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85 lines
3.3 KiB
C
85 lines
3.3 KiB
C
/* Single-precision inline helper for vector (SVE) expm1 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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#ifndef AARCH64_FPU_SV_EXPM1F_INLINE_H
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#define AARCH64_FPU_SV_EXPM1F_INLINE_H
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#include "sv_math.h"
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struct sv_expm1f_data
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{
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/* These 4 are grouped together so they can be loaded as one quadword, then
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used with _lane forms of svmla/svmls. */
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float32_t c2, c4, ln2_hi, ln2_lo;
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float32_t c0, c1, c3, inv_ln2, shift;
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};
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/* Coefficients generated using fpminimax. */
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#define SV_EXPM1F_DATA \
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{ \
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.c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \
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.c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \
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\
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.shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \
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.ln2_lo = 0x1.7f7d1cp-20f, \
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}
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#define C(i) sv_f32 (d->c##i)
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static inline svfloat32_t
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expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d)
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{
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/* This vector is reliant on layout of data - it contains constants
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that can be used with _lane forms of svmla/svmls. Values are:
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[ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */
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svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2);
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/* Reduce argument to smaller range:
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Let i = round(x / ln2)
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and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
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exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
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where 2^i is exact because i is an integer. */
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svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2);
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j = svsub_x (pg, j, d->shift);
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svint32_t i = svcvt_s32_x (pg, j);
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svfloat32_t f = svmls_lane (x, j, lane_constants, 2);
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f = svmls_lane (f, j, lane_constants, 3);
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/* Approximate expm1(f) using polynomial.
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Taylor expansion for expm1(x) has the form:
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x + ax^2 + bx^3 + cx^4 ....
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So we calculate the polynomial P(f) = a + bf + cf^2 + ...
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and assemble the approximation expm1(f) ~= f + f^2 * P(f). */
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svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0);
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svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1);
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svfloat32_t f2 = svmul_x (pg, f, f);
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svfloat32_t p = svmla_x (pg, p12, f2, p34);
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p = svmla_x (pg, C (0), f, p);
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p = svmla_x (pg, f, f2, p);
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/* Assemble the result.
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expm1(x) ~= 2^i * (p + 1) - 1
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Let t = 2^i. */
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svfloat32_t t = svscale_x (pg, sv_f32 (1), i);
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return svmla_x (pg, svsub_x (pg, t, 1), p, t);
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}
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#endif
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