1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Helper for single-precision routines which calculate exp(x) - 1 and do not 3*f3087befSAndrew Turner * need special-case handling 4*f3087befSAndrew Turner * 5*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited. 6*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7*f3087befSAndrew Turner */ 8*f3087befSAndrew Turner 9*f3087befSAndrew Turner #ifndef MATH_V_EXPM1F_INLINE_H 10*f3087befSAndrew Turner #define MATH_V_EXPM1F_INLINE_H 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner #include "v_math.h" 13*f3087befSAndrew Turner 14*f3087befSAndrew Turner struct v_expm1f_data 15*f3087befSAndrew Turner { 16*f3087befSAndrew Turner float32x4_t c0, c2; 17*f3087befSAndrew Turner int32x4_t exponent_bias; 18*f3087befSAndrew Turner float c1, c3, inv_ln2, c4; 19*f3087befSAndrew Turner float ln2_hi, ln2_lo; 20*f3087befSAndrew Turner }; 21*f3087befSAndrew Turner 22*f3087befSAndrew Turner /* Coefficients generated using fpminimax with degree=5 in [-log(2)/2, 23*f3087befSAndrew Turner log(2)/2]. Exponent bias is asuint(1.0f). */ 24*f3087befSAndrew Turner #define V_EXPM1F_DATA \ 25*f3087befSAndrew Turner { \ 26*f3087befSAndrew Turner .c0 = V4 (0x1.fffffep-2), .c1 = 0x1.5554aep-3, .c2 = V4 (0x1.555736p-5), \ 27*f3087befSAndrew Turner .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \ 28*f3087befSAndrew Turner .exponent_bias = V4 (0x3f800000), .inv_ln2 = 0x1.715476p+0f, \ 29*f3087befSAndrew Turner .ln2_hi = 0x1.62e4p-1f, .ln2_lo = 0x1.7f7d1cp-20f, \ 30*f3087befSAndrew Turner } 31*f3087befSAndrew Turner 32*f3087befSAndrew Turner static inline float32x4_t 33*f3087befSAndrew Turner expm1f_inline (float32x4_t x, const struct v_expm1f_data *d) 34*f3087befSAndrew Turner { 35*f3087befSAndrew Turner /* Helper routine for calculating exp(x) - 1. */ 36*f3087befSAndrew Turner 37*f3087befSAndrew Turner float32x2_t ln2 = vld1_f32 (&d->ln2_hi); 38*f3087befSAndrew Turner float32x4_t lane_consts = vld1q_f32 (&d->c1); 39*f3087befSAndrew Turner 40*f3087befSAndrew Turner /* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */ 41*f3087befSAndrew Turner float32x4_t j = vrndaq_f32 (vmulq_laneq_f32 (x, lane_consts, 2)); 42*f3087befSAndrew Turner int32x4_t i = vcvtq_s32_f32 (j); 43*f3087befSAndrew Turner float32x4_t f = vfmsq_lane_f32 (x, j, ln2, 0); 44*f3087befSAndrew Turner f = vfmsq_lane_f32 (f, j, ln2, 1); 45*f3087befSAndrew Turner 46*f3087befSAndrew Turner /* Approximate expm1(f) with polynomial P, expm1(f) ~= f + f^2 * P(f). */ 47*f3087befSAndrew Turner float32x4_t f2 = vmulq_f32 (f, f); 48*f3087befSAndrew Turner float32x4_t f4 = vmulq_f32 (f2, f2); 49*f3087befSAndrew Turner float32x4_t p01 = vfmaq_laneq_f32 (d->c0, f, lane_consts, 0); 50*f3087befSAndrew Turner float32x4_t p23 = vfmaq_laneq_f32 (d->c2, f, lane_consts, 1); 51*f3087befSAndrew Turner float32x4_t p = vfmaq_f32 (p01, f2, p23); 52*f3087befSAndrew Turner p = vfmaq_laneq_f32 (p, f4, lane_consts, 3); 53*f3087befSAndrew Turner p = vfmaq_f32 (f, f2, p); 54*f3087befSAndrew Turner 55*f3087befSAndrew Turner /* t = 2^i. */ 56*f3087befSAndrew Turner int32x4_t u = vaddq_s32 (vshlq_n_s32 (i, 23), d->exponent_bias); 57*f3087befSAndrew Turner float32x4_t t = vreinterpretq_f32_s32 (u); 58*f3087befSAndrew Turner /* expm1(x) ~= p * t + (t - 1). */ 59*f3087befSAndrew Turner return vfmaq_f32 (vsubq_f32 (t, v_f32 (1.0f)), p, t); 60*f3087befSAndrew Turner } 61*f3087befSAndrew Turner 62*f3087befSAndrew Turner #endif // MATH_V_EXPM1F_INLINE_H 63