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Diffstat (limited to 'sysdeps/aarch64/fpu/sv_expm1f_inline.h')
| -rw-r--r-- | sysdeps/aarch64/fpu/sv_expm1f_inline.h | 84 |
1 files changed, 84 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/sv_expm1f_inline.h b/sysdeps/aarch64/fpu/sv_expm1f_inline.h new file mode 100644 index 0000000000..5b72451222 --- /dev/null +++ b/sysdeps/aarch64/fpu/sv_expm1f_inline.h @@ -0,0 +1,84 @@ +/* Single-precision inline helper for vector (SVE) expm1 function + + Copyright (C) 2024 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ + +#ifndef AARCH64_FPU_SV_EXPM1F_INLINE_H +#define AARCH64_FPU_SV_EXPM1F_INLINE_H + +#include "sv_math.h" + +struct sv_expm1f_data +{ + /* These 4 are grouped together so they can be loaded as one quadword, then + used with _lane forms of svmla/svmls. */ + float32_t c2, c4, ln2_hi, ln2_lo; + float32_t c0, c1, c3, inv_ln2, shift; +}; + +/* Coefficients generated using fpminimax. */ +#define SV_EXPM1F_DATA \ + { \ + .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \ + .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \ + \ + .shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \ + .ln2_lo = 0x1.7f7d1cp-20f, \ + } + +#define C(i) sv_f32 (d->c##i) + +static inline svfloat32_t +expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d) +{ + /* This vector is reliant on layout of data - it contains constants + that can be used with _lane forms of svmla/svmls. Values are: + [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */ + svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2); + + /* Reduce argument to smaller range: + Let i = round(x / ln2) + and f = x - i * ln2, then f is in [-ln2/2, ln2/2]. + exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 + where 2^i is exact because i is an integer. */ + svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2); + j = svsub_x (pg, j, d->shift); + svint32_t i = svcvt_s32_x (pg, j); + + svfloat32_t f = svmls_lane (x, j, lane_constants, 2); + f = svmls_lane (f, j, lane_constants, 3); + + /* Approximate expm1(f) using polynomial. + Taylor expansion for expm1(x) has the form: + x + ax^2 + bx^3 + cx^4 .... + So we calculate the polynomial P(f) = a + bf + cf^2 + ... + and assemble the approximation expm1(f) ~= f + f^2 * P(f). */ + svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0); + svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1); + svfloat32_t f2 = svmul_x (pg, f, f); + svfloat32_t p = svmla_x (pg, p12, f2, p34); + p = svmla_x (pg, C (0), f, p); + p = svmla_x (pg, f, f2, p); + + /* Assemble the result. + expm1(x) ~= 2^i * (p + 1) - 1 + Let t = 2^i. */ + svfloat32_t t = svscale_x (pg, sv_f32 (1), i); + return svmla_x (pg, svsub_x (pg, t, 1), p, t); +} + +#endif |