1 /* 2 * SVE helper for single-precision routines which calculate exp(x) - 1 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_EXPM1F_INLINE_H 10 #define PL_MATH_SV_EXPM1F_INLINE_H 11 12 #include "sv_math.h" 13 14 struct sv_expm1f_data 15 { 16 /* These 4 are grouped together so they can be loaded as one quadword, then 17 used with _lane forms of svmla/svmls. */ 18 float32_t c2, c4, ln2_hi, ln2_lo; 19 float32_t c0, c1, c3, inv_ln2, shift; 20 }; 21 22 /* Coefficients generated using fpminimax. */ 23 #define SV_EXPM1F_DATA \ 24 { \ 25 .c0 = 0x1.fffffep-2, .c1 = 0x1.5554aep-3, .c2 = 0x1.555736p-5, \ 26 .c3 = 0x1.12287cp-7, .c4 = 0x1.6b55a2p-10, \ 27 \ 28 .shift = 0x1.8p23f, .inv_ln2 = 0x1.715476p+0f, .ln2_hi = 0x1.62e4p-1f, \ 29 .ln2_lo = 0x1.7f7d1cp-20f, \ 30 } 31 32 #define C(i) sv_f32 (d->c##i) 33 34 static inline svfloat32_t 35 expm1f_inline (svfloat32_t x, svbool_t pg, const struct sv_expm1f_data *d) 36 { 37 /* This vector is reliant on layout of data - it contains constants 38 that can be used with _lane forms of svmla/svmls. Values are: 39 [ coeff_2, coeff_4, ln2_hi, ln2_lo ]. */ 40 svfloat32_t lane_constants = svld1rq (svptrue_b32 (), &d->c2); 41 42 /* Reduce argument to smaller range: 43 Let i = round(x / ln2) 44 and f = x - i * ln2, then f is in [-ln2/2, ln2/2]. 45 exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 46 where 2^i is exact because i is an integer. */ 47 svfloat32_t j = svmla_x (pg, sv_f32 (d->shift), x, d->inv_ln2); 48 j = svsub_x (pg, j, d->shift); 49 svint32_t i = svcvt_s32_x (pg, j); 50 51 svfloat32_t f = svmls_lane (x, j, lane_constants, 2); 52 f = svmls_lane (f, j, lane_constants, 3); 53 54 /* Approximate expm1(f) using polynomial. 55 Taylor expansion for expm1(x) has the form: 56 x + ax^2 + bx^3 + cx^4 .... 57 So we calculate the polynomial P(f) = a + bf + cf^2 + ... 58 and assemble the approximation expm1(f) ~= f + f^2 * P(f). */ 59 svfloat32_t p12 = svmla_lane (C (1), f, lane_constants, 0); 60 svfloat32_t p34 = svmla_lane (C (3), f, lane_constants, 1); 61 svfloat32_t f2 = svmul_x (pg, f, f); 62 svfloat32_t p = svmla_x (pg, p12, f2, p34); 63 p = svmla_x (pg, C (0), f, p); 64 p = svmla_x (pg, f, f2, p); 65 66 /* Assemble the result. 67 expm1(x) ~= 2^i * (p + 1) - 1 68 Let t = 2^i. */ 69 svfloat32_t t = svscale_x (pg, sv_f32 (1), i); 70 return svmla_x (pg, svsub_x (pg, t, 1), p, t); 71 } 72 73 #endif // PL_MATH_SV_EXPM1F_INLINE_H