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/* Single-precision inline helper for vector (Advanced SIMD) expm1 function
Copyright (C) 2024-2025 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_V_EXPM1F_INLINE_H
#define AARCH64_FPU_V_EXPM1F_INLINE_H
#include "v_math.h"
struct v_expm1f_data
{
float32x4_t c0, c2;
int32x4_t exponent_bias;
float c1, c3, inv_ln2, c4;
float ln2_hi, ln2_lo;
};
/* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
log(2)/2]. Exponent bias is asuint(1.0f). */
#define V_EXPM1F_DATA \
{ \
.c0 = V4 (0x1.fffffep-2), .c1 = 0x1.5554aep-3, .c2 = V4 (0x1.555736p-5), \
.c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \
.exponent_bias = V4 (0x3f800000), .inv_ln2 = 0x1.715476p+0f, \
.ln2_hi = 0x1.62e4p-1f, .ln2_lo = 0x1.7f7d1cp-20f, \
}
static inline float32x4_t
expm1f_inline (float32x4_t x, const struct v_expm1f_data *d)
{
/* Helper routine for calculating exp(x) - 1. */
float32x2_t ln2 = vld1_f32 (&d->ln2_hi);
float32x4_t lane_consts = vld1q_f32 (&d->c1);
/* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
float32x4_t j = vrndaq_f32 (vmulq_laneq_f32 (x, lane_consts, 2));
int32x4_t i = vcvtq_s32_f32 (j);
float32x4_t f = vfmsq_lane_f32 (x, j, ln2, 0);
f = vfmsq_lane_f32 (f, j, ln2, 1);
/* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f). */
float32x4_t f2 = vmulq_f32 (f, f);
float32x4_t f4 = vmulq_f32 (f2, f2);
float32x4_t p01 = vfmaq_laneq_f32 (d->c0, f, lane_consts, 0);
float32x4_t p23 = vfmaq_laneq_f32 (d->c2, f, lane_consts, 1);
float32x4_t p = vfmaq_f32 (p01, f2, p23);
p = vfmaq_laneq_f32 (p, f4, lane_consts, 3);
p = vfmaq_f32 (f, f2, p);
/* t = 2^i. */
int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias);
float32x4_t t = vreinterpretq_f32_s32 (u);
/* expm1(x) ~= p * t + (t - 1). */
return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t);
}
#endif
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