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112 lines
4.0 KiB
C
112 lines
4.0 KiB
C
/* Double-precision vector (SVE) exp2 function
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Copyright (C) 2023 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 N (1 << V_EXP_TABLE_BITS)
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#define BigBound 1022
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#define UOFlowBound 1280
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static const struct data
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{
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double poly[4];
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double shift, big_bound, uoflow_bound;
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} data = {
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/* Coefficients are computed using Remez algorithm with
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minimisation of the absolute error. */
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.poly = { 0x1.62e42fefa3686p-1, 0x1.ebfbdff82c241p-3, 0x1.c6b09b16de99ap-5,
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0x1.3b2abf5571ad8p-7 },
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.shift = 0x1.8p52 / N,
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.uoflow_bound = UOFlowBound,
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.big_bound = BigBound,
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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->uoflow_bound);
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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 exp2.
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Maximum measured error is 1.65 ulp.
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_ZGVsMxv_exp2(-0x1.4c264ab5b559bp-6) got 0x1.f8db0d4df721fp-1
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want 0x1.f8db0d4df721dp-1. */
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svfloat64_t SV_NAME_D1 (exp2) (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->big_bound);
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svbool_t special = svnot_z (pg, no_big_scale);
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/* Reduce x to k/N + r, where k is integer and r in [-1/2N, 1/2N]. */
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svfloat64_t shift = sv_f64 (d->shift);
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svfloat64_t kd = svadd_x (pg, x, shift);
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svuint64_t ki = svreinterpret_u64 (kd);
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/* kd = k/N. */
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kd = svsub_x (pg, kd, shift);
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svfloat64_t r = svsub_x (pg, x, kd);
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/* scale ~= 2^(k/N). */
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svuint64_t idx = svand_x (pg, ki, N - 1);
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svuint64_t sbits = svld1_gather_index (pg, __v_exp_data, idx);
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/* This is only a valid scale when -1023*N < k < 1024*N. */
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svuint64_t top = svlsl_x (pg, ki, 52 - V_EXP_TABLE_BITS);
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svfloat64_t scale = svreinterpret_f64 (svadd_x (pg, sbits, top));
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/* Approximate exp2(r) using polynomial. */
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svfloat64_t r2 = svmul_x (pg, r, r);
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svfloat64_t p = sv_pairwise_poly_3_f64_x (pg, r, r2, d->poly);
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svfloat64_t y = svmul_x (pg, r, p);
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/* Assemble exp2(x) = exp2(r) * scale. */
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if (__glibc_unlikely (svptest_any (pg, special)))
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return special_case (pg, scale, y, kd, d);
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return svmla_x (pg, scale, scale, y);
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}
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