1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Helper for single-precision routines which calculate exp(ax) and do not 3*f3087befSAndrew Turner * need special-case handling 4*f3087befSAndrew Turner * 5*f3087befSAndrew Turner * Copyright (c) 2019-2024, 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_EXPF_INLINE_H 10*f3087befSAndrew Turner #define MATH_V_EXPF_INLINE_H 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner #include "v_math.h" 13*f3087befSAndrew Turner 14*f3087befSAndrew Turner struct v_expf_data 15*f3087befSAndrew Turner { 16*f3087befSAndrew Turner float ln2_hi, ln2_lo, c0, c2; 17*f3087befSAndrew Turner float32x4_t inv_ln2, c1, c3, c4; 18*f3087befSAndrew Turner /* asuint(1.0f). */ 19*f3087befSAndrew Turner uint32x4_t exponent_bias; 20*f3087befSAndrew Turner }; 21*f3087befSAndrew Turner 22*f3087befSAndrew Turner /* maxerr: 1.45358 +0.5 ulp. */ 23*f3087befSAndrew Turner #define V_EXPF_DATA \ 24*f3087befSAndrew Turner { \ 25*f3087befSAndrew Turner .c0 = 0x1.0e4020p-7f, .c1 = V4 (0x1.573e2ep-5f), .c2 = 0x1.555e66p-3f, \ 26*f3087befSAndrew Turner .c3 = V4 (0x1.fffdb6p-2f), .c4 = V4 (0x1.ffffecp-1f), \ 27*f3087befSAndrew Turner .ln2_hi = 0x1.62e4p-1f, .ln2_lo = 0x1.7f7d1cp-20f, \ 28*f3087befSAndrew Turner .inv_ln2 = V4 (0x1.715476p+0f), .exponent_bias = V4 (0x3f800000), \ 29*f3087befSAndrew Turner } 30*f3087befSAndrew Turner 31*f3087befSAndrew Turner static inline float32x4_t 32*f3087befSAndrew Turner v_expf_inline (float32x4_t x, const struct v_expf_data *d) 33*f3087befSAndrew Turner { 34*f3087befSAndrew Turner /* Helper routine for calculating exp(ax). 35*f3087befSAndrew Turner Copied from v_expf.c, with all special-case handling removed - the 36*f3087befSAndrew Turner calling routine should handle special values if required. */ 37*f3087befSAndrew Turner 38*f3087befSAndrew Turner /* exp(ax) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] 39*f3087befSAndrew Turner ax = ln2*n + r, with r in [-ln2/2, ln2/2]. */ 40*f3087befSAndrew Turner float32x4_t ax = vabsq_f32 (x); 41*f3087befSAndrew Turner float32x4_t ln2_c02 = vld1q_f32 (&d->ln2_hi); 42*f3087befSAndrew Turner float32x4_t n = vrndaq_f32 (vmulq_f32 (ax, d->inv_ln2)); 43*f3087befSAndrew Turner float32x4_t r = vfmsq_laneq_f32 (ax, n, ln2_c02, 0); 44*f3087befSAndrew Turner r = vfmsq_laneq_f32 (r, n, ln2_c02, 1); 45*f3087befSAndrew Turner uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtq_s32_f32 (n)), 23); 46*f3087befSAndrew Turner float32x4_t scale = vreinterpretq_f32_u32 (vaddq_u32 (e, d->exponent_bias)); 47*f3087befSAndrew Turner 48*f3087befSAndrew Turner /* Custom order-4 Estrin avoids building high order monomial. */ 49*f3087befSAndrew Turner float32x4_t r2 = vmulq_f32 (r, r); 50*f3087befSAndrew Turner float32x4_t p = vfmaq_laneq_f32 (d->c1, r, ln2_c02, 2); 51*f3087befSAndrew Turner float32x4_t q = vfmaq_laneq_f32 (d->c3, r, ln2_c02, 3); 52*f3087befSAndrew Turner q = vfmaq_f32 (q, p, r2); 53*f3087befSAndrew Turner p = vmulq_f32 (d->c4, r); 54*f3087befSAndrew Turner float32x4_t poly = vfmaq_f32 (p, q, r2); 55*f3087befSAndrew Turner return vfmaq_f32 (scale, poly, scale); 56*f3087befSAndrew Turner } 57*f3087befSAndrew Turner 58*f3087befSAndrew Turner #endif // MATH_V_EXPF_INLINE_H 59