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/*
* Helper for single-precision routines which calculate exp(x) - 1 and do not
* need special-case handling
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#ifndef PL_MATH_V_EXPM1F_INLINE_H
#define PL_MATH_V_EXPM1F_INLINE_H
#include "v_math.h"
#include "math_config.h"
#include "poly_advsimd_f32.h"
struct v_expm1f_data
{
float32x4_t poly[5];
float32x4_t invln2_and_ln2, shift;
int32x4_t exponent_bias;
};
/* Coefficients generated using fpminimax with degree=5 in [-log(2)/2,
log(2)/2]. Exponent bias is asuint(1.0f).
invln2_and_ln2 Stores constants: invln2, ln2_lo, ln2_hi, 0. */
#define V_EXPM1F_DATA \
{ \
.poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5), \
V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) }, \
.shift = V4 (0x1.8p23f), .exponent_bias = V4 (0x3f800000), \
.invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, \
}
static inline float32x4_t
expm1f_inline (float32x4_t x, const struct v_expm1f_data *d)
{
/* Helper routine for calculating exp(x) - 1.
Copied from v_expm1f_1u6.c, with all special-case handling removed - the
calling routine should handle special values if required. */
/* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
float32x4_t j = vsubq_f32 (
vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0), d->shift);
int32x4_t i = vcvtq_s32_f32 (j);
float32x4_t f = vfmsq_laneq_f32 (x, j, d->invln2_and_ln2, 1);
f = vfmsq_laneq_f32 (f, j, d->invln2_and_ln2, 2);
/* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f).
Uses Estrin scheme, where the main _ZGVnN4v_expm1f routine uses
Horner. */
float32x4_t f2 = vmulq_f32 (f, f);
float32x4_t f4 = vmulq_f32 (f2, f2);
float32x4_t p = v_estrin_4_f32 (f, f2, f4, d->poly);
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 // PL_MATH_V_EXPM1F_INLINE_H
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