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101 lines
3.7 KiB
C
101 lines
3.7 KiB
C
/* Single-precision SVE log1p
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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_f32.h"
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static const struct data
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{
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float poly[8];
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float ln2, exp_bias;
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uint32_t four, three_quarters;
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} data = {.poly = {/* Do not store first term of polynomial, which is -0.5, as
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this can be fmov-ed directly instead of including it in
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the main load-and-mla polynomial schedule. */
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0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f,
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-0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f,
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0x1.abcb6p-4f, -0x1.6f0d5ep-5f},
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.ln2 = 0x1.62e43p-1f,
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.exp_bias = 0x1p-23f,
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.four = 0x40800000,
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.three_quarters = 0x3f400000};
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#define SignExponentMask 0xff800000
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static svfloat32_t NOINLINE
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special_case (svfloat32_t x, svfloat32_t y, svbool_t special)
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{
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return sv_call_f32 (log1pf, x, y, special);
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}
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/* Vector log1pf approximation using polynomial on reduced interval. Worst-case
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error is 1.27 ULP very close to 0.5.
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_ZGVsMxv_log1pf(0x1.fffffep-2) got 0x1.9f324p-2
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want 0x1.9f323ep-2. */
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svfloat32_t SV_NAME_F1 (log1p) (svfloat32_t x, svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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/* x < -1, Inf/Nan. */
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svbool_t special = svcmpeq (pg, svreinterpret_u32 (x), 0x7f800000);
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special = svorn_z (pg, special, svcmpge (pg, x, -1));
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/* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m
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is in [-0.25, 0.5]):
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log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2).
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We approximate log1p(m) with a polynomial, then scale by
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k*log(2). Instead of doing this directly, we use an intermediate
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scale factor s = 4*k*log(2) to ensure the scale is representable
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as a normalised fp32 number. */
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svfloat32_t m = svadd_x (pg, x, 1);
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/* Choose k to scale x to the range [-1/4, 1/2]. */
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svint32_t k
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= svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters),
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sv_s32 (SignExponentMask));
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/* Scale x by exponent manipulation. */
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svfloat32_t m_scale = svreinterpret_f32 (
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svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k)));
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/* Scale up to ensure that the scale factor is representable as normalised
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fp32 number, and scale m down accordingly. */
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svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four));
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m_scale = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1), s, 0.25));
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/* Evaluate polynomial on reduced interval. */
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svfloat32_t ms2 = svmul_x (pg, m_scale, m_scale),
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ms4 = svmul_x (pg, ms2, ms2);
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svfloat32_t p = sv_estrin_7_f32_x (pg, m_scale, ms2, ms4, d->poly);
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p = svmad_x (pg, m_scale, p, -0.5);
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p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p));
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/* The scale factor to be applied back at the end - by multiplying float(k)
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by 2^-23 we get the unbiased exponent of k. */
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svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->exp_bias);
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/* Apply the scaling back. */
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svfloat32_t y = svmla_x (pg, p, scale_back, d->ln2);
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if (__glibc_unlikely (svptest_any (pg, special)))
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return special_case (x, y, special);
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return y;
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}
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