1 /* 2 * Helper for single-precision routines which calculate exp(x) - 1 and do not 3 * need special-case handling 4 * 5 * Copyright (c) 2022-2023, Arm Limited. 6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7 */ 8 9 #ifndef PL_MATH_V_EXPM1F_INLINE_H 10 #define PL_MATH_V_EXPM1F_INLINE_H 11 12 #include "v_math.h" 13 #include "math_config.h" 14 #include "poly_advsimd_f32.h" 15 16 struct v_expm1f_data 17 { 18 float32x4_t poly[5]; 19 float32x4_t invln2_and_ln2, shift; 20 int32x4_t exponent_bias; 21 }; 22 23 /* Coefficients generated using fpminimax with degree=5 in [-log(2)/2, 24 log(2)/2]. Exponent bias is asuint(1.0f). 25 invln2_and_ln2 Stores constants: invln2, ln2_lo, ln2_hi, 0. */ 26 #define V_EXPM1F_DATA \ 27 { \ 28 .poly = { V4 (0x1.fffffep-2), V4 (0x1.5554aep-3), V4 (0x1.555736p-5), \ 29 V4 (0x1.12287cp-7), V4 (0x1.6b55a2p-10) }, \ 30 .shift = V4 (0x1.8p23f), .exponent_bias = V4 (0x3f800000), \ 31 .invln2_and_ln2 = { 0x1.715476p+0f, 0x1.62e4p-1f, 0x1.7f7d1cp-20f, 0 }, \ 32 } 33 34 static inline float32x4_t 35 expm1f_inline (float32x4_t x, const struct v_expm1f_data *d) 36 { 37 /* Helper routine for calculating exp(x) - 1. 38 Copied from v_expm1f_1u6.c, with all special-case handling removed - the 39 calling routine should handle special values if required. */ 40 41 /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ 42 float32x4_t j = vsubq_f32 ( 43 vfmaq_laneq_f32 (d->shift, x, d->invln2_and_ln2, 0), d->shift); 44 int32x4_t i = vcvtq_s32_f32 (j); 45 float32x4_t f = vfmsq_laneq_f32 (x, j, d->invln2_and_ln2, 1); 46 f = vfmsq_laneq_f32 (f, j, d->invln2_and_ln2, 2); 47 48 /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f). 49 Uses Estrin scheme, where the main _ZGVnN4v_expm1f routine uses 50 Horner. */ 51 float32x4_t f2 = vmulq_f32 (f, f); 52 float32x4_t f4 = vmulq_f32 (f2, f2); 53 float32x4_t p = v_estrin_4_f32 (f, f2, f4, d->poly); 54 p = vfmaq_f32 (f, f2, p); 55 56 /* t = 2^i. */ 57 int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias); 58 float32x4_t t = vreinterpretq_f32_s32 (u); 59 /* expm1(x) ~= p * t + (t - 1). */ 60 return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t); 61 } 62 63 #endif // PL_MATH_V_EXPM1F_INLINE_H 64