@@ -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
@@ -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;
@@ -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));
@@ -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);
new file mode 100644
@@ -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
+ <https://www.gnu.org/licenses/>. */
+
+#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);
+}
new file mode 100644
@@ -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
+ <https://www.gnu.org/licenses/>. */
+
+#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 },
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+ { 0x1.d1bd6b173b9f2p-856, 0x1.7b25cc6523c3bp-850 },
+ { 0x1.35fc8451ff49ep-856, 0x1.f8db2dc70232bp-851 },
+ { 0x1.9c9712232f548p-857, 0x1.5014bc06e7f91p-851 },
+ { 0x1.128b47439dcd5p-857, 0x1.bf66ba3b9066cp-852 },
+ { 0x1.6d53d2be0a0b6p-858, 0x1.29c2c1dc958dbp-852 },
+ { 0x1.e6122171333dfp-859, 0x1.8c4a9d76af90fp-853 },
+ { 0x1.435229d0cc681p-859, 0x1.07ae5a7347d0bp-853 },
+ { 0x1.ae1371b74ea2dp-860, 0x1.5ed9539dfd0c9p-854 },
+ { 0x1.1e01427183001p-860, 0x1.d2c69c7599edcp-855 },
+ { 0x1.7c589442700ecp-861, 0x1.3677341a98a13p-855 },
+ { 0x1.f9be9e1d7b4e4p-862, 0x1.9cf2c5625685ep-856 },
+ { 0x1.5033c96eb757p-862, 0x1.1298aebe8af0fp-856 },
+ { 0x1.bef014f36ffa9p-863, 0x1.6d2655c8560ebp-857 },
+ { 0x1.290979be09b3bp-863, 0x1.e58166789d0bcp-858 },
+ { 0x1.8ac6ba86dcc3cp-864, 0x1.42b9e90b536b6p-858 },
+ { 0x1.064e638fb2517p-864, 0x1.acfe7e64002b1p-859 },
+ { 0x1.5c884857d8adep-865, 0x1.1d179e12ade6ep-859 },
+ { 0x1.cf0beaeb1b319p-866, 0x1.7ae01eb0f55cbp-860 },
+ { 0x1.338e29511ffcdp-866, 0x1.f772a9e0423a1p-861 },
+ { 0x1.9881a23b2ff9bp-867, 0x1.4e72e15f0f016p-861 },
+ { 0x1.0f43798c4f845p-867, 0x1.bc4e2f5a8c9afp-862 },
+ { 0x1.6836e63bd7d88p-868, 0x1.27165d875ec78p-862 },
+ { 0x1.de466f9c32fdap-869, 0x1.87eb54ae1860dp-863 },
+ { 0x1.3d79f883687bfp-869, 0x1.043b38d103ec9p-863 },
+ { 0x1.a56d48500b8a3p-870, 0x1.598a7d65e3b67p-864 },
+ { 0x1.17ac327f9b5e5p-870, 0x1.cac2d1ee89db1p-865 },
+ { 0x1.73278f241bb95p-871, 0x1.308090afcd9f3p-865 },
+ { 0x1.ec801820c3f3dp-872, 0x1.942d41e7bf2a3p-866 },
+ { 0x1.46b841565ab3ep-872, 0x1.0c34dc595f4bfp-866 },
+ { 0x1.b16ea850bfa34p-873, 0x1.63e9cb83e74b2p-867 },
+ { 0x1.1f76e44abf0ecp-873, 0x1.d83e5a3ffd7adp-868 },
+ { 0x1.7d432d7dd0ca1p-874, 0x1.39428e0fd00c5p-868 },
+ { 0x1.f99abec00b682p-875, 0x1.9f8c2eadfb109p-869 },
+ { 0x1.4f35579392d4bp-875, 0x1.13957092e7741p-869 },
+ { 0x1.bc6c19eee10e8p-876, 0x1.6d7ad6ac744f9p-870 },
+ { 0x1.2692d6adc530fp-876, 0x1.e4a41e3c393c2p-871 },
+ { 0x1.8673fad41c337p-877, 0x1.4149a31665d1ep-871 },
+ { 0x1.02bd066e6e446p-877, 0x1.a9efbad7c9909p-872 },
+ { 0x1.56dece3f159c3p-878, 0x1.1a4d14ca40e6p-872 },
+ { 0x1.c64dabfd6babdp-879, 0x1.7628f37011dc7p-873 },
+ { 0x1.2cf07ed3ac7cap-879, 0x1.efd93aae49244p-874 },
+ { 0x1.8ea5cdb1b77f8p-880, 0x1.4884565714d83p-874 },
+ { 0x1.0801f05da3babp-880, 0x1.b341347ab9d2ep-875 },
+ { 0x1.5da3ba0723cbcp-881, 0x1.204d0f497ca7dp-875 },
+ { 0x1.cefd7b19fc691p-882, 0x1.7de10a24a9be3p-876 },
+ { 0x1.3281b7ca3d771p-882, 0x1.f9c4f419d97b9p-877 },
+ { 0x1.95c663259c5d8p-883, 0x1.4ee2a6bb63f1dp-877 },
+ { 0x1.0c90568fe453bp-883, 0x1.bb6bea4d790c6p-878 },
+ { 0x1.6374ef6370a23p-884, 0x1.258802fee3a1bp-878 },
+ { 0x1.d668024e6e773p-885, 0x1.8491dcb50d65p-879 },
+ { 0x1.3739f6c74a992p-885, 0x1.012888bcf5e1bp-879 },
+ { 0x1.9bc5a2748239p-886, 0x1.5456466d99824p-880 },
+ { 0x1.105de86fb726ep-886, 0x1.c25d7813e5a28p-881 },
+ { 0x1.68453b252f9afp-887, 0x1.29f220ff323bdp-881 },
+ { 0x1.dc7c640bf856fp-888, 0x1.8a2c46b36447dp-882 },
+ { 0x1.3b0e7a2d8004dp-888, 0x1.04b5178932d9ep-882 },
+ { 0x1.a095d99893beap-889, 0x1.58d2d04dcdef9p-883 },
+ { 0x1.1361f24d04a1ep-889, 0x1.c8060b8a624d8p-884 },
+ { 0x1.6c0994513d45bp-890, 0x1.2d8154e3020f5p-884 },
+ { 0x1.e12caa0268707p-891, 0x1.8ea37661d565fp-885 },
+ { 0x1.3df6725a60cf5p-891, 0x1.078003d294269p-885 },
+ { 0x1.a42bf15180a09p-892, 0x1.5c4df6da1a5fp-886 },
+ { 0x1.15957e82800c6p-892, 0x1.cc58a0676d26ep-887 },
+ { 0x1.6eb9463d29a0dp-893, 0x1.302d6b1661efp-887 },
+ { 0x1.e46dfa81a2018p-894, 0x1.91ed1d851d1ddp-888 },
+ { 0x1.3feb236502138p-894, 0x1.0982d94421652p-888 },
+ { 0x1.a67f97b02e026p-895, 0x1.5ebfab91b4a2bp-889 },
+ { 0x1.16f37032d6085p-895, 0x1.cf4b3235443f5p-890 },
+ { 0x1.704e120e656fdp-896, 0x1.31f0304f01ddbp-890 },
+ { 0x1.e638c247f445dp-897, 0x1.940198fd0e1c2p-891 },
+ { 0x1.40e7ff18c854cp-897, 0x1.0ab8eaa8fae67p-891 },
+ { 0x1.a78b6039c7039p-898, 0x1.60223e0067b2cp-892 },
+ { 0x1.1778970df4481p-898, 0x1.d0d6e2f89dd66p-893 },
+ { 0x1.70c446e7535ccp-899, 0x1.32c589802b4bap-893 },
+ { 0x1.e688d1dc06742p-900, 0x1.94dc0e4e3bd62p-894 },
+ { 0x1.40eab69ffb357p-900, 0x1.0b1f64079cf15p-894 },
+ { 0x1.a74cd8f49285bp-901, 0x1.607271cb1c23p-895 },
+ { 0x1.1723bbb37e71p-901, 0x1.d0f815d3e30e4p-896 },
+ { 0x1.701ad03f5aba2p-902, 0x1.32ab83cb1b9aap-896 },
+ { 0x1.e55d6dd34aeb5p-903, 0x1.947a7e7d08e62p-897 },
+ { 0x1.3ff3437e5e592p-903, 0x1.0ab555a059592p-897 },
+ { 0x1.a5c493ec4b75bp-904, 0x1.5faf8b45ee11cp-898 },
+ { 0x1.15f5a46f2a8c5p-904, 0x1.cfae7d166a387p-899 },
+ { 0x1.6e533a1804da5p-905, 0x1.31a25c153692fp-899 },
+ { 0x1.e2b951ac76b4bp-906, 0x1.92ddcdd3a585ap-900 },
+ { 0x1.3e03e7aaf4a23p-906, 0x1.097bb793410b5p-900 },
+ { 0x1.a2f624fa2da41p-907, 0x1.5ddb524f58124p-901 },
+ { 0x1.13f112353b2e2p-907, 0x1.ccfd1b6b2b0d1p-902 },
+ { 0x1.6b71aaf8395acp-908, 0x1.2fac7e1ac1a55p-902 },
+ { 0x1.dea2a52e6f8d6p-909, 0x1.9009c068a7447p-903 },
+ { 0x1.3b2124c85eb7dp-909, 0x1.077566199da13p-903 },
+ { 0x1.9ee813dcc82f4p-910, 0x1.5afa0b60e30adp-904 },
+ { 0x1.111ab5ef7d9cep-910, 0x1.c8ea38207b48cp-905 },
+ { 0x1.677cd3ce598a2p-911, 0x1.2cce7b0334e93p-905 },
+ { 0x1.d922e485849dfp-912, 0x1.8c04eb792831bp-906 },
+ { 0x1.3751aaab95803p-912, 0x1.04a716678c7d9p-906 },
+ { 0x1.99a3c2eb312dfp-913, 0x1.571266fb205e7p-907 },
+ { 0x1.0d791e54efc95p-913, 0x1.c37f46c8a36cep-908 },
+ { 0x1.627dd610c1f2fp-914, 0x1.290ef7aa6784ep-908 },
+ { 0x1.d246bba093dddp-915, 0x1.86d89be61c44fp-909 },
+ { 0x1.329e3d8fc35e5p-915, 0x1.011744722e8f8p-909 },
+ { 0x1.93354aecb0f91p-916, 0x1.522d67c700dd9p-910 },
+ { 0x1.09149eae599f4p-916, 0x1.bcc8c2b79e5e6p-911 },
+ { 0x1.5c8020a89d6a7p-917, 0x1.247692feaf7c7p-911 },
+ { 0x1.ca1dd59404578p-918, 0x1.8090b25f1fb1cp-912 },
+ { 0x1.2d1194826d1d9p-918, 0x1.f99c33fa36826p-913 },
+ { 0x1.8bab4cd7bc185p-919, 0x1.4c563ff8738edp-913 },
+ { 0x1.03f72f0fa181cp-919, 0x1.b4d5ff233ee8bp-914 },
+ { 0x1.559144638d7d2p-920, 0x1.1f0fc4fe41aefp-914 },
+ { 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 },
+},
+};
new file mode 100644
@@ -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
+ <https://www.gnu.org/licenses/>. */
+
+#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);
+}
new file mode 100644
@@ -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
+ <https://www.gnu.org/licenses/>. */
+
+#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)
new file mode 100644
@@ -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
+ <https://www.gnu.org/licenses/>. */
+
+#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 },
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+ { 0x1.566cep-39, 0x1.4527acp-35 },
+ { 0x1.0dffep-39, 0x1.00e7acp-35 },
+ { 0x1.a99426p-40, 0x1.95c358p-36 },
+ { 0x1.4f3d92p-40, 0x1.4047cep-36 },
+ { 0x1.07f35ep-40, 0x1.f95dcep-37 },
+ { 0x1.9f70cp-41, 0x1.8e82cep-37 },
+ { 0x1.46c77ap-41, 0x1.3a1882p-37 },
+ { 0x1.00ea48p-41, 0x1.eee1d4p-38 },
+ { 0x1.93c7acp-42, 0x1.85ac18p-38 },
+ { 0x1.3d256ap-42, 0x1.32ae04p-38 },
+ { 0x1.f1f59p-43, 0x1.e27d88p-39 },
+ { 0x1.86bd6ap-43, 0x1.7b5bdap-39 },
+ { 0x1.327554p-43, 0x1.2a2036p-39 },
+ { 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 },
+ },
+ };
new file mode 100644
@@ -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
+ <https://www.gnu.org/licenses/>. */
+
+#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);
+}
@@ -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)
@@ -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)
@@ -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)
@@ -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)
@@ -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
@@ -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
@@ -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