1 /* 2 * SVE helper for single-precision routines which calculate exp(x) and do 3 * not need special-case handling 4 * 5 * Copyright (c) 2023, Arm Limited. 6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7 */ 8 9 #ifndef PL_MATH_SV_EXPF_INLINE_H 10 #define PL_MATH_SV_EXPF_INLINE_H 11 12 #include "sv_math.h" 13 #include "pl_sig.h" 14 #include "pl_test.h" 15 16 struct sv_expf_data 17 { 18 float poly[5]; 19 float inv_ln2, ln2_hi, ln2_lo, shift; 20 }; 21 22 /* Coefficients copied from the polynomial in AdvSIMD variant, reversed for 23 compatibility with polynomial helpers. Shift is 1.5*2^17 + 127. */ 24 #define SV_EXPF_DATA \ 25 { \ 26 .poly = { 0x1.ffffecp-1f, 0x1.fffdb6p-2f, 0x1.555e66p-3f, 0x1.573e2ep-5f, \ 27 0x1.0e4020p-7f }, \ 28 \ 29 .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \ 30 .ln2_lo = 0x1.7f7d1cp-20f, .shift = 0x1.803f8p17f, \ 31 } 32 33 #define C(i) sv_f32 (d->poly[i]) 34 35 static inline svfloat32_t 36 expf_inline (svfloat32_t x, const svbool_t pg, const struct sv_expf_data *d) 37 { 38 /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] 39 x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ 40 41 /* Load some constants in quad-word chunks to minimise memory access. */ 42 svfloat32_t c4_invln2_and_ln2 = svld1rq (svptrue_b32 (), &d->poly[4]); 43 44 /* n = round(x/(ln2/N)). */ 45 svfloat32_t z = svmla_lane (sv_f32 (d->shift), x, c4_invln2_and_ln2, 1); 46 svfloat32_t n = svsub_x (pg, z, d->shift); 47 48 /* r = x - n*ln2/N. */ 49 svfloat32_t r = svmls_lane (x, n, c4_invln2_and_ln2, 2); 50 r = svmls_lane (r, n, c4_invln2_and_ln2, 3); 51 52 /* scale = 2^(n/N). */ 53 svfloat32_t scale = svexpa (svreinterpret_u32_f32 (z)); 54 55 /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6. */ 56 svfloat32_t p12 = svmla_x (pg, C (1), C (2), r); 57 svfloat32_t p34 = svmla_lane (C (3), r, c4_invln2_and_ln2, 0); 58 svfloat32_t r2 = svmul_f32_x (pg, r, r); 59 svfloat32_t p14 = svmla_x (pg, p12, p34, r2); 60 svfloat32_t p0 = svmul_f32_x (pg, r, C (0)); 61 svfloat32_t poly = svmla_x (pg, p0, r2, p14); 62 63 return svmla_x (pg, scale, scale, poly); 64 } 65 66 #endif // PL_MATH_SV_EXPF_INLINE_H