@@ -1,17 +1,18 @@
-float-advsimd-funcs = cos sin log
+float-advsimd-funcs = cos sin log exp
-double-advsimd-funcs = cos sin log
+double-advsimd-funcs = cos sin log exp
-float-sve-funcs = cos sin log
+float-sve-funcs = cos sin log exp
-double-sve-funcs = cos sin log
+double-sve-funcs = cos sin log exp
ifeq ($(subdir),mathvec)
libmvec-support = $(addsuffix f_advsimd,$(float-advsimd-funcs)) \
$(addsuffix _advsimd,$(double-advsimd-funcs)) \
$(addsuffix f_sve,$(float-sve-funcs)) \
$(addsuffix _sve,$(double-sve-funcs)) \
- v_log_data
+ v_log_data \
+ v_exp_data
endif
sve-cflags = -march=armv8-a+sve
@@ -1,13 +1,17 @@
libmvec {
GLIBC_2.38 {
_ZGVnN2v_cos;
+ _ZGVnN2v_exp;
_ZGVnN2v_log;
_ZGVnN2v_sin;
_ZGVnN4v_cosf;
+ _ZGVnN4v_expf;
_ZGVnN4v_logf;
_ZGVnN4v_sinf;
_ZGVsMxv_cos;
_ZGVsMxv_cosf;
+ _ZGVsMxv_exp;
+ _ZGVsMxv_expf;
_ZGVsMxv_log;
_ZGVsMxv_logf;
_ZGVsMxv_sin;
@@ -50,10 +50,12 @@ typedef __SVBool_t __sv_bool_t;
# define __vpcs __attribute__ ((__aarch64_vector_pcs__))
__vpcs __f32x4_t _ZGVnN4v_cosf (__f32x4_t);
+__vpcs __f32x4_t _ZGVnN4v_expf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_logf (__f32x4_t);
__vpcs __f32x4_t _ZGVnN4v_sinf (__f32x4_t);
__vpcs __f64x2_t _ZGVnN2v_cos (__f64x2_t);
+__vpcs __f64x2_t _ZGVnN2v_exp (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_log (__f64x2_t);
__vpcs __f64x2_t _ZGVnN2v_sin (__f64x2_t);
@@ -63,10 +65,12 @@ __vpcs __f64x2_t _ZGVnN2v_sin (__f64x2_t);
#ifdef __SVE_VEC_MATH_SUPPORTED
__sv_f32_t _ZGVsMxv_cosf (__sv_f32_t, __sv_bool_t);
+__sv_f32_t _ZGVsMxv_expf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_logf (__sv_f32_t, __sv_bool_t);
__sv_f32_t _ZGVsMxv_sinf (__sv_f32_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_cos (__sv_f64_t, __sv_bool_t);
+__sv_f64_t _ZGVsMxv_exp (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_log (__sv_f64_t, __sv_bool_t);
__sv_f64_t _ZGVsMxv_sin (__sv_f64_t, __sv_bool_t);
new file mode 100644
@@ -0,0 +1,136 @@
+/* Double-precision vector (Advanced SIMD) exp function.
+
+ Copyright (C) 2023 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"
+
+#define N (1 << V_EXP_TABLE_BITS)
+#define IndexMask (N - 1)
+
+const static volatile struct
+{
+ float64x2_t poly[3];
+ float64x2_t inv_ln2, ln2_hi, ln2_lo, shift;
+#if !WANT_SIMD_EXCEPT
+ float64x2_t special_bound, scale_thresh;
+#endif
+} data = {
+ /* maxerr: 1.88 +0.5 ulp
+ rel error: 1.4337*2^-53
+ abs error: 1.4299*2^-53 in [ -ln2/256, ln2/256 ]. */
+ .poly = { V2 (0x1.ffffffffffd43p-2), V2 (0x1.55555c75adbb2p-3),
+ V2 (0x1.55555da646206p-5) },
+#if !WANT_SIMD_EXCEPT
+ .scale_thresh = V2 (163840.0), /* 1280.0 * N. */
+ .special_bound = V2 (704.0),
+#endif
+ .inv_ln2 = V2 (0x1.71547652b82fep7), /* N/ln2. */
+ .ln2_hi = V2 (0x1.62e42fefa39efp-8), /* ln2/N. */
+ .ln2_lo = V2 (0x1.abc9e3b39803f3p-63),
+ .shift = V2 (0x1.8p+52)
+};
+
+#define C(i) data.poly[i]
+#define Tab __v_exp_data
+
+#if WANT_SIMD_EXCEPT
+
+# define TinyBound v_u64 (0x2000000000000000) /* asuint64 (0x1p-511). */
+# define BigBound v_u64 (0x4080000000000000) /* asuint64 (0x1p9). */
+# define SpecialBound v_u64 (0x2080000000000000) /* BigBound - TinyBound. */
+
+static inline float64x2_t VPCS_ATTR
+special_case (float64x2_t x, float64x2_t y, uint64x2_t cmp)
+{
+ /* If fenv exceptions are to be triggered correctly, fall back to the scalar
+ routine to special lanes. */
+ return v_call_f64 (exp, x, y, cmp);
+}
+
+#else
+
+# define SpecialOffset v_u64 (0x6000000000000000) /* 0x1p513. */
+/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
+# define SpecialBias1 v_u64 (0x7000000000000000) /* 0x1p769. */
+# define SpecialBias2 v_u64 (0x3010000000000000) /* 0x1p-254. */
+
+static float64x2_t VPCS_ATTR NOINLINE
+special_case (float64x2_t s, float64x2_t y, float64x2_t n)
+{
+ /* 2^(n/N) may overflow, break it up into s1*s2. */
+ uint64x2_t b = vandq_u64 (vcltzq_f64 (n), SpecialOffset);
+ float64x2_t s1 = vreinterpretq_f64_u64 (vsubq_u64 (SpecialBias1, b));
+ float64x2_t s2 = vreinterpretq_f64_u64 (
+ vaddq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (s), SpecialBias2), b));
+ uint64x2_t cmp = vcagtq_f64 (n, data.scale_thresh);
+ float64x2_t r1 = vmulq_f64 (s1, s1);
+ float64x2_t r0 = vmulq_f64 (vfmaq_f64 (s2, y, s2), s1);
+ return vbslq_f64 (cmp, r1, r0);
+}
+
+#endif
+
+float64x2_t VPCS_ATTR V_NAME_D1 (exp) (float64x2_t x)
+{
+ float64x2_t n, r, r2, s, y, z;
+ uint64x2_t cmp, u, e;
+
+#if WANT_SIMD_EXCEPT
+ /* If any lanes are special, mask them with 1 and retain a copy of x to allow
+ special_case to fix special lanes later. This is only necessary if fenv
+ exceptions are to be triggered correctly. */
+ float64x2_t xm = x;
+ uint64x2_t iax = vreinterpretq_u64_f64 (vabsq_f64 (x));
+ cmp = vcgeq_u64 (vsubq_u64 (iax, TinyBound), SpecialBound);
+ if (unlikely (v_any_u64 (cmp)))
+ x = vbslq_f64 (cmp, v_f64 (1), x);
+#else
+ cmp = vcagtq_f64 (x, data.special_bound);
+#endif
+
+ /* n = round(x/(ln2/N)). */
+ z = vfmaq_f64 (data.shift, x, data.inv_ln2);
+ u = vreinterpretq_u64_f64 (z);
+ n = vsubq_f64 (z, data.shift);
+
+ /* r = x - n*ln2/N. */
+ r = x;
+ r = vfmsq_f64 (r, data.ln2_hi, n);
+ r = vfmsq_f64 (r, data.ln2_lo, n);
+
+ e = vshlq_n_u64 (u, 52 - V_EXP_TABLE_BITS);
+
+ /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4. */
+ r2 = vmulq_f64 (r, r);
+ y = vfmaq_f64 (C (0), C (1), r);
+ y = vfmaq_f64 (y, C (2), r2);
+ y = vfmaq_f64 (r, y, r2);
+
+ /* s = 2^(n/N). */
+ u = (uint64x2_t){ Tab[u[0] & IndexMask], Tab[u[1] & IndexMask] };
+ s = vreinterpretq_f64_u64 (vaddq_u64 (u, e));
+
+ if (unlikely (v_any_u64 (cmp)))
+#if WANT_SIMD_EXCEPT
+ return special_case (xm, vfmaq_f64 (s, y, s), cmp);
+#else
+ return special_case (s, y, n);
+#endif
+
+ return vfmaq_f64 (s, y, s);
+}
new file mode 100644
@@ -0,0 +1,138 @@
+/* Double-precision vector (SVE) exp function.
+
+ Copyright (C) 2023 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 "sv_estrin.h"
+
+static struct
+{
+ double poly[4];
+ double ln2_hi, ln2_lo, inv_ln2, shift, thres;
+} data = {
+ .poly = { /* ulp error: 0.53. */
+ 0x1.fffffffffdbcdp-2, 0x1.555555555444cp-3, 0x1.555573c6a9f7dp-5,
+ 0x1.1111266d28935p-7 },
+ .ln2_hi = 0x1.62e42fefa3800p-1,
+ .ln2_lo = 0x1.ef35793c76730p-45,
+ /* 1/ln2. */
+ .inv_ln2 = 0x1.71547652b82fep+0,
+ /* 1.5*2^46+1023. This value is further explained below. */
+ .shift = 0x1.800000000ffc0p+46,
+ .thres = 704.0,
+};
+
+#define C(i) sv_f64 (data.poly[i])
+#define SpecialOffset 0x6000000000000000 /* 0x1p513. */
+/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
+#define SpecialBias1 0x7000000000000000 /* 0x1p769. */
+#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
+
+/* Update of both special and non-special cases, if any special case is
+ detected. */
+static inline svfloat64_t
+special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n)
+{
+ /* s=2^n may overflow, break it up into s=s1*s2,
+ such that exp = s + s*y can be computed as s1*(s2+s2*y)
+ and s1*s1 overflows only if n>0. */
+
+ /* If n<=0 then set b to 0x6, 0 otherwise. */
+ svbool_t p_sign = svcmple_n_f64 (pg, n, 0.0); /* n <= 0. */
+ svuint64_t b
+ = svdup_n_u64_z (p_sign, SpecialOffset); /* Inactive lanes set to 0. */
+
+ /* Set s1 to generate overflow depending on sign of exponent n. */
+ svfloat64_t s1 = svreinterpret_f64_u64 (
+ svsubr_n_u64_x (pg, b, SpecialBias1)); /* 0x70...0 - b. */
+ /* Offset s to avoid overflow in final result if n is below threshold. */
+ svfloat64_t s2 = svreinterpret_f64_u64 (svadd_u64_x (
+ pg, svsub_n_u64_x (pg, svreinterpret_u64_f64 (s), SpecialBias2),
+ b)); /* as_u64 (s) - 0x3010...0 + b. */
+
+ /* |n| > 1280 => 2^(n) overflows. */
+ svbool_t p_cmp = svacgt_n_f64 (pg, n, 1280.0);
+
+ svfloat64_t r1 = svmul_f64_x (pg, s1, s1);
+ svfloat64_t r2 = svmla_f64_x (pg, s2, s2, y);
+ svfloat64_t r0 = svmul_f64_x (pg, r2, s1);
+
+ return svsel_f64 (p_cmp, r1, r0);
+}
+
+/* SVE exp algorithm. Maximum measured error is 1.01ulps:
+ SV_NAME_D1 (exp)(0x1.4619d7b04da41p+6) got 0x1.885d9acc41da7p+117
+ want 0x1.885d9acc41da6p+117. */
+svfloat64_t SV_NAME_D1 (exp) (svfloat64_t x, const svbool_t pg)
+{
+ svbool_t special = svacgt_n_f64 (pg, x, data.thres);
+
+ /* Use a modifed version of the shift used for flooring, such that x/ln2 is
+ rounded to a multiple of 2^-6=1/64, shift = 1.5 * 2^52 * 2^-6 = 1.5 *
+ 2^46.
+
+ n is not an integer but can be written as n = m + i/64, with i and m
+ integer, 0 <= i < 64 and m <= n.
+
+ Bits 5:0 of z will be null every time x/ln2 reaches a new integer value
+ (n=m, i=0), and is incremented every time z (or n) is incremented by 1/64.
+ FEXPA expects i in bits 5:0 of the input so it can be used as index into
+ FEXPA hardwired table T[i] = 2^(i/64) for i = 0:63, that will in turn
+ populate the mantissa of the output. Therefore, we use u=asuint(z) as
+ input to FEXPA.
+
+ We add 1023 to the modified shift value in order to set bits 16:6 of u to
+ 1, such that once these bits are moved to the exponent of the output of
+ FEXPA, we get the exponent of 2^n right, i.e. we get 2^m. */
+ svfloat64_t z = svmla_n_f64_x (pg, sv_f64 (data.shift), x, data.inv_ln2);
+ svuint64_t u = svreinterpret_u64_f64 (z);
+ svfloat64_t n = svsub_n_f64_x (pg, z, data.shift);
+
+ /* r = x - n * ln2, r is in [-ln2/(2N), ln2/(2N)]. */
+ svfloat64_t ln2 = svld1rq_f64 (svptrue_b64 (), &data.ln2_hi);
+ svfloat64_t r = svmls_lane_f64 (x, n, ln2, 0);
+ r = svmls_lane_f64 (r, n, ln2, 1);
+
+ /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5. */
+ svfloat64_t r2 = svmul_f64_x (pg, r, r);
+ svfloat64_t y = svmla_f64_x (pg, r, ESTRIN_3 (pg, r, r2, C), r2);
+
+ /* s = 2^n, computed using FEXPA. FEXPA does not propagate NaNs, so for
+ consistent NaN handling we have to manually propagate them. This comes at
+ significant performance cost. */
+ svfloat64_t s = svexpa_f64 (u);
+
+ /* Assemble result as exp(x) = 2^n * exp(r). If |x| > Thresh the
+ multiplication may overflow, so use special case routine. */
+
+ if (unlikely (svptest_any (pg, special)))
+ {
+ /* FEXPA zeroes the sign bit, however the sign is meaningful to the
+ special case function so needs to be copied.
+ e = sign bit of u << 46. */
+ svuint64_t e
+ = svand_n_u64_x (pg, svlsl_n_u64_x (pg, u, 46), 0x8000000000000000);
+ /* Copy sign to s. */
+ s = svreinterpret_f64_u64 (
+ svadd_u64_x (pg, e, svreinterpret_u64_f64 (s)));
+ return special_case (pg, s, y, n);
+ }
+
+ /* No special case. */
+ return svmla_f64_x (pg, s, s, y);
+}
new file mode 100644
@@ -0,0 +1,132 @@
+/* Single-precision vector (Advanced SIMD) exp function.
+
+ Copyright (C) 2023 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 volatile struct
+{
+ float32x4_t poly[5];
+ float32x4_t shift, inv_ln2, ln2_hi, ln2_lo;
+ uint32x4_t exponent_bias;
+#if !WANT_SIMD_EXCEPT
+ float32x4_t special_bound, scale_thresh;
+#endif
+} data = {
+ /* maxerr: 1.45358 +0.5 ulp. */
+ .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),
+ .inv_ln2 = V4 (0x1.715476p+0f),
+ .ln2_hi = V4 (0x1.62e4p-1f),
+ .ln2_lo = V4 (0x1.7f7d1cp-20f),
+ .exponent_bias = V4 (0x3f800000),
+#if !WANT_SIMD_EXCEPT
+ .special_bound = V4 (126.0f),
+ .scale_thresh = V4 (192.0f),
+#endif
+};
+
+#define C(i) data.poly[i]
+
+#if WANT_SIMD_EXCEPT
+
+# define TinyBound v_u32 (0x20000000) /* asuint (0x1p-63). */
+# define BigBound v_u32 (0x42800000) /* asuint (0x1p6). */
+# define SpecialBound v_u32 (0x22800000) /* BigBound - TinyBound. */
+
+static float32x4_t VPCS_ATTR NOINLINE
+special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp)
+{
+ /* If fenv exceptions are to be triggered correctly, fall back to the scalar
+ routine to special lanes. */
+ return v_call_f32 (expf, x, y, cmp);
+}
+
+#else
+
+# define SpecialOffset v_u32 (0x82000000)
+# define SpecialBias v_u32 (0x7f000000)
+
+static float32x4_t VPCS_ATTR NOINLINE
+special_case (float32x4_t poly, float32x4_t n, uint32x4_t e, uint32x4_t cmp1,
+ float32x4_t scale)
+{
+ /* 2^n may overflow, break it up into s1*s2. */
+ uint32x4_t b = vandq_u32 (vclezq_f32 (n), SpecialOffset);
+ float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, SpecialBias));
+ float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b));
+ uint32x4_t cmp2 = vcagtq_f32 (n, data.scale_thresh);
+ float32x4_t r2 = vmulq_f32 (s1, s1);
+ float32x4_t r1 = vmulq_f32 (vfmaq_f32 (s2, poly, s2), s1);
+ /* Similar to r1 but avoids double rounding in the subnormal range. */
+ float32x4_t r0 = vfmaq_f32 (scale, poly, scale);
+ float32x4_t r = vbslq_f32 (cmp1, r1, r0);
+ return vbslq_f32 (cmp2, r2, r);
+}
+
+#endif
+
+float32x4_t VPCS_ATTR V_NAME_F1 (exp) (float32x4_t x)
+{
+ float32x4_t n, r, r2, scale, p, q, poly, z;
+ uint32x4_t cmp, e;
+
+#if WANT_SIMD_EXCEPT
+ /* asuint(x) - TinyBound >= BigBound - TinyBound. */
+ cmp = vcgeq_u32 (
+ vsubq_u32 (vandq_u32 (vreinterpretq_u32_f32 (x), v_u32 (0x7fffffff)),
+ TinyBound),
+ SpecialBound);
+ 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 (unlikely (v_any_u32 (cmp)))
+ x = vbslq_f32 (cmp, v_f32 (1), x);
+#endif
+
+ /* 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]. */
+ z = vfmaq_f32 (data.shift, x, data.inv_ln2);
+ n = vsubq_f32 (z, data.shift);
+ r = vfmsq_f32 (x, n, data.ln2_hi);
+ r = vfmsq_f32 (r, n, data.ln2_lo);
+ e = vshlq_n_u32 (vreinterpretq_u32_f32 (z), 23);
+ scale = vreinterpretq_f32_u32 (vaddq_u32 (e, data.exponent_bias));
+
+#if !WANT_SIMD_EXCEPT
+ cmp = vcagtq_f32 (n, data.special_bound);
+#endif
+
+ r2 = vmulq_f32 (r, r);
+ 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);
+
+ if (unlikely (v_any_u32 (cmp)))
+#if WANT_SIMD_EXCEPT
+ return special_case (xm, vfmaq_f32 (scale, poly, scale), cmp);
+#else
+ return special_case (poly, n, e, cmp, scale);
+#endif
+
+ return vfmaq_f32 (scale, poly, scale);
+}
new file mode 100644
@@ -0,0 +1,89 @@
+/* Single-precision vector (SVE) exp function.
+
+ Copyright (C) 2023 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 "sv_estrinf.h"
+
+static struct
+{
+ float poly[5];
+ float inv_ln2, ln2_hi, ln2_lo, shift, thres;
+} data = {
+ /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for
+ compatibility with polynomial helpers. */
+ .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,
+ /* 1.5*2^17 + 127. */
+ .shift = 0x1.903f8p17f,
+ /* Roughly 87.3. For x < -Thres, the result is subnormal and not handled
+ correctly by FEXPA. */
+ .thres = 0x1.5d5e2ap+6f,
+};
+
+#define C(i) sv_f32 (data.poly[i])
+#define ExponentBias 0x3f800000
+
+static svfloat32_t NOINLINE
+special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
+{
+ return sv_call_f32 (expf, x, y, special);
+}
+
+/* Optimised single-precision SVE exp function.
+ Worst-case error is 1.04 ulp:
+ SV_NAME_F1 (exp)(0x1.a8eda4p+1) got 0x1.ba74bcp+4
+ want 0x1.ba74bap+4. */
+svfloat32_t SV_NAME_F1 (exp) (svfloat32_t x, const svbool_t pg)
+{
+ /* 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 (last
+ lane is wasted). */
+ svfloat32_t invln2_and_ln2 = svld1rq_f32 (svptrue_b32 (), &data.inv_ln2);
+
+ /* n = round(x/(ln2/N)). */
+ svfloat32_t z = svmla_lane_f32 (sv_f32 (data.shift), x, invln2_and_ln2, 0);
+ svfloat32_t n = svsub_n_f32_x (pg, z, data.shift);
+
+ /* r = x - n*ln2/N. */
+ svfloat32_t r = svmls_lane_f32 (x, n, invln2_and_ln2, 1);
+ r = svmls_lane_f32 (r, n, invln2_and_ln2, 2);
+
+/* scale = 2^(n/N). */
+ svbool_t is_special_case = svacgt_n_f32 (pg, x, data.thres);
+ svfloat32_t scale = svexpa_f32 (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 r2 = svmul_f32_x (pg, r, r);
+ /* Evaluate polynomial use hybrid scheme - offset variant of ESTRIN macro for
+ coefficients 1 to 4, and apply most significant coefficient directly. */
+ svfloat32_t p14 = ESTRIN_3_ (pg, r, r2, C, 1);
+ svfloat32_t p0 = svmul_f32_x (pg, r, C (0));
+ svfloat32_t poly = svmla_f32_x (pg, p0, r2, p14);
+
+ if (unlikely (svptest_any (pg, is_special_case)))
+ return special_case (x, svmla_f32_x (pg, scale, scale, poly),
+ is_special_case);
+
+ return svmla_f32_x (pg, scale, scale, poly);
+}
new file mode 100644
@@ -0,0 +1,23 @@
+/* Helper macros for double-precision Estrin polynomial evaluation
+ in SVE routines.
+
+ Copyright (C) 2023 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/>. */
+
+#define FMA(pg, x, y, z) svmla_f64_x (pg, z, x, y)
+
+#include "sv_estrin_wrap.h"
new file mode 100644
@@ -0,0 +1,89 @@
+/* Helper macros for Estrin polynomial evaluation in SVE routines.
+
+ Copyright (C) 2023 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/>. */
+
+#define ESTRIN_1_(pg, x, c, i) FMA (pg, c (1 + i), x, c (i))
+#define ESTRIN_2_(pg, x, x2, c, i) \
+ FMA (pg, c (2 + i), x2, ESTRIN_1_ (pg, x, c, i))
+#define ESTRIN_3_(pg, x, x2, c, i) \
+ FMA (pg, ESTRIN_1_ (pg, x, c, 2 + i), x2, ESTRIN_1_ (pg, x, c, i))
+#define ESTRIN_4_(pg, x, x2, x4, c, i) \
+ FMA (pg, c (4 + i), x4, ESTRIN_3_ (pg, x, x2, c, i))
+#define ESTRIN_5_(pg, x, x2, x4, c, i) \
+ FMA (pg, ESTRIN_1_ (pg, x, c, 4 + i), x4, ESTRIN_3_ (pg, x, x2, c, i))
+#define ESTRIN_6_(pg, x, x2, x4, c, i) \
+ FMA (pg, ESTRIN_2_ (pg, x, x2, c, 4 + i), x4, ESTRIN_3_ (pg, x, x2, c, i))
+#define ESTRIN_7_(pg, x, x2, x4, c, i) \
+ FMA (pg, ESTRIN_3_ (pg, x, x2, c, 4 + i), x4, ESTRIN_3_ (pg, x, x2, c, i))
+#define ESTRIN_8_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, c (8 + i), x8, ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_9_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, ESTRIN_1_ (pg, x, c, 8 + i), x8, ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_10_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, ESTRIN_2_ (pg, x, x2, c, 8 + i), x8, \
+ ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_11_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, ESTRIN_3_ (pg, x, x2, c, 8 + i), x8, \
+ ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_12_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, ESTRIN_4_ (pg, x, x2, x4, c, 8 + i), x8, \
+ ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_13_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, ESTRIN_5_ (pg, x, x2, x4, c, 8 + i), x8, \
+ ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_14_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, ESTRIN_6_ (pg, x, x2, x4, c, 8 + i), x8, \
+ ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_15_(pg, x, x2, x4, x8, c, i) \
+ FMA (pg, ESTRIN_7_ (pg, x, x2, x4, c, 8 + i), x8, \
+ ESTRIN_7_ (pg, x, x2, x4, c, i))
+#define ESTRIN_16_(pg, x, x2, x4, x8, x16, c, i) \
+ FMA (pg, c (16 + i), x16, ESTRIN_15_ (pg, x, x2, x4, x8, c, i))
+#define ESTRIN_17_(pg, x, x2, x4, x8, x16, c, i) \
+ FMA (pg, ESTRIN_1_ (pg, x, c, 16 + i), x16, \
+ ESTRIN_15_ (pg, x, x2, x4, x8, c, i))
+#define ESTRIN_18_(pg, x, x2, x4, x8, x16, c, i) \
+ FMA (pg, ESTRIN_2_ (pg, x, x2, c, 16 + i), x16, \
+ ESTRIN_15_ (pg, x, x2, x4, x8, c, i))
+#define ESTRIN_19_(pg, x, x2, x4, x8, x16, c, i) \
+ FMA (pg, ESTRIN_3_ (pg, x, x2, c, 16 + i), x16, \
+ ESTRIN_15_ (pg, x, x2, x4, x8, c, i))
+
+#define ESTRIN_1(pg, x, c) ESTRIN_1_ (pg, x, c, 0)
+#define ESTRIN_2(pg, x, x2, c) ESTRIN_2_ (pg, x, x2, c, 0)
+#define ESTRIN_3(pg, x, x2, c) ESTRIN_3_ (pg, x, x2, c, 0)
+#define ESTRIN_4(pg, x, x2, x4, c) ESTRIN_4_ (pg, x, x2, x4, c, 0)
+#define ESTRIN_5(pg, x, x2, x4, c) ESTRIN_5_ (pg, x, x2, x4, c, 0)
+#define ESTRIN_6(pg, x, x2, x4, c) ESTRIN_6_ (pg, x, x2, x4, c, 0)
+#define ESTRIN_7(pg, x, x2, x4, c) ESTRIN_7_ (pg, x, x2, x4, c, 0)
+#define ESTRIN_8(pg, x, x2, x4, x8, c) ESTRIN_8_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_9(pg, x, x2, x4, x8, c) ESTRIN_9_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_10(pg, x, x2, x4, x8, c) ESTRIN_10_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_11(pg, x, x2, x4, x8, c) ESTRIN_11_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_12(pg, x, x2, x4, x8, c) ESTRIN_12_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_13(pg, x, x2, x4, x8, c) ESTRIN_13_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_14(pg, x, x2, x4, x8, c) ESTRIN_14_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_15(pg, x, x2, x4, x8, c) ESTRIN_15_ (pg, x, x2, x4, x8, c, 0)
+#define ESTRIN_16(pg, x, x2, x4, x8, x16, c) \
+ ESTRIN_16_ (pg, x, x2, x4, x8, x16, c, 0)
+#define ESTRIN_17(pg, x, x2, x4, x8, x16, c) \
+ ESTRIN_17_ (pg, x, x2, x4, x8, x16, c, 0)
+#define ESTRIN_18(pg, x, x2, x4, x8, x16, c) \
+ ESTRIN_18_ (pg, x, x2, x4, x8, x16, c, 0)
+#define ESTRIN_19(pg, x, x2, x4, x8, x16, c) \
+ ESTRIN_19_ (pg, x, x2, x4, x8, x16, c, 0)
new file mode 100644
@@ -0,0 +1,23 @@
+/* Helper macros for single-precision Estrin polynomial evaluation
+ in SVE routines.
+
+ Copyright (C) 2023 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/>. */
+
+#define FMA(pg, x, y, z) svmla_f32_x (pg, z, x, y)
+
+#include "sv_estrin_wrap.h"
@@ -24,5 +24,6 @@
#define VEC_TYPE float64x2_t
VPCS_VECTOR_WRAPPER (cos_advsimd, _ZGVnN2v_cos)
+VPCS_VECTOR_WRAPPER (exp_advsimd, _ZGVnN2v_exp)
VPCS_VECTOR_WRAPPER (log_advsimd, _ZGVnN2v_log)
VPCS_VECTOR_WRAPPER (sin_advsimd, _ZGVnN2v_sin)
@@ -33,5 +33,6 @@
}
SVE_VECTOR_WRAPPER (cos_sve, _ZGVsMxv_cos)
+SVE_VECTOR_WRAPPER (exp_sve, _ZGVsMxv_exp)
SVE_VECTOR_WRAPPER (log_sve, _ZGVsMxv_log)
SVE_VECTOR_WRAPPER (sin_sve, _ZGVsMxv_sin)
@@ -24,5 +24,6 @@
#define VEC_TYPE float32x4_t
VPCS_VECTOR_WRAPPER (cosf_advsimd, _ZGVnN4v_cosf)
+VPCS_VECTOR_WRAPPER (expf_advsimd, _ZGVnN4v_expf)
VPCS_VECTOR_WRAPPER (logf_advsimd, _ZGVnN4v_logf)
VPCS_VECTOR_WRAPPER (sinf_advsimd, _ZGVnN4v_sinf)
@@ -33,5 +33,6 @@
}
SVE_VECTOR_WRAPPER (cosf_sve, _ZGVsMxv_cosf)
+SVE_VECTOR_WRAPPER (expf_sve, _ZGVsMxv_expf)
SVE_VECTOR_WRAPPER (logf_sve, _ZGVsMxv_logf)
SVE_VECTOR_WRAPPER (sinf_sve, _ZGVsMxv_sinf)
new file mode 100644
@@ -0,0 +1,66 @@
+/* Scale values for vector exp and exp2
+
+ Copyright (C) 2023 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"
+
+const uint64_t __v_exp_data[] = {
+ 0x3ff0000000000000, 0x3feff63da9fb3335, 0x3fefec9a3e778061,
+ 0x3fefe315e86e7f85, 0x3fefd9b0d3158574, 0x3fefd06b29ddf6de,
+ 0x3fefc74518759bc8, 0x3fefbe3ecac6f383, 0x3fefb5586cf9890f,
+ 0x3fefac922b7247f7, 0x3fefa3ec32d3d1a2, 0x3fef9b66affed31b,
+ 0x3fef9301d0125b51, 0x3fef8abdc06c31cc, 0x3fef829aaea92de0,
+ 0x3fef7a98c8a58e51, 0x3fef72b83c7d517b, 0x3fef6af9388c8dea,
+ 0x3fef635beb6fcb75, 0x3fef5be084045cd4, 0x3fef54873168b9aa,
+ 0x3fef4d5022fcd91d, 0x3fef463b88628cd6, 0x3fef3f49917ddc96,
+ 0x3fef387a6e756238, 0x3fef31ce4fb2a63f, 0x3fef2b4565e27cdd,
+ 0x3fef24dfe1f56381, 0x3fef1e9df51fdee1, 0x3fef187fd0dad990,
+ 0x3fef1285a6e4030b, 0x3fef0cafa93e2f56, 0x3fef06fe0a31b715,
+ 0x3fef0170fc4cd831, 0x3feefc08b26416ff, 0x3feef6c55f929ff1,
+ 0x3feef1a7373aa9cb, 0x3feeecae6d05d866, 0x3feee7db34e59ff7,
+ 0x3feee32dc313a8e5, 0x3feedea64c123422, 0x3feeda4504ac801c,
+ 0x3feed60a21f72e2a, 0x3feed1f5d950a897, 0x3feece086061892d,
+ 0x3feeca41ed1d0057, 0x3feec6a2b5c13cd0, 0x3feec32af0d7d3de,
+ 0x3feebfdad5362a27, 0x3feebcb299fddd0d, 0x3feeb9b2769d2ca7,
+ 0x3feeb6daa2cf6642, 0x3feeb42b569d4f82, 0x3feeb1a4ca5d920f,
+ 0x3feeaf4736b527da, 0x3feead12d497c7fd, 0x3feeab07dd485429,
+ 0x3feea9268a5946b7, 0x3feea76f15ad2148, 0x3feea5e1b976dc09,
+ 0x3feea47eb03a5585, 0x3feea34634ccc320, 0x3feea23882552225,
+ 0x3feea155d44ca973, 0x3feea09e667f3bcd, 0x3feea012750bdabf,
+ 0x3fee9fb23c651a2f, 0x3fee9f7df9519484, 0x3fee9f75e8ec5f74,
+ 0x3fee9f9a48a58174, 0x3fee9feb564267c9, 0x3feea0694fde5d3f,
+ 0x3feea11473eb0187, 0x3feea1ed0130c132, 0x3feea2f336cf4e62,
+ 0x3feea427543e1a12, 0x3feea589994cce13, 0x3feea71a4623c7ad,
+ 0x3feea8d99b4492ed, 0x3feeaac7d98a6699, 0x3feeace5422aa0db,
+ 0x3feeaf3216b5448c, 0x3feeb1ae99157736, 0x3feeb45b0b91ffc6,
+ 0x3feeb737b0cdc5e5, 0x3feeba44cbc8520f, 0x3feebd829fde4e50,
+ 0x3feec0f170ca07ba, 0x3feec49182a3f090, 0x3feec86319e32323,
+ 0x3feecc667b5de565, 0x3feed09bec4a2d33, 0x3feed503b23e255d,
+ 0x3feed99e1330b358, 0x3feede6b5579fdbf, 0x3feee36bbfd3f37a,
+ 0x3feee89f995ad3ad, 0x3feeee07298db666, 0x3feef3a2b84f15fb,
+ 0x3feef9728de5593a, 0x3feeff76f2fb5e47, 0x3fef05b030a1064a,
+ 0x3fef0c1e904bc1d2, 0x3fef12c25bd71e09, 0x3fef199bdd85529c,
+ 0x3fef20ab5fffd07a, 0x3fef27f12e57d14b, 0x3fef2f6d9406e7b5,
+ 0x3fef3720dcef9069, 0x3fef3f0b555dc3fa, 0x3fef472d4a07897c,
+ 0x3fef4f87080d89f2, 0x3fef5818dcfba487, 0x3fef60e316c98398,
+ 0x3fef69e603db3285, 0x3fef7321f301b460, 0x3fef7c97337b9b5f,
+ 0x3fef864614f5a129, 0x3fef902ee78b3ff6, 0x3fef9a51fbc74c83,
+ 0x3fefa4afa2a490da, 0x3fefaf482d8e67f1, 0x3fefba1bee615a27,
+ 0x3fefc52b376bba97, 0x3fefd0765b6e4540, 0x3fefdbfdad9cbe14,
+ 0x3fefe7c1819e90d8, 0x3feff3c22b8f71f1,
+};
@@ -41,4 +41,7 @@ extern const struct v_log_data
double invc[1 << V_LOG_TABLE_BITS];
double logc[1 << V_LOG_TABLE_BITS];
} __v_log_data HIDDEN;
+
+#define V_EXP_TABLE_BITS 7
+extern const uint64_t __v_exp_data[1 << V_EXP_TABLE_BITS] HIDDEN;
#endif
@@ -1005,10 +1005,18 @@ double: 1
float: 1
ldouble: 2
+Function: "exp_advsimd":
+double: 1
+float: 1
+
Function: "exp_downward":
double: 1
float: 1
+Function: "exp_sve":
+double: 1
+float: 1
+
Function: "exp_towardzero":
double: 1
float: 1
@@ -1,11 +1,15 @@
GLIBC_2.38 _ZGVnN2v_cos F
+GLIBC_2.38 _ZGVnN2v_exp F
GLIBC_2.38 _ZGVnN2v_log F
GLIBC_2.38 _ZGVnN2v_sin F
GLIBC_2.38 _ZGVnN4v_cosf F
+GLIBC_2.38 _ZGVnN4v_expf F
GLIBC_2.38 _ZGVnN4v_logf F
GLIBC_2.38 _ZGVnN4v_sinf F
GLIBC_2.38 _ZGVsMxv_cos F
GLIBC_2.38 _ZGVsMxv_cosf F
+GLIBC_2.38 _ZGVsMxv_exp F
+GLIBC_2.38 _ZGVsMxv_expf F
GLIBC_2.38 _ZGVsMxv_log F
GLIBC_2.38 _ZGVsMxv_logf F
GLIBC_2.38 _ZGVsMxv_sin F