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151 lines
5.5 KiB
C
151 lines
5.5 KiB
C
/* Double-precision vector (SVE) asinh function
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Copyright (C) 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 SignMask (0x8000000000000000)
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#define One (0x3ff0000000000000)
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#define Thres (0x5fe0000000000000) /* asuint64 (0x1p511). */
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static const struct data
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{
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double poly[18];
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double ln2, p3, p1, p4, p0, p2;
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uint64_t n;
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uint64_t off;
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} data = {
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/* Polynomial generated using Remez on [2^-26, 1]. */
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.poly
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= { -0x1.55555555554a7p-3, 0x1.3333333326c7p-4, -0x1.6db6db68332e6p-5,
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0x1.f1c71b26fb40dp-6, -0x1.6e8b8b654a621p-6, 0x1.1c4daa9e67871p-6,
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-0x1.c9871d10885afp-7, 0x1.7a16e8d9d2ecfp-7, -0x1.3ddca533e9f54p-7,
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0x1.0becef748dafcp-7, -0x1.b90c7099dd397p-8, 0x1.541f2bb1ffe51p-8,
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-0x1.d217026a669ecp-9, 0x1.0b5c7977aaf7p-9, -0x1.e0f37daef9127p-11,
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0x1.388b5fe542a6p-12, -0x1.021a48685e287p-14, 0x1.93d4ba83d34dap-18 },
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.ln2 = 0x1.62e42fefa39efp-1,
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.p0 = -0x1.ffffffffffff7p-2,
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.p1 = 0x1.55555555170d4p-2,
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.p2 = -0x1.0000000399c27p-2,
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.p3 = 0x1.999b2e90e94cap-3,
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.p4 = -0x1.554e550bd501ep-3,
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.n = 1 << V_LOG_TABLE_BITS,
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.off = 0x3fe6900900000000
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};
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static svfloat64_t NOINLINE
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special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
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{
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return sv_call_f64 (asinh, x, y, special);
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}
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static inline svfloat64_t
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__sv_log_inline (svfloat64_t x, const struct data *d, const svbool_t pg)
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{
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/* Double-precision SVE log, copied from SVE log implementation with some
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cosmetic modification and special-cases removed. See that file for details
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of the algorithm used. */
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svuint64_t ix = svreinterpret_u64 (x);
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svuint64_t tmp = svsub_x (pg, ix, d->off);
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svuint64_t i = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)),
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(d->n - 1) << 1);
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svint64_t k = svasr_x (pg, svreinterpret_s64 (tmp), 52);
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svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52));
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svfloat64_t z = svreinterpret_f64 (iz);
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svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i);
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svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i);
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svfloat64_t ln2_p3 = svld1rq (svptrue_b64 (), &d->ln2);
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svfloat64_t p1_p4 = svld1rq (svptrue_b64 (), &d->p1);
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svfloat64_t r = svmla_x (pg, sv_f64 (-1.0), invc, z);
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svfloat64_t kd = svcvt_f64_x (pg, k);
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svfloat64_t hi = svmla_lane (svadd_x (pg, logc, r), kd, ln2_p3, 0);
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svfloat64_t r2 = svmul_x (pg, r, r);
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svfloat64_t y = svmla_lane (sv_f64 (d->p2), r, ln2_p3, 1);
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svfloat64_t p = svmla_lane (sv_f64 (d->p0), r, p1_p4, 0);
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y = svmla_lane (y, r2, p1_p4, 1);
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y = svmla_x (pg, p, r2, y);
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y = svmla_x (pg, hi, r2, y);
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return y;
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}
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/* Double-precision implementation of SVE asinh(x).
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asinh is very sensitive around 1, so it is impractical to devise a single
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low-cost algorithm which is sufficiently accurate on a wide range of input.
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Instead we use two different algorithms:
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asinh(x) = sign(x) * log(|x| + sqrt(x^2 + 1) if |x| >= 1
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= sign(x) * (|x| + |x|^3 * P(x^2)) otherwise
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where log(x) is an optimized log approximation, and P(x) is a polynomial
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shared with the scalar routine. The greatest observed error 2.51 ULP, in
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|x| >= 1:
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_ZGVsMxv_asinh(0x1.170469d024505p+0) got 0x1.e3181c43b0f36p-1
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want 0x1.e3181c43b0f39p-1. */
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svfloat64_t SV_NAME_D1 (asinh) (svfloat64_t x, const svbool_t pg)
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{
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const struct data *d = ptr_barrier (&data);
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svuint64_t ix = svreinterpret_u64 (x);
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svuint64_t iax = svbic_x (pg, ix, SignMask);
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svuint64_t sign = svand_x (pg, ix, SignMask);
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svfloat64_t ax = svreinterpret_f64 (iax);
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svbool_t ge1 = svcmpge (pg, iax, One);
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svbool_t special = svcmpge (pg, iax, Thres);
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/* Option 1: |x| >= 1.
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Compute asinh(x) according by asinh(x) = log(x + sqrt(x^2 + 1)). */
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svfloat64_t option_1 = sv_f64 (0);
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if (__glibc_likely (svptest_any (pg, ge1)))
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{
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svfloat64_t x2 = svmul_x (pg, ax, ax);
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option_1 = __sv_log_inline (
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svadd_x (pg, ax, svsqrt_x (pg, svadd_x (pg, x2, 1))), d, pg);
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}
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/* Option 2: |x| < 1.
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Compute asinh(x) using a polynomial.
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The largest observed error in this region is 1.51 ULPs:
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_ZGVsMxv_asinh(0x1.fe12bf8c616a2p-1) got 0x1.c1e649ee2681bp-1
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want 0x1.c1e649ee2681dp-1. */
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svfloat64_t option_2 = sv_f64 (0);
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if (__glibc_likely (svptest_any (pg, svnot_z (pg, ge1))))
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{
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svfloat64_t x2 = svmul_x (pg, ax, ax);
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svfloat64_t x4 = svmul_x (pg, x2, x2);
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svfloat64_t p = sv_pw_horner_17_f64_x (pg, x2, x4, d->poly);
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option_2 = svmla_x (pg, ax, p, svmul_x (pg, x2, ax));
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}
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/* Choose the right option for each lane. */
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svfloat64_t y = svsel (ge1, option_1, option_2);
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if (__glibc_unlikely (svptest_any (pg, special)))
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return special_case (
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x, svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign)),
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special);
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return svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign));
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}
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