..60e1cdeace 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -79,6 +79,11 @@ libmvec { _ZGVsMxv_tan; } GLIBC_2.40 { + _ZGVnN2v_acosh; + _ZGVnN2v_acoshf; + _ZGVnN4v_acoshf; + _ZGVsMxv_acosh; + _ZGVsMxv_acoshf; _ZGVnN2v_cosh; _ZGVnN2v_coshf; _ZGVnN4v_coshf; diff --git a/sysdeps/aarch64/fpu/acosh_advsimd.c b/sysdeps/aarch64/fpu/acosh_advsimd.c new file mode 100644 index 0000000000..c88283cf11 --- /dev/null +++ b/sysdeps/aarch64/fpu/acosh_advsimd.c @@ -0,0 +1,67 @@ +/* Double-precision vector (Advanced SIMD) acosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#define WANT_V_LOG1P_K0_SHORTCUT 1 +#include "v_log1p_inline.h" + +const static struct data +{ + struct v_log1p_data log1p_consts; + uint64x2_t one, thresh; +} data = { + .log1p_consts = V_LOG1P_CONSTANTS_TABLE, + .one = V2 (0x3ff0000000000000), + .thresh = V2 (0x1ff0000000000000) /* asuint64(0x1p511) - asuint64(1). */ +}; + +static float64x2_t NOINLINE VPCS_ATTR +special_case (float64x2_t x, float64x2_t y, uint64x2_t special, + const struct v_log1p_data *d) +{ + return v_call_f64 (acosh, x, log1p_inline (y, d), special); +} + +/* Vector approximation for double-precision acosh, based on log1p. + The largest observed error is 3.02 ULP in the region where the + argument to log1p falls in the k=0 interval, i.e. x close to 1: + _ZGVnN2v_acosh(0x1.00798aaf80739p+0) got 0x1.f2d6d823bc9dfp-5 + want 0x1.f2d6d823bc9e2p-5. */ +VPCS_ATTR float64x2_t V_NAME_D1 (acosh) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + uint64x2_t special + = vcgeq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (x), d->one), d->thresh); + float64x2_t special_arg = x; + +#if WANT_SIMD_EXCEPT + if (__glibc_unlikely (v_any_u64 (special))) + x = vbslq_f64 (special, vreinterpretq_f64_u64 (d->one), x); +#endif + + float64x2_t xm1 = vsubq_f64 (x, v_f64 (1)); + float64x2_t y; + y = vaddq_f64 (x, v_f64 (1)); + y = vmulq_f64 (y, xm1); + y = vsqrtq_f64 (y); + y = vaddq_f64 (xm1, y); + + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (special_arg, y, special, &d->log1p_consts); + return log1p_inline (y, &d->log1p_consts); +} diff --git a/sysdeps/aarch64/fpu/acosh_sve.c b/sysdeps/aarch64/fpu/acosh_sve.c new file mode 100644 index 0000000000..3e4faaa5ca --- /dev/null +++ b/sysdeps/aarch64/fpu/acosh_sve.c @@ -0,0 +1,51 @@ +/* Double-precision vector (SVE) acosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#define WANT_SV_LOG1P_K0_SHORTCUT 1 +#include "sv_log1p_inline.h" + +#define One (0x3ff0000000000000) +#define Thres (0x1ff0000000000000) /* asuint64 (0x1p511) - One. */ + +static svfloat64_t NOINLINE +special_case (svfloat64_t x, svfloat64_t y, svbool_t special) +{ + return sv_call_f64 (acosh, x, y, special); +} + +/* SVE approximation for double-precision acosh, based on log1p. + The largest observed error is 3.19 ULP in the region where the + argument to log1p falls in the k=0 interval, i.e. x close to 1: + SV_NAME_D1 (acosh)(0x1.1e4388d4ca821p+0) got 0x1.ed23399f5137p-2 + want 0x1.ed23399f51373p-2. */ +svfloat64_t SV_NAME_D1 (acosh) (svfloat64_t x, const svbool_t pg) +{ + /* (ix - One) >= (BigBound - One). */ + svuint64_t ix = svreinterpret_u64 (x); + svbool_t special = svcmpge (pg, svsub_x (pg, ix, One), Thres); + + svfloat64_t xm1 = svsub_x (pg, x, 1.0); + svfloat64_t u = svmul_x (pg, xm1, svadd_x (pg, x, 1.0)); + svfloat64_t y = svadd_x (pg, xm1, svsqrt_x (pg, u)); + + /* Fall back to scalar routine for special lanes. */ + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, sv_log1p_inline (y, pg), special); + return sv_log1p_inline (y, pg); +} diff --git a/sysdeps/aarch64/fpu/acoshf_advsimd.c b/sysdeps/aarch64/fpu/acoshf_advsimd.c new file mode 100644 index 0000000000..8916dcbf40 --- /dev/null +++ b/sysdeps/aarch64/fpu/acoshf_advsimd.c @@ -0,0 +1,78 @@ +/* Single-precision vector (Advanced SIMD) acosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_log1pf_inline.h" + +#define SquareLim 0x1p64 + +const static struct data +{ + struct v_log1pf_data log1pf_consts; + uint32x4_t one; + uint16x4_t thresh; +} data = { + .log1pf_consts = V_LOG1PF_CONSTANTS_TABLE, + .one = V4 (0x3f800000), + .thresh = V4 (0x2000) /* top(asuint(SquareLim) - asuint(1)). */ +}; + +static float32x4_t NOINLINE VPCS_ATTR +special_case (float32x4_t x, float32x4_t y, uint16x4_t special, + const struct v_log1pf_data d) +{ + return v_call_f32 (acoshf, x, log1pf_inline (y, d), vmovl_u16 (special)); +} + +/* Vector approximation for single-precision acosh, based on log1p. Maximum + error depends on WANT_SIMD_EXCEPT. With SIMD fp exceptions enabled, it + is 2.78 ULP: + __v_acoshf(0x1.07887p+0) got 0x1.ef9e9cp-3 + want 0x1.ef9ea2p-3. + With exceptions disabled, we can compute u with a shorter dependency chain, + which gives maximum error of 3.07 ULP: + __v_acoshf(0x1.01f83ep+0) got 0x1.fbc7fap-4 + want 0x1.fbc7f4p-4. */ + +VPCS_ATTR float32x4_t NOINLINE V_NAME_F1 (acosh) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + uint32x4_t ix = vreinterpretq_u32_f32 (x); + uint16x4_t special = vcge_u16 (vsubhn_u32 (ix, d->one), d->thresh); + +#if WANT_SIMD_EXCEPT + /* Mask special lanes with 1 to side-step spurious invalid or overflow. Use + only xm1 to calculate u, as operating on x will trigger invalid for NaN. + Widening sign-extend special predicate in order to mask with it. */ + uint32x4_t p + = vreinterpretq_u32_s32 (vmovl_s16 (vreinterpret_s16_u16 (special))); + float32x4_t xm1 = v_zerofy_f32 (vsubq_f32 (x, v_f32 (1)), p); + float32x4_t u = vfmaq_f32 (vaddq_f32 (xm1, xm1), xm1, xm1); +#else + float32x4_t xm1 = vsubq_f32 (x, v_f32 (1)); + float32x4_t u = vmulq_f32 (xm1, vaddq_f32 (x, v_f32 (1.0f))); +#endif + + float32x4_t y = vaddq_f32 (xm1, vsqrtq_f32 (u)); + + if (__glibc_unlikely (v_any_u16h (special))) + return special_case (x, y, special, d->log1pf_consts); + return log1pf_inline (y, d->log1pf_consts); +} +libmvec_hidden_def (V_NAME_F1 (acosh)) +HALF_WIDTH_ALIAS_F1 (acosh) diff --git a/sysdeps/aarch64/fpu/acoshf_sve.c b/sysdeps/aarch64/fpu/acoshf_sve.c new file mode 100644 index 0000000000..2110894e62 --- /dev/null +++ b/sysdeps/aarch64/fpu/acoshf_sve.c @@ -0,0 +1,49 @@ +/* Single-precision vector (SVE) acosh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#define One 0x3f800000 +#define Thres 0x20000000 /* asuint(0x1p64) - One. */ + +#include "sv_log1pf_inline.h" + +static svfloat32_t NOINLINE +special_case (svfloat32_t x, svfloat32_t y, svbool_t special) +{ + return sv_call_f32 (acoshf, x, y, special); +} + +/* Single-precision SVE acosh(x) routine. Implements the same algorithm as + vector acoshf and log1p. + + Maximum error is 2.78 ULPs: + SV_NAME_F1 (acosh) (0x1.01e996p+0) got 0x1.f45b42p-4 + want 0x1.f45b3cp-4. */ +svfloat32_t SV_NAME_F1 (acosh) (svfloat32_t x, const svbool_t pg) +{ + svuint32_t ix = svreinterpret_u32 (x); + svbool_t special = svcmpge (pg, svsub_x (pg, ix, One), Thres); + + svfloat32_t xm1 = svsub_x (pg, x, 1.0f); + svfloat32_t u = svmul_x (pg, xm1, svadd_x (pg, x, 1.0f)); + svfloat32_t y = sv_log1pf_inline (svadd_x (pg, xm1, svsqrt_x (pg, u)), pg); + + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, y, special); + return y; +} diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index c63b2948d4..22fec4de77 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -18,6 +18,7 @@ . */ libmvec_hidden_proto (V_NAME_F1(acos)); +libmvec_hidden_proto (V_NAME_F1(acosh)); libmvec_hidden_proto (V_NAME_F1(asin)); libmvec_hidden_proto (V_NAME_F1(atan)); libmvec_hidden_proto (V_NAME_F1(cos)); diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 8ca5509870..841330956c 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -33,6 +33,10 @@ # define __DECL_SIMD_acos __DECL_SIMD_aarch64 # undef __DECL_SIMD_acosf # define __DECL_SIMD_acosf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_acosh +# define __DECL_SIMD_acosh __DECL_SIMD_aarch64 +# undef __DECL_SIMD_acoshf +# define __DECL_SIMD_acoshf __DECL_SIMD_aarch64 # undef __DECL_SIMD_asin # define __DECL_SIMD_asin __DECL_SIMD_aarch64 # undef __DECL_SIMD_asinf @@ -125,6 +129,7 @@ typedef __SVBool_t __sv_bool_t; __vpcs __f32x4_t _ZGVnN4vv_atan2f (__f32x4_t, __f32x4_t); __vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_acoshf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); @@ -143,6 +148,7 @@ __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t); __vpcs __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t); __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_acosh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); @@ -166,6 +172,7 @@ __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t); __sv_f32_t _ZGVsMxvv_atan2f (__sv_f32_t, __sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_acoshf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); @@ -184,6 +191,7 @@ __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t); __sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_acosh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); diff --git a/sysdeps/aarch64/fpu/sv_log1p_inline.h b/sysdeps/aarch64/fpu/sv_log1p_inline.h new file mode 100644 index 0000000000..da019674f9 --- /dev/null +++ b/sysdeps/aarch64/fpu/sv_log1p_inline.h @@ -0,0 +1,109 @@ +/* Helper for double-precision SVE routines which depend on log1p + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_SV_LOG1P_INLINE_H +#define AARCH64_FPU_SV_LOG1P_INLINE_H + +#include "sv_math.h" +#include "poly_sve_f64.h" + +static const struct sv_log1p_data +{ + double poly[19], ln2[2]; + uint64_t hf_rt2_top; + uint64_t one_m_hf_rt2_top; + uint32_t bottom_mask; + int64_t one_top; +} sv_log1p_data = { + /* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. + */ + .poly = { -0x1.ffffffffffffbp-2, 0x1.55555555551a9p-2, -0x1.00000000008e3p-2, + 0x1.9999999a32797p-3, -0x1.555555552fecfp-3, 0x1.249248e071e5ap-3, + -0x1.ffffff8bf8482p-4, 0x1.c71c8f07da57ap-4, -0x1.9999ca4ccb617p-4, + 0x1.7459ad2e1dfa3p-4, -0x1.554d2680a3ff2p-4, 0x1.3b4c54d487455p-4, + -0x1.2548a9ffe80e6p-4, 0x1.0f389a24b2e07p-4, -0x1.eee4db15db335p-5, + 0x1.e95b494d4a5ddp-5, -0x1.15fdf07cb7c73p-4, 0x1.0310b70800fcfp-4, + -0x1.cfa7385bdb37ep-6 }, + .ln2 = { 0x1.62e42fefa3800p-1, 0x1.ef35793c76730p-45 }, + .hf_rt2_top = 0x3fe6a09e00000000, + .one_m_hf_rt2_top = 0x00095f6200000000, + .bottom_mask = 0xffffffff, + .one_top = 0x3ff +}; + +static inline svfloat64_t +sv_log1p_inline (svfloat64_t x, const svbool_t pg) +{ + /* Helper for calculating log(x + 1). Adapted from v_log1p_inline.h, which + differs from v_log1p_2u5.c by: + - No special-case handling - this should be dealt with by the caller. + - Pairwise Horner polynomial evaluation for improved accuracy. + - Optionally simulate the shortcut for k=0, used in the scalar routine, + using svsel, for improved accuracy when the argument to log1p is close + to 0. This feature is enabled by defining WANT_SV_LOG1P_K0_SHORTCUT as 1 + in the source of the caller before including this file. + See sv_log1p_2u1.c for details of the algorithm. */ + const struct sv_log1p_data *d = ptr_barrier (&sv_log1p_data); + svfloat64_t m = svadd_x (pg, x, 1); + svuint64_t mi = svreinterpret_u64 (m); + svuint64_t u = svadd_x (pg, mi, d->one_m_hf_rt2_top); + + svint64_t ki + = svsub_x (pg, svreinterpret_s64 (svlsr_x (pg, u, 52)), d->one_top); + svfloat64_t k = svcvt_f64_x (pg, ki); + + /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ + svuint64_t utop + = svadd_x (pg, svand_x (pg, u, 0x000fffff00000000), d->hf_rt2_top); + svuint64_t u_red = svorr_x (pg, utop, svand_x (pg, mi, d->bottom_mask)); + svfloat64_t f = svsub_x (pg, svreinterpret_f64 (u_red), 1); + + /* Correction term c/m. */ + svfloat64_t c = svsub_x (pg, x, svsub_x (pg, m, 1)); + svfloat64_t cm; + +#ifndef WANT_SV_LOG1P_K0_SHORTCUT +#error \ + "Cannot use sv_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0" +#elif WANT_SV_LOG1P_K0_SHORTCUT + /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is + that the approximation is solely the polynomial. */ + svbool_t knot0 = svcmpne (pg, k, 0); + cm = svdiv_z (knot0, c, m); + if (__glibc_likely (!svptest_any (pg, knot0))) + { + f = svsel (knot0, f, x); + } +#else + /* No shortcut. */ + cm = svdiv_x (pg, c, m); +#endif + + /* Approximate log1p(f) on the reduced input using a polynomial. */ + svfloat64_t f2 = svmul_x (pg, f, f); + svfloat64_t p = sv_pw_horner_18_f64_x (pg, f, f2, d->poly); + + /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */ + svfloat64_t ylo = svmla_x (pg, cm, k, d->ln2[0]); + svfloat64_t yhi = svmla_x (pg, f, k, d->ln2[1]); + + return svmla_x (pg, svadd_x (pg, ylo, yhi), f2, p); +} + +#endif diff --git a/sysdeps/aarch64/fpu/sv_log1pf_inline.h b/sysdeps/aarch64/fpu/sv_log1pf_inline.h new file mode 100644 index 0000000000..b94b2da055 --- /dev/null +++ b/sysdeps/aarch64/fpu/sv_log1pf_inline.h @@ -0,0 +1,76 @@ +/* Helper for single-precision SVE routines which depend on log1p + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_SV_LOG1PF_INLINE_H +#define AARCH64_FPU_SV_LOG1PF_INLINE_H + +#include "sv_math.h" +#include "vecmath_config.h" +#include "poly_sve_f32.h" + +static const struct sv_log1pf_data +{ + float32_t poly[9]; + float32_t ln2; + float32_t scale_back; +} sv_log1pf_data = { + /* Polynomial generated using FPMinimax in [-0.25, 0.5]. */ + .poly = { -0x1p-1f, 0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f, + -0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f, 0x1.abcb6p-4f, + -0x1.6f0d5ep-5f }, + .scale_back = 0x1.0p-23f, + .ln2 = 0x1.62e43p-1f, +}; + +static inline svfloat32_t +eval_poly (svfloat32_t m, const float32_t *c, svbool_t pg) +{ + svfloat32_t p_12 = svmla_x (pg, sv_f32 (c[0]), m, sv_f32 (c[1])); + svfloat32_t m2 = svmul_x (pg, m, m); + svfloat32_t q = svmla_x (pg, m, m2, p_12); + svfloat32_t p = sv_pw_horner_6_f32_x (pg, m, m2, c + 2); + p = svmul_x (pg, m2, p); + + return svmla_x (pg, q, m2, p); +} + +static inline svfloat32_t +sv_log1pf_inline (svfloat32_t x, svbool_t pg) +{ + const struct sv_log1pf_data *d = ptr_barrier (&sv_log1pf_data); + + svfloat32_t m = svadd_x (pg, x, 1.0f); + + svint32_t ks = svsub_x (pg, svreinterpret_s32 (m), + svreinterpret_s32 (svdup_f32 (0.75f))); + ks = svand_x (pg, ks, 0xff800000); + svuint32_t k = svreinterpret_u32 (ks); + svfloat32_t s = svreinterpret_f32 ( + svsub_x (pg, svreinterpret_u32 (svdup_f32 (4.0f)), k)); + + svfloat32_t m_scale + = svreinterpret_f32 (svsub_x (pg, svreinterpret_u32 (x), k)); + m_scale + = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1.0f), sv_f32 (0.25f), s)); + svfloat32_t p = eval_poly (m_scale, d->poly, pg); + svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->scale_back); + return svmla_x (pg, p, scale_back, d->ln2); +} + +#endif diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index b37cb7d5e9..f4ce1d7009 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -24,6 +24,7 @@ #define VEC_TYPE float64x2_t VPCS_VECTOR_WRAPPER (acos_advsimd, _ZGVnN2v_acos) +VPCS_VECTOR_WRAPPER (acosh_advsimd, _ZGVnN2v_acosh) VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan) VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 011f07d2c1..0e973cc9d7 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -43,6 +43,7 @@ } SVE_VECTOR_WRAPPER (acos_sve, _ZGVsMxv_acos) +SVE_VECTOR_WRAPPER (acosh_sve, _ZGVsMxv_acosh) SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan) SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 3545299143..0ce026b5ea 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -24,6 +24,7 @@ #define VEC_TYPE float32x4_t VPCS_VECTOR_WRAPPER (acosf_advsimd, _ZGVnN4v_acosf) +VPCS_VECTOR_WRAPPER (acoshf_advsimd, _ZGVnN4v_acoshf) VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf) VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index bbc74ede88..398b7373e8 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -43,6 +43,7 @@ } SVE_VECTOR_WRAPPER (acosf_sve, _ZGVsMxv_acosf) +SVE_VECTOR_WRAPPER (acoshf_sve, _ZGVsMxv_acoshf) SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf) SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f) diff --git a/sysdeps/aarch64/fpu/v_log1p_inline.h b/sysdeps/aarch64/fpu/v_log1p_inline.h new file mode 100644 index 0000000000..242e43b6ee --- /dev/null +++ b/sysdeps/aarch64/fpu/v_log1p_inline.h @@ -0,0 +1,103 @@ +/* Helper for double-precision Advanced SIMD routines which depend on log1p + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_V_LOG1P_INLINE_H +#define AARCH64_FPU_V_LOG1P_INLINE_H + +#include "v_math.h" +#include "poly_advsimd_f64.h" + +struct v_log1p_data +{ + float64x2_t poly[19], ln2[2]; + uint64x2_t hf_rt2_top, one_m_hf_rt2_top, umask; + int64x2_t one_top; +}; + +/* Coefficients generated using Remez, deg=20, in [sqrt(2)/2-1, sqrt(2)-1]. */ +#define V_LOG1P_CONSTANTS_TABLE \ + { \ + .poly = { V2 (-0x1.ffffffffffffbp-2), V2 (0x1.55555555551a9p-2), \ + V2 (-0x1.00000000008e3p-2), V2 (0x1.9999999a32797p-3), \ + V2 (-0x1.555555552fecfp-3), V2 (0x1.249248e071e5ap-3), \ + V2 (-0x1.ffffff8bf8482p-4), V2 (0x1.c71c8f07da57ap-4), \ + V2 (-0x1.9999ca4ccb617p-4), V2 (0x1.7459ad2e1dfa3p-4), \ + V2 (-0x1.554d2680a3ff2p-4), V2 (0x1.3b4c54d487455p-4), \ + V2 (-0x1.2548a9ffe80e6p-4), V2 (0x1.0f389a24b2e07p-4), \ + V2 (-0x1.eee4db15db335p-5), V2 (0x1.e95b494d4a5ddp-5), \ + V2 (-0x1.15fdf07cb7c73p-4), V2 (0x1.0310b70800fcfp-4), \ + V2 (-0x1.cfa7385bdb37ep-6) }, \ + .ln2 = { V2 (0x1.62e42fefa3800p-1), V2 (0x1.ef35793c76730p-45) }, \ + .hf_rt2_top = V2 (0x3fe6a09e00000000), \ + .one_m_hf_rt2_top = V2 (0x00095f6200000000), \ + .umask = V2 (0x000fffff00000000), .one_top = V2 (0x3ff) \ + } + +#define BottomMask v_u64 (0xffffffff) + +static inline float64x2_t +log1p_inline (float64x2_t x, const struct v_log1p_data *d) +{ + /* Helper for calculating log(x + 1). Copied from v_log1p_2u5.c, with several + modifications: + - No special-case handling - this should be dealt with by the caller. + - Pairwise Horner polynomial evaluation for improved accuracy. + - Optionally simulate the shortcut for k=0, used in the scalar routine, + using v_sel, for improved accuracy when the argument to log1p is close to + 0. This feature is enabled by defining WANT_V_LOG1P_K0_SHORTCUT as 1 in + the source of the caller before including this file. + See v_log1pf_2u1.c for details of the algorithm. */ + float64x2_t m = vaddq_f64 (x, v_f64 (1)); + uint64x2_t mi = vreinterpretq_u64_f64 (m); + uint64x2_t u = vaddq_u64 (mi, d->one_m_hf_rt2_top); + + int64x2_t ki + = vsubq_s64 (vreinterpretq_s64_u64 (vshrq_n_u64 (u, 52)), d->one_top); + float64x2_t k = vcvtq_f64_s64 (ki); + + /* Reduce x to f in [sqrt(2)/2, sqrt(2)]. */ + uint64x2_t utop = vaddq_u64 (vandq_u64 (u, d->umask), d->hf_rt2_top); + uint64x2_t u_red = vorrq_u64 (utop, vandq_u64 (mi, BottomMask)); + float64x2_t f = vsubq_f64 (vreinterpretq_f64_u64 (u_red), v_f64 (1)); + + /* Correction term c/m. */ + float64x2_t cm = vdivq_f64 (vsubq_f64 (x, vsubq_f64 (m, v_f64 (1))), m); + +#ifndef WANT_V_LOG1P_K0_SHORTCUT +#error \ + "Cannot use v_log1p_inline.h without specifying whether you need the k0 shortcut for greater accuracy close to 0" +#elif WANT_V_LOG1P_K0_SHORTCUT + /* Shortcut if k is 0 - set correction term to 0 and f to x. The result is + that the approximation is solely the polynomial. */ + uint64x2_t k0 = vceqzq_f64 (k); + cm = v_zerofy_f64 (cm, k0); + f = vbslq_f64 (k0, x, f); +#endif + + /* Approximate log1p(f) on the reduced input using a polynomial. */ + float64x2_t f2 = vmulq_f64 (f, f); + float64x2_t p = v_pw_horner_18_f64 (f, f2, d->poly); + + /* Assemble log1p(x) = k * log2 + log1p(f) + c/m. */ + float64x2_t ylo = vfmaq_f64 (cm, k, d->ln2[1]); + float64x2_t yhi = vfmaq_f64 (f, k, d->ln2[0]); + return vfmaq_f64 (vaddq_f64 (ylo, yhi), f2, p); +} + +#endif diff --git a/sysdeps/aarch64/fpu/v_log1pf_inline.h b/sysdeps/aarch64/fpu/v_log1pf_inline.h new file mode 100644 index 0000000000..643a6cdcfc --- /dev/null +++ b/sysdeps/aarch64/fpu/v_log1pf_inline.h @@ -0,0 +1,78 @@ +/* Helper for single-precision Advanced SIMD routines which depend on log1p + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_V_LOG1PF_INLINE_H +#define AARCH64_FPU_V_LOG1PF_INLINE_H + +#include "v_math.h" +#include "poly_advsimd_f32.h" + +struct v_log1pf_data +{ + float32x4_t poly[8], ln2; + uint32x4_t four; + int32x4_t three_quarters; +}; + +/* Polynomial generated using FPMinimax in [-0.25, 0.5]. First two coefficients + (1, -0.5) are not stored as they can be generated more efficiently. */ +#define V_LOG1PF_CONSTANTS_TABLE \ + { \ + .poly \ + = { V4 (0x1.5555aap-2f), V4 (-0x1.000038p-2f), V4 (0x1.99675cp-3f), \ + V4 (-0x1.54ef78p-3f), V4 (0x1.28a1f4p-3f), V4 (-0x1.0da91p-3f), \ + V4 (0x1.abcb6p-4f), V4 (-0x1.6f0d5ep-5f) }, \ + .ln2 = V4 (0x1.62e43p-1f), .four = V4 (0x40800000), \ + .three_quarters = V4 (0x3f400000) \ + } + +static inline float32x4_t +eval_poly (float32x4_t m, const float32x4_t *c) +{ + /* Approximate log(1+m) on [-0.25, 0.5] using pairwise Horner (main routine + uses split Estrin, but this way reduces register pressure in the calling + routine). */ + float32x4_t q = vfmaq_f32 (v_f32 (-0.5), m, c[0]); + float32x4_t m2 = vmulq_f32 (m, m); + q = vfmaq_f32 (m, m2, q); + float32x4_t p = v_pw_horner_6_f32 (m, m2, c + 1); + p = vmulq_f32 (m2, p); + return vfmaq_f32 (q, m2, p); +} + +static inline float32x4_t +log1pf_inline (float32x4_t x, const struct v_log1pf_data d) +{ + /* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no + special-case handling. See that file for details of the algorithm. */ + float32x4_t m = vaddq_f32 (x, v_f32 (1.0f)); + int32x4_t k + = vandq_s32 (vsubq_s32 (vreinterpretq_s32_f32 (m), d.three_quarters), + v_s32 (0xff800000)); + uint32x4_t ku = vreinterpretq_u32_s32 (k); + float32x4_t s = vreinterpretq_f32_u32 (vsubq_u32 (d.four, ku)); + float32x4_t m_scale + = vreinterpretq_f32_u32 (vsubq_u32 (vreinterpretq_u32_f32 (x), ku)); + m_scale = vaddq_f32 (m_scale, vfmaq_f32 (v_f32 (-1.0f), v_f32 (0.25f), s)); + float32x4_t p = eval_poly (m_scale, d.poly); + float32x4_t scale_back = vmulq_f32 (vcvtq_f32_s32 (k), v_f32 (0x1.0p-23f)); + return vfmaq_f32 (p, scale_back, d.ln2); +} + +#endif diff --git a/sysdeps/aarch64/fpu/v_math.h b/sysdeps/aarch64/fpu/v_math.h index d4d78bc402..12824fce8c 100644 --- a/sysdeps/aarch64/fpu/v_math.h +++ b/sysdeps/aarch64/fpu/v_math.h @@ -108,6 +108,11 @@ v_call2_f32 (float (*f) (float, float), float32x4_t x1, float32x4_t x2, p[2] ? f (x1[2], x2[2]) : y[2], p[3] ? f (x1[3], x2[3]) : y[3] }; } +static inline float32x4_t +v_zerofy_f32 (float32x4_t x, uint32x4_t mask) +{ + return vreinterpretq_f32_u32 (vbicq_u32 (vreinterpretq_u32_f32 (x), mask)); +} static inline float64x2_t v_f64 (double x) @@ -167,5 +172,10 @@ v_call2_f64 (double (*f) (double, double), float64x2_t x1, float64x2_t x2, return (float64x2_t){ p[0] ? f (x1[0], x2[0]) : y[0], p[1] ? f (x1[1], x2[1]) : y[1] }; } +static inline float64x2_t +v_zerofy_f64 (float64x2_t x, uint64x2_t mask) +{ + return vreinterpretq_f64_u64 (vbicq_u64 (vreinterpretq_u64_f64 (x), mask)); +} #endif diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index 97f45236dd..3afdd35043 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -34,11 +34,19 @@ double: 2 float: 2 ldouble: 4 +Function: "acosh_advsimd": +double: 2 +float: 2 + Function: "acosh_downward": double: 2 float: 2 ldouble: 3 +Function: "acosh_sve": +double: 2 +float: 2 + Function: "acosh_towardzero": double: 2 float: 2 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index f66da42c36..f5aaa519f2 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -73,12 +73,17 @@ GLIBC_2.39 _ZGVsMxv_tan F GLIBC_2.39 _ZGVsMxv_tanf F GLIBC_2.39 _ZGVsMxvv_atan2 F GLIBC_2.39 _ZGVsMxvv_atan2f F +GLIBC_2.40 _ZGVnN2v_acosh F +GLIBC_2.40 _ZGVnN2v_acoshf F GLIBC_2.40 _ZGVnN2v_cosh F GLIBC_2.40 _ZGVnN2v_coshf F GLIBC_2.40 _ZGVnN2v_erf F GLIBC_2.40 _ZGVnN2v_erff F +GLIBC_2.40 _ZGVnN4v_acoshf F GLIBC_2.40 _ZGVnN4v_coshf F GLIBC_2.40 _ZGVnN4v_erff F +GLIBC_2.40 _ZGVsMxv_acosh F +GLIBC_2.40 _ZGVsMxv_acoshf F GLIBC_2.40 _ZGVsMxv_cosh F GLIBC_2.40 _ZGVsMxv_coshf F GLIBC_2.40 _ZGVsMxv_erf F From patchwork Tue Feb 20 16:59:41 2024 Content-Type: text/plain; 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CTRY:IE; LANG:en; SCL:1; SRV:; IPV:CAL; SFV:NSPM; H:64aa7808-outbound-1.mta.getcheckrecipient.com; PTR:ec2-63-35-35-123.eu-west-1.compute.amazonaws.com; CAT:NONE; SFS:(13230031)(36860700004)(46966006)(40470700004); DIR:OUT; SFP:1101; X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-OriginalArrivalTime: 20 Feb 2024 17:00:01.0187 (UTC) X-MS-Exchange-CrossTenant-Network-Message-Id: fcd00ec9-c985-4d22-2614-08dc32356058 X-MS-Exchange-CrossTenant-Id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-CrossTenant-OriginalAttributedTenantConnectingIp: TenantId=f34e5979-57d9-4aaa-ad4d-b122a662184d; Ip=[63.35.35.123]; Helo=[64aa7808-outbound-1.mta.getcheckrecipient.com] X-MS-Exchange-CrossTenant-AuthSource: AM3PEPF0000A79C.eurprd04.prod.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: HybridOnPrem X-MS-Exchange-Transport-CrossTenantHeadersStamped: AS8PR08MB8134 X-Spam-Status: No, score=-12.6 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, FORGED_SPF_HELO, GIT_PATCH_0, KAM_DMARC_NONE, KAM_SHORT, RCVD_IN_DNSWL_NONE, RCVD_IN_MSPIKE_H2, SPF_HELO_PASS, SPF_NONE, TXREP, T_SCC_BODY_TEXT_LINE, UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org --- Thanks, Joe sysdeps/aarch64/fpu/Makefile | 1 + sysdeps/aarch64/fpu/Versions | 5 + sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/asinh_advsimd.c | 171 ++++++++++++++++++ sysdeps/aarch64/fpu/asinh_sve.c | 150 +++++++++++++++ sysdeps/aarch64/fpu/asinhf_advsimd.c | 80 ++++++++ sysdeps/aarch64/fpu/asinhf_sve.c | 56 ++++++ sysdeps/aarch64/fpu/bits/math-vector.h | 8 + .../fpu/test-double-advsimd-wrappers.c | 1 + .../aarch64/fpu/test-double-sve-wrappers.c | 1 + .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + sysdeps/aarch64/libm-test-ulps | 8 + .../unix/sysv/linux/aarch64/libmvec.abilist | 5 + 14 files changed, 489 insertions(+) create mode 100644 sysdeps/aarch64/fpu/asinh_advsimd.c create mode 100644 sysdeps/aarch64/fpu/asinh_sve.c create mode 100644 sysdeps/aarch64/fpu/asinhf_advsimd.c create mode 100644 sysdeps/aarch64/fpu/asinhf_sve.c Reviewed-by: Szabolcs Nagy diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index 2e5bbb5a07..d474f2969d 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -1,6 +1,7 @@ libmvec-supported-funcs = acos \ acosh \ asin \ + asinh \ atan \ atan2 \ cos \ diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index 60e1cdeace..08ea15efae 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -84,6 +84,11 @@ libmvec { _ZGVnN4v_acoshf; _ZGVsMxv_acosh; _ZGVsMxv_acoshf; + _ZGVnN2v_asinh; + _ZGVnN2v_asinhf; + _ZGVnN4v_asinhf; + _ZGVsMxv_asinh; + _ZGVsMxv_asinhf; _ZGVnN2v_cosh; _ZGVnN2v_coshf; _ZGVnN4v_coshf; diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index 22fec4de77..1e80721c9f 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -20,6 +20,7 @@ libmvec_hidden_proto (V_NAME_F1(acos)); libmvec_hidden_proto (V_NAME_F1(acosh)); libmvec_hidden_proto (V_NAME_F1(asin)); +libmvec_hidden_proto (V_NAME_F1(asinh)); libmvec_hidden_proto (V_NAME_F1(atan)); libmvec_hidden_proto (V_NAME_F1(cos)); libmvec_hidden_proto (V_NAME_F1(cosh)); diff --git a/sysdeps/aarch64/fpu/asinh_advsimd.c b/sysdeps/aarch64/fpu/asinh_advsimd.c new file mode 100644 index 0000000000..544a52f651 --- /dev/null +++ b/sysdeps/aarch64/fpu/asinh_advsimd.c @@ -0,0 +1,171 @@ +/* Double-precision vector (Advanced SIMD) asinh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" +#include "poly_advsimd_f64.h" + +#define A(i) v_f64 (__v_log_data.poly[i]) +#define N (1 << V_LOG_TABLE_BITS) + +const static struct data +{ + float64x2_t poly[18]; + uint64x2_t off, huge_bound, abs_mask; + float64x2_t ln2, tiny_bound; +} data = { + .off = V2 (0x3fe6900900000000), + .ln2 = V2 (0x1.62e42fefa39efp-1), + .huge_bound = V2 (0x5fe0000000000000), + .tiny_bound = V2 (0x1p-26), + .abs_mask = V2 (0x7fffffffffffffff), + /* Even terms of polynomial s.t. asinh(x) is approximated by + asinh(x) ~= x + x^3 * (C0 + C1 * x + C2 * x^2 + C3 * x^3 + ...). + Generated using Remez, f = (asinh(sqrt(x)) - sqrt(x))/x^(3/2). */ + .poly = { V2 (-0x1.55555555554a7p-3), V2 (0x1.3333333326c7p-4), + V2 (-0x1.6db6db68332e6p-5), V2 (0x1.f1c71b26fb40dp-6), + V2 (-0x1.6e8b8b654a621p-6), V2 (0x1.1c4daa9e67871p-6), + V2 (-0x1.c9871d10885afp-7), V2 (0x1.7a16e8d9d2ecfp-7), + V2 (-0x1.3ddca533e9f54p-7), V2 (0x1.0becef748dafcp-7), + V2 (-0x1.b90c7099dd397p-8), V2 (0x1.541f2bb1ffe51p-8), + V2 (-0x1.d217026a669ecp-9), V2 (0x1.0b5c7977aaf7p-9), + V2 (-0x1.e0f37daef9127p-11), V2 (0x1.388b5fe542a6p-12), + V2 (-0x1.021a48685e287p-14), V2 (0x1.93d4ba83d34dap-18) }, +}; + +static float64x2_t NOINLINE VPCS_ATTR +special_case (float64x2_t x, float64x2_t y, uint64x2_t special) +{ + return v_call_f64 (asinh, x, y, special); +} + +struct entry +{ + float64x2_t invc; + float64x2_t logc; +}; + +static inline struct entry +lookup (uint64x2_t i) +{ + float64x2_t e0 = vld1q_f64 ( + &__v_log_data.table[(i[0] >> (52 - V_LOG_TABLE_BITS)) & (N - 1)].invc); + float64x2_t e1 = vld1q_f64 ( + &__v_log_data.table[(i[1] >> (52 - V_LOG_TABLE_BITS)) & (N - 1)].invc); + return (struct entry){ vuzp1q_f64 (e0, e1), vuzp2q_f64 (e0, e1) }; +} + +static inline float64x2_t +log_inline (float64x2_t x, const struct data *d) +{ + /* Double-precision vector log, copied from ordinary vector log with some + cosmetic modification and special-cases removed. */ + uint64x2_t ix = vreinterpretq_u64_f64 (x); + uint64x2_t tmp = vsubq_u64 (ix, d->off); + int64x2_t k = vshrq_n_s64 (vreinterpretq_s64_u64 (tmp), 52); + uint64x2_t iz + = vsubq_u64 (ix, vandq_u64 (tmp, vdupq_n_u64 (0xfffULL << 52))); + float64x2_t z = vreinterpretq_f64_u64 (iz); + struct entry e = lookup (tmp); + float64x2_t r = vfmaq_f64 (v_f64 (-1.0), z, e.invc); + float64x2_t kd = vcvtq_f64_s64 (k); + float64x2_t hi = vfmaq_f64 (vaddq_f64 (e.logc, r), kd, d->ln2); + float64x2_t r2 = vmulq_f64 (r, r); + float64x2_t y = vfmaq_f64 (A (2), A (3), r); + float64x2_t p = vfmaq_f64 (A (0), A (1), r); + y = vfmaq_f64 (y, A (4), r2); + y = vfmaq_f64 (p, y, r2); + y = vfmaq_f64 (hi, y, r2); + return y; +} + +/* Double-precision implementation of vector asinh(x). + asinh is very sensitive around 1, so it is impractical to devise a single + low-cost algorithm which is sufficiently accurate on a wide range of input. + Instead we use two different algorithms: + asinh(x) = sign(x) * log(|x| + sqrt(x^2 + 1) if |x| >= 1 + = sign(x) * (|x| + |x|^3 * P(x^2)) otherwise + where log(x) is an optimized log approximation, and P(x) is a polynomial + shared with the scalar routine. The greatest observed error 3.29 ULP, in + |x| >= 1: + __v_asinh(0x1.2cd9d717e2c9bp+0) got 0x1.ffffcfd0e234fp-1 + want 0x1.ffffcfd0e2352p-1. */ +VPCS_ATTR float64x2_t V_NAME_D1 (asinh) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + float64x2_t ax = vabsq_f64 (x); + uint64x2_t iax = vreinterpretq_u64_f64 (ax); + + uint64x2_t gt1 = vcgeq_f64 (ax, v_f64 (1)); + uint64x2_t special = vcgeq_u64 (iax, d->huge_bound); + +#if WANT_SIMD_EXCEPT + uint64x2_t tiny = vcltq_f64 (ax, d->tiny_bound); + special = vorrq_u64 (special, tiny); +#endif + + /* Option 1: |x| >= 1. + Compute asinh(x) according by asinh(x) = log(x + sqrt(x^2 + 1)). + If WANT_SIMD_EXCEPT is enabled, sidestep special values, which will + overflow, by setting special lanes to 1. These will be fixed later. */ + float64x2_t option_1 = v_f64 (0); + if (__glibc_likely (v_any_u64 (gt1))) + { +#if WANT_SIMD_EXCEPT + float64x2_t xm = v_zerofy_f64 (ax, special); +#else + float64x2_t xm = ax; +#endif + option_1 = log_inline ( + vaddq_f64 (xm, vsqrtq_f64 (vfmaq_f64 (v_f64 (1), xm, xm))), d); + } + + /* Option 2: |x| < 1. + Compute asinh(x) using a polynomial. + If WANT_SIMD_EXCEPT is enabled, sidestep special lanes, which will + overflow, and tiny lanes, which will underflow, by setting them to 0. They + will be fixed later, either by selecting x or falling back to the scalar + special-case. The largest observed error in this region is 1.47 ULPs: + __v_asinh(0x1.fdfcd00cc1e6ap-1) got 0x1.c1d6bf874019bp-1 + want 0x1.c1d6bf874019cp-1. */ + float64x2_t option_2 = v_f64 (0); + if (__glibc_likely (v_any_u64 (vceqzq_u64 (gt1)))) + { +#if WANT_SIMD_EXCEPT + ax = v_zerofy_f64 (ax, vorrq_u64 (tiny, gt1)); +#endif + float64x2_t x2 = vmulq_f64 (ax, ax), x3 = vmulq_f64 (ax, x2), + z2 = vmulq_f64 (x2, x2), z4 = vmulq_f64 (z2, z2), + z8 = vmulq_f64 (z4, z4), z16 = vmulq_f64 (z8, z8); + float64x2_t p = v_estrin_17_f64 (x2, z2, z4, z8, z16, d->poly); + option_2 = vfmaq_f64 (ax, p, x3); +#if WANT_SIMD_EXCEPT + option_2 = vbslq_f64 (tiny, x, option_2); +#endif + } + + /* Choose the right option for each lane. */ + float64x2_t y = vbslq_f64 (gt1, option_1, option_2); + /* Copy sign. */ + y = vbslq_f64 (d->abs_mask, y, x); + + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (x, y, special); + return y; +} diff --git a/sysdeps/aarch64/fpu/asinh_sve.c b/sysdeps/aarch64/fpu/asinh_sve.c new file mode 100644 index 0000000000..28dc5c4587 --- /dev/null +++ b/sysdeps/aarch64/fpu/asinh_sve.c @@ -0,0 +1,150 @@ +/* Double-precision vector (SVE) asinh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" +#include "poly_sve_f64.h" + +#define SignMask (0x8000000000000000) +#define One (0x3ff0000000000000) +#define Thres (0x5fe0000000000000) /* asuint64 (0x1p511). */ + +static const struct data +{ + double poly[18]; + double ln2, p3, p1, p4, p0, p2; + uint64_t n; + uint64_t off; + +} data = { + /* Polynomial generated using Remez on [2^-26, 1]. */ + .poly + = { -0x1.55555555554a7p-3, 0x1.3333333326c7p-4, -0x1.6db6db68332e6p-5, + 0x1.f1c71b26fb40dp-6, -0x1.6e8b8b654a621p-6, 0x1.1c4daa9e67871p-6, + -0x1.c9871d10885afp-7, 0x1.7a16e8d9d2ecfp-7, -0x1.3ddca533e9f54p-7, + 0x1.0becef748dafcp-7, -0x1.b90c7099dd397p-8, 0x1.541f2bb1ffe51p-8, + -0x1.d217026a669ecp-9, 0x1.0b5c7977aaf7p-9, -0x1.e0f37daef9127p-11, + 0x1.388b5fe542a6p-12, -0x1.021a48685e287p-14, 0x1.93d4ba83d34dap-18 }, + .ln2 = 0x1.62e42fefa39efp-1, + .p0 = -0x1.ffffffffffff7p-2, + .p1 = 0x1.55555555170d4p-2, + .p2 = -0x1.0000000399c27p-2, + .p3 = 0x1.999b2e90e94cap-3, + .p4 = -0x1.554e550bd501ep-3, + .n = 1 << V_LOG_TABLE_BITS, + .off = 0x3fe6900900000000 +}; + +static svfloat64_t NOINLINE +special_case (svfloat64_t x, svfloat64_t y, svbool_t special) +{ + return sv_call_f64 (asinh, x, y, special); +} + +static inline svfloat64_t +__sv_log_inline (svfloat64_t x, const struct data *d, const svbool_t pg) +{ + /* Double-precision SVE log, copied from SVE log implementation with some + cosmetic modification and special-cases removed. See that file for details + of the algorithm used. */ + + svuint64_t ix = svreinterpret_u64 (x); + svuint64_t tmp = svsub_x (pg, ix, d->off); + svuint64_t i = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), + (d->n - 1) << 1); + svint64_t k = svasr_x (pg, svreinterpret_s64 (tmp), 52); + svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)); + svfloat64_t z = svreinterpret_f64 (iz); + + svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i); + svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i); + + svfloat64_t ln2_p3 = svld1rq (svptrue_b64 (), &d->ln2); + svfloat64_t p1_p4 = svld1rq (svptrue_b64 (), &d->p1); + + svfloat64_t r = svmla_x (pg, sv_f64 (-1.0), invc, z); + svfloat64_t kd = svcvt_f64_x (pg, k); + + svfloat64_t hi = svmla_lane (svadd_x (pg, logc, r), kd, ln2_p3, 0); + svfloat64_t r2 = svmul_x (pg, r, r); + + svfloat64_t y = svmla_lane (sv_f64 (d->p2), r, ln2_p3, 1); + + svfloat64_t p = svmla_lane (sv_f64 (d->p0), r, p1_p4, 0); + y = svmla_lane (y, r2, p1_p4, 1); + y = svmla_x (pg, p, r2, y); + y = svmla_x (pg, hi, r2, y); + return y; +} + +/* Double-precision implementation of SVE asinh(x). + asinh is very sensitive around 1, so it is impractical to devise a single + low-cost algorithm which is sufficiently accurate on a wide range of input. + Instead we use two different algorithms: + asinh(x) = sign(x) * log(|x| + sqrt(x^2 + 1) if |x| >= 1 + = sign(x) * (|x| + |x|^3 * P(x^2)) otherwise + where log(x) is an optimized log approximation, and P(x) is a polynomial + shared with the scalar routine. The greatest observed error 2.51 ULP, in + |x| >= 1: + _ZGVsMxv_asinh(0x1.170469d024505p+0) got 0x1.e3181c43b0f36p-1 + want 0x1.e3181c43b0f39p-1. */ +svfloat64_t SV_NAME_D1 (asinh) (svfloat64_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svuint64_t ix = svreinterpret_u64 (x); + svuint64_t iax = svbic_x (pg, ix, SignMask); + svuint64_t sign = svand_x (pg, ix, SignMask); + svfloat64_t ax = svreinterpret_f64 (iax); + + svbool_t ge1 = svcmpge (pg, iax, One); + svbool_t special = svcmpge (pg, iax, Thres); + + /* Option 1: |x| >= 1. + Compute asinh(x) according by asinh(x) = log(x + sqrt(x^2 + 1)). */ + svfloat64_t option_1 = sv_f64 (0); + if (__glibc_likely (svptest_any (pg, ge1))) + { + svfloat64_t x2 = svmul_x (pg, ax, ax); + option_1 = __sv_log_inline ( + svadd_x (pg, ax, svsqrt_x (pg, svadd_x (pg, x2, 1))), d, pg); + } + + /* Option 2: |x| < 1. + Compute asinh(x) using a polynomial. + The largest observed error in this region is 1.51 ULPs: + _ZGVsMxv_asinh(0x1.fe12bf8c616a2p-1) got 0x1.c1e649ee2681bp-1 + want 0x1.c1e649ee2681dp-1. */ + svfloat64_t option_2 = sv_f64 (0); + if (__glibc_likely (svptest_any (pg, svnot_z (pg, ge1)))) + { + svfloat64_t x2 = svmul_x (pg, ax, ax); + svfloat64_t x4 = svmul_x (pg, x2, x2); + svfloat64_t p = sv_pw_horner_17_f64_x (pg, x2, x4, d->poly); + option_2 = svmla_x (pg, ax, p, svmul_x (pg, x2, ax)); + } + + /* Choose the right option for each lane. */ + svfloat64_t y = svsel (ge1, option_1, option_2); + + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case ( + x, svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign)), + special); + return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign)); +} diff --git a/sysdeps/aarch64/fpu/asinhf_advsimd.c b/sysdeps/aarch64/fpu/asinhf_advsimd.c new file mode 100644 index 0000000000..09fd8a6143 --- /dev/null +++ b/sysdeps/aarch64/fpu/asinhf_advsimd.c @@ -0,0 +1,80 @@ +/* Single-precision vector (Advanced SIMD) asinh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" +#include "v_log1pf_inline.h" + +#define SignMask v_u32 (0x80000000) + +const static struct data +{ + struct v_log1pf_data log1pf_consts; + uint32x4_t big_bound; +#if WANT_SIMD_EXCEPT + uint32x4_t tiny_bound; +#endif +} data = { + .log1pf_consts = V_LOG1PF_CONSTANTS_TABLE, + .big_bound = V4 (0x5f800000), /* asuint(0x1p64). */ +#if WANT_SIMD_EXCEPT + .tiny_bound = V4 (0x30800000) /* asuint(0x1p-30). */ +#endif +}; + +static float32x4_t NOINLINE VPCS_ATTR +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +{ + return v_call_f32 (asinhf, x, y, special); +} + +/* Single-precision implementation of vector asinh(x), using vector log1p. + Worst-case error is 2.66 ULP, at roughly +/-0.25: + __v_asinhf(0x1.01b04p-2) got 0x1.fe163ep-3 want 0x1.fe1638p-3. */ +VPCS_ATTR float32x4_t NOINLINE V_NAME_F1 (asinh) (float32x4_t x) +{ + const struct data *dat = ptr_barrier (&data); + uint32x4_t iax = vbicq_u32 (vreinterpretq_u32_f32 (x), SignMask); + float32x4_t ax = vreinterpretq_f32_u32 (iax); + uint32x4_t special = vcgeq_u32 (iax, dat->big_bound); + float32x4_t special_arg = x; + +#if WANT_SIMD_EXCEPT + /* Sidestep tiny and large values to avoid inadvertently triggering + under/overflow. */ + special = vorrq_u32 (special, vcltq_u32 (iax, dat->tiny_bound)); + if (__glibc_unlikely (v_any_u32 (special))) + { + ax = v_zerofy_f32 (ax, special); + x = v_zerofy_f32 (x, special); + } +#endif + + /* asinh(x) = log(x + sqrt(x * x + 1)). + For positive x, asinh(x) = log1p(x + x * x / (1 + sqrt(x * x + 1))). */ + float32x4_t d + = vaddq_f32 (v_f32 (1), vsqrtq_f32 (vfmaq_f32 (v_f32 (1), x, x))); + float32x4_t y = log1pf_inline ( + vaddq_f32 (ax, vdivq_f32 (vmulq_f32 (ax, ax), d)), dat->log1pf_consts); + + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (special_arg, vbslq_f32 (SignMask, x, y), special); + return vbslq_f32 (SignMask, x, y); +} +libmvec_hidden_def (V_NAME_F1 (asinh)) +HALF_WIDTH_ALIAS_F1 (asinh) diff --git a/sysdeps/aarch64/fpu/asinhf_sve.c b/sysdeps/aarch64/fpu/asinhf_sve.c new file mode 100644 index 0000000000..d85c3a685c --- /dev/null +++ b/sysdeps/aarch64/fpu/asinhf_sve.c @@ -0,0 +1,56 @@ +/* Single-precision vector (SVE) asinh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" +#include "sv_log1pf_inline.h" + +#define BigBound (0x5f800000) /* asuint(0x1p64). */ + +static svfloat32_t NOINLINE +special_case (svfloat32_t x, svfloat32_t y, svbool_t special) +{ + return sv_call_f32 (asinhf, x, y, special); +} + +/* Single-precision SVE asinh(x) routine. Implements the same algorithm as + vector asinhf and log1p. + + Maximum error is 2.48 ULPs: + SV_NAME_F1 (asinh) (0x1.008864p-3) got 0x1.ffbbbcp-4 + want 0x1.ffbbb8p-4. */ +svfloat32_t SV_NAME_F1 (asinh) (svfloat32_t x, const svbool_t pg) +{ + svfloat32_t ax = svabs_x (pg, x); + svuint32_t iax = svreinterpret_u32 (ax); + svuint32_t sign = sveor_x (pg, svreinterpret_u32 (x), iax); + svbool_t special = svcmpge (pg, iax, BigBound); + + /* asinh(x) = log(x + sqrt(x * x + 1)). + For positive x, asinh(x) = log1p(x + x * x / (1 + sqrt(x * x + 1))). */ + svfloat32_t ax2 = svmul_x (pg, ax, ax); + svfloat32_t d = svadd_x (pg, svsqrt_x (pg, svadd_x (pg, ax2, 1.0f)), 1.0f); + svfloat32_t y + = sv_log1pf_inline (svadd_x (pg, ax, svdiv_x (pg, ax2, d)), pg); + + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case ( + x, svreinterpret_f32 (svorr_x (pg, sign, svreinterpret_u32 (y))), + special); + return svreinterpret_f32 (svorr_x (pg, sign, svreinterpret_u32 (y))); +} diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 841330956c..eb2af35b27 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -41,6 +41,10 @@ # define __DECL_SIMD_asin __DECL_SIMD_aarch64 # undef __DECL_SIMD_asinf # define __DECL_SIMD_asinf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_asinh +# define __DECL_SIMD_asinh __DECL_SIMD_aarch64 +# undef __DECL_SIMD_asinhf +# define __DECL_SIMD_asinhf __DECL_SIMD_aarch64 # undef __DECL_SIMD_atan # define __DECL_SIMD_atan __DECL_SIMD_aarch64 # undef __DECL_SIMD_atanf @@ -131,6 +135,7 @@ __vpcs __f32x4_t _ZGVnN4vv_atan2f (__f32x4_t, __f32x4_t); __vpcs __f32x4_t _ZGVnN4v_acosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_acoshf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_coshf (__f32x4_t); @@ -150,6 +155,7 @@ __vpcs __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t); __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_acosh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cosh (__f64x2_t); @@ -174,6 +180,7 @@ __sv_f32_t _ZGVsMxvv_atan2f (__sv_f32_t, __sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_acosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_acoshf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_asinhf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_coshf (__sv_f32_t, __sv_bool_t); @@ -193,6 +200,7 @@ __sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_acosh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_asinh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cosh (__sv_f64_t, __sv_bool_t); diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index f4ce1d7009..3d7177c32d 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -26,6 +26,7 @@ VPCS_VECTOR_WRAPPER (acos_advsimd, _ZGVnN2v_acos) VPCS_VECTOR_WRAPPER (acosh_advsimd, _ZGVnN2v_acosh) VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) +VPCS_VECTOR_WRAPPER (asinh_advsimd, _ZGVnN2v_asinh) VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan) VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2) VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 0e973cc9d7..b88a2afe5c 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -45,6 +45,7 @@ SVE_VECTOR_WRAPPER (acos_sve, _ZGVsMxv_acos) SVE_VECTOR_WRAPPER (acosh_sve, _ZGVsMxv_acosh) SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) +SVE_VECTOR_WRAPPER (asinh_sve, _ZGVsMxv_asinh) SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan) SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2) SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 0ce026b5ea..533655402d 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -26,6 +26,7 @@ VPCS_VECTOR_WRAPPER (acosf_advsimd, _ZGVnN4v_acosf) VPCS_VECTOR_WRAPPER (acoshf_advsimd, _ZGVnN4v_acoshf) VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) +VPCS_VECTOR_WRAPPER (asinhf_advsimd, _ZGVnN4v_asinhf) VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf) VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f) VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index 398b7373e8..f7b673e335 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -45,6 +45,7 @@ SVE_VECTOR_WRAPPER (acosf_sve, _ZGVsMxv_acosf) SVE_VECTOR_WRAPPER (acoshf_sve, _ZGVsMxv_acoshf) SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) +SVE_VECTOR_WRAPPER (asinhf_sve, _ZGVsMxv_asinhf) SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf) SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f) SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf) diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index 3afdd35043..dc8cb08b3a 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -90,11 +90,19 @@ double: 2 float: 2 ldouble: 4 +Function: "asinh_advsimd": +double: 1 +float: 2 + Function: "asinh_downward": double: 3 float: 3 ldouble: 4 +Function: "asinh_sve": +double: 1 +float: 2 + Function: "asinh_towardzero": double: 2 float: 2 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index f5aaa519f2..f288afdfdd 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -75,15 +75,20 @@ GLIBC_2.39 _ZGVsMxvv_atan2 F GLIBC_2.39 _ZGVsMxvv_atan2f F GLIBC_2.40 _ZGVnN2v_acosh F GLIBC_2.40 _ZGVnN2v_acoshf F +GLIBC_2.40 _ZGVnN2v_asinh F +GLIBC_2.40 _ZGVnN2v_asinhf F GLIBC_2.40 _ZGVnN2v_cosh F GLIBC_2.40 _ZGVnN2v_coshf F GLIBC_2.40 _ZGVnN2v_erf F GLIBC_2.40 _ZGVnN2v_erff F GLIBC_2.40 _ZGVnN4v_acoshf F +GLIBC_2.40 _ZGVnN4v_asinhf F GLIBC_2.40 _ZGVnN4v_coshf F GLIBC_2.40 _ZGVnN4v_erff F GLIBC_2.40 _ZGVsMxv_acosh F GLIBC_2.40 _ZGVsMxv_acoshf F +GLIBC_2.40 _ZGVsMxv_asinh F +GLIBC_2.40 _ZGVsMxv_asinhf F GLIBC_2.40 _ZGVsMxv_cosh F GLIBC_2.40 _ZGVsMxv_coshf F GLIBC_2.40 _ZGVsMxv_erf F From patchwork Tue Feb 20 16:59:42 2024 Content-Type: text/plain; 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Tue, 20 Feb 2024 16:59:48 +0000 From: Joe Ramsay To: CC: Joe Ramsay Subject: [PATCH 5/8] aarch64/fpu: Add vector variants of atanh Date: Tue, 20 Feb 2024 16:59:42 +0000 Message-ID: <20240220165945.21585-5-Joe.Ramsay@arm.com> X-Mailer: git-send-email 2.27.0 In-Reply-To: <20240220165945.21585-1-Joe.Ramsay@arm.com> References: <20240220165945.21585-1-Joe.Ramsay@arm.com> MIME-Version: 1.0 X-EOPAttributedMessage: 1 X-MS-TrafficTypeDiagnostic: AM4PEPF00025F98:EE_|DU0PR08MB8639:EE_|DU6PEPF0000A7DE:EE_|PAWPR08MB9122:EE_ X-MS-Office365-Filtering-Correlation-Id: e07d4680-9ef8-49a4-f22e-08dc32356027 x-checkrecipientrouted: true NoDisclaimer: true X-MS-Exchange-SenderADCheck: 1 X-MS-Exchange-AntiSpam-Relay: 0 X-Microsoft-Antispam-Untrusted: BCL:0; X-Microsoft-Antispam-Message-Info-Original: 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 X-Forefront-Antispam-Report-Untrusted: CIP:40.67.248.234; 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CTRY:IE; LANG:en; SCL:1; SRV:; IPV:CAL; SFV:NSPM; H:64aa7808-outbound-1.mta.getcheckrecipient.com; PTR:ec2-63-35-35-123.eu-west-1.compute.amazonaws.com; CAT:NONE; SFS:(13230031)(36860700004)(40470700004)(46966006); DIR:OUT; SFP:1101; X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-OriginalArrivalTime: 20 Feb 2024 17:00:00.7653 (UTC) X-MS-Exchange-CrossTenant-Network-Message-Id: e07d4680-9ef8-49a4-f22e-08dc32356027 X-MS-Exchange-CrossTenant-Id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-CrossTenant-OriginalAttributedTenantConnectingIp: TenantId=f34e5979-57d9-4aaa-ad4d-b122a662184d; Ip=[63.35.35.123]; Helo=[64aa7808-outbound-1.mta.getcheckrecipient.com] X-MS-Exchange-CrossTenant-AuthSource: DU6PEPF0000A7DE.eurprd02.prod.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: HybridOnPrem X-MS-Exchange-Transport-CrossTenantHeadersStamped: PAWPR08MB9122 X-Spam-Status: No, score=-12.5 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, FORGED_SPF_HELO, GIT_PATCH_0, KAM_DMARC_NONE, KAM_SHORT, RCVD_IN_DNSWL_NONE, RCVD_IN_MSPIKE_H2, SPF_HELO_PASS, SPF_NONE, TXREP, T_SCC_BODY_TEXT_LINE, UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org --- Thanks, Joe sysdeps/aarch64/fpu/Makefile | 1 + sysdeps/aarch64/fpu/Versions | 5 ++ sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/atanh_advsimd.c | 64 +++++++++++++++ sysdeps/aarch64/fpu/atanh_sve.c | 59 ++++++++++++++ sysdeps/aarch64/fpu/atanhf_advsimd.c | 79 +++++++++++++++++++ sysdeps/aarch64/fpu/atanhf_sve.c | 54 +++++++++++++ sysdeps/aarch64/fpu/bits/math-vector.h | 8 ++ .../fpu/test-double-advsimd-wrappers.c | 1 + .../aarch64/fpu/test-double-sve-wrappers.c | 1 + .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + sysdeps/aarch64/libm-test-ulps | 8 ++ .../unix/sysv/linux/aarch64/libmvec.abilist | 5 ++ 14 files changed, 288 insertions(+) create mode 100644 sysdeps/aarch64/fpu/atanh_advsimd.c create mode 100644 sysdeps/aarch64/fpu/atanh_sve.c create mode 100644 sysdeps/aarch64/fpu/atanhf_advsimd.c create mode 100644 sysdeps/aarch64/fpu/atanhf_sve.c Reviewed-by: Szabolcs Nagy diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index d474f2969d..4c878e5906 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -3,6 +3,7 @@ libmvec-supported-funcs = acos \ asin \ asinh \ atan \ + atanh \ atan2 \ cos \ cosh \ diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index 08ea15efae..86c08c1fa3 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -99,5 +99,10 @@ libmvec { _ZGVnN4v_erff; _ZGVsMxv_erf; _ZGVsMxv_erff; + _ZGVnN2v_atanh; + _ZGVnN2v_atanhf; + _ZGVnN4v_atanhf; + _ZGVsMxv_atanh; + _ZGVsMxv_atanhf; } } diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index 1e80721c9f..afbb01e191 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -22,6 +22,7 @@ libmvec_hidden_proto (V_NAME_F1(acosh)); libmvec_hidden_proto (V_NAME_F1(asin)); libmvec_hidden_proto (V_NAME_F1(asinh)); libmvec_hidden_proto (V_NAME_F1(atan)); +libmvec_hidden_proto (V_NAME_F1(atanh)); libmvec_hidden_proto (V_NAME_F1(cos)); libmvec_hidden_proto (V_NAME_F1(cosh)); libmvec_hidden_proto (V_NAME_F1(erf)); diff --git a/sysdeps/aarch64/fpu/atanh_advsimd.c b/sysdeps/aarch64/fpu/atanh_advsimd.c new file mode 100644 index 0000000000..3c3d0bd6ad --- /dev/null +++ b/sysdeps/aarch64/fpu/atanh_advsimd.c @@ -0,0 +1,64 @@ +/* Double-precision vector (Advanced SIMD) atanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#define WANT_V_LOG1P_K0_SHORTCUT 0 +#include "v_log1p_inline.h" + +const static struct data +{ + struct v_log1p_data log1p_consts; + uint64x2_t one, half; +} data = { .log1p_consts = V_LOG1P_CONSTANTS_TABLE, + .one = V2 (0x3ff0000000000000), + .half = V2 (0x3fe0000000000000) }; + +static float64x2_t VPCS_ATTR NOINLINE +special_case (float64x2_t x, float64x2_t y, uint64x2_t special) +{ + return v_call_f64 (atanh, x, y, special); +} + +/* Approximation for vector double-precision atanh(x) using modified log1p. + The greatest observed error is 3.31 ULP: + _ZGVnN2v_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6 + want 0x1.ffd8ff31b501cp-6. */ +VPCS_ATTR +float64x2_t V_NAME_D1 (atanh) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + float64x2_t ax = vabsq_f64 (x); + uint64x2_t ia = vreinterpretq_u64_f64 (ax); + uint64x2_t sign = veorq_u64 (vreinterpretq_u64_f64 (x), ia); + uint64x2_t special = vcgeq_u64 (ia, d->one); + float64x2_t halfsign = vreinterpretq_f64_u64 (vorrq_u64 (sign, d->half)); + +#if WANT_SIMD_EXCEPT + ax = v_zerofy_f64 (ax, special); +#endif + + float64x2_t y; + y = vaddq_f64 (ax, ax); + y = vdivq_f64 (y, vsubq_f64 (v_f64 (1), ax)); + y = log1p_inline (y, &d->log1p_consts); + + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (x, vmulq_f64 (y, halfsign), special); + return vmulq_f64 (y, halfsign); +} diff --git a/sysdeps/aarch64/fpu/atanh_sve.c b/sysdeps/aarch64/fpu/atanh_sve.c new file mode 100644 index 0000000000..7a52728d70 --- /dev/null +++ b/sysdeps/aarch64/fpu/atanh_sve.c @@ -0,0 +1,59 @@ +/* Double-precision vector (SVE) atanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#define WANT_SV_LOG1P_K0_SHORTCUT 0 +#include "sv_log1p_inline.h" + +#define One (0x3ff0000000000000) +#define Half (0x3fe0000000000000) + +static svfloat64_t NOINLINE +special_case (svfloat64_t x, svfloat64_t y, svbool_t special) +{ + return sv_call_f64 (atanh, x, y, special); +} + +/* SVE approximation for double-precision atanh, based on log1p. + The greatest observed error is 2.81 ULP: + _ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6 + want 0x1.ffd8ff31b501cp-6. */ +svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg) +{ + + svfloat64_t ax = svabs_x (pg, x); + svuint64_t iax = svreinterpret_u64 (ax); + svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax); + svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half)); + + /* It is special if iax >= 1. */ +// svbool_t special = svcmpge (pg, iax, One); + svbool_t special = svacge (pg, x, 1.0); + + /* Computation is performed based on the following sequence of equality: + (1+x)/(1-x) = 1 + 2x/(1-x). */ + svfloat64_t y; + y = svadd_x (pg, ax, ax); + y = svdiv_x (pg, y, svsub_x (pg, sv_f64 (1), ax)); + /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */ + y = sv_log1p_inline (y, pg); + + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, svmul_x (pg, halfsign, y), special); + return svmul_x (pg, halfsign, y); +} diff --git a/sysdeps/aarch64/fpu/atanhf_advsimd.c b/sysdeps/aarch64/fpu/atanhf_advsimd.c new file mode 100644 index 0000000000..ae488f7b54 --- /dev/null +++ b/sysdeps/aarch64/fpu/atanhf_advsimd.c @@ -0,0 +1,79 @@ +/* Single-precision vector (Advanced SIMD) atanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" +#include "v_log1pf_inline.h" + +const static struct data +{ + struct v_log1pf_data log1pf_consts; + uint32x4_t one; +#if WANT_SIMD_EXCEPT + uint32x4_t tiny_bound; +#endif +} data = { + .log1pf_consts = V_LOG1PF_CONSTANTS_TABLE, + .one = V4 (0x3f800000), +#if WANT_SIMD_EXCEPT + /* 0x1p-12, below which atanhf(x) rounds to x. */ + .tiny_bound = V4 (0x39800000), +#endif +}; + +#define AbsMask v_u32 (0x7fffffff) +#define Half v_u32 (0x3f000000) + +static float32x4_t NOINLINE VPCS_ATTR +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +{ + return v_call_f32 (atanhf, x, y, special); +} + +/* Approximation for vector single-precision atanh(x) using modified log1p. + The maximum error is 3.08 ULP: + __v_atanhf(0x1.ff215p-5) got 0x1.ffcb7cp-5 + want 0x1.ffcb82p-5. */ +VPCS_ATTR float32x4_t NOINLINE V_NAME_F1 (atanh) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + + float32x4_t halfsign = vbslq_f32 (AbsMask, v_f32 (0.5), x); + float32x4_t ax = vabsq_f32 (x); + uint32x4_t iax = vreinterpretq_u32_f32 (ax); + +#if WANT_SIMD_EXCEPT + uint32x4_t special + = vorrq_u32 (vcgeq_u32 (iax, d->one), vcltq_u32 (iax, d->tiny_bound)); + /* Side-step special cases by setting those lanes to 0, which will trigger no + exceptions. These will be fixed up later. */ + if (__glibc_unlikely (v_any_u32 (special))) + ax = v_zerofy_f32 (ax, special); +#else + uint32x4_t special = vcgeq_u32 (iax, d->one); +#endif + + float32x4_t y = vdivq_f32 (vaddq_f32 (ax, ax), vsubq_f32 (v_f32 (1), ax)); + y = log1pf_inline (y, d->log1pf_consts); + + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (x, vmulq_f32 (halfsign, y), special); + return vmulq_f32 (halfsign, y); +} +libmvec_hidden_def (V_NAME_F1 (atanh)) +HALF_WIDTH_ALIAS_F1 (atanh) diff --git a/sysdeps/aarch64/fpu/atanhf_sve.c b/sysdeps/aarch64/fpu/atanhf_sve.c new file mode 100644 index 0000000000..dae83041ef --- /dev/null +++ b/sysdeps/aarch64/fpu/atanhf_sve.c @@ -0,0 +1,54 @@ +/* Single-precision vector (SVE) atanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_log1pf_inline.h" + +#define One (0x3f800000) +#define Half (0x3f000000) + +static svfloat32_t NOINLINE +special_case (svfloat32_t x, svfloat32_t y, svbool_t special) +{ + return sv_call_f32 (atanhf, x, y, special); +} + +/* Approximation for vector single-precision atanh(x) using modified log1p. + The maximum error is 2.28 ULP: + _ZGVsMxv_atanhf(0x1.ff1194p-5) got 0x1.ffbbbcp-5 + want 0x1.ffbbb6p-5. */ +svfloat32_t SV_NAME_F1 (atanh) (svfloat32_t x, const svbool_t pg) +{ + svfloat32_t ax = svabs_x (pg, x); + svuint32_t iax = svreinterpret_u32 (ax); + svuint32_t sign = sveor_x (pg, svreinterpret_u32 (x), iax); + svfloat32_t halfsign = svreinterpret_f32 (svorr_x (pg, sign, Half)); + svbool_t special = svcmpge (pg, iax, One); + + /* Computation is performed based on the following sequence of equality: + * (1+x)/(1-x) = 1 + 2x/(1-x). */ + svfloat32_t y = svadd_x (pg, ax, ax); + y = svdiv_x (pg, y, svsub_x (pg, sv_f32 (1), ax)); + /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y). */ + y = sv_log1pf_inline (y, pg); + + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, svmul_x (pg, halfsign, y), special); + + return svmul_x (pg, halfsign, y); +} diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index eb2af35b27..ab7a8f7454 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -49,6 +49,10 @@ # define __DECL_SIMD_atan __DECL_SIMD_aarch64 # undef __DECL_SIMD_atanf # define __DECL_SIMD_atanf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_atanh +# define __DECL_SIMD_atanh __DECL_SIMD_aarch64 +# undef __DECL_SIMD_atanhf +# define __DECL_SIMD_atanhf __DECL_SIMD_aarch64 # undef __DECL_SIMD_atan2 # define __DECL_SIMD_atan2 __DECL_SIMD_aarch64 # undef __DECL_SIMD_atan2f @@ -137,6 +141,7 @@ __vpcs __f32x4_t _ZGVnN4v_acoshf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_asinhf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_atanf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_atanhf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_coshf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_erff (__f32x4_t); @@ -157,6 +162,7 @@ __vpcs __f64x2_t _ZGVnN2v_acosh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asin (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_asinh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_atan (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_atanh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cosh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_erf (__f64x2_t); @@ -182,6 +188,7 @@ __sv_f32_t _ZGVsMxv_acoshf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_asinhf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_atanf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_atanhf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_coshf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_erff (__sv_f32_t, __sv_bool_t); @@ -202,6 +209,7 @@ __sv_f64_t _ZGVsMxv_acosh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asin (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_asinh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_atan (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_atanh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cosh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_erf (__sv_f64_t, __sv_bool_t); diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index 3d7177c32d..a01aa99c16 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -28,6 +28,7 @@ VPCS_VECTOR_WRAPPER (acosh_advsimd, _ZGVnN2v_acosh) VPCS_VECTOR_WRAPPER (asin_advsimd, _ZGVnN2v_asin) VPCS_VECTOR_WRAPPER (asinh_advsimd, _ZGVnN2v_asinh) VPCS_VECTOR_WRAPPER (atan_advsimd, _ZGVnN2v_atan) +VPCS_VECTOR_WRAPPER (atanh_advsimd, _ZGVnN2v_atanh) VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2) VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos) VPCS_VECTOR_WRAPPER (cosh_advsimd, _ZGVnN2v_cosh) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index b88a2afe5c..83cb3ad5d0 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -47,6 +47,7 @@ SVE_VECTOR_WRAPPER (acosh_sve, _ZGVsMxv_acosh) SVE_VECTOR_WRAPPER (asin_sve, _ZGVsMxv_asin) SVE_VECTOR_WRAPPER (asinh_sve, _ZGVsMxv_asinh) SVE_VECTOR_WRAPPER (atan_sve, _ZGVsMxv_atan) +SVE_VECTOR_WRAPPER (atanh_sve, _ZGVsMxv_atanh) SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2) SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos) SVE_VECTOR_WRAPPER (cosh_sve, _ZGVsMxv_cosh) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 533655402d..831d4d7552 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -28,6 +28,7 @@ VPCS_VECTOR_WRAPPER (acoshf_advsimd, _ZGVnN4v_acoshf) VPCS_VECTOR_WRAPPER (asinf_advsimd, _ZGVnN4v_asinf) VPCS_VECTOR_WRAPPER (asinhf_advsimd, _ZGVnN4v_asinhf) VPCS_VECTOR_WRAPPER (atanf_advsimd, _ZGVnN4v_atanf) +VPCS_VECTOR_WRAPPER (atanhf_advsimd, _ZGVnN4v_atanhf) VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f) VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf) VPCS_VECTOR_WRAPPER (coshf_advsimd, _ZGVnN4v_coshf) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index f7b673e335..96fd612c3e 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -47,6 +47,7 @@ SVE_VECTOR_WRAPPER (acoshf_sve, _ZGVsMxv_acoshf) SVE_VECTOR_WRAPPER (asinf_sve, _ZGVsMxv_asinf) SVE_VECTOR_WRAPPER (asinhf_sve, _ZGVsMxv_asinhf) SVE_VECTOR_WRAPPER (atanf_sve, _ZGVsMxv_atanf) +SVE_VECTOR_WRAPPER (atanhf_sve, _ZGVsMxv_atanhf) SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f) SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf) SVE_VECTOR_WRAPPER (coshf_sve, _ZGVsMxv_coshf) diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index dc8cb08b3a..e2b43107e5 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -173,11 +173,19 @@ double: 2 float: 2 ldouble: 4 +Function: "atanh_advsimd": +double: 1 +float: 1 + Function: "atanh_downward": double: 3 float: 3 ldouble: 4 +Function: "atanh_sve": +double: 2 +float: 1 + Function: "atanh_towardzero": double: 2 float: 2 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index f288afdfdd..ce42372a3a 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -77,18 +77,23 @@ GLIBC_2.40 _ZGVnN2v_acosh F GLIBC_2.40 _ZGVnN2v_acoshf F GLIBC_2.40 _ZGVnN2v_asinh F GLIBC_2.40 _ZGVnN2v_asinhf F +GLIBC_2.40 _ZGVnN2v_atanh F +GLIBC_2.40 _ZGVnN2v_atanhf F GLIBC_2.40 _ZGVnN2v_cosh F GLIBC_2.40 _ZGVnN2v_coshf F GLIBC_2.40 _ZGVnN2v_erf F GLIBC_2.40 _ZGVnN2v_erff F GLIBC_2.40 _ZGVnN4v_acoshf F GLIBC_2.40 _ZGVnN4v_asinhf F +GLIBC_2.40 _ZGVnN4v_atanhf F GLIBC_2.40 _ZGVnN4v_coshf F GLIBC_2.40 _ZGVnN4v_erff F GLIBC_2.40 _ZGVsMxv_acosh F GLIBC_2.40 _ZGVsMxv_acoshf F GLIBC_2.40 _ZGVsMxv_asinh F GLIBC_2.40 _ZGVsMxv_asinhf F +GLIBC_2.40 _ZGVsMxv_atanh F +GLIBC_2.40 _ZGVsMxv_atanhf F GLIBC_2.40 _ZGVsMxv_cosh F GLIBC_2.40 _ZGVsMxv_coshf F GLIBC_2.40 _ZGVsMxv_erf F From patchwork Tue Feb 20 16:59:43 2024 Content-Type: text/plain; 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CTRY:IE; LANG:en; SCL:1; SRV:; IPV:CAL; SFV:NSPM; H:64aa7808-outbound-1.mta.getcheckrecipient.com; PTR:ec2-63-35-35-123.eu-west-1.compute.amazonaws.com; CAT:NONE; SFS:(13230031)(36860700004)(46966006)(40470700004); DIR:OUT; SFP:1101; X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-OriginalArrivalTime: 20 Feb 2024 17:00:03.2963 (UTC) X-MS-Exchange-CrossTenant-Network-Message-Id: 87a509b8-694a-45ca-2271-08dc323561aa X-MS-Exchange-CrossTenant-Id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-CrossTenant-OriginalAttributedTenantConnectingIp: TenantId=f34e5979-57d9-4aaa-ad4d-b122a662184d; Ip=[63.35.35.123]; Helo=[64aa7808-outbound-1.mta.getcheckrecipient.com] X-MS-Exchange-CrossTenant-AuthSource: DU6PEPF0000B621.eurprd02.prod.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: HybridOnPrem X-MS-Exchange-Transport-CrossTenantHeadersStamped: AS8PR08MB6150 X-Spam-Status: No, score=-12.6 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, FORGED_SPF_HELO, GIT_PATCH_0, KAM_DMARC_NONE, KAM_SHORT, RCVD_IN_DNSWL_NONE, RCVD_IN_MSPIKE_H2, SPF_HELO_PASS, SPF_NONE, TXREP, T_SCC_BODY_TEXT_LINE, UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org --- Thanks, Joe sysdeps/aarch64/fpu/Makefile | 1 + sysdeps/aarch64/fpu/Versions | 15 ++- sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/bits/math-vector.h | 8 ++ sysdeps/aarch64/fpu/sinh_advsimd.c | 121 ++++++++++++++++++ sysdeps/aarch64/fpu/sinh_sve.c | 107 ++++++++++++++++ sysdeps/aarch64/fpu/sinhf_advsimd.c | 88 +++++++++++++ sysdeps/aarch64/fpu/sinhf_sve.c | 67 ++++++++++ sysdeps/aarch64/fpu/sv_expm1f_inline.h | 84 ++++++++++++ .../fpu/test-double-advsimd-wrappers.c | 1 + .../aarch64/fpu/test-double-sve-wrappers.c | 1 + .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + sysdeps/aarch64/fpu/v_expm1f_inline.h | 73 +++++++++++ sysdeps/aarch64/libm-test-ulps | 8 ++ .../unix/sysv/linux/aarch64/libmvec.abilist | 5 + 16 files changed, 577 insertions(+), 5 deletions(-) create mode 100644 sysdeps/aarch64/fpu/sinh_advsimd.c create mode 100644 sysdeps/aarch64/fpu/sinh_sve.c create mode 100644 sysdeps/aarch64/fpu/sinhf_advsimd.c create mode 100644 sysdeps/aarch64/fpu/sinhf_sve.c create mode 100644 sysdeps/aarch64/fpu/sv_expm1f_inline.h create mode 100644 sysdeps/aarch64/fpu/v_expm1f_inline.h Reviewed-by: Szabolcs Nagy diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index 4c878e5906..fb5f3a365b 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -17,6 +17,7 @@ libmvec-supported-funcs = acos \ log1p \ log2 \ sin \ + sinh \ tan float-advsimd-funcs = $(libmvec-supported-funcs) diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index 86c08c1fa3..4774b3efea 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -89,6 +89,11 @@ libmvec { _ZGVnN4v_asinhf; _ZGVsMxv_asinh; _ZGVsMxv_asinhf; + _ZGVnN2v_atanh; + _ZGVnN2v_atanhf; + _ZGVnN4v_atanhf; + _ZGVsMxv_atanh; + _ZGVsMxv_atanhf; _ZGVnN2v_cosh; _ZGVnN2v_coshf; _ZGVnN4v_coshf; @@ -99,10 +104,10 @@ libmvec { _ZGVnN4v_erff; _ZGVsMxv_erf; _ZGVsMxv_erff; - _ZGVnN2v_atanh; - _ZGVnN2v_atanhf; - _ZGVnN4v_atanhf; - _ZGVsMxv_atanh; - _ZGVsMxv_atanhf; + _ZGVnN2v_sinh; + _ZGVnN2v_sinhf; + _ZGVnN4v_sinhf; + _ZGVsMxv_sinh; + _ZGVsMxv_sinhf; } } diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index afbb01e191..7d9445d5c0 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -35,5 +35,6 @@ libmvec_hidden_proto (V_NAME_F1(log1p)); libmvec_hidden_proto (V_NAME_F1(log2)); libmvec_hidden_proto (V_NAME_F1(log)); libmvec_hidden_proto (V_NAME_F1(sin)); +libmvec_hidden_proto (V_NAME_F1(sinh)); libmvec_hidden_proto (V_NAME_F1(tan)); libmvec_hidden_proto (V_NAME_F2(atan2)); diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index ab7a8f7454..1e9b76cf41 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -105,6 +105,10 @@ # define __DECL_SIMD_sin __DECL_SIMD_aarch64 # undef __DECL_SIMD_sinf # define __DECL_SIMD_sinf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_sinh +# define __DECL_SIMD_sinh __DECL_SIMD_aarch64 +# undef __DECL_SIMD_sinhf +# define __DECL_SIMD_sinhf __DECL_SIMD_aarch64 # undef __DECL_SIMD_tan # define __DECL_SIMD_tan __DECL_SIMD_aarch64 # undef __DECL_SIMD_tanf @@ -154,6 +158,7 @@ __vpcs __f32x4_t _ZGVnN4v_log10f (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_log1pf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_log2f (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_sinhf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t); __vpcs __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t); @@ -175,6 +180,7 @@ __vpcs __f64x2_t _ZGVnN2v_log10 (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_log1p (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_log2 (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_sin (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_sinh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t); # undef __ADVSIMD_VEC_MATH_SUPPORTED @@ -201,6 +207,7 @@ __sv_f32_t _ZGVsMxv_log10f (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_log1pf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_log2f (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_sinf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_sinhf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t); __sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t); @@ -222,6 +229,7 @@ __sv_f64_t _ZGVsMxv_log10 (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_log1p (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_log2 (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_sin (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_sinh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_tan (__sv_f64_t, __sv_bool_t); # undef __SVE_VEC_MATH_SUPPORTED diff --git a/sysdeps/aarch64/fpu/sinh_advsimd.c b/sysdeps/aarch64/fpu/sinh_advsimd.c new file mode 100644 index 0000000000..fa3723b10c --- /dev/null +++ b/sysdeps/aarch64/fpu/sinh_advsimd.c @@ -0,0 +1,121 @@ +/* Double-precision vector (Advanced SIMD) sinh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" +#include "poly_advsimd_f64.h" + +static const struct data +{ + float64x2_t poly[11]; + float64x2_t inv_ln2, m_ln2, shift; + uint64x2_t halff; + int64x2_t onef; +#if WANT_SIMD_EXCEPT + uint64x2_t tiny_bound, thresh; +#else + uint64x2_t large_bound; +#endif +} data = { + /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ + .poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5), + V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10), + V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16), + V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22), + V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), }, + + .inv_ln2 = V2 (0x1.71547652b82fep0), + .m_ln2 = (float64x2_t) {-0x1.62e42fefa39efp-1, -0x1.abc9e3b39803fp-56}, + .shift = V2 (0x1.8p52), + + .halff = V2 (0x3fe0000000000000), + .onef = V2 (0x3ff0000000000000), +#if WANT_SIMD_EXCEPT + /* 2^-26, below which sinh(x) rounds to x. */ + .tiny_bound = V2 (0x3e50000000000000), + /* asuint(large_bound) - asuint(tiny_bound). */ + .thresh = V2 (0x0230000000000000), +#else +/* 2^9. expm1 helper overflows for large input. */ + .large_bound = V2 (0x4080000000000000), +#endif +}; + +static inline float64x2_t +expm1_inline (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + /* Reduce argument: + exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 + where i = round(x / ln2) + and f = x - i * ln2 (f in [-ln2/2, ln2/2]). */ + float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift); + int64x2_t i = vcvtq_s64_f64 (j); + float64x2_t f = vfmaq_laneq_f64 (x, j, d->m_ln2, 0); + f = vfmaq_laneq_f64 (f, j, d->m_ln2, 1); + /* Approximate expm1(f) using polynomial. */ + float64x2_t f2 = vmulq_f64 (f, f); + float64x2_t f4 = vmulq_f64 (f2, f2); + float64x2_t f8 = vmulq_f64 (f4, f4); + float64x2_t p = vfmaq_f64 (f, f2, v_estrin_10_f64 (f, f2, f4, f8, d->poly)); + /* t = 2^i. */ + float64x2_t t = vreinterpretq_f64_u64 ( + vreinterpretq_u64_s64 (vaddq_s64 (vshlq_n_s64 (i, 52), d->onef))); + /* expm1(x) ~= p * t + (t - 1). */ + return vfmaq_f64 (vsubq_f64 (t, v_f64 (1.0)), p, t); +} + +static float64x2_t NOINLINE VPCS_ATTR +special_case (float64x2_t x) +{ + return v_call_f64 (sinh, x, x, v_u64 (-1)); +} + +/* Approximation for vector double-precision sinh(x) using expm1. + sinh(x) = (exp(x) - exp(-x)) / 2. + The greatest observed error is 2.57 ULP: + _ZGVnN2v_sinh (0x1.9fb1d49d1d58bp-2) got 0x1.ab34e59d678dcp-2 + want 0x1.ab34e59d678d9p-2. */ +float64x2_t VPCS_ATTR V_NAME_D1 (sinh) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + float64x2_t ax = vabsq_f64 (x); + uint64x2_t sign + = veorq_u64 (vreinterpretq_u64_f64 (x), vreinterpretq_u64_f64 (ax)); + float64x2_t halfsign = vreinterpretq_f64_u64 (vorrq_u64 (sign, d->halff)); + +#if WANT_SIMD_EXCEPT + uint64x2_t special = vcgeq_u64 ( + vsubq_u64 (vreinterpretq_u64_f64 (ax), d->tiny_bound), d->thresh); +#else + uint64x2_t special = vcgeq_u64 (vreinterpretq_u64_f64 (ax), d->large_bound); +#endif + + /* Fall back to scalar variant for all lanes if any of them are special. */ + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (x); + + /* Up to the point that expm1 overflows, we can use it to calculate sinh + using a slight rearrangement of the definition of sinh. This allows us to + retain acceptable accuracy for very small inputs. */ + float64x2_t t = expm1_inline (ax); + t = vaddq_f64 (t, vdivq_f64 (t, vaddq_f64 (t, v_f64 (1.0)))); + return vmulq_f64 (t, halfsign); +} diff --git a/sysdeps/aarch64/fpu/sinh_sve.c b/sysdeps/aarch64/fpu/sinh_sve.c new file mode 100644 index 0000000000..df5f6c8c06 --- /dev/null +++ b/sysdeps/aarch64/fpu/sinh_sve.c @@ -0,0 +1,107 @@ +/* Double-precision vector (SVE) atanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" +#include "poly_sve_f64.h" + +static const struct data +{ + float64_t poly[11]; + float64_t inv_ln2, m_ln2_hi, m_ln2_lo, shift; + uint64_t halff; + int64_t onef; + uint64_t large_bound; +} data = { + /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ + .poly = { 0x1p-1, 0x1.5555555555559p-3, 0x1.555555555554bp-5, + 0x1.111111110f663p-7, 0x1.6c16c16c1b5f3p-10, + 0x1.a01a01affa35dp-13, 0x1.a01a018b4ecbbp-16, + 0x1.71ddf82db5bb4p-19, 0x1.27e517fc0d54bp-22, + 0x1.af5eedae67435p-26, 0x1.1f143d060a28ap-29, }, + + .inv_ln2 = 0x1.71547652b82fep0, + .m_ln2_hi = -0x1.62e42fefa39efp-1, + .m_ln2_lo = -0x1.abc9e3b39803fp-56, + .shift = 0x1.8p52, + + .halff = 0x3fe0000000000000, + .onef = 0x3ff0000000000000, + /* 2^9. expm1 helper overflows for large input. */ + .large_bound = 0x4080000000000000, +}; + +static inline svfloat64_t +expm1_inline (svfloat64_t x, svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + /* Reduce argument: + exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 + where i = round(x / ln2) + and f = x - i * ln2 (f in [-ln2/2, ln2/2]). */ + svfloat64_t j + = svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2), d->shift); + svint64_t i = svcvt_s64_x (pg, j); + svfloat64_t f = svmla_x (pg, x, j, d->m_ln2_hi); + f = svmla_x (pg, f, j, d->m_ln2_lo); + /* Approximate expm1(f) using polynomial. */ + svfloat64_t f2 = svmul_x (pg, f, f); + svfloat64_t f4 = svmul_x (pg, f2, f2); + svfloat64_t f8 = svmul_x (pg, f4, f4); + svfloat64_t p + = svmla_x (pg, f, f2, sv_estrin_10_f64_x (pg, f, f2, f4, f8, d->poly)); + /* t = 2^i. */ + svfloat64_t t = svscale_x (pg, sv_f64 (1), i); + /* expm1(x) ~= p * t + (t - 1). */ + return svmla_x (pg, svsub_x (pg, t, 1.0), p, t); +} + +static svfloat64_t NOINLINE +special_case (svfloat64_t x, svbool_t pg) +{ + return sv_call_f64 (sinh, x, x, pg); +} + +/* Approximation for SVE double-precision sinh(x) using expm1. + sinh(x) = (exp(x) - exp(-x)) / 2. + The greatest observed error is 2.57 ULP: + _ZGVsMxv_sinh (0x1.a008538399931p-2) got 0x1.ab929fc64bd66p-2 + want 0x1.ab929fc64bd63p-2. */ +svfloat64_t SV_NAME_D1 (sinh) (svfloat64_t x, svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svfloat64_t ax = svabs_x (pg, x); + svuint64_t sign + = sveor_x (pg, svreinterpret_u64 (x), svreinterpret_u64 (ax)); + svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, d->halff)); + + svbool_t special = svcmpge (pg, svreinterpret_u64 (ax), d->large_bound); + + /* Fall back to scalar variant for all lanes if any are special. */ + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, pg); + + /* Up to the point that expm1 overflows, we can use it to calculate sinh + using a slight rearrangement of the definition of sinh. This allows us to + retain acceptable accuracy for very small inputs. */ + svfloat64_t t = expm1_inline (ax, pg); + t = svadd_x (pg, t, svdiv_x (pg, t, svadd_x (pg, t, 1.0))); + return svmul_x (pg, t, halfsign); +} diff --git a/sysdeps/aarch64/fpu/sinhf_advsimd.c b/sysdeps/aarch64/fpu/sinhf_advsimd.c new file mode 100644 index 0000000000..6bb7482dc2 --- /dev/null +++ b/sysdeps/aarch64/fpu/sinhf_advsimd.c @@ -0,0 +1,88 @@ +/* Single-precision vector (Advanced SIMD) sinh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" +#include "v_expm1f_inline.h" + +static const struct data +{ + struct v_expm1f_data expm1f_consts; + uint32x4_t halff; +#if WANT_SIMD_EXCEPT + uint32x4_t tiny_bound, thresh; +#else + uint32x4_t oflow_bound; +#endif +} data = { + .expm1f_consts = V_EXPM1F_DATA, + .halff = V4 (0x3f000000), +#if WANT_SIMD_EXCEPT + /* 0x1.6a09e8p-32, below which expm1f underflows. */ + .tiny_bound = V4 (0x2fb504f4), + /* asuint(oflow_bound) - asuint(tiny_bound). */ + .thresh = V4 (0x12fbbbb3), +#else + /* 0x1.61814ep+6, above which expm1f helper overflows. */ + .oflow_bound = V4 (0x42b0c0a7), +#endif +}; + +static float32x4_t NOINLINE VPCS_ATTR +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +{ + return v_call_f32 (sinhf, x, y, special); +} + +/* Approximation for vector single-precision sinh(x) using expm1. + sinh(x) = (exp(x) - exp(-x)) / 2. + The maximum error is 2.26 ULP: + _ZGVnN4v_sinhf (0x1.e34a9ep-4) got 0x1.e469ep-4 + want 0x1.e469e4p-4. */ +float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (sinh) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + + uint32x4_t ix = vreinterpretq_u32_f32 (x); + float32x4_t ax = vabsq_f32 (x); + uint32x4_t iax = vreinterpretq_u32_f32 (ax); + uint32x4_t sign = veorq_u32 (ix, iax); + float32x4_t halfsign = vreinterpretq_f32_u32 (vorrq_u32 (sign, d->halff)); + +#if WANT_SIMD_EXCEPT + uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, d->tiny_bound), d->thresh); + ax = v_zerofy_f32 (ax, special); +#else + uint32x4_t special = vcgeq_u32 (iax, d->oflow_bound); +#endif + + /* Up to the point that expm1f overflows, we can use it to calculate sinhf + using a slight rearrangement of the definition of asinh. This allows us + to retain acceptable accuracy for very small inputs. */ + float32x4_t t = expm1f_inline (ax, &d->expm1f_consts); + t = vaddq_f32 (t, vdivq_f32 (t, vaddq_f32 (t, v_f32 (1.0)))); + + /* Fall back to the scalar variant for any lanes that should trigger an + exception. */ + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (x, vmulq_f32 (t, halfsign), special); + + return vmulq_f32 (t, halfsign); +} +libmvec_hidden_def (V_NAME_F1 (sinh)) +HALF_WIDTH_ALIAS_F1 (sinh) diff --git a/sysdeps/aarch64/fpu/sinhf_sve.c b/sysdeps/aarch64/fpu/sinhf_sve.c new file mode 100644 index 0000000000..6c204b57a2 --- /dev/null +++ b/sysdeps/aarch64/fpu/sinhf_sve.c @@ -0,0 +1,67 @@ +/* Single-precision vector (SVE) sinh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_expm1f_inline.h" +#include "sv_math.h" + +static const struct data +{ + struct sv_expm1f_data expm1f_consts; + uint32_t halff, large_bound; +} data = { + .expm1f_consts = SV_EXPM1F_DATA, + .halff = 0x3f000000, + /* 0x1.61814ep+6, above which expm1f helper overflows. */ + .large_bound = 0x42b0c0a7, +}; + +static svfloat32_t NOINLINE +special_case (svfloat32_t x, svfloat32_t y, svbool_t pg) +{ + return sv_call_f32 (sinhf, x, y, pg); +} + +/* Approximation for SVE single-precision sinh(x) using expm1. + sinh(x) = (exp(x) - exp(-x)) / 2. + The maximum error is 2.26 ULP: + _ZGVsMxv_sinhf (0x1.e34a9ep-4) got 0x1.e469ep-4 + want 0x1.e469e4p-4. */ +svfloat32_t SV_NAME_F1 (sinh) (svfloat32_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + svfloat32_t ax = svabs_x (pg, x); + svuint32_t sign + = sveor_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (ax)); + svfloat32_t halfsign = svreinterpret_f32 (svorr_x (pg, sign, d->halff)); + + svbool_t special = svcmpge (pg, svreinterpret_u32 (ax), d->large_bound); + + /* Up to the point that expm1f overflows, we can use it to calculate sinhf + using a slight rearrangement of the definition of asinh. This allows us to + retain acceptable accuracy for very small inputs. */ + svfloat32_t t = expm1f_inline (ax, pg, &d->expm1f_consts); + t = svadd_x (pg, t, svdiv_x (pg, t, svadd_x (pg, t, 1.0))); + + /* Fall back to the scalar variant for any lanes which would cause + expm1f to overflow. */ + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, svmul_x (pg, t, halfsign), special); + + return svmul_x (pg, t, halfsign); +} diff --git a/sysdeps/aarch64/fpu/sv_expm1f_inline.h b/sysdeps/aarch64/fpu/sv_expm1f_inline.h new file mode 100644 index 0000000000..5b72451222 --- /dev/null +++ b/sysdeps/aarch64/fpu/sv_expm1f_inline.h @@ -0,0 +1,84 @@ +/* Single-precision inline helper for vector (SVE) expm1 function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_SV_EXPM1F_INLINE_H +#define AARCH64_FPU_SV_EXPM1F_INLINE_H + +#include "sv_math.h" + +struct sv_expm1f_data +{ + /* These 4 are grouped together so they can be loaded as one quadword, then + used with _lane forms of svmla/svmls. */ + float32_t c2, c4, ln2_hi, ln2_lo; + float32_t c0, c1, c3, inv_ln2, shift; +}; + +/* Coefficients generated using fpminimax. */ +#define SV_EXPM1F_DATA \ + { \ + .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \ + .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \ + \ + .shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \ + .ln2_lo = 0x1.7f7d1cp-20f, \ + } + +#define C(i) sv_f32 (d->c##i) + +static inline svfloat32_t +expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d) +{ + /* This vector is reliant on layout of data - it contains constants + that can be used with _lane forms of svmla/svmls. Values are: + [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */ + svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2); + + /* Reduce argument to smaller range: + Let i = round(x / ln2) + and f = x - i * ln2, then f is in [-ln2/2, ln2/2]. + exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 + where 2^i is exact because i is an integer. */ + svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2); + j = svsub_x (pg, j, d->shift); + svint32_t i = svcvt_s32_x (pg, j); + + svfloat32_t f = svmls_lane (x, j, lane_constants, 2); + f = svmls_lane (f, j, lane_constants, 3); + + /* Approximate expm1(f) using polynomial. + Taylor expansion for expm1(x) has the form: + x + ax^2 + bx^3 + cx^4 .... + So we calculate the polynomial P(f) = a + bf + cf^2 + ... + and assemble the approximation expm1(f) ~= f + f^2 * P(f). */ + svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0); + svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1); + svfloat32_t f2 = svmul_x (pg, f, f); + svfloat32_t p = svmla_x (pg, p12, f2, p34); + p = svmla_x (pg, C (0), f, p); + p = svmla_x (pg, f, f2, p); + + /* Assemble the result. + expm1(x) ~= 2^i * (p + 1) - 1 + Let t = 2^i. */ + svfloat32_t t = svscale_x (pg, sv_f32 (1), i); + return svmla_x (pg, svsub_x (pg, t, 1), p, t); +} + +#endif diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index a01aa99c16..1a57b22c3a 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -42,4 +42,5 @@ VPCS_VECTOR_WRAPPER (log10_advsimd, _ZGVnN2v_log10) VPCS_VECTOR_WRAPPER (log1p_advsimd, _ZGVnN2v_log1p) VPCS_VECTOR_WRAPPER (log2_advsimd, _ZGVnN2v_log2) VPCS_VECTOR_WRAPPER (sin_advsimd, _ZGVnN2v_sin) +VPCS_VECTOR_WRAPPER (sinh_advsimd, _ZGVnN2v_sinh) VPCS_VECTOR_WRAPPER (tan_advsimd, _ZGVnN2v_tan) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 83cb3ad5d0..0c9858f6b7 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -61,4 +61,5 @@ SVE_VECTOR_WRAPPER (log10_sve, _ZGVsMxv_log10) SVE_VECTOR_WRAPPER (log1p_sve, _ZGVsMxv_log1p) SVE_VECTOR_WRAPPER (log2_sve, _ZGVsMxv_log2) SVE_VECTOR_WRAPPER (sin_sve, _ZGVsMxv_sin) +SVE_VECTOR_WRAPPER (sinh_sve, _ZGVsMxv_sinh) SVE_VECTOR_WRAPPER (tan_sve, _ZGVsMxv_tan) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 831d4d7552..4758490c6f 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -42,4 +42,5 @@ VPCS_VECTOR_WRAPPER (log10f_advsimd, _ZGVnN4v_log10f) VPCS_VECTOR_WRAPPER (log1pf_advsimd, _ZGVnN4v_log1pf) VPCS_VECTOR_WRAPPER (log2f_advsimd, _ZGVnN4v_log2f) VPCS_VECTOR_WRAPPER (sinf_advsimd, _ZGVnN4v_sinf) +VPCS_VECTOR_WRAPPER (sinhf_advsimd, _ZGVnN4v_sinhf) VPCS_VECTOR_WRAPPER (tanf_advsimd, _ZGVnN4v_tanf) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index 96fd612c3e..7c04f07bbe 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -61,4 +61,5 @@ SVE_VECTOR_WRAPPER (log10f_sve, _ZGVsMxv_log10f) SVE_VECTOR_WRAPPER (log1pf_sve, _ZGVsMxv_log1pf) SVE_VECTOR_WRAPPER (log2f_sve, _ZGVsMxv_log2f) SVE_VECTOR_WRAPPER (sinf_sve, _ZGVsMxv_sinf) +SVE_VECTOR_WRAPPER (sinhf_sve, _ZGVsMxv_sinhf) SVE_VECTOR_WRAPPER (tanf_sve, _ZGVsMxv_tanf) diff --git a/sysdeps/aarch64/fpu/v_expm1f_inline.h b/sysdeps/aarch64/fpu/v_expm1f_inline.h new file mode 100644 index 0000000000..337ccfbfab --- /dev/null +++ b/sysdeps/aarch64/fpu/v_expm1f_inline.h @@ -0,0 +1,73 @@ +/* Single-precision inline helper for vector (Advanced SIMD) expm1 function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#ifndef AARCH64_FPU_V_EXPM1F_INLINE_H +#define AARCH64_FPU_V_EXPM1F_INLINE_H + +#include "v_math.h" +#include "poly_advsimd_f32.h" + +struct v_expm1f_data +{ + float32x4_t poly[5]; + float32x4_t invln2_and_ln2, shift; + int32x4_t exponent_bias; +}; + +/* Coefficients generated using fpminimax with degree=5 in [-log(2)/2, + log(2)/2]. Exponent bias is asuint(1.0f). + invln2_and_ln2 Stores constants: invln2, ln2_lo, ln2_hi, 0. */ +#define V_EXPM1F_DATA \ + { \ + .poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5), \ + V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) }, \ + .shift = V4 (0x1.8p23f), .exponent_bias = V4 (0x3f800000), \ + .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, \ + } + +static inline float32x4_t +expm1f_inline (float32x4_t x, const struct v_expm1f_data *d) +{ + /* Helper routine for calculating exp(x) - 1. + Copied from v_expm1f_1u6.c, with all special-case handling removed - the + calling routine should handle special values if required. */ + + /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ + float32x4_t j = vsubq_f32 ( + vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0), d->shift); + int32x4_t i = vcvtq_s32_f32 (j); + float32x4_t f = vfmsq_laneq_f32 (x, j, d->invln2_and_ln2, 1); + f = vfmsq_laneq_f32 (f, j, d->invln2_and_ln2, 2); + + /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f). + Uses Estrin scheme, where the main _ZGVnN4v_expm1f routine uses + Horner. */ + float32x4_t f2 = vmulq_f32 (f, f); + float32x4_t f4 = vmulq_f32 (f2, f2); + float32x4_t p = v_estrin_4_f32 (f, f2, f4, d->poly); + p = vfmaq_f32 (f, f2, p); + + /* t = 2^i. */ + int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias); + float32x4_t t = vreinterpretq_f32_s32 (u); + /* expm1(x) ~= p * t + (t - 1). */ + return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t); +} + +#endif diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index e2b43107e5..004eb34694 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -1441,11 +1441,19 @@ double: 2 float: 2 ldouble: 2 +Function: "sinh_advsimd": +double: 2 +float: 1 + Function: "sinh_downward": double: 3 float: 3 ldouble: 3 +Function: "sinh_sve": +double: 2 +float: 1 + Function: "sinh_towardzero": double: 3 float: 2 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index ce42372a3a..1db5ba61d6 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -83,11 +83,14 @@ GLIBC_2.40 _ZGVnN2v_cosh F GLIBC_2.40 _ZGVnN2v_coshf F GLIBC_2.40 _ZGVnN2v_erf F GLIBC_2.40 _ZGVnN2v_erff F +GLIBC_2.40 _ZGVnN2v_sinh F +GLIBC_2.40 _ZGVnN2v_sinhf F GLIBC_2.40 _ZGVnN4v_acoshf F GLIBC_2.40 _ZGVnN4v_asinhf F GLIBC_2.40 _ZGVnN4v_atanhf F GLIBC_2.40 _ZGVnN4v_coshf F GLIBC_2.40 _ZGVnN4v_erff F +GLIBC_2.40 _ZGVnN4v_sinhf F GLIBC_2.40 _ZGVsMxv_acosh F GLIBC_2.40 _ZGVsMxv_acoshf F GLIBC_2.40 _ZGVsMxv_asinh F @@ -98,3 +101,5 @@ GLIBC_2.40 _ZGVsMxv_cosh F GLIBC_2.40 _ZGVsMxv_coshf F GLIBC_2.40 _ZGVsMxv_erf F GLIBC_2.40 _ZGVsMxv_erff F +GLIBC_2.40 _ZGVsMxv_sinh F +GLIBC_2.40 _ZGVsMxv_sinhf F From patchwork Tue Feb 20 16:59:44 2024 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit 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GIT_PATCH_0, KAM_DMARC_NONE, KAM_SHORT, RCVD_IN_DNSWL_NONE, RCVD_IN_MSPIKE_H2, SPF_HELO_PASS, SPF_NONE, TXREP, T_SCC_BODY_TEXT_LINE, UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org --- Thanks, Joe math/auto-libm-test-in | 2 +- math/auto-libm-test-out-tanh | 50 ++++---- sysdeps/aarch64/fpu/Makefile | 3 +- sysdeps/aarch64/fpu/Versions | 5 + sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/bits/math-vector.h | 8 ++ sysdeps/aarch64/fpu/tanh_advsimd.c | 109 ++++++++++++++++++ sysdeps/aarch64/fpu/tanh_sve.c | 100 ++++++++++++++++ sysdeps/aarch64/fpu/tanhf_advsimd.c | 76 ++++++++++++ sysdeps/aarch64/fpu/tanhf_sve.c | 61 ++++++++++ .../fpu/test-double-advsimd-wrappers.c | 1 + .../aarch64/fpu/test-double-sve-wrappers.c | 1 + .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + sysdeps/aarch64/libm-test-ulps | 8 ++ .../unix/sysv/linux/aarch64/libmvec.abilist | 5 + 16 files changed, 405 insertions(+), 27 deletions(-) create mode 100644 sysdeps/aarch64/fpu/tanh_advsimd.c create mode 100644 sysdeps/aarch64/fpu/tanh_sve.c create mode 100644 sysdeps/aarch64/fpu/tanhf_advsimd.c create mode 100644 sysdeps/aarch64/fpu/tanhf_sve.c Reviewed-by: Szabolcs Nagy diff --git a/math/auto-libm-test-in b/math/auto-libm-test-in index d728f97770..05d7ae5002 100644 --- a/math/auto-libm-test-in +++ b/math/auto-libm-test-in @@ -7747,7 +7747,7 @@ tan min_subnorm tan -min_subnorm tanh 0 -tanh -0 +tanh -0 no-mathvec tanh 0.75 tanh -0.75 tanh 1.0 diff --git a/math/auto-libm-test-out-tanh b/math/auto-libm-test-out-tanh index 8b9427c917..19ce2e7b93 100644 --- a/math/auto-libm-test-out-tanh +++ b/math/auto-libm-test-out-tanh @@ -23,31 +23,31 @@ tanh 0 = tanh tonearest ibm128 0x0p+0 : 0x0p+0 : inexact-ok = tanh towardzero ibm128 0x0p+0 : 0x0p+0 : inexact-ok = tanh upward ibm128 0x0p+0 : 0x0p+0 : inexact-ok -tanh -0 -= tanh downward binary32 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh tonearest binary32 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh towardzero binary32 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh upward binary32 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh downward binary64 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh tonearest binary64 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh towardzero binary64 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh upward binary64 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh downward intel96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh tonearest intel96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh towardzero intel96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh upward intel96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh downward m68k96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh tonearest m68k96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh towardzero m68k96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh upward m68k96 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh downward binary128 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh tonearest binary128 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh towardzero binary128 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh upward binary128 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh downward ibm128 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh tonearest ibm128 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh towardzero ibm128 -0x0p+0 : -0x0p+0 : inexact-ok -= tanh upward ibm128 -0x0p+0 : -0x0p+0 : inexact-ok +tanh -0 no-mathvec += tanh downward binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh tonearest binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh towardzero binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh upward binary32 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh downward binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh tonearest binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh towardzero binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh upward binary64 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh downward intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh tonearest intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh towardzero intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh upward intel96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh downward m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh tonearest m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh towardzero m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh upward m68k96 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh downward binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh tonearest binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh towardzero binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh upward binary128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh downward ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh tonearest ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh towardzero ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok += tanh upward ibm128 -0x0p+0 : -0x0p+0 : no-mathvec inexact-ok tanh 0.75 = tanh downward binary32 0xcp-4 : 0xa.2991fp-4 : inexact-ok = tanh tonearest binary32 0xcp-4 : 0xa.2991fp-4 : inexact-ok diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index fb5f3a365b..e5f418ae42 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -18,7 +18,8 @@ libmvec-supported-funcs = acos \ log2 \ sin \ sinh \ - tan + tan \ + tanh float-advsimd-funcs = $(libmvec-supported-funcs) double-advsimd-funcs = $(libmvec-supported-funcs) diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index 4774b3efea..4dbf3d3244 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -109,5 +109,10 @@ libmvec { _ZGVnN4v_sinhf; _ZGVsMxv_sinh; _ZGVsMxv_sinhf; + _ZGVnN2v_tanh; + _ZGVnN2v_tanhf; + _ZGVnN4v_tanhf; + _ZGVsMxv_tanh; + _ZGVsMxv_tanhf; } } diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index 7d9445d5c0..4ff191c324 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -37,4 +37,5 @@ libmvec_hidden_proto (V_NAME_F1(log)); libmvec_hidden_proto (V_NAME_F1(sin)); libmvec_hidden_proto (V_NAME_F1(sinh)); libmvec_hidden_proto (V_NAME_F1(tan)); +libmvec_hidden_proto (V_NAME_F1(tanh)); libmvec_hidden_proto (V_NAME_F2(atan2)); diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 1e9b76cf41..585e022082 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -113,6 +113,10 @@ # define __DECL_SIMD_tan __DECL_SIMD_aarch64 # undef __DECL_SIMD_tanf # define __DECL_SIMD_tanf __DECL_SIMD_aarch64 +# undef __DECL_SIMD_tanh +# define __DECL_SIMD_tanh __DECL_SIMD_aarch64 +# undef __DECL_SIMD_tanhf +# define __DECL_SIMD_tanhf __DECL_SIMD_aarch64 #endif #if __GNUC_PREREQ(9, 0) @@ -160,6 +164,7 @@ __vpcs __f32x4_t _ZGVnN4v_log2f (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_sinhf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_tanf (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_tanhf (__f32x4_t); __vpcs __f64x2_t _ZGVnN2vv_atan2 (__f64x2_t, __f64x2_t); __vpcs __f64x2_t _ZGVnN2v_acos (__f64x2_t); @@ -182,6 +187,7 @@ __vpcs __f64x2_t _ZGVnN2v_log2 (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_sin (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_sinh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_tan (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_tanh (__f64x2_t); # undef __ADVSIMD_VEC_MATH_SUPPORTED #endif /* __ADVSIMD_VEC_MATH_SUPPORTED */ @@ -209,6 +215,7 @@ __sv_f32_t _ZGVsMxv_log2f (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_sinf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_sinhf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_tanf (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_tanhf (__sv_f32_t, __sv_bool_t); __sv_f64_t _ZGVsMxvv_atan2 (__sv_f64_t, __sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_acos (__sv_f64_t, __sv_bool_t); @@ -231,6 +238,7 @@ __sv_f64_t _ZGVsMxv_log2 (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_sin (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_sinh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_tan (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_tanh (__sv_f64_t, __sv_bool_t); # undef __SVE_VEC_MATH_SUPPORTED #endif /* __SVE_VEC_MATH_SUPPORTED */ diff --git a/sysdeps/aarch64/fpu/tanh_advsimd.c b/sysdeps/aarch64/fpu/tanh_advsimd.c new file mode 100644 index 0000000000..1da1dfa5db --- /dev/null +++ b/sysdeps/aarch64/fpu/tanh_advsimd.c @@ -0,0 +1,109 @@ +/* Double-precision vector (Advanced SIMD) tanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" +#include "poly_advsimd_f64.h" + +static const struct data +{ + float64x2_t poly[11]; + float64x2_t inv_ln2, ln2_hi, ln2_lo, shift; + uint64x2_t onef; + uint64x2_t thresh, tiny_bound; +} data = { + /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ + .poly = { V2 (0x1p-1), V2 (0x1.5555555555559p-3), V2 (0x1.555555555554bp-5), + V2 (0x1.111111110f663p-7), V2 (0x1.6c16c16c1b5f3p-10), + V2 (0x1.a01a01affa35dp-13), V2 (0x1.a01a018b4ecbbp-16), + V2 (0x1.71ddf82db5bb4p-19), V2 (0x1.27e517fc0d54bp-22), + V2 (0x1.af5eedae67435p-26), V2 (0x1.1f143d060a28ap-29), }, + + .inv_ln2 = V2 (0x1.71547652b82fep0), + .ln2_hi = V2 (-0x1.62e42fefa39efp-1), + .ln2_lo = V2 (-0x1.abc9e3b39803fp-56), + .shift = V2 (0x1.8p52), + + .onef = V2 (0x3ff0000000000000), + .tiny_bound = V2 (0x3e40000000000000), /* asuint64 (0x1p-27). */ + /* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */ + .thresh = V2 (0x01f241bf835f9d5f), +}; + +static inline float64x2_t +expm1_inline (float64x2_t x, const struct data *d) +{ + /* Helper routine for calculating exp(x) - 1. Vector port of the helper from + the scalar variant of tanh. */ + + /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ + float64x2_t j = vsubq_f64 (vfmaq_f64 (d->shift, d->inv_ln2, x), d->shift); + int64x2_t i = vcvtq_s64_f64 (j); + float64x2_t f = vfmaq_f64 (x, j, d->ln2_hi); + f = vfmaq_f64 (f, j, d->ln2_lo); + + /* Approximate expm1(f) using polynomial. */ + float64x2_t f2 = vmulq_f64 (f, f); + float64x2_t f4 = vmulq_f64 (f2, f2); + float64x2_t p = vfmaq_f64 ( + f, f2, v_estrin_10_f64 (f, f2, f4, vmulq_f64 (f4, f4), d->poly)); + + /* t = 2 ^ i. */ + float64x2_t t = vreinterpretq_f64_u64 ( + vaddq_u64 (vreinterpretq_u64_s64 (i << 52), d->onef)); + /* expm1(x) = p * t + (t - 1). */ + return vfmaq_f64 (vsubq_f64 (t, v_f64 (1)), p, t); +} + +static float64x2_t NOINLINE VPCS_ATTR +special_case (float64x2_t x, float64x2_t y, uint64x2_t special) +{ + return v_call_f64 (tanh, x, y, special); +} + +/* Vector approximation for double-precision tanh(x), using a simplified + version of expm1. The greatest observed error is 2.77 ULP: + _ZGVnN2v_tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3 + want -0x1.bd6a21a163624p-3. */ +float64x2_t VPCS_ATTR V_NAME_D1 (tanh) (float64x2_t x) +{ + const struct data *d = ptr_barrier (&data); + + uint64x2_t ia = vreinterpretq_u64_f64 (vabsq_f64 (x)); + + float64x2_t u = x; + + /* Trigger special-cases for tiny, boring and infinity/NaN. */ + uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia, d->tiny_bound), d->thresh); +#if WANT_SIMD_EXCEPT + /* To trigger fp exceptions correctly, set special lanes to a neutral value. + They will be fixed up later by the special-case handler. */ + if (__glibc_unlikely (v_any_u64 (special))) + u = v_zerofy_f64 (u, special); +#endif + + u = vaddq_f64 (u, u); + + /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ + float64x2_t q = expm1_inline (u, d); + float64x2_t qp2 = vaddq_f64 (q, v_f64 (2)); + + if (__glibc_unlikely (v_any_u64 (special))) + return special_case (x, vdivq_f64 (q, qp2), special); + return vdivq_f64 (q, qp2); +} diff --git a/sysdeps/aarch64/fpu/tanh_sve.c b/sysdeps/aarch64/fpu/tanh_sve.c new file mode 100644 index 0000000000..d25e011cea --- /dev/null +++ b/sysdeps/aarch64/fpu/tanh_sve.c @@ -0,0 +1,100 @@ +/* Double-precision vector (SVE) tanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" +#include "poly_sve_f64.h" + +static const struct data +{ + float64_t poly[11]; + float64_t inv_ln2, ln2_hi, ln2_lo, shift; + uint64_t thresh, tiny_bound; +} data = { + /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ + .poly = { 0x1p-1, 0x1.5555555555559p-3, 0x1.555555555554bp-5, + 0x1.111111110f663p-7, 0x1.6c16c16c1b5f3p-10, + 0x1.a01a01affa35dp-13, 0x1.a01a018b4ecbbp-16, + 0x1.71ddf82db5bb4p-19, 0x1.27e517fc0d54bp-22, + 0x1.af5eedae67435p-26, 0x1.1f143d060a28ap-29, }, + + .inv_ln2 = 0x1.71547652b82fep0, + .ln2_hi = -0x1.62e42fefa39efp-1, + .ln2_lo = -0x1.abc9e3b39803fp-56, + .shift = 0x1.8p52, + + .tiny_bound = 0x3e40000000000000, /* asuint64 (0x1p-27). */ + /* asuint64(0x1.241bf835f9d5fp+4) - asuint64(tiny_bound). */ + .thresh = 0x01f241bf835f9d5f, +}; + +static inline svfloat64_t +expm1_inline (svfloat64_t x, const svbool_t pg, const struct data *d) +{ + /* Helper routine for calculating exp(x) - 1. Vector port of the helper from + the scalar variant of tanh. */ + + /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ + svfloat64_t j + = svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2), d->shift); + svint64_t i = svcvt_s64_x (pg, j); + svfloat64_t f = svmla_x (pg, x, j, d->ln2_hi); + f = svmla_x (pg, f, j, d->ln2_lo); + + /* Approximate expm1(f) using polynomial. */ + svfloat64_t f2 = svmul_x (pg, f, f); + svfloat64_t f4 = svmul_x (pg, f2, f2); + svfloat64_t p = svmla_x ( + pg, f, f2, + sv_estrin_10_f64_x (pg, f, f2, f4, svmul_x (pg, f4, f4), d->poly)); + + /* t = 2 ^ i. */ + svfloat64_t t = svscale_x (pg, sv_f64 (1), i); + /* expm1(x) = p * t + (t - 1). */ + return svmla_x (pg, svsub_x (pg, t, 1), p, t); +} + +static svfloat64_t NOINLINE +special_case (svfloat64_t x, svfloat64_t y, svbool_t special) +{ + return sv_call_f64 (tanh, x, y, special); +} + +/* SVE approximation for double-precision tanh(x), using a simplified + version of expm1. The greatest observed error is 2.77 ULP: + _ZGVsMxv_tanh(-0x1.c4a4ca0f9f3b7p-3) got -0x1.bd6a21a163627p-3 + want -0x1.bd6a21a163624p-3. */ +svfloat64_t SV_NAME_D1 (tanh) (svfloat64_t x, svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svuint64_t ia = svreinterpret_u64 (svabs_x (pg, x)); + + /* Trigger special-cases for tiny, boring and infinity/NaN. */ + svbool_t special = svcmpgt (pg, svsub_x (pg, ia, d->tiny_bound), d->thresh); + + svfloat64_t u = svadd_x (pg, x, x); + + /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ + svfloat64_t q = expm1_inline (u, pg, d); + svfloat64_t qp2 = svadd_x (pg, q, 2); + + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, svdiv_x (pg, q, qp2), special); + return svdiv_x (pg, q, qp2); +} diff --git a/sysdeps/aarch64/fpu/tanhf_advsimd.c b/sysdeps/aarch64/fpu/tanhf_advsimd.c new file mode 100644 index 0000000000..50defd6ef0 --- /dev/null +++ b/sysdeps/aarch64/fpu/tanhf_advsimd.c @@ -0,0 +1,76 @@ +/* Single-precision vector (Advanced SIMD) tanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_expm1f_inline.h" + +static const struct data +{ + struct v_expm1f_data expm1f_consts; + uint32x4_t boring_bound, large_bound, onef; +} data = { + .expm1f_consts = V_EXPM1F_DATA, + /* 0x1.205966p+3, above which tanhf rounds to 1 (or -1 for negative). */ + .boring_bound = V4 (0x41102cb3), + .large_bound = V4 (0x7f800000), + .onef = V4 (0x3f800000), +}; + +static float32x4_t NOINLINE VPCS_ATTR +special_case (float32x4_t x, float32x4_t y, uint32x4_t special) +{ + return v_call_f32 (tanhf, x, y, special); +} + +/* Approximation for single-precision vector tanh(x), using a simplified + version of expm1f. The maximum error is 2.58 ULP: + _ZGVnN4v_tanhf (0x1.fa5eep-5) got 0x1.f9ba02p-5 + want 0x1.f9ba08p-5. */ +float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tanh) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + + uint32x4_t ix = vreinterpretq_u32_f32 (x); + float32x4_t ax = vabsq_f32 (x); + uint32x4_t iax = vreinterpretq_u32_f32 (ax); + uint32x4_t sign = veorq_u32 (ix, iax); + uint32x4_t is_boring = vcgtq_u32 (iax, d->boring_bound); + float32x4_t boring = vreinterpretq_f32_u32 (vorrq_u32 (sign, d->onef)); + +#if WANT_SIMD_EXCEPT + /* If fp exceptions are to be triggered properly, set all special and boring + lanes to 0, which will trigger no exceptions, and fix them up later. */ + uint32x4_t special = vorrq_u32 (vcgtq_u32 (iax, d->large_bound), + vcltq_u32 (iax, v_u32 (0x34000000))); + x = v_zerofy_f32 (x, is_boring); + if (__glibc_unlikely (v_any_u32 (special))) + x = v_zerofy_f32 (x, special); +#else + uint32x4_t special = vcgtq_u32 (iax, d->large_bound); +#endif + + /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ + float32x4_t q = expm1f_inline (vmulq_n_f32 (x, 2), &d->expm1f_consts); + float32x4_t y = vdivq_f32 (q, vaddq_f32 (q, v_f32 (2.0))); + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (vreinterpretq_f32_u32 (ix), + vbslq_f32 (is_boring, boring, y), special); + return vbslq_f32 (is_boring, boring, y); +} +libmvec_hidden_def (V_NAME_F1 (tanh)) +HALF_WIDTH_ALIAS_F1 (tanh) diff --git a/sysdeps/aarch64/fpu/tanhf_sve.c b/sysdeps/aarch64/fpu/tanhf_sve.c new file mode 100644 index 0000000000..0b94523cf5 --- /dev/null +++ b/sysdeps/aarch64/fpu/tanhf_sve.c @@ -0,0 +1,61 @@ +/* Single-precision vector (SVE) tanh function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_expm1f_inline.h" + +static const struct data +{ + struct sv_expm1f_data expm1f_consts; + uint32_t boring_bound, onef; +} data = { + .expm1f_consts = SV_EXPM1F_DATA, + /* 0x1.205966p+3, above which tanhf rounds to 1 (or -1 for negative). */ + .boring_bound = 0x41102cb3, + .onef = 0x3f800000, +}; + +static svfloat32_t NOINLINE +special_case (svfloat32_t x, svfloat32_t y, svbool_t special) +{ + return sv_call_f32 (tanhf, x, y, special); +} + +/* Approximation for single-precision SVE tanh(x), using a simplified + version of expm1f. The maximum error is 2.57 ULP: + _ZGVsMxv_tanhf (0x1.fc1832p-5) got 0x1.fb71a4p-5 + want 0x1.fb71aap-5. */ +svfloat32_t SV_NAME_F1 (tanh) (svfloat32_t x, const svbool_t pg) +{ + const struct data *d = ptr_barrier (&data); + + svfloat32_t ax = svabs_x (pg, x); + svuint32_t iax = svreinterpret_u32 (ax); + svuint32_t sign = sveor_x (pg, svreinterpret_u32 (x), iax); + svbool_t is_boring = svcmpgt (pg, iax, d->boring_bound); + svfloat32_t boring = svreinterpret_f32 (svorr_x (pg, sign, d->onef)); + + svbool_t special = svcmpgt (pg, iax, 0x7f800000); + + /* tanh(x) = (e^2x - 1) / (e^2x + 1). */ + svfloat32_t q = expm1f_inline (svmul_x (pg, x, 2.0), pg, &d->expm1f_consts); + svfloat32_t y = svdiv_x (pg, q, svadd_x (pg, q, 2.0)); + if (__glibc_unlikely (svptest_any (pg, special))) + return special_case (x, svsel_f32 (is_boring, boring, y), special); + return svsel_f32 (is_boring, boring, y); +} diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index 1a57b22c3a..7aeda880bd 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -44,3 +44,4 @@ VPCS_VECTOR_WRAPPER (log2_advsimd, _ZGVnN2v_log2) VPCS_VECTOR_WRAPPER (sin_advsimd, _ZGVnN2v_sin) VPCS_VECTOR_WRAPPER (sinh_advsimd, _ZGVnN2v_sinh) VPCS_VECTOR_WRAPPER (tan_advsimd, _ZGVnN2v_tan) +VPCS_VECTOR_WRAPPER (tanh_advsimd, _ZGVnN2v_tanh) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 0c9858f6b7..95f1ec5222 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -63,3 +63,4 @@ SVE_VECTOR_WRAPPER (log2_sve, _ZGVsMxv_log2) SVE_VECTOR_WRAPPER (sin_sve, _ZGVsMxv_sin) SVE_VECTOR_WRAPPER (sinh_sve, _ZGVsMxv_sinh) SVE_VECTOR_WRAPPER (tan_sve, _ZGVsMxv_tan) +SVE_VECTOR_WRAPPER (tanh_sve, _ZGVsMxv_tanh) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index 4758490c6f..bd6800e91c 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -44,3 +44,4 @@ VPCS_VECTOR_WRAPPER (log2f_advsimd, _ZGVnN4v_log2f) VPCS_VECTOR_WRAPPER (sinf_advsimd, _ZGVnN4v_sinf) VPCS_VECTOR_WRAPPER (sinhf_advsimd, _ZGVnN4v_sinhf) VPCS_VECTOR_WRAPPER (tanf_advsimd, _ZGVnN4v_tanf) +VPCS_VECTOR_WRAPPER (tanhf_advsimd, _ZGVnN4v_tanhf) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index 7c04f07bbe..35ca305fdd 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -63,3 +63,4 @@ SVE_VECTOR_WRAPPER (log2f_sve, _ZGVsMxv_log2f) SVE_VECTOR_WRAPPER (sinf_sve, _ZGVsMxv_sinf) SVE_VECTOR_WRAPPER (sinhf_sve, _ZGVsMxv_sinhf) SVE_VECTOR_WRAPPER (tanf_sve, _ZGVsMxv_tanf) +SVE_VECTOR_WRAPPER (tanhf_sve, _ZGVsMxv_tanhf) diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index 004eb34694..c26d39e644 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -1496,11 +1496,19 @@ double: 2 float: 2 ldouble: 2 +Function: "tanh_advsimd": +double: 2 +float: 2 + Function: "tanh_downward": double: 3 float: 3 ldouble: 4 +Function: "tanh_sve": +double: 2 +float: 2 + Function: "tanh_towardzero": double: 2 float: 2 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index 1db5ba61d6..396082f6a7 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -85,12 +85,15 @@ GLIBC_2.40 _ZGVnN2v_erf F GLIBC_2.40 _ZGVnN2v_erff F GLIBC_2.40 _ZGVnN2v_sinh F GLIBC_2.40 _ZGVnN2v_sinhf F +GLIBC_2.40 _ZGVnN2v_tanh F +GLIBC_2.40 _ZGVnN2v_tanhf F GLIBC_2.40 _ZGVnN4v_acoshf F GLIBC_2.40 _ZGVnN4v_asinhf F GLIBC_2.40 _ZGVnN4v_atanhf F GLIBC_2.40 _ZGVnN4v_coshf F GLIBC_2.40 _ZGVnN4v_erff F GLIBC_2.40 _ZGVnN4v_sinhf F +GLIBC_2.40 _ZGVnN4v_tanhf F GLIBC_2.40 _ZGVsMxv_acosh F GLIBC_2.40 _ZGVsMxv_acoshf F GLIBC_2.40 _ZGVsMxv_asinh F @@ -103,3 +106,5 @@ GLIBC_2.40 _ZGVsMxv_erf F GLIBC_2.40 _ZGVsMxv_erff F GLIBC_2.40 _ZGVsMxv_sinh F GLIBC_2.40 _ZGVsMxv_sinhf F +GLIBC_2.40 _ZGVsMxv_tanh F +GLIBC_2.40 _ZGVsMxv_tanhf F From patchwork Tue Feb 20 16:59:45 2024 Content-Type: text/plain; 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CTRY:IE; LANG:en; SCL:1; SRV:; IPV:CAL; SFV:NSPM; H:64aa7808-outbound-1.mta.getcheckrecipient.com; PTR:ec2-63-35-35-123.eu-west-1.compute.amazonaws.com; CAT:NONE; SFS:(13230031)(36860700004)(40470700004)(46966006); DIR:OUT; SFP:1101; X-OriginatorOrg: arm.com X-MS-Exchange-CrossTenant-OriginalArrivalTime: 20 Feb 2024 17:00:06.2759 (UTC) X-MS-Exchange-CrossTenant-Network-Message-Id: 7fb65042-6e05-443c-ca74-08dc32356370 X-MS-Exchange-CrossTenant-Id: f34e5979-57d9-4aaa-ad4d-b122a662184d X-MS-Exchange-CrossTenant-OriginalAttributedTenantConnectingIp: TenantId=f34e5979-57d9-4aaa-ad4d-b122a662184d; Ip=[63.35.35.123]; Helo=[64aa7808-outbound-1.mta.getcheckrecipient.com] X-MS-Exchange-CrossTenant-AuthSource: DU6PEPF0000B61C.eurprd02.prod.outlook.com X-MS-Exchange-CrossTenant-AuthAs: Anonymous X-MS-Exchange-CrossTenant-FromEntityHeader: HybridOnPrem X-MS-Exchange-Transport-CrossTenantHeadersStamped: AS4PR08MB7601 X-Spam-Status: No, score=-12.6 required=5.0 tests=BAYES_00, DKIM_SIGNED, DKIM_VALID, FORGED_SPF_HELO, GIT_PATCH_0, KAM_DMARC_NONE, KAM_SHORT, RCVD_IN_DNSWL_NONE, RCVD_IN_MSPIKE_H2, SPF_HELO_PASS, SPF_NONE, TXREP, T_SCC_BODY_TEXT_LINE, UNPARSEABLE_RELAY autolearn=ham autolearn_force=no version=3.4.6 X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on server2.sourceware.org X-BeenThere: libc-alpha@sourceware.org X-Mailman-Version: 2.1.30 Precedence: list List-Id: Libc-alpha mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: libc-alpha-bounces+patchwork=sourceware.org@sourceware.org --- Thanks, Joe sysdeps/aarch64/fpu/Makefile | 5 +- sysdeps/aarch64/fpu/Versions | 5 + sysdeps/aarch64/fpu/advsimd_f32_protos.h | 1 + sysdeps/aarch64/fpu/bits/math-vector.h | 8 + sysdeps/aarch64/fpu/erfc_advsimd.c | 201 + sysdeps/aarch64/fpu/erfc_data.c | 3519 +++++++++++++++++ sysdeps/aarch64/fpu/erfc_sve.c | 167 + sysdeps/aarch64/fpu/erfcf_advsimd.c | 170 + sysdeps/aarch64/fpu/erfcf_data.c | 676 ++++ sysdeps/aarch64/fpu/erfcf_sve.c | 113 + .../fpu/test-double-advsimd-wrappers.c | 1 + .../aarch64/fpu/test-double-sve-wrappers.c | 1 + .../aarch64/fpu/test-float-advsimd-wrappers.c | 1 + sysdeps/aarch64/fpu/test-float-sve-wrappers.c | 1 + sysdeps/aarch64/fpu/vecmath_config.h | 16 + sysdeps/aarch64/libm-test-ulps | 8 + .../unix/sysv/linux/aarch64/libmvec.abilist | 5 + 17 files changed, 4897 insertions(+), 1 deletion(-) create mode 100644 sysdeps/aarch64/fpu/erfc_advsimd.c create mode 100644 sysdeps/aarch64/fpu/erfc_data.c create mode 100644 sysdeps/aarch64/fpu/erfc_sve.c create mode 100644 sysdeps/aarch64/fpu/erfcf_advsimd.c create mode 100644 sysdeps/aarch64/fpu/erfcf_data.c create mode 100644 sysdeps/aarch64/fpu/erfcf_sve.c Reviewed-by: Szabolcs Nagy diff --git a/sysdeps/aarch64/fpu/Makefile b/sysdeps/aarch64/fpu/Makefile index e5f418ae42..e8af35099d 100644 --- a/sysdeps/aarch64/fpu/Makefile +++ b/sysdeps/aarch64/fpu/Makefile @@ -8,6 +8,7 @@ libmvec-supported-funcs = acos \ cos \ cosh \ erf \ + erfc \ exp \ exp10 \ exp2 \ @@ -39,7 +40,9 @@ libmvec-support = $(addsuffix f_advsimd,$(float-advsimd-funcs)) \ erff_data \ sv_erf_data \ sv_erff_data \ - v_exp_tail_data + v_exp_tail_data \ + erfc_data \ + erfcf_data endif sve-cflags = -march=armv8-a+sve diff --git a/sysdeps/aarch64/fpu/Versions b/sysdeps/aarch64/fpu/Versions index 4dbf3d3244..3cb1b82bd2 100644 --- a/sysdeps/aarch64/fpu/Versions +++ b/sysdeps/aarch64/fpu/Versions @@ -104,6 +104,11 @@ libmvec { _ZGVnN4v_erff; _ZGVsMxv_erf; _ZGVsMxv_erff; + _ZGVnN2v_erfc; + _ZGVnN2v_erfcf; + _ZGVnN4v_erfcf; + _ZGVsMxv_erfc; + _ZGVsMxv_erfcf; _ZGVnN2v_sinh; _ZGVnN2v_sinhf; _ZGVnN4v_sinhf; diff --git a/sysdeps/aarch64/fpu/advsimd_f32_protos.h b/sysdeps/aarch64/fpu/advsimd_f32_protos.h index 4ff191c324..383c436972 100644 --- a/sysdeps/aarch64/fpu/advsimd_f32_protos.h +++ b/sysdeps/aarch64/fpu/advsimd_f32_protos.h @@ -26,6 +26,7 @@ libmvec_hidden_proto (V_NAME_F1(atanh)); libmvec_hidden_proto (V_NAME_F1(cos)); libmvec_hidden_proto (V_NAME_F1(cosh)); libmvec_hidden_proto (V_NAME_F1(erf)); +libmvec_hidden_proto (V_NAME_F1(erfc)); libmvec_hidden_proto (V_NAME_F1(exp10)); libmvec_hidden_proto (V_NAME_F1(exp2)); libmvec_hidden_proto (V_NAME_F1(exp)); diff --git a/sysdeps/aarch64/fpu/bits/math-vector.h b/sysdeps/aarch64/fpu/bits/math-vector.h index 585e022082..e29b2d1c09 100644 --- a/sysdeps/aarch64/fpu/bits/math-vector.h +++ b/sysdeps/aarch64/fpu/bits/math-vector.h @@ -69,6 +69,10 @@ # define __DECL_SIMD_erf __DECL_SIMD_aarch64 # undef __DECL_SIMD_erff # define __DECL_SIMD_erff __DECL_SIMD_aarch64 +# undef __DECL_SIMD_erfc +# define __DECL_SIMD_erfc __DECL_SIMD_aarch64 +# undef __DECL_SIMD_erfcf +# define __DECL_SIMD_erfcf __DECL_SIMD_aarch64 # undef __DECL_SIMD_exp # define __DECL_SIMD_exp __DECL_SIMD_aarch64 # undef __DECL_SIMD_expf @@ -153,6 +157,7 @@ __vpcs __f32x4_t _ZGVnN4v_atanhf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_coshf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_erff (__f32x4_t); +__vpcs __f32x4_t _ZGVnN4v_erfcf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_exp10f (__f32x4_t); __vpcs __f32x4_t _ZGVnN4v_exp2f (__f32x4_t); @@ -176,6 +181,7 @@ __vpcs __f64x2_t _ZGVnN2v_atanh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_cosh (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_erf (__f64x2_t); +__vpcs __f64x2_t _ZGVnN2v_erfc (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp10 (__f64x2_t); __vpcs __f64x2_t _ZGVnN2v_exp2 (__f64x2_t); @@ -204,6 +210,7 @@ __sv_f32_t _ZGVsMxv_atanhf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_coshf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_erff (__sv_f32_t, __sv_bool_t); +__sv_f32_t _ZGVsMxv_erfcf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_exp10f (__sv_f32_t, __sv_bool_t); __sv_f32_t _ZGVsMxv_exp2f (__sv_f32_t, __sv_bool_t); @@ -227,6 +234,7 @@ __sv_f64_t _ZGVsMxv_atanh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_cosh (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_erf (__sv_f64_t, __sv_bool_t); +__sv_f64_t _ZGVsMxv_erfc (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp10 (__sv_f64_t, __sv_bool_t); __sv_f64_t _ZGVsMxv_exp2 (__sv_f64_t, __sv_bool_t); diff --git a/sysdeps/aarch64/fpu/erfc_advsimd.c b/sysdeps/aarch64/fpu/erfc_advsimd.c new file mode 100644 index 0000000000..548f21a3d6 --- /dev/null +++ b/sysdeps/aarch64/fpu/erfc_advsimd.c @@ -0,0 +1,201 @@ +/* Double-precision vector (Advanced SIMD) erfc function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" +#include "vecmath_config.h" + +static const struct data +{ + uint64x2_t offset, table_scale; + float64x2_t max, shift; + float64x2_t p20, p40, p41, p42; + float64x2_t p51, p52; + float64x2_t qr5, qr6, qr7, qr8, qr9; +#if WANT_SIMD_EXCEPT + float64x2_t uflow_bound; +#endif +} data = { + /* Set an offset so the range of the index used for lookup is 3487, and it + can be clamped using a saturated add on an offset index. + Index offset is 0xffffffffffffffff - asuint64(shift) - 3487. */ + .offset = V2 (0xbd3ffffffffff260), + .table_scale = V2 (0x37f0000000000000 << 1), /* asuint64 (2^-128) << 1. */ + .max = V2 (0x1.b3ep+4), /* 3487/128. */ + .shift = V2 (0x1p45), + .p20 = V2 (0x1.5555555555555p-2), /* 1/3, used to compute 2/3 and 1/6. */ + .p40 = V2 (-0x1.999999999999ap-4), /* 1/10. */ + .p41 = V2 (-0x1.999999999999ap-2), /* 2/5. */ + .p42 = V2 (0x1.1111111111111p-3), /* 2/15. */ + .p51 = V2 (-0x1.c71c71c71c71cp-3), /* 2/9. */ + .p52 = V2 (0x1.6c16c16c16c17p-5), /* 2/45. */ + /* Qi = (i+1) / i, Ri = -2 * i / ((i+1)*(i+2)), for i = 5, ..., 9. */ + .qr5 = { 0x1.3333333333333p0, -0x1.e79e79e79e79ep-3 }, + .qr6 = { 0x1.2aaaaaaaaaaabp0, -0x1.b6db6db6db6dbp-3 }, + .qr7 = { 0x1.2492492492492p0, -0x1.8e38e38e38e39p-3 }, + .qr8 = { 0x1.2p0, -0x1.6c16c16c16c17p-3 }, + .qr9 = { 0x1.1c71c71c71c72p0, -0x1.4f2094f2094f2p-3 }, +#if WANT_SIMD_EXCEPT + .uflow_bound = V2 (0x1.a8b12fc6e4892p+4), +#endif +}; + +#define TinyBound 0x4000000000000000 /* 0x1p-511 << 1. */ +#define Off 0xfffffffffffff260 /* 0xffffffffffffffff - 3487. */ + +struct entry +{ + float64x2_t erfc; + float64x2_t scale; +}; + +static inline struct entry +lookup (uint64x2_t i) +{ + struct entry e; + float64x2_t e1 = vld1q_f64 ((float64_t *) (__erfc_data.tab - Off + i[0])), + e2 = vld1q_f64 ((float64_t *) (__erfc_data.tab - Off + i[1])); + e.erfc = vuzp1q_f64 (e1, e2); + e.scale = vuzp2q_f64 (e1, e2); + return e; +} + +#if WANT_SIMD_EXCEPT +static float64x2_t VPCS_ATTR NOINLINE +special_case (float64x2_t x, float64x2_t y, uint64x2_t cmp) +{ + return v_call_f64 (erfc, x, y, cmp); +} +#endif + +/* Optimized double-precision vector erfc(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/128. + + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + + erfc(x) ~ erfc(r) - scale * d * poly(r, d), with + + poly(r, d) = 1 - r d + (2/3 r^2 - 1/3) d^2 - r (1/3 r^2 - 1/2) d^3 + + (2/15 r^4 - 2/5 r^2 + 1/10) d^4 + - r * (2/45 r^4 - 2/9 r^2 + 1/6) d^5 + + p6(r) d^6 + ... + p10(r) d^10 + + Polynomials p6(r) to p10(r) are computed using recurrence relation + + 2(i+1)p_i + 2r(i+2)p_{i+1} + (i+2)(i+3)p_{i+2} = 0, + with p0 = 1, and p1(r) = -r. + + Values of erfc(r) and scale are read from lookup tables. Stored values + are scaled to avoid hitting the subnormal range. + + Note that for x < 0, erfc(x) = 2.0 - erfc(-x). + + Maximum measured error: 1.71 ULP + V_NAME_D1 (erfc)(0x1.46cfe976733p+4) got 0x1.e15fcbea3e7afp-608 + want 0x1.e15fcbea3e7adp-608. */ +VPCS_ATTR +float64x2_t V_NAME_D1 (erfc) (float64x2_t x) +{ + const struct data *dat = ptr_barrier (&data); + +#if WANT_SIMD_EXCEPT + /* |x| < 2^-511. Avoid fabs by left-shifting by 1. */ + uint64x2_t ix = vreinterpretq_u64_f64 (x); + uint64x2_t cmp = vcltq_u64 (vaddq_u64 (ix, ix), v_u64 (TinyBound)); + /* x >= ~26.54 (into subnormal case and uflow case). Comparison is done in + integer domain to avoid raising exceptions in presence of nans. */ + uint64x2_t uflow = vcgeq_s64 (vreinterpretq_s64_f64 (x), + vreinterpretq_s64_f64 (dat->uflow_bound)); + cmp = vorrq_u64 (cmp, uflow); + float64x2_t xm = x; + /* If any lanes are special, mask them with 0 and retain a copy of x to allow + special case handler to fix special lanes later. This is only necessary if + fenv exceptions are to be triggered correctly. */ + if (__glibc_unlikely (v_any_u64 (cmp))) + x = v_zerofy_f64 (x, cmp); +#endif + + float64x2_t a = vabsq_f64 (x); + a = vminq_f64 (a, dat->max); + + /* Lookup erfc(r) and scale(r) in tables, e.g. set erfc(r) to 0 and scale to + 2/sqrt(pi), when x reduced to r = 0. */ + float64x2_t shift = dat->shift; + float64x2_t z = vaddq_f64 (a, shift); + + /* Clamp index to a range of 3487. A naive approach would use a subtract and + min. Instead we offset the table address and the index, then use a + saturating add. */ + uint64x2_t i = vqaddq_u64 (vreinterpretq_u64_f64 (z), dat->offset); + + struct entry e = lookup (i); + + /* erfc(x) ~ erfc(r) - scale * d * poly(r, d). */ + float64x2_t r = vsubq_f64 (z, shift); + float64x2_t d = vsubq_f64 (a, r); + float64x2_t d2 = vmulq_f64 (d, d); + float64x2_t r2 = vmulq_f64 (r, r); + + float64x2_t p1 = r; + float64x2_t p2 = vfmsq_f64 (dat->p20, r2, vaddq_f64 (dat->p20, dat->p20)); + float64x2_t p3 = vmulq_f64 (r, vfmaq_f64 (v_f64 (-0.5), r2, dat->p20)); + float64x2_t p4 = vfmaq_f64 (dat->p41, r2, dat->p42); + p4 = vfmsq_f64 (dat->p40, r2, p4); + float64x2_t p5 = vfmaq_f64 (dat->p51, r2, dat->p52); + p5 = vmulq_f64 (r, vfmaq_f64 (vmulq_f64 (v_f64 (0.5), dat->p20), r2, p5)); + /* Compute p_i using recurrence relation: + p_{i+2} = (p_i + r * Q_{i+1} * p_{i+1}) * R_{i+1}. */ + float64x2_t p6 = vfmaq_f64 (p4, p5, vmulq_laneq_f64 (r, dat->qr5, 0)); + p6 = vmulq_laneq_f64 (p6, dat->qr5, 1); + float64x2_t p7 = vfmaq_f64 (p5, p6, vmulq_laneq_f64 (r, dat->qr6, 0)); + p7 = vmulq_laneq_f64 (p7, dat->qr6, 1); + float64x2_t p8 = vfmaq_f64 (p6, p7, vmulq_laneq_f64 (r, dat->qr7, 0)); + p8 = vmulq_laneq_f64 (p8, dat->qr7, 1); + float64x2_t p9 = vfmaq_f64 (p7, p8, vmulq_laneq_f64 (r, dat->qr8, 0)); + p9 = vmulq_laneq_f64 (p9, dat->qr8, 1); + float64x2_t p10 = vfmaq_f64 (p8, p9, vmulq_laneq_f64 (r, dat->qr9, 0)); + p10 = vmulq_laneq_f64 (p10, dat->qr9, 1); + /* Compute polynomial in d using pairwise Horner scheme. */ + float64x2_t p90 = vfmaq_f64 (p9, d, p10); + float64x2_t p78 = vfmaq_f64 (p7, d, p8); + float64x2_t p56 = vfmaq_f64 (p5, d, p6); + float64x2_t p34 = vfmaq_f64 (p3, d, p4); + float64x2_t p12 = vfmaq_f64 (p1, d, p2); + float64x2_t y = vfmaq_f64 (p78, d2, p90); + y = vfmaq_f64 (p56, d2, y); + y = vfmaq_f64 (p34, d2, y); + y = vfmaq_f64 (p12, d2, y); + + y = vfmsq_f64 (e.erfc, e.scale, vfmsq_f64 (d, d2, y)); + + /* Offset equals 2.0 if sign, else 0.0. */ + uint64x2_t sign = vshrq_n_u64 (vreinterpretq_u64_f64 (x), 63); + float64x2_t off = vreinterpretq_f64_u64 (vshlq_n_u64 (sign, 62)); + /* Copy sign and scale back in a single fma. Since the bit patterns do not + overlap, then logical or and addition are equivalent here. */ + float64x2_t fac = vreinterpretq_f64_u64 ( + vsraq_n_u64 (vshlq_n_u64 (sign, 63), dat->table_scale, 1)); + +#if WANT_SIMD_EXCEPT + if (__glibc_unlikely (v_any_u64 (cmp))) + return special_case (xm, vfmaq_f64 (off, fac, y), cmp); +#endif + + return vfmaq_f64 (off, fac, y); +} diff --git a/sysdeps/aarch64/fpu/erfc_data.c b/sysdeps/aarch64/fpu/erfc_data.c new file mode 100644 index 0000000000..76a94e4681 --- /dev/null +++ b/sysdeps/aarch64/fpu/erfc_data.c @@ -0,0 +1,3519 @@ +/* Table for Advanced SIMD erfc + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "vecmath_config.h" + +/* Lookup table used in erfc. + For each possible rounded input r (multiples of 1/128), between + r = 0.0 and r = ~27.0 (3488 values): + - the first entry __erfc_data.tab.erfc contains the values of erfc(r), + - the second entry __erfc_data.tab.scale contains the values of + 2/sqrt(pi)*exp(-r^2). Both values may go into subnormal range, therefore + they are scaled by a large enough value 2^128 (fits in 8bit). */ +const struct erfc_data __erfc_data = { + .tab = { { 0x1p128, 0x1.20dd750429b6dp128 }, + { 0x1.fb7c9030853b3p127, 0x1.20d8f1975c85dp128 }, + { 0x1.f6f9447be0743p127, 0x1.20cb67bd452c7p128 }, + { 0x1.f27640f9853d9p127, 0x1.20b4d8bac36c1p128 }, + { 0x1.edf3a9ba22dadp127, 0x1.209546ad13ccfp128 }, + { 0x1.e971a2c4436aep127, 0x1.206cb4897b148p128 }, + { 0x1.e4f05010eca8cp127, 0x1.203b261cd0053p128 }, + { 0x1.e06fd58842c7ep127, 0x1.2000a00ae3804p128 }, + { 0x1.dbf056fe2df35p127, 0x1.1fbd27cdc72d3p128 }, + { 0x1.d771f82f02f4ep127, 0x1.1f70c3b4f2cc8p128 }, + { 0x1.d2f4dcbc2f894p127, 0x1.1f1b7ae44867fp128 }, + { 0x1.ce792828eae5cp127, 0x1.1ebd5552f795bp128 }, + { 0x1.c9fefdd6eaf19p127, 0x1.1e565bca400d4p128 }, + { 0x1.c58681031eb6ap127, 0x1.1de697e413d29p128 }, + { 0x1.c10fd4c26e896p127, 0x1.1d6e14099944ap128 }, + { 0x1.bc9b1bfe82687p127, 0x1.1cecdb718d61cp128 }, + { 0x1.b82879728f11ep127, 0x1.1c62fa1e869b6p128 }, + { 0x1.b3b80fa82a4bbp127, 0x1.1bd07cdd189acp128 }, + { 0x1.af4a00f426daap127, 0x1.1b357141d95d5p128 }, + { 0x1.aade6f7378a0ep127, 0x1.1a91e5a748165p128 }, + { 0x1.a6757d08215d8p127, 0x1.19e5e92b964abp128 }, + { 0x1.a20f4b5626818p127, 0x1.19318bae53a04p128 }, + { 0x1.9dabfbc090901p127, 0x1.1874ddcdfce24p128 }, + { 0x1.994baf66747adp127, 0x1.17aff0e56ec1p128 }, + { 0x1.94ee8720076b6p127, 0x1.16e2d7093cd8cp128 }, + { 0x1.9094a37bbd66ep127, 0x1.160da304ed92fp128 }, + { 0x1.8c3e24bb73372p127, 0x1.153068581b781p128 }, + { 0x1.87eb2ad1a4032p127, 0x1.144b3b337c90cp128 }, + { 0x1.839bd55eaafc8p127, 0x1.135e3075d076bp128 }, + { 0x1.7f5043ae11862p127, 0x1.12695da8b5bdep128 }, + { 0x1.7b0894b3ea35cp127, 0x1.116cd8fd67618p128 }, + { 0x1.76c4e70a390e7p127, 0x1.1068b94962e5ep128 }, + { 0x1.728558ee694fcp127, 0x1.0f5d1602f7e41p128 }, + { 0x1.6e4a083ed132fp127, 0x1.0e4a073dc1b91p128 }, + { 0x1.6a13127843ec1p127, 0x1.0d2fa5a70c168p128 }, + { 0x1.65e094b3b2413p127, 0x1.0c0e0a8223359p128 }, + { 0x1.61b2aba3da093p127, 0x1.0ae54fa490723p128 }, + { 0x1.5d89739304dcfp127, 0x1.09b58f724416bp128 }, + { 0x1.59650860d6469p127, 0x1.087ee4d9ad247p128 }, + { 0x1.5545858029b39p127, 0x1.07416b4fbfe7cp128 }, + { 0x1.512b05f5006e1p127, 0x1.05fd3ecbec298p128 }, + { 0x1.4d15a4527fdc7p127, 0x1.04b27bc403d3p128 }, + { 0x1.49057ab900447p127, 0x1.03613f2812dafp128 }, + { 0x1.44faa2d42c4ap127, 0x1.0209a65e29545p128 }, + { 0x1.40f535d93160ep127, 0x1.00abcf3e187a9p128 }, + { 0x1.3cf54c850162p127, 0x1.fe8fb01a47307p127 }, + { 0x1.38faff1aa574ap127, 0x1.fbbbbef34b4b2p127 }, + { 0x1.35066561a275dp127, 0x1.f8dc092d58ff8p127 }, + { 0x1.311796a46f064p127, 0x1.f5f0cdaf15313p127 }, + { 0x1.2d2ea9aefb636p127, 0x1.f2fa4c16c0019p127 }, + { 0x1.294bb4cd4b2bdp127, 0x1.eff8c4b1375dbp127 }, + { 0x1.256ecdca212ccp127, 0x1.ecec7870ebca8p127 }, + { 0x1.219809edbd524p127, 0x1.e9d5a8e4c934ep127 }, + { 0x1.1dc77dfcacd02p127, 0x1.e6b4982f158b9p127 }, + { 0x1.19fd3e36ac96ap127, 0x1.e38988fc46e72p127 }, + { 0x1.16395e559e218p127, 0x1.e054be79d3042p127 }, + { 0x1.127bf18c8eadcp127, 0x1.dd167c4cf9d2ap127 }, + { 0x1.0ec50a86d0dd4p127, 0x1.d9cf06898cdafp127 }, + { 0x1.0b14bb6728cd8p127, 0x1.d67ea1a8b5368p127 }, + { 0x1.076b15c70aa28p127, 0x1.d325927fb9d89p127 }, + { 0x1.03c82ab5eb831p127, 0x1.cfc41e36c7df9p127 }, + { 0x1.002c0ab8a5018p127, 0x1.cc5a8a3fbea4p127 }, + { 0x1.f92d8b91d5cc7p126, 0x1.c8e91c4d01368p127 }, + { 0x1.f210d6a9a6a31p126, 0x1.c5701a484ef9dp127 }, + { 0x1.eb02147ce245cp126, 0x1.c1efca49a5011p127 }, + { 0x1.e40161b701275p126, 0x1.be68728e29d5ep127 }, + { 0x1.dd0ed9ea4bdd6p126, 0x1.bada596f25436p127 }, + { 0x1.d62a978f7c957p126, 0x1.b745c55905bf8p127 }, + { 0x1.cf54b4058455fp126, 0x1.b3aafcc27502ep127 }, + { 0x1.c88d479173ccep126, 0x1.b00a46237d5bep127 }, + { 0x1.c1d4695e87644p126, 0x1.ac63e7ecc1411p127 }, + { 0x1.bb2a2f7e5652p126, 0x1.a8b8287ec6a09p127 }, + { 0x1.b48eaee924501p126, 0x1.a5074e215762p127 }, + { 0x1.ae01fb7e55a66p126, 0x1.a1519efaf889ep127 }, + { 0x1.a78428050527ep126, 0x1.9d97610879642p127 }, + { 0x1.a115462cbbc17p126, 0x1.99d8da149c13fp127 }, + { 0x1.9ab5668e4930ap126, 0x1.96164fafd8de3p127 }, + { 0x1.946498acbd766p126, 0x1.925007283d7aap127 }, + { 0x1.8e22eaf68291ep126, 0x1.8e86458169af8p127 }, + { 0x1.87f06ac6960c4p126, 0x1.8ab94f6caa71dp127 }, + { 0x1.81cd2465e1d96p126, 0x1.86e9694134b9ep127 }, + { 0x1.7bb9230cb40b4p126, 0x1.8316d6f48133dp127 }, + { 0x1.75b470e454d35p126, 0x1.7f41dc12c9e89p127 }, + { 0x1.6fbf1708ba47cp126, 0x1.7b6abbb7aaf19p127 }, + { 0x1.69d91d8a595dap126, 0x1.7791b886e7403p127 }, + { 0x1.64028b7013867p126, 0x1.73b714a552763p127 }, + { 0x1.5e3b66b9405a9p126, 0x1.6fdb11b1e0c34p127 }, + { 0x1.5883b45fd2b63p126, 0x1.6bfdf0beddaf5p127 }, + { 0x1.52db785a98acap126, 0x1.681ff24b4ab04p127 }, + { 0x1.4d42b59f95afap126, 0x1.6441563c665d4p127 }, + { 0x1.47b96e267647ap126, 0x1.60625bd75d07bp127 }, + { 0x1.423fa2eb1cb59p126, 0x1.5c8341bb23767p127 }, + { 0x1.3cd553f045d45p126, 0x1.58a445da7c74cp127 }, + { 0x1.377a8042458d1p126, 0x1.54c5a57629dbp127 }, + { 0x1.322f25f9da2fdp126, 0x1.50e79d1749ac9p127 }, + { 0x1.2cf3423f15fdfp126, 0x1.4d0a6889dfd9fp127 }, + { 0x1.27c6d14c5e341p126, 0x1.492e42d78d2c5p127 }, + { 0x1.22a9ce717edcbp126, 0x1.4553664273d24p127 }, + { 0x1.1d9c3416d2b4bp126, 0x1.417a0c4049fdp127 }, + { 0x1.189dfbc07e69p126, 0x1.3da26d759aef5p127 }, + { 0x1.13af1e11be721p126, 0x1.39ccc1b136d5ap127 }, + { 0x1.0ecf92d046d22p126, 0x1.35f93fe7d1b3dp127 }, + { 0x1.09ff50e7b3f93p126, 0x1.32281e2fd1a92p127 }, + { 0x1.053e4e6d0c10bp126, 0x1.2e5991bd4cbfcp127 }, + { 0x1.008c80a24ff1p126, 0x1.2a8dcede3673bp127 }, + { 0x1.f7d3b7f436013p125, 0x1.26c508f6bd0ffp127 }, + { 0x1.eeaca836a27ccp125, 0x1.22ff727dd6f7bp127 }, + { 0x1.e5a3b7c9b56dap125, 0x1.1f3d3cf9ffe5ap127 }, + { 0x1.dcb8cae2d747fp125, 0x1.1b7e98fe26217p127 }, + { 0x1.d3ebc436b0f26p125, 0x1.17c3b626c7a12p127 }, + { 0x1.cb3c8500ea349p125, 0x1.140cc3173f007p127 }, + { 0x1.c2aaed0bfcfeep125, 0x1.1059ed7740313p127 }, + { 0x1.ba36dab91c0e9p125, 0x1.0cab61f084b93p127 }, + { 0x1.b1e02b082b72p125, 0x1.09014c2ca74dap127 }, + { 0x1.a9a6b99fc973bp125, 0x1.055bd6d32e8d7p127 }, + { 0x1.a18a60d56673ep125, 0x1.01bb2b87c6968p127 }, + { 0x1.998af9b56a3aep125, 0x1.fc3ee5d1524bp126 }, + { 0x1.91a85c0b65519p125, 0x1.f511a91a67d2ap126 }, + { 0x1.89e25e6a4cef9p125, 0x1.edeeee0959518p126 }, + { 0x1.8238d634c0127p125, 0x1.e6d6ffaa65a25p126 }, + { 0x1.7aab97a554544p125, 0x1.dfca26f5bbf88p126 }, + { 0x1.733a75d6e91b8p125, 0x1.d8c8aace11e63p126 }, + { 0x1.6be542ccffc2fp125, 0x1.d1d2cfff91594p126 }, + { 0x1.64abcf7c175b4p125, 0x1.cae8d93f1d7b7p126 }, + { 0x1.5d8debd20aacep125, 0x1.c40b0729ed548p126 }, + { 0x1.568b66be6f268p125, 0x1.bd3998457afdbp126 }, + { 0x1.4fa40e3af3674p125, 0x1.b674c8ffc6283p126 }, + { 0x1.48d7af53bc19fp125, 0x1.afbcd3afe8ab6p126 }, + { 0x1.4226162fbddd5p125, 0x1.a911f096fbc26p126 }, + { 0x1.3b8f0e1912f7p125, 0x1.a27455e14c93cp126 }, + { 0x1.351261854b991p125, 0x1.9be437a7de946p126 }, + { 0x1.2eafda1db784ap125, 0x1.9561c7f23a47bp126 }, + { 0x1.286740c7a7dabp125, 0x1.8eed36b886d93p126 }, + { 0x1.22385daca7f47p125, 0x1.8886b1e5ecfd1p126 }, + { 0x1.1c22f842ac1f2p125, 0x1.822e655b417e7p126 }, + { 0x1.1626d7543522p125, 0x1.7be47af1f5d89p126 }, + { 0x1.1043c1086777dp125, 0x1.75a91a7f4d2edp126 }, + { 0x1.0a797aeb152f2p125, 0x1.6f7c69d7d3ef8p126 }, + { 0x1.04c7c9f4b969p125, 0x1.695e8cd31867ep126 }, + { 0x1.fe5ce524c8ee5p124, 0x1.634fa54fa285fp126 }, + { 0x1.f35a715b2f3e1p124, 0x1.5d4fd33729015p126 }, + { 0x1.e887bf681f218p124, 0x1.575f3483021c3p126 }, + { 0x1.dde4553ef94dep124, 0x1.517de540ce2a3p126 }, + { 0x1.d36fb7fa50177p124, 0x1.4babff975a04cp126 }, + { 0x1.c9296beb09cf1p124, 0x1.45e99bcbb7915p126 }, + { 0x1.bf10f4a759889p124, 0x1.4036d0468a7a2p126 }, + { 0x1.b525d5198cb1cp124, 0x1.3a93b1998736cp126 }, + { 0x1.ab678f8eabedbp124, 0x1.35005285227f1p126 }, + { 0x1.a1d5a5c4edb96p124, 0x1.2f7cc3fe6f423p126 }, + { 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{ 0x1.c0baa10766979p-921, 0x1.793b75fbd2367p-915 }, + { 0x1.26b830bbc4f33p-921, 0x1.efaa9eeaa4992p-916 }, + { 0x1.8316ba6f8ef74p-922, 0x1.459a26ac43fcfp-916 }, + { 0x1.fc588d5eeb3p-923, 0x1.abb8ece685efep-917 }, + { 0x1.4dc0c0d42f863p-923, 0x1.18e6b704952c1p-917 }, + { 0x1.b6320aea7077ap-924, 0x1.70e95e366ca95p-918 }, + { 0x1.1fa02ebad6485p-924, 0x1.e4700e7fab75ep-919 }, + { 0x1.798a96e59845bp-925, 0x1.3e0826243926dp-919 }, + { 0x1.ef81624855ca5p-926, 0x1.a185d71d9ae78p-920 }, + { 0x1.451fcaaed5e7p-926, 0x1.1209163a43d8ap-920 }, + { 0x1.aa9b30dd7b333p-927, 0x1.67acd56555624p-921 }, + { 0x1.17d9121b4ff43p-927, 0x1.d805487b20ec2p-922 }, + { 0x1.6f1bb0c9eff18p-928, 0x1.35b0e3e76f72ap-922 }, + { 0x1.e184bec96bcc5p-929, 0x1.965317fc3f8ebp-923 }, + { 0x1.3bc10ccdff1d7p-929, 0x1.0a85e11600392p-923 }, + { 0x1.9e0f0cdf83a76p-930, 0x1.5d99f4f4fa7a2p-924 }, + { 0x1.0f738d3253e75p-930, 0x1.ca8538b911cc2p-925 }, + { 0x1.63e056b37b486p-931, 0x1.2ca663e8f6c6ep-925 }, + { 0x1.d2806afda0512p-932, 0x1.8a38c763ae5p-926 }, + { 0x1.31b865207923bp-932, 0x1.026d30f31261ep-926 }, + { 0x1.90a81bef15367p-933, 0x1.52c63cbe5201dp-927 }, + { 0x1.068145905baddp-933, 0x1.bc0c903e2dd51p-928 }, + { 0x1.57f0081c7461bp-934, 0x1.22fbc7eb40c8ep-928 }, + { 0x1.c293abfeb81c1p-935, 0x1.7d5064d5d2e6ap-929 }, + { 0x1.271a9ed146425p-935, 0x1.f3a001a1da12ap-930 }, + { 0x1.8282015bfd093p-936, 0x1.474846e880b8p-930 }, + { 0x1.fa292d1f4b615p-937, 0x1.acb96019278e3p-931 }, + { 0x1.4b6323fa7fafcp-937, 0x1.18c50c637e437p-931 }, + { 0x1.b1ded81f6cf48p-938, 0x1.6fb47e7243b1p-932 }, + { 0x1.1bfd2aff12d23p-938, 0x1.e17fe4af1cdcdp-933 }, + { 0x1.73b9288cf980bp-939, 0x1.3b3779cd081bcp-933 }, + { 0x1.e680a6315c8f9p-940, 0x1.9caab20737c4bp-934 }, + { 0x1.3e52969a46a03p-940, 0x1.0e16c42489121p-934 }, + { 0x1.a082ea93d471fp-941, 0x1.618056ad2fa0dp-935 }, + { 0x1.1075d9566cab2p-941, 0x1.ce9e247afa7efp-936 }, + { 0x1.646a66f6fb197p-942, 0x1.2eabb9557e4c3p-936 }, + { 0x1.d22f0f82317a8p-943, 0x1.8c0020c90fd02p-937 }, + { 0x1.30d7883df3e07p-943, 0x1.0305d4157bdecp-937 }, + { 0x1.8ea1187daf8b3p-944, 0x1.52cf8a69cbdeep-938 }, + { 0x1.049a91d747c02p-944, 0x1.bb1f3a4ce848cp-939 }, + { 0x1.54b29ff375e83p-945, 0x1.21bd19407d3a8p-939 }, + { 0x1.bd5a7cbaf896dp-946, 0x1.7ad97206eb3e9p-940 }, + { 0x1.230b0dec754dap-946, 0x1.ef4e6059f1fe4p-941 }, + { 0x1.7c5a693980a4p-947, 0x1.43bdb9112e65bp-941 }, + { 0x1.f10221f87a1cap-948, 0x1.a7278c0b2c815p-942 }, + { 0x1.44ae6c097e3b8p-948, 0x1.148391a9b5b7p-942 }, + { 0x1.a8288818abb4p-949, 0x1.69563388e87eep-943 }, +}, +}; diff --git a/sysdeps/aarch64/fpu/erfc_sve.c b/sysdeps/aarch64/fpu/erfc_sve.c new file mode 100644 index 0000000000..c17d3e4484 --- /dev/null +++ b/sysdeps/aarch64/fpu/erfc_sve.c @@ -0,0 +1,167 @@ +/* Double-precision vector (SVE) erfc function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" +#include "vecmath_config.h" + +static const struct data +{ + uint64_t off_idx, off_arr; + double max, shift; + double p20, p40, p41, p42; + double p51, p52; + double q5, r5; + double q6, r6; + double q7, r7; + double q8, r8; + double q9, r9; + uint64_t table_scale; +} data = { + /* Set an offset so the range of the index used for lookup is 3487, and it + can be clamped using a saturated add on an offset index. + Index offset is 0xffffffffffffffff - asuint64(shift) - 3487. */ + .off_idx = 0xbd3ffffffffff260, + .off_arr = 0xfffffffffffff260, /* 0xffffffffffffffff - 3487. */ + .max = 0x1.b3ep+4, /* 3487/128. */ + .shift = 0x1p45, + .table_scale = 0x37f0000000000000, /* asuint64(0x1p-128). */ + .p20 = 0x1.5555555555555p-2, /* 1/3, used to compute 2/3 and 1/6. */ + .p40 = -0x1.999999999999ap-4, /* 1/10. */ + .p41 = -0x1.999999999999ap-2, /* 2/5. */ + .p42 = 0x1.1111111111111p-3, /* 2/15. */ + .p51 = -0x1.c71c71c71c71cp-3, /* 2/9. */ + .p52 = 0x1.6c16c16c16c17p-5, /* 2/45. */ + /* Qi = (i+1) / i, for i = 5, ..., 9. */ + .q5 = 0x1.3333333333333p0, + .q6 = 0x1.2aaaaaaaaaaabp0, + .q7 = 0x1.2492492492492p0, + .q8 = 0x1.2p0, + .q9 = 0x1.1c71c71c71c72p0, + /* Ri = -2 * i / ((i+1)*(i+2)), for i = 5, ..., 9. */ + .r5 = -0x1.e79e79e79e79ep-3, + .r6 = -0x1.b6db6db6db6dbp-3, + .r7 = -0x1.8e38e38e38e39p-3, + .r8 = -0x1.6c16c16c16c17p-3, + .r9 = -0x1.4f2094f2094f2p-3, +}; + +/* Optimized double-precision vector erfc(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/128. + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + + erfc(x) ~ erfc(r) - scale * d * poly(r, d), with + + poly(r, d) = 1 - r d + (2/3 r^2 - 1/3) d^2 - r (1/3 r^2 - 1/2) d^3 + + (2/15 r^4 - 2/5 r^2 + 1/10) d^4 + - r * (2/45 r^4 - 2/9 r^2 + 1/6) d^5 + + p6(r) d^6 + ... + p10(r) d^10 + + Polynomials p6(r) to p10(r) are computed using recurrence relation + + 2(i+1)p_i + 2r(i+2)p_{i+1} + (i+2)(i+3)p_{i+2} = 0, + with p0 = 1, and p1(r) = -r. + + Values of erfc(r) and scale are read from lookup tables. Stored values + are scaled to avoid hitting the subnormal range. + + Note that for x < 0, erfc(x) = 2.0 - erfc(-x). + + Maximum measured error: 1.71 ULP + _ZGVsMxv_erfc(0x1.46cfe976733p+4) got 0x1.e15fcbea3e7afp-608 + want 0x1.e15fcbea3e7adp-608. */ +svfloat64_t SV_NAME_D1 (erfc) (svfloat64_t x, const svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + + svfloat64_t a = svabs_x (pg, x); + + /* Clamp input at |x| <= 3487/128. */ + a = svmin_x (pg, a, dat->max); + + /* Reduce x to the nearest multiple of 1/128. */ + svfloat64_t shift = sv_f64 (dat->shift); + svfloat64_t z = svadd_x (pg, a, shift); + + /* Saturate index for the NaN case. */ + svuint64_t i = svqadd (svreinterpret_u64 (z), dat->off_idx); + + /* Lookup erfc(r) and 2/sqrt(pi)*exp(-r^2) in tables. */ + i = svadd_x (pg, i, i); + const float64_t *p = &__erfc_data.tab[0].erfc - 2 * dat->off_arr; + svfloat64_t erfcr = svld1_gather_index (pg, p, i); + svfloat64_t scale = svld1_gather_index (pg, p + 1, i); + + /* erfc(x) ~ erfc(r) - scale * d * poly(r, d). */ + svfloat64_t r = svsub_x (pg, z, shift); + svfloat64_t d = svsub_x (pg, a, r); + svfloat64_t d2 = svmul_x (pg, d, d); + svfloat64_t r2 = svmul_x (pg, r, r); + + /* poly (d, r) = 1 + p1(r) * d + p2(r) * d^2 + ... + p9(r) * d^9. */ + svfloat64_t p1 = r; + svfloat64_t third = sv_f64 (dat->p20); + svfloat64_t twothird = svmul_x (pg, third, 2.0); + svfloat64_t sixth = svmul_x (pg, third, 0.5); + svfloat64_t p2 = svmls_x (pg, third, r2, twothird); + svfloat64_t p3 = svmad_x (pg, r2, third, -0.5); + p3 = svmul_x (pg, r, p3); + svfloat64_t p4 = svmla_x (pg, sv_f64 (dat->p41), r2, dat->p42); + p4 = svmls_x (pg, sv_f64 (dat->p40), r2, p4); + svfloat64_t p5 = svmla_x (pg, sv_f64 (dat->p51), r2, dat->p52); + p5 = svmla_x (pg, sixth, r2, p5); + p5 = svmul_x (pg, r, p5); + /* Compute p_i using recurrence relation: + p_{i+2} = (p_i + r * Q_{i+1} * p_{i+1}) * R_{i+1}. */ + svfloat64_t qr5 = svld1rq (svptrue_b64 (), &dat->q5); + svfloat64_t qr6 = svld1rq (svptrue_b64 (), &dat->q6); + svfloat64_t qr7 = svld1rq (svptrue_b64 (), &dat->q7); + svfloat64_t qr8 = svld1rq (svptrue_b64 (), &dat->q8); + svfloat64_t qr9 = svld1rq (svptrue_b64 (), &dat->q9); + svfloat64_t p6 = svmla_x (pg, p4, p5, svmul_lane (r, qr5, 0)); + p6 = svmul_lane (p6, qr5, 1); + svfloat64_t p7 = svmla_x (pg, p5, p6, svmul_lane (r, qr6, 0)); + p7 = svmul_lane (p7, qr6, 1); + svfloat64_t p8 = svmla_x (pg, p6, p7, svmul_lane (r, qr7, 0)); + p8 = svmul_lane (p8, qr7, 1); + svfloat64_t p9 = svmla_x (pg, p7, p8, svmul_lane (r, qr8, 0)); + p9 = svmul_lane (p9, qr8, 1); + svfloat64_t p10 = svmla_x (pg, p8, p9, svmul_lane (r, qr9, 0)); + p10 = svmul_lane (p10, qr9, 1); + /* Compute polynomial in d using pairwise Horner scheme. */ + svfloat64_t p90 = svmla_x (pg, p9, d, p10); + svfloat64_t p78 = svmla_x (pg, p7, d, p8); + svfloat64_t p56 = svmla_x (pg, p5, d, p6); + svfloat64_t p34 = svmla_x (pg, p3, d, p4); + svfloat64_t p12 = svmla_x (pg, p1, d, p2); + svfloat64_t y = svmla_x (pg, p78, d2, p90); + y = svmla_x (pg, p56, d2, y); + y = svmla_x (pg, p34, d2, y); + y = svmla_x (pg, p12, d2, y); + + y = svmls_x (pg, erfcr, scale, svmls_x (pg, d, d2, y)); + + /* Offset equals 2.0 if sign, else 0.0. */ + svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000); + svfloat64_t off = svreinterpret_f64 (svlsr_x (pg, sign, 1)); + /* Handle sign and scale back in a single fma. */ + svfloat64_t fac = svreinterpret_f64 (svorr_x (pg, sign, dat->table_scale)); + + return svmla_x (pg, off, fac, y); +} diff --git a/sysdeps/aarch64/fpu/erfcf_advsimd.c b/sysdeps/aarch64/fpu/erfcf_advsimd.c new file mode 100644 index 0000000000..30b9e48dd4 --- /dev/null +++ b/sysdeps/aarch64/fpu/erfcf_advsimd.c @@ -0,0 +1,170 @@ +/* Single-precision vector (Advanced SIMD) erfc function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "v_math.h" + +static const struct data +{ + uint32x4_t offset, table_scale; + float32x4_t max, shift; + float32x4_t coeffs, third, two_over_five, tenth; +#if WANT_SIMD_EXCEPT + float32x4_t uflow_bound; +#endif + +} data = { + /* Set an offset so the range of the index used for lookup is 644, and it can + be clamped using a saturated add. */ + .offset = V4 (0xb7fffd7b), /* 0xffffffff - asuint(shift) - 644. */ + .table_scale = V4 (0x28000000 << 1), /* asuint (2^-47) << 1. */ + .max = V4 (10.0625f), /* 10 + 1/16 = 644/64. */ + .shift = V4 (0x1p17f), + /* Store 1/3, 2/3 and 2/15 in a single register for use with indexed muls and + fmas. */ + .coeffs = (float32x4_t){ 0x1.555556p-2f, 0x1.555556p-1f, 0x1.111112p-3f, 0 }, + .third = V4 (0x1.555556p-2f), + .two_over_five = V4 (-0x1.99999ap-2f), + .tenth = V4 (-0x1.99999ap-4f), +#if WANT_SIMD_EXCEPT + .uflow_bound = V4 (0x1.2639cp+3f), +#endif +}; + +#define TinyBound 0x41000000 /* 0x1p-62f << 1. */ +#define Thres 0xbe000000 /* asuint(infinity) << 1 - TinyBound. */ +#define Off 0xfffffd7b /* 0xffffffff - 644. */ + +struct entry +{ + float32x4_t erfc; + float32x4_t scale; +}; + +static inline struct entry +lookup (uint32x4_t i) +{ + struct entry e; + float64_t t0 = *((float64_t *) (__erfcf_data.tab - Off + i[0])); + float64_t t1 = *((float64_t *) (__erfcf_data.tab - Off + i[1])); + float64_t t2 = *((float64_t *) (__erfcf_data.tab - Off + i[2])); + float64_t t3 = *((float64_t *) (__erfcf_data.tab - Off + i[3])); + float32x4_t e1 = vreinterpretq_f32_f64 ((float64x2_t){ t0, t1 }); + float32x4_t e2 = vreinterpretq_f32_f64 ((float64x2_t){ t2, t3 }); + e.erfc = vuzp1q_f32 (e1, e2); + e.scale = vuzp2q_f32 (e1, e2); + return e; +} + +#if WANT_SIMD_EXCEPT +static float32x4_t VPCS_ATTR NOINLINE +special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp) +{ + return v_call_f32 (erfcf, x, y, cmp); +} +#endif + +/* Optimized single-precision vector erfcf(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/64. + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + + erfc(x) ~ erfc(r) - scale * d * poly(r, d), with + + poly(r, d) = 1 - r d + (2/3 r^2 - 1/3) d^2 - r (1/3 r^2 - 1/2) d^3 + + (2/15 r^4 - 2/5 r^2 + 1/10) d^4 + + Values of erfc(r) and scale are read from lookup tables. Stored values + are scaled to avoid hitting the subnormal range. + + Note that for x < 0, erfc(x) = 2.0 - erfc(-x). + Maximum error: 1.63 ULP (~1.0 ULP for x < 0.0). + _ZGVnN4v_erfcf(0x1.1dbf7ap+3) got 0x1.f51212p-120 + want 0x1.f51216p-120. */ +VPCS_ATTR +float32x4_t NOINLINE V_NAME_F1 (erfc) (float32x4_t x) +{ + const struct data *dat = ptr_barrier (&data); + +#if WANT_SIMD_EXCEPT + /* |x| < 2^-62. Avoid fabs by left-shifting by 1. */ + uint32x4_t ix = vreinterpretq_u32_f32 (x); + uint32x4_t cmp = vcltq_u32 (vaddq_u32 (ix, ix), v_u32 (TinyBound)); + /* x >= ~9.19 (into subnormal case and uflow case). Comparison is done in + integer domain to avoid raising exceptions in presence of nans. */ + uint32x4_t uflow = vcgeq_s32 (vreinterpretq_s32_f32 (x), + vreinterpretq_s32_f32 (dat->uflow_bound)); + cmp = vorrq_u32 (cmp, uflow); + float32x4_t xm = x; + /* If any lanes are special, mask them with 0 and retain a copy of x to allow + special case handler to fix special lanes later. This is only necessary if + fenv exceptions are to be triggered correctly. */ + if (__glibc_unlikely (v_any_u32 (cmp))) + x = v_zerofy_f32 (x, cmp); +#endif + + float32x4_t a = vabsq_f32 (x); + a = vminq_f32 (a, dat->max); + + /* Lookup erfc(r) and scale(r) in tables, e.g. set erfc(r) to 0 and scale to + 2/sqrt(pi), when x reduced to r = 0. */ + float32x4_t shift = dat->shift; + float32x4_t z = vaddq_f32 (a, shift); + + /* Clamp index to a range of 644. A naive approach would use a subtract and + min. Instead we offset the table address and the index, then use a + saturating add. */ + uint32x4_t i = vqaddq_u32 (vreinterpretq_u32_f32 (z), dat->offset); + + struct entry e = lookup (i); + + /* erfc(x) ~ erfc(r) - scale * d * poly(r, d). */ + float32x4_t r = vsubq_f32 (z, shift); + float32x4_t d = vsubq_f32 (a, r); + float32x4_t d2 = vmulq_f32 (d, d); + float32x4_t r2 = vmulq_f32 (r, r); + + float32x4_t p1 = r; + float32x4_t p2 = vfmsq_laneq_f32 (dat->third, r2, dat->coeffs, 1); + float32x4_t p3 + = vmulq_f32 (r, vfmaq_laneq_f32 (v_f32 (-0.5), r2, dat->coeffs, 0)); + float32x4_t p4 = vfmaq_laneq_f32 (dat->two_over_five, r2, dat->coeffs, 2); + p4 = vfmsq_f32 (dat->tenth, r2, p4); + + float32x4_t y = vfmaq_f32 (p3, d, p4); + y = vfmaq_f32 (p2, d, y); + y = vfmaq_f32 (p1, d, y); + y = vfmsq_f32 (e.erfc, e.scale, vfmsq_f32 (d, d2, y)); + + /* Offset equals 2.0f if sign, else 0.0f. */ + uint32x4_t sign = vshrq_n_u32 (vreinterpretq_u32_f32 (x), 31); + float32x4_t off = vreinterpretq_f32_u32 (vshlq_n_u32 (sign, 30)); + /* Copy sign and scale back in a single fma. Since the bit patterns do not + overlap, then logical or and addition are equivalent here. */ + float32x4_t fac = vreinterpretq_f32_u32 ( + vsraq_n_u32 (vshlq_n_u32 (sign, 31), dat->table_scale, 1)); + +#if WANT_SIMD_EXCEPT + if (__glibc_unlikely (v_any_u32 (cmp))) + return special_case (xm, vfmaq_f32 (off, fac, y), cmp); +#endif + + return vfmaq_f32 (off, fac, y); +} +libmvec_hidden_def (V_NAME_F1 (erfc)) +HALF_WIDTH_ALIAS_F1 (erfc) diff --git a/sysdeps/aarch64/fpu/erfcf_data.c b/sysdeps/aarch64/fpu/erfcf_data.c new file mode 100644 index 0000000000..77fb889a78 --- /dev/null +++ b/sysdeps/aarch64/fpu/erfcf_data.c @@ -0,0 +1,676 @@ +/* Table for Advanced SIMD erfcf + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "vecmath_config.h" + +/* Lookup table used in erfcf. + For each possible rounded input r (multiples of 1/64), between + r = 0.0 and r = 10.0625 (645 values): + - the first entry __erfcf_data.tab.erfc contains the values of erfc(r), + - the second entry __erfcf_data.tab.scale contains the values of + 2/sqrt(pi)*exp(-r^2). Both values may go into subnormal range, therefore + they are scaled by a large enough value 2^47 (fits in 8 bits). */ +const struct erfcf_data __erfcf_data = { + .tab = { { 0x1p47, 0x1.20dd76p47 }, + { 0x1.f6f944p46, 0x1.20cb68p47 }, + { 0x1.edf3aap46, 0x1.209546p47 }, + { 0x1.e4f05p46, 0x1.203b26p47 }, + { 0x1.dbf056p46, 0x1.1fbd28p47 }, + { 0x1.d2f4dcp46, 0x1.1f1b7ap47 }, + { 0x1.c9fefep46, 0x1.1e565cp47 }, + { 0x1.c10fd4p46, 0x1.1d6e14p47 }, + { 0x1.b8287ap46, 0x1.1c62fap47 }, + { 0x1.af4ap46, 0x1.1b3572p47 }, + { 0x1.a6757ep46, 0x1.19e5eap47 }, + { 0x1.9dabfcp46, 0x1.1874dep47 }, + { 0x1.94ee88p46, 0x1.16e2d8p47 }, + { 0x1.8c3e24p46, 0x1.153068p47 }, + { 0x1.839bd6p46, 0x1.135e3p47 }, + { 0x1.7b0894p46, 0x1.116cd8p47 }, + { 0x1.728558p46, 0x1.0f5d16p47 }, + { 0x1.6a1312p46, 0x1.0d2fa6p47 }, + { 0x1.61b2acp46, 0x1.0ae55p47 }, + { 0x1.596508p46, 0x1.087ee4p47 }, + { 0x1.512b06p46, 0x1.05fd3ep47 }, + { 0x1.49057ap46, 0x1.03614p47 }, + { 0x1.40f536p46, 0x1.00abdp47 }, + { 0x1.38fbp46, 0x1.fbbbbep46 }, + { 0x1.311796p46, 0x1.f5f0cep46 }, + { 0x1.294bb4p46, 0x1.eff8c4p46 }, + { 0x1.21980ap46, 0x1.e9d5a8p46 }, + { 0x1.19fd3ep46, 0x1.e38988p46 }, + { 0x1.127bf2p46, 0x1.dd167cp46 }, + { 0x1.0b14bcp46, 0x1.d67ea2p46 }, + { 0x1.03c82ap46, 0x1.cfc41ep46 }, + { 0x1.f92d8cp45, 0x1.c8e91cp46 }, + { 0x1.eb0214p45, 0x1.c1efcap46 }, + { 0x1.dd0edap45, 0x1.bada5ap46 }, + { 0x1.cf54b4p45, 0x1.b3aafcp46 }, + { 0x1.c1d46ap45, 0x1.ac63e8p46 }, + { 0x1.b48eaep45, 0x1.a5074ep46 }, + { 0x1.a78428p45, 0x1.9d9762p46 }, + { 0x1.9ab566p45, 0x1.96165p46 }, + { 0x1.8e22eap45, 0x1.8e8646p46 }, + { 0x1.81cd24p45, 0x1.86e96ap46 }, + { 0x1.75b47p45, 0x1.7f41dcp46 }, + { 0x1.69d91ep45, 0x1.7791b8p46 }, + { 0x1.5e3b66p45, 0x1.6fdb12p46 }, + { 0x1.52db78p45, 0x1.681ff2p46 }, + { 0x1.47b96ep45, 0x1.60625cp46 }, + { 0x1.3cd554p45, 0x1.58a446p46 }, + { 0x1.322f26p45, 0x1.50e79ep46 }, + { 0x1.27c6d2p45, 0x1.492e42p46 }, + { 0x1.1d9c34p45, 0x1.417a0cp46 }, + { 0x1.13af1ep45, 0x1.39ccc2p46 }, + { 0x1.09ff5p45, 0x1.32281ep46 }, + { 0x1.008c8p45, 0x1.2a8dcep46 }, + { 0x1.eeaca8p44, 0x1.22ff72p46 }, + { 0x1.dcb8cap44, 0x1.1b7e98p46 }, + { 0x1.cb3c86p44, 0x1.140cc4p46 }, + { 0x1.ba36dap44, 0x1.0cab62p46 }, + { 0x1.a9a6bap44, 0x1.055bd6p46 }, + { 0x1.998afap44, 0x1.fc3ee6p45 }, + { 0x1.89e25ep44, 0x1.edeeeep45 }, + { 0x1.7aab98p44, 0x1.dfca26p45 }, + { 0x1.6be542p44, 0x1.d1d2dp45 }, + { 0x1.5d8decp44, 0x1.c40b08p45 }, + { 0x1.4fa40ep44, 0x1.b674c8p45 }, + { 0x1.422616p44, 0x1.a911fp45 }, + { 0x1.351262p44, 0x1.9be438p45 }, + { 0x1.28674p44, 0x1.8eed36p45 }, + { 0x1.1c22f8p44, 0x1.822e66p45 }, + { 0x1.1043c2p44, 0x1.75a91ap45 }, + { 0x1.04c7cap44, 0x1.695e8cp45 }, + { 0x1.f35a72p43, 0x1.5d4fd4p45 }, + { 0x1.dde456p43, 0x1.517de6p45 }, + { 0x1.c9296cp43, 0x1.45e99cp45 }, + { 0x1.b525d6p43, 0x1.3a93b2p45 }, + { 0x1.a1d5a6p43, 0x1.2f7cc4p45 }, + { 0x1.8f34eap43, 0x1.24a554p45 }, + { 0x1.7d3fa6p43, 0x1.1a0dc6p45 }, + { 0x1.6bf1dcp43, 0x1.0fb662p45 }, + { 0x1.5b4784p43, 0x1.059f5ap45 }, + { 0x1.4b3c98p43, 0x1.f79184p44 }, + { 0x1.3bcd14p43, 0x1.e4653p44 }, + { 0x1.2cf4eep43, 0x1.d1b982p44 }, + { 0x1.1eb024p43, 0x1.bf8e1cp44 }, + { 0x1.10fab8p43, 0x1.ade26cp44 }, + { 0x1.03d0acp43, 0x1.9cb5bep44 }, + { 0x1.ee5c18p42, 0x1.8c0732p44 }, + { 0x1.d61dd6p42, 0x1.7bd5c8p44 }, + { 0x1.bedec8p42, 0x1.6c2056p44 }, + { 0x1.a8973cp42, 0x1.5ce596p44 }, + { 0x1.933f9p42, 0x1.4e241ep44 }, + { 0x1.7ed03ap42, 0x1.3fda6cp44 }, + { 0x1.6b41ccp42, 0x1.3206dcp44 }, + { 0x1.588cf2p42, 0x1.24a7b8p44 }, + { 0x1.46aa72p42, 0x1.17bb2cp44 }, + { 0x1.359332p42, 0x1.0b3f52p44 }, + { 0x1.254038p42, 0x1.fe646p43 }, + { 0x1.15aaa8p42, 0x1.e72372p43 }, + { 0x1.06cbcap42, 0x1.d0b7ap43 }, + { 0x1.f13a04p41, 0x1.bb1c98p43 }, + { 0x1.d62fbep41, 0x1.a64de6p43 }, + { 0x1.bc6c1ep41, 0x1.92470ap43 }, + { 0x1.a3e2ccp41, 0x1.7f036cp43 }, + { 0x1.8c87b8p41, 0x1.6c7e64p43 }, + { 0x1.764f2p41, 0x1.5ab342p43 }, + { 0x1.612d8ap41, 0x1.499d48p43 }, + { 0x1.4d17cap41, 0x1.3937b2p43 }, + { 0x1.3a03p41, 0x1.297dbap43 }, + { 0x1.27e498p41, 0x1.1a6a96p43 }, + { 0x1.16b24cp41, 0x1.0bf97ep43 }, + { 0x1.066222p41, 0x1.fc4b5ep42 }, + { 0x1.edd4d2p40, 0x1.e1d4dp42 }, + { 0x1.d08382p40, 0x1.c885ep42 }, + { 0x1.b4be2p40, 0x1.b0553p42 }, + { 0x1.9a7316p40, 0x1.99397ap42 }, + { 0x1.81915cp40, 0x1.83298ep42 }, + { 0x1.6a088p40, 0x1.6e1c58p42 }, + { 0x1.53c89ep40, 0x1.5a08e8p42 }, + { 0x1.3ec25ep40, 0x1.46e66cp42 }, + { 0x1.2ae6fap40, 0x1.34ac36p42 }, + { 0x1.18282ep40, 0x1.2351c2p42 }, + { 0x1.067844p40, 0x1.12ceb4p42 }, + { 0x1.eb940ep39, 0x1.031ad6p42 }, + { 0x1.cc2186p39, 0x1.e85c44p41 }, + { 0x1.ae808cp39, 0x1.cc018p41 }, + { 0x1.9299bp39, 0x1.b1160ap41 }, + { 0x1.785674p39, 0x1.978ae8p41 }, + { 0x1.5fa14ap39, 0x1.7f5188p41 }, + { 0x1.486586p39, 0x1.685bb6p41 }, + { 0x1.328f5ep39, 0x1.529b9ep41 }, + { 0x1.1e0be6p39, 0x1.3e03d8p41 }, + { 0x1.0ac8fcp39, 0x1.2a875cp41 }, + { 0x1.f16aaep38, 0x1.181984p41 }, + { 0x1.cf80d4p38, 0x1.06ae14p41 }, + { 0x1.afb4e2p38, 0x1.ec7262p40 }, + { 0x1.91e8bep38, 0x1.cd5ecap40 }, + { 0x1.75ffb4p38, 0x1.b00b38p40 }, + { 0x1.5bde72p38, 0x1.94624ep40 }, + { 0x1.436af4p38, 0x1.7a4f6ap40 }, + { 0x1.2c8c7ap38, 0x1.61beaep40 }, + { 0x1.172b7ap38, 0x1.4a9cf6p40 }, + { 0x1.033198p38, 0x1.34d7dcp40 }, + { 0x1.e11332p37, 0x1.205dacp40 }, + { 0x1.be3ebp37, 0x1.0d1d6ap40 }, + { 0x1.9dbf72p37, 0x1.f60d8ap39 }, + { 0x1.7f714p37, 0x1.d4143ap39 }, + { 0x1.6331cap37, 0x1.b430ecp39 }, + { 0x1.48e09cp37, 0x1.9646f4p39 }, + { 0x1.305ef8p37, 0x1.7a3adep39 }, + { 0x1.198fd6p37, 0x1.5ff276p39 }, + { 0x1.0457c6p37, 0x1.4754acp39 }, + { 0x1.e139bcp36, 0x1.30499cp39 }, + { 0x1.bc8d52p36, 0x1.1aba78p39 }, + { 0x1.9a7c3p36, 0x1.06918cp39 }, + { 0x1.7adadep36, 0x1.e77448p38 }, + { 0x1.5d806ap36, 0x1.c4412cp38 }, + { 0x1.424642p36, 0x1.a36454p38 }, + { 0x1.290826p36, 0x1.84ba3p38 }, + { 0x1.11a3f8p36, 0x1.6821p38 }, + { 0x1.f7f358p35, 0x1.4d78bcp38 }, + { 0x1.cfd652p35, 0x1.34a306p38 }, + { 0x1.aab85ap35, 0x1.1d8318p38 }, + { 0x1.88647p35, 0x1.07fdb4p38 }, + { 0x1.68a8e4p35, 0x1.e7f232p37 }, + { 0x1.4b5726p35, 0x1.c2b9dp37 }, + { 0x1.30439cp35, 0x1.a02436p37 }, + { 0x1.174578p35, 0x1.8005fp37 }, + { 0x1.003692p35, 0x1.6235fcp37 }, + { 0x1.d5e678p34, 0x1.468daep37 }, + { 0x1.aeb442p34, 0x1.2ce898p37 }, + { 0x1.8a9848p34, 0x1.15246ep37 }, + { 0x1.695876p34, 0x1.fe41cep36 }, + { 0x1.4abea2p34, 0x1.d57f52p36 }, + { 0x1.2e984ep34, 0x1.afc85ep36 }, + { 0x1.14b676p34, 0x1.8ce75ep36 }, + { 0x1.f9daap33, 0x1.6caa0ep36 }, + { 0x1.ce283ap33, 0x1.4ee142p36 }, + { 0x1.a609f8p33, 0x1.3360ccp36 }, + { 0x1.81396ap33, 0x1.19ff46p36 }, + { 0x1.5f7524p33, 0x1.0295fp36 }, + { 0x1.40806ep33, 0x1.da011p35 }, + { 0x1.2422eep33, 0x1.b23a5ap35 }, + { 0x1.0a286p33, 0x1.8d986ap35 }, + { 0x1.e4c0bp32, 0x1.6be022p35 }, + { 0x1.b93bf4p32, 0x1.4cda54p35 }, + { 0x1.916f7cp32, 0x1.30539p35 }, + { 0x1.6d0e7p32, 0x1.161be4p35 }, + { 0x1.4bd1cp32, 0x1.fc0d56p34 }, + { 0x1.2d77bep32, 0x1.cfd4a6p34 }, + { 0x1.11c3bep32, 0x1.a74068p34 }, + { 0x1.f0fb86p31, 0x1.8208bcp34 }, + { 0x1.c2e43ep31, 0x1.5feadap34 }, + { 0x1.98e254p31, 0x1.40a8c2p34 }, + { 0x1.729df6p31, 0x1.2408eap34 }, + { 0x1.4fc63cp31, 0x1.09d5f8p34 }, + { 0x1.3010aap31, 0x1.e3bcf4p33 }, + { 0x1.1338b8p31, 0x1.b7e946p33 }, + { 0x1.f1fecp30, 0x1.8fdc1cp33 }, + { 0x1.c2556ap30, 0x1.6b4702p33 }, + { 0x1.970b06p30, 0x1.49e178p33 }, + { 0x1.6fbddep30, 0x1.2b6876p33 }, + { 0x1.4c144ep30, 0x1.0f9e1cp33 }, + { 0x1.2bbc1ep30, 0x1.ec929ap32 }, + { 0x1.0e69f2p30, 0x1.be6abcp32 }, + { 0x1.e7b188p29, 0x1.94637ep32 }, + { 0x1.b792bcp29, 0x1.6e2368p32 }, + { 0x1.8c03d2p29, 0x1.4b581cp32 }, + { 0x1.649b02p29, 0x1.2bb5ccp32 }, + { 0x1.40f794p29, 0x1.0ef6c4p32 }, + { 0x1.20c13p29, 0x1.e9b5e8p31 }, + { 0x1.03a72ap29, 0x1.ba4f04p31 }, + { 0x1.d2bfc6p28, 0x1.8f4cccp31 }, + { 0x1.a35068p28, 0x1.684c22p31 }, + { 0x1.7885cep28, 0x1.44f21ep31 }, + { 0x1.51f06ap28, 0x1.24eb72p31 }, + { 0x1.2f2aaap28, 0x1.07ebd2p31 }, + { 0x1.0fd816p28, 0x1.db5adp30 }, + { 0x1.e7493p27, 0x1.abe09ep30 }, + { 0x1.b48774p27, 0x1.80f43ap30 }, + { 0x1.86e006p27, 0x1.5a2aep30 }, + 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0x1.e07ab4p-44, 0x1.d458ap-40 }, + { 0x1.7879ecp-44, 0x1.6fb2eap-40 }, + { 0x1.26d7bp-44, 0x1.208a2cp-40 }, + { 0x1.cd98a2p-45, 0x1.c49f8ap-41 }, + { 0x1.6927c2p-45, 0x1.62d5aap-41 }, + { 0x1.1a6ed6p-45, 0x1.16098ep-41 }, + { 0x1.b986acp-46, 0x1.b3828ep-42 }, + { 0x1.58f35ap-46, 0x1.54eb3ep-42 }, + { 0x1.0d5e6p-46, 0x1.0abe0ep-42 }, + { 0x1.a47db6p-47, 0x1.a134d4p-43 }, + { 0x1.480a18p-47, 0x1.461cdap-43 }, + { 0x1.ff94e4p-48, 0x1.fd9182p-44 }, + { 0x1.8eb738p-48, 0x1.8deb62p-44 }, + { 0x1.369994p-48, 0x1.3694e8p-44 }, + { 0x1.e3ae4ap-49, 0x1.e49706p-45 }, + { 0x1.786c3ep-49, 0x1.79dc28p-45 }, + { 0x1.24cec8p-49, 0x1.267e46p-45 }, + { 0x1.c74fc4p-50, 0x1.cad0bp-46 }, + { 0x1.61d46cp-50, 0x1.653d08p-46 }, + { 0x1.12d55cp-50, 0x1.16038cp-46 }, + { 0x1.aabdacp-51, 0x1.b081aap-47 }, + { 0x1.4b252ep-51, 0x1.5042e2p-47 }, + { 0x1.00d6f8p-51, 0x1.054e44p-47 }, + { 0x1.8e38ep-52, 0x1.95eb2cp-48 }, + { 0x1.3490e8p-52, 0x1.3b20c6p-48 }, + { 0x1.ddf56ap-53, 0x1.e90cb6p-49 }, + { 0x1.71fdep-53, 0x1.7b4b76p-49 }, + { 0x1.1e465ap-53, 0x1.26072ap-49 }, + { 0x1.bac92ep-54, 0x1.c7a2ecp-50 }, + { 0x1.56441cp-54, 0x1.60dcfp-50 }, + { 0x1.08700cp-54, 0x1.112346p-50 }, + { 0x1.986a66p-55, 0x1.a6a50ap-51 }, + { 0x1.3b3d56p-55, 0x1.46d572p-51 }, + { 0x1.e667dap-56, 0x1.f93d0ep-52 }, + { 0x1.7712b8p-56, 0x1.86529ep-52 }, + { 0x1.211544p-56, 0x1.2d65aep-52 }, + { 0x1.bd660ap-57, 0x1.d13c32p-53 }, + { 0x1.56f3eep-57, 0x1.66e45ap-53 }, + { 0x1.07f14ap-57, 0x1.14b8b6p-53 }, + { 0x1.96129cp-58, 0x1.aa854cp-54 }, + { 0x1.3837cp-58, 0x1.488b94p-54 }, + { 0x1.dfe0c2p-59, 0x1.f9e772p-55 }, + { 0x1.709b5ap-59, 0x1.85503p-55 }, + { 0x1.1affd2p-59, 0x1.2b7218p-55 }, + { 0x1.b2564p-60, 0x1.cc6bb6p-56 }, + { 0x1.4d23fap-60, 0x1.61cb1ap-56 }, + { 0x1.fecbdp-61, 0x1.0fba0ep-56 }, + { 0x1.8767d8p-61, 0x1.a13072p-57 }, + { 0x1.2bc67ep-61, 0x1.401abcp-57 }, + { 0x1.caf846p-62, 0x1.eafc2cp-58 }, + { 0x1.5f2e7ap-62, 0x1.785cp-58 }, + { 0x1.0c93acp-62, 0x1.205a7ep-58 }, + { 0x1.9a9b06p-63, 0x1.b9a31ap-59 }, + { 0x1.39b7fcp-63, 0x1.520968p-59 }, + { 0x1.df277ap-64, 0x1.029ce6p-59 }, + { 0x1.6dbcdp-64, 0x1.8b81d6p-60 }, + { 0x1.17080ap-64, 0x1.2e48f2p-60 }, + { 0x1.a98e26p-65, 0x1.cdd86cp-61 }, + { 0x1.445a6ap-65, 0x1.60a47ap-61 }, + { 0x1.ee324ep-66, 0x1.0d210cp-61 }, + { 0x1.784e3p-66, 0x1.9a961ep-62 }, + { 0x1.1e65fep-66, 0x1.390b74p-62 }, + { 0x1.b3bb86p-67, 0x1.dd1e52p-63 }, + { 0x1.4b4e36p-67, 0x1.6b6a7ap-63 }, + { 0x1.f790f6p-68, 0x1.14acc2p-63 }, + { 0x1.7e82cep-68, 0x1.a511aap-64 }, + { 0x1.226a7ap-68, 0x1.404114p-64 }, + { 0x1.b8c634p-69, 0x1.e6ea96p-65 }, + { 0x1.4e53acp-69, 0x1.71f97ap-65 }, + { 0x1.faed5cp-70, 0x1.18fb2ep-65 }, + { 0x1.80217ep-70, 0x1.aa947ep-66 }, + { 0x1.22f066p-70, 0x1.43a796p-66 }, + { 0x1.b87f86p-71, 0x1.eae2fp-67 }, + { 0x1.4d4ec8p-71, 0x1.7414e6p-67 }, + { 0x1.f8283ep-72, 0x1.19e474p-67 }, + { 0x1.7d1b22p-72, 0x1.aaeb7ep-68 }, + { 0x1.1ff2dp-72, 0x1.431f66p-68 }, + { 0x1.b2e9e8p-73, 0x1.e8e272p-69 }, + { 0x1.4848dep-73, 0x1.71a91ep-69 }, + { 0x1.ef5b16p-74, 0x1.176014p-69 }, + { 0x1.758b92p-74, 0x1.a6137cp-70 }, + { 0x1.198d42p-74, 0x1.3ead74p-70 }, + { 0x1.a838bp-75, 0x1.e0fbc2p-71 }, + { 0x1.3f700cp-75, 0x1.6accaep-71 }, + { 0x1.e0d68ep-76, 0x1.118578p-71 }, + { 0x1.69b7f4p-76, 0x1.9c3974p-72 }, + { 0x1.0ffa12p-76, 0x1.367afap-72 }, + { 0x1.98cd1cp-77, 0x1.d377fap-73 }, + { 0x1.33148p-77, 0x1.5fbee6p-73 }, + { 0x1.cd1dbap-78, 0x1.088a8p-73 }, + { 0x1.5a0a9cp-78, 0x1.8db7ccp-74 }, + { 0x1.038ef4p-78, 0x1.2ad2ecp-74 }, + { 0x1.85308ap-79, 0x1.c0d23ep-75 }, + { 0x1.23a3cp-79, 0x1.50e41ap-75 }, + { 0x1.b4de68p-80, 0x1.f980a8p-76 }, + { 0x1.470ce4p-80, 0x1.7b10fep-76 }, + { 0x1.e9700cp-81, 0x1.1c1d98p-76 }, + { 0x1.6e0c9p-81, 0x1.a9b08p-77 }, + { 0x1.11a25ap-81, 0x1.3ebfb4p-77 }, + { 0x1.98e73ap-82, 0x1.dd1d36p-78 }, + { 0x1.315f58p-82, 0x1.64e7fp-78 }, + { 0x1.c7e35cp-83, 0x1.0ada94p-78 }, + { 0x1.542176p-83, 0x1.8ed9e8p-79 }, + { 0x1.fb491ep-84, 0x1.29ecb2p-79 }, + { 0x1.7a1c34p-84, 0x1.bcdb34p-80 }, + { 0x1.19b0f2p-84, 0x1.4bf6cap-80 }, + { 0x1.a383cap-85, 0x1.ef3318p-81 }, + { 0x1.383bf2p-85, 0x1.712bc2p-81 }, + { 0x1.d08cdap-86, 0x1.13151p-81 }, + { 0x1.596adp-86, 0x1.99bf36p-82 }, + { 0x1.00b602p-86, 0x1.3104d6p-82 }, + { 0x1.7d62a2p-87, 0x1.c5e534p-83 }, + { 0x1.1b2abcp-87, 0x1.518db2p-83 }, + { 0x1.a4480ep-88, 0x1.f5d1c6p-84 }, + { 0x1.37be42p-88, 0x1.74d45ap-84 }, + { 0x1.ce3ee4p-89, 0x1.14dc4ap-84 }, + { 0x1.568986p-89, 0x1.9afd0ep-85 }, + { 0x1.fb69c6p-90, 0x1.30e632p-85 }, + { 0x1.77a47ep-90, 0x1.c42b48p-86 }, + { 0x1.15f4ep-90, 0x1.4f1f52p-86 }, + { 0x1.9b25dcp-91, 0x1.f08156p-87 }, + { 0x1.2feeeep-91, 0x1.6f9f62p-87 }, + { 0x1.c122bcp-92, 0x1.100ffap-87 }, + { 0x1.4bb154p-92, 0x1.927ce6p-88 }, + { 0x1.e9ae56p-93, 0x1.2992f4p-88 }, + { 0x1.6948e8p-93, 0x1.b7cccap-89 }, + { 0x1.0a6cd2p-93, 0x1.44d7c4p-89 }, + { 0x1.88c0cap-94, 0x1.dfa22p-90 }, + { 0x1.215988p-94, 0x1.61eb26p-90 }, + { 0x1.aa222ap-95, 0x1.0506e2p-90 }, + { 0x1.39a30ep-95, 0x1.80d828p-91 }, + { 0x1.cd740ep-96, 0x1.1b8f04p-91 }, + { 0x1.534d82p-96, 0x1.a1a7ecp-92 }, + { 0x1.f2bb06p-97, 0x1.336f3p-92 }, + { 0x1.6e5b34p-97, 0x1.c46172p-93 }, + { 0x1.0cfc82p-97, 0x1.4cab82p-93 }, + { 0x1.8acc82p-98, 0x1.e9094cp-94 }, + { 0x1.219686p-98, 0x1.67465p-94 }, + { 0x1.a89fa6p-99, 0x1.07d0b8p-94 }, + { 0x1.372982p-99, 0x1.833ffap-95 }, + { 0x1.c7d094p-100, 0x1.1c147ap-95 }, + { 0x1.4db1c8p-100, 0x1.a096ccp-96 }, + { 0x1.e858d8p-101, 0x1.314decp-96 }, + { 0x1.6529ep-101, 0x1.bf46cep-97 }, + { 0x1.0517bap-101, 0x1.47796ap-97 }, + { 0x1.7d8a8p-102, 0x1.df49a2p-98 }, + { 0x1.16a46p-102, 0x1.5e9198p-98 }, + { 0x1.96ca76p-103, 0x1.004b34p-98 }, + { 0x1.28cb2cp-103, 0x1.768f3ep-99 }, + { 0x1.b0de98p-104, 0x1.1190d2p-99 }, + }, + }; diff --git a/sysdeps/aarch64/fpu/erfcf_sve.c b/sysdeps/aarch64/fpu/erfcf_sve.c new file mode 100644 index 0000000000..48d1677eb4 --- /dev/null +++ b/sysdeps/aarch64/fpu/erfcf_sve.c @@ -0,0 +1,113 @@ +/* Single-precision vector (SVE) erfc function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + . */ + +#include "sv_math.h" + +static const struct data +{ + uint32_t off_idx, off_arr; + float max, shift; + float third, two_thirds, two_over_fifteen, two_over_five, tenth; +} data = { + /* Set an offset so the range of the index used for lookup is 644, and it can + be clamped using a saturated add. */ + .off_idx = 0xb7fffd7b, /* 0xffffffff - asuint(shift) - 644. */ + .off_arr = 0xfffffd7b, /* 0xffffffff - 644. */ + .max = 10.0625f, /* 644/64. */ + .shift = 0x1p17f, + .third = 0x1.555556p-2f, + .two_thirds = 0x1.555556p-1f, + .two_over_fifteen = 0x1.111112p-3f, + .two_over_five = -0x1.99999ap-2f, + .tenth = -0x1.99999ap-4f, +}; + +#define SignMask 0x80000000 +#define TableScale 0x28000000 /* 0x1p-47. */ + +/* Optimized single-precision vector erfcf(x). + Approximation based on series expansion near x rounded to + nearest multiple of 1/64. + Let d = x - r, and scale = 2 / sqrt(pi) * exp(-r^2). For x near r, + + erfc(x) ~ erfc(r) - scale * d * poly(r, d), with + + poly(r, d) = 1 - r d + (2/3 r^2 - 1/3) d^2 - r (1/3 r^2 - 1/2) d^3 + + (2/15 r^4 - 2/5 r^2 + 1/10) d^4 + + Values of erfc(r) and scale are read from lookup tables. Stored values + are scaled to avoid hitting the subnormal range. + + Note that for x < 0, erfc(x) = 2.0 - erfc(-x). + + Maximum error: 1.63 ULP (~1.0 ULP for x < 0.0). + _ZGVsMxv_erfcf(0x1.1dbf7ap+3) got 0x1.f51212p-120 + want 0x1.f51216p-120. */ +svfloat32_t SV_NAME_F1 (erfc) (svfloat32_t x, const svbool_t pg) +{ + const struct data *dat = ptr_barrier (&data); + + svfloat32_t a = svabs_x (pg, x); + + /* Clamp input at |x| <= 10.0 + 4/64. */ + a = svmin_x (pg, a, dat->max); + + /* Reduce x to the nearest multiple of 1/64. */ + svfloat32_t shift = sv_f32 (dat->shift); + svfloat32_t z = svadd_x (pg, a, shift); + + /* Saturate index for the NaN case. */ + svuint32_t i = svqadd (svreinterpret_u32 (z), dat->off_idx); + + /* Lookup erfc(r) and 2/sqrt(pi)*exp(-r^2) in tables. */ + i = svmul_x (pg, i, 2); + const float32_t *p = &__erfcf_data.tab[0].erfc - 2 * dat->off_arr; + svfloat32_t erfcr = svld1_gather_index (pg, p, i); + svfloat32_t scale = svld1_gather_index (pg, p + 1, i); + + /* erfc(x) ~ erfc(r) - scale * d * poly(r, d). */ + svfloat32_t r = svsub_x (pg, z, shift); + svfloat32_t d = svsub_x (pg, a, r); + svfloat32_t d2 = svmul_x (pg, d, d); + svfloat32_t r2 = svmul_x (pg, r, r); + + svfloat32_t coeffs = svld1rq (svptrue_b32 (), &dat->third); + svfloat32_t third = svdup_lane (coeffs, 0); + + svfloat32_t p1 = r; + svfloat32_t p2 = svmls_lane (third, r2, coeffs, 1); + svfloat32_t p3 = svmul_x (pg, r, svmla_lane (sv_f32 (-0.5), r2, coeffs, 0)); + svfloat32_t p4 = svmla_lane (sv_f32 (dat->two_over_five), r2, coeffs, 2); + p4 = svmls_x (pg, sv_f32 (dat->tenth), r2, p4); + + svfloat32_t y = svmla_x (pg, p3, d, p4); + y = svmla_x (pg, p2, d, y); + y = svmla_x (pg, p1, d, y); + + /* Solves the |x| = inf/nan case. */ + y = svmls_x (pg, erfcr, scale, svmls_x (pg, d, d2, y)); + + /* Offset equals 2.0f if sign, else 0.0f. */ + svuint32_t sign = svand_x (pg, svreinterpret_u32 (x), SignMask); + svfloat32_t off = svreinterpret_f32 (svlsr_x (pg, sign, 1)); + /* Handle sign and scale back in a single fma. */ + svfloat32_t fac = svreinterpret_f32 (svorr_x (pg, sign, TableScale)); + + return svmla_x (pg, off, fac, y); +} diff --git a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c index 7aeda880bd..f2d8714075 100644 --- a/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-advsimd-wrappers.c @@ -33,6 +33,7 @@ VPCS_VECTOR_WRAPPER_ff (atan2_advsimd, _ZGVnN2vv_atan2) VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos) VPCS_VECTOR_WRAPPER (cosh_advsimd, _ZGVnN2v_cosh) VPCS_VECTOR_WRAPPER (erf_advsimd, _ZGVnN2v_erf) +VPCS_VECTOR_WRAPPER (erfc_advsimd, _ZGVnN2v_erfc) VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp) VPCS_VECTOR_WRAPPER (exp10_advsimd, _ZGVnN2v_exp10) VPCS_VECTOR_WRAPPER (exp2_advsimd, _ZGVnN2v_exp2) diff --git a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c index 95f1ec5222..37873d5e43 100644 --- a/sysdeps/aarch64/fpu/test-double-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-double-sve-wrappers.c @@ -52,6 +52,7 @@ SVE_VECTOR_WRAPPER_ff (atan2_sve, _ZGVsMxvv_atan2) SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos) SVE_VECTOR_WRAPPER (cosh_sve, _ZGVsMxv_cosh) SVE_VECTOR_WRAPPER (erf_sve, _ZGVsMxv_erf) +SVE_VECTOR_WRAPPER (erfc_sve, _ZGVsMxv_erfc) SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp) SVE_VECTOR_WRAPPER (exp10_sve, _ZGVsMxv_exp10) SVE_VECTOR_WRAPPER (exp2_sve, _ZGVsMxv_exp2) diff --git a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c index bd6800e91c..08e33115b9 100644 --- a/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-advsimd-wrappers.c @@ -33,6 +33,7 @@ VPCS_VECTOR_WRAPPER_ff (atan2f_advsimd, _ZGVnN4vv_atan2f) VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf) VPCS_VECTOR_WRAPPER (coshf_advsimd, _ZGVnN4v_coshf) VPCS_VECTOR_WRAPPER (erff_advsimd, _ZGVnN4v_erff) +VPCS_VECTOR_WRAPPER (erfcf_advsimd, _ZGVnN4v_erfcf) VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf) VPCS_VECTOR_WRAPPER (exp10f_advsimd, _ZGVnN4v_exp10f) VPCS_VECTOR_WRAPPER (exp2f_advsimd, _ZGVnN4v_exp2f) diff --git a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c index 35ca305fdd..025daa662e 100644 --- a/sysdeps/aarch64/fpu/test-float-sve-wrappers.c +++ b/sysdeps/aarch64/fpu/test-float-sve-wrappers.c @@ -52,6 +52,7 @@ SVE_VECTOR_WRAPPER_ff (atan2f_sve, _ZGVsMxvv_atan2f) SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf) SVE_VECTOR_WRAPPER (coshf_sve, _ZGVsMxv_coshf) SVE_VECTOR_WRAPPER (erff_sve, _ZGVsMxv_erff) +SVE_VECTOR_WRAPPER (erfcf_sve, _ZGVsMxv_erfcf) SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf) SVE_VECTOR_WRAPPER (exp10f_sve, _ZGVsMxv_exp10f) SVE_VECTOR_WRAPPER (exp2f_sve, _ZGVsMxv_exp2f) diff --git a/sysdeps/aarch64/fpu/vecmath_config.h b/sysdeps/aarch64/fpu/vecmath_config.h index 3f0b5f4764..c8cfc03bc0 100644 --- a/sysdeps/aarch64/fpu/vecmath_config.h +++ b/sysdeps/aarch64/fpu/vecmath_config.h @@ -114,4 +114,20 @@ extern const struct sv_erf_data double scale[769]; } __sv_erf_data attribute_hidden; +extern const struct erfc_data +{ + struct + { + double erfc, scale; + } tab[3488]; +} __erfc_data attribute_hidden; + +extern const struct erfcf_data +{ + struct + { + float erfc, scale; + } tab[645]; +} __erfcf_data attribute_hidden; + #endif diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index c26d39e644..116a5404f5 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -1017,11 +1017,19 @@ double: 2 float: 2 ldouble: 4 +Function: "erfc_advsimd": +double: 1 +float: 1 + Function: "erfc_downward": double: 4 float: 4 ldouble: 5 +Function: "erfc_sve": +double: 1 +float: 1 + Function: "erfc_towardzero": double: 3 float: 3 diff --git a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist index 396082f6a7..26c3fbf18b 100644 --- a/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/aarch64/libmvec.abilist @@ -82,6 +82,8 @@ GLIBC_2.40 _ZGVnN2v_atanhf F GLIBC_2.40 _ZGVnN2v_cosh F GLIBC_2.40 _ZGVnN2v_coshf F GLIBC_2.40 _ZGVnN2v_erf F +GLIBC_2.40 _ZGVnN2v_erfc F +GLIBC_2.40 _ZGVnN2v_erfcf F GLIBC_2.40 _ZGVnN2v_erff F GLIBC_2.40 _ZGVnN2v_sinh F GLIBC_2.40 _ZGVnN2v_sinhf F @@ -91,6 +93,7 @@ GLIBC_2.40 _ZGVnN4v_acoshf F GLIBC_2.40 _ZGVnN4v_asinhf F GLIBC_2.40 _ZGVnN4v_atanhf F GLIBC_2.40 _ZGVnN4v_coshf F +GLIBC_2.40 _ZGVnN4v_erfcf F GLIBC_2.40 _ZGVnN4v_erff F GLIBC_2.40 _ZGVnN4v_sinhf F GLIBC_2.40 _ZGVnN4v_tanhf F @@ -103,6 +106,8 @@ GLIBC_2.40 _ZGVsMxv_atanhf F GLIBC_2.40 _ZGVsMxv_cosh F GLIBC_2.40 _ZGVsMxv_coshf F GLIBC_2.40 _ZGVsMxv_erf F +GLIBC_2.40 _ZGVsMxv_erfc F +GLIBC_2.40 _ZGVsMxv_erfcf F GLIBC_2.40 _ZGVsMxv_erff F GLIBC_2.40 _ZGVsMxv_sinh F GLIBC_2.40 _ZGVsMxv_sinhf F