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128 lines
4.9 KiB
C
128 lines
4.9 KiB
C
/* Double-precision vector (SVE) exp10 function.
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Copyright (C) 2023-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include "sv_math.h"
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#include "poly_sve_f64.h"
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#define SpecialBound 307.0 /* floor (log10 (2^1023)). */
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static const struct data
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{
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double poly[5];
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double shift, log10_2, log2_10_hi, log2_10_lo, scale_thres, special_bound;
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} data = {
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/* Coefficients generated using Remez algorithm.
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rel error: 0x1.9fcb9b3p-60
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abs error: 0x1.a20d9598p-60 in [ -log10(2)/128, log10(2)/128 ]
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max ulp err 0.52 +0.5. */
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.poly = { 0x1.26bb1bbb55516p1, 0x1.53524c73cd32ap1, 0x1.0470591daeafbp1,
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0x1.2bd77b1361ef6p0, 0x1.142b5d54e9621p-1 },
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/* 1.5*2^46+1023. This value is further explained below. */
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.shift = 0x1.800000000ffc0p+46,
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.log10_2 = 0x1.a934f0979a371p1, /* 1/log2(10). */
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.log2_10_hi = 0x1.34413509f79ffp-2, /* log2(10). */
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.log2_10_lo = -0x1.9dc1da994fd21p-59,
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.scale_thres = 1280.0,
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.special_bound = SpecialBound,
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};
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#define SpecialOffset 0x6000000000000000 /* 0x1p513. */
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/* SpecialBias1 + SpecialBias1 = asuint(1.0). */
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#define SpecialBias1 0x7000000000000000 /* 0x1p769. */
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#define SpecialBias2 0x3010000000000000 /* 0x1p-254. */
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/* Update of both special and non-special cases, if any special case is
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detected. */
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static inline svfloat64_t
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special_case (svbool_t pg, svfloat64_t s, svfloat64_t y, svfloat64_t n,
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const struct data *d)
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{
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/* s=2^n may overflow, break it up into s=s1*s2,
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such that exp = s + s*y can be computed as s1*(s2+s2*y)
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and s1*s1 overflows only if n>0. */
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/* If n<=0 then set b to 0x6, 0 otherwise. */
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svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0. */
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svuint64_t b = svdup_u64_z (p_sign, SpecialOffset);
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/* Set s1 to generate overflow depending on sign of exponent n. */
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svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
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/* Offset s to avoid overflow in final result if n is below threshold. */
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svfloat64_t s2 = svreinterpret_f64 (
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svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));
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/* |n| > 1280 => 2^(n) overflows. */
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svbool_t p_cmp = svacgt (pg, n, d->scale_thres);
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svfloat64_t r1 = svmul_x (pg, s1, s1);
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svfloat64_t r2 = svmla_x (pg, s2, s2, y);
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svfloat64_t r0 = svmul_x (pg, r2, s1);
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return svsel (p_cmp, r1, r0);
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}
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/* Fast vector implementation of exp10 using FEXPA instruction.
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Maximum measured error is 1.02 ulp.
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SV_NAME_D1 (exp10)(-0x1.2862fec805e58p+2) got 0x1.885a89551d782p-16
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want 0x1.885a89551d781p-16. */
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svfloat64_t SV_NAME_D1 (exp10) (svfloat64_t x, svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svbool_t no_big_scale = svacle (pg, x, d->special_bound);
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svbool_t special = svnot_z (pg, no_big_scale);
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/* n = round(x/(log10(2)/N)). */
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svfloat64_t shift = sv_f64 (d->shift);
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svfloat64_t z = svmla_x (pg, shift, x, d->log10_2);
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svfloat64_t n = svsub_x (pg, z, shift);
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/* r = x - n*log10(2)/N. */
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svfloat64_t log2_10 = svld1rq (svptrue_b64 (), &d->log2_10_hi);
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svfloat64_t r = x;
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r = svmls_lane (r, n, log2_10, 0);
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r = svmls_lane (r, n, log2_10, 1);
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/* scale = 2^(n/N), computed using FEXPA. FEXPA does not propagate NaNs, so
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for consistent NaN handling we have to manually propagate them. This
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comes at significant performance cost. */
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svuint64_t u = svreinterpret_u64 (z);
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svfloat64_t scale = svexpa (u);
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/* Approximate exp10(r) using polynomial. */
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svfloat64_t r2 = svmul_x (pg, r, r);
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svfloat64_t y = svmla_x (pg, svmul_x (pg, r, d->poly[0]), r2,
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sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly + 1));
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/* Assemble result as exp10(x) = 2^n * exp10(r). If |x| > SpecialBound
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multiplication may overflow, so use special case routine. */
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if (__glibc_unlikely (svptest_any (pg, special)))
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{
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/* FEXPA zeroes the sign bit, however the sign is meaningful to the
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special case function so needs to be copied.
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e = sign bit of u << 46. */
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svuint64_t e = svand_x (pg, svlsl_x (pg, u, 46), 0x8000000000000000);
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/* Copy sign to scale. */
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scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale)));
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return special_case (pg, scale, y, n, d);
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}
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/* No special case. */
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return svmla_x (pg, scale, scale, y);
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}
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