1 /* 2 * Single-precision SVE 10^x function. 3 * 4 * Copyright (c) 2023-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #define _GNU_SOURCE 9 #include "sv_math.h" 10 #include "test_sig.h" 11 #include "test_defs.h" 12 #include "sv_poly_f32.h" 13 14 /* For x < -Thres, the result is subnormal and not handled correctly by 15 FEXPA. */ 16 #define Thres 37.9 17 18 static const struct data 19 { 20 float log2_10_lo, c0, c2, c4; 21 float c1, c3, log10_2; 22 float shift, log2_10_hi, thres; 23 } data = { 24 /* Coefficients generated using Remez algorithm with minimisation of relative 25 error. 26 rel error: 0x1.89dafa3p-24 27 abs error: 0x1.167d55p-23 in [-log10(2)/2, log10(2)/2] 28 maxerr: 0.52 +0.5 ulp. */ 29 .c0 = 0x1.26bb16p+1f, 30 .c1 = 0x1.5350d2p+1f, 31 .c2 = 0x1.04744ap+1f, 32 .c3 = 0x1.2d8176p+0f, 33 .c4 = 0x1.12b41ap-1f, 34 /* 1.5*2^17 + 127, a shift value suitable for FEXPA. */ 35 .shift = 0x1.803f8p17f, 36 .log10_2 = 0x1.a934fp+1, 37 .log2_10_hi = 0x1.344136p-2, 38 .log2_10_lo = -0x1.ec10cp-27, 39 .thres = Thres, 40 }; 41 42 static inline svfloat32_t 43 sv_exp10f_inline (svfloat32_t x, const svbool_t pg, const struct data *d) 44 { 45 /* exp10(x) = 2^(n/N) * 10^r = 2^n * (1 + poly (r)), 46 with poly(r) in [1/sqrt(2), sqrt(2)] and 47 x = r + n * log10(2) / N, with r in [-log10(2)/2N, log10(2)/2N]. */ 48 49 svfloat32_t lane_consts = svld1rq (svptrue_b32 (), &d->log2_10_lo); 50 51 /* n = round(x/(log10(2)/N)). */ 52 svfloat32_t shift = sv_f32 (d->shift); 53 svfloat32_t z = svmad_x (pg, sv_f32 (d->log10_2), x, shift); 54 svfloat32_t n = svsub_x (svptrue_b32 (), z, shift); 55 56 /* r = x - n*log10(2)/N. */ 57 svfloat32_t r = svmsb_x (pg, sv_f32 (d->log2_10_hi), n, x); 58 r = svmls_lane (r, n, lane_consts, 0); 59 60 svfloat32_t scale = svexpa (svreinterpret_u32 (z)); 61 62 /* Polynomial evaluation: poly(r) ~ exp10(r)-1. */ 63 svfloat32_t p12 = svmla_lane (sv_f32 (d->c1), r, lane_consts, 2); 64 svfloat32_t p34 = svmla_lane (sv_f32 (d->c3), r, lane_consts, 3); 65 svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r); 66 svfloat32_t p14 = svmla_x (pg, p12, p34, r2); 67 svfloat32_t p0 = svmul_lane (r, lane_consts, 1); 68 svfloat32_t poly = svmla_x (pg, p0, r2, p14); 69 70 return svmla_x (pg, scale, scale, poly); 71 } 72 73 static svfloat32_t NOINLINE 74 special_case (svfloat32_t x, svbool_t special, const struct data *d) 75 { 76 return sv_call_f32 (exp10f, x, sv_exp10f_inline (x, svptrue_b32 (), d), 77 special); 78 } 79 80 /* Single-precision SVE exp10f routine. Implements the same algorithm 81 as AdvSIMD exp10f. 82 Worst case error is 1.02 ULPs. 83 _ZGVsMxv_exp10f(-0x1.040488p-4) got 0x1.ba5f9ep-1 84 want 0x1.ba5f9cp-1. */ 85 svfloat32_t SV_NAME_F1 (exp10) (svfloat32_t x, const svbool_t pg) 86 { 87 const struct data *d = ptr_barrier (&data); 88 svbool_t special = svacgt (pg, x, d->thres); 89 if (unlikely (svptest_any (special, special))) 90 return special_case (x, special, d); 91 return sv_exp10f_inline (x, pg, d); 92 } 93 94 #if WANT_EXP10_TESTS 95 TEST_SIG (SV, F, 1, exp10, -9.9, 9.9) 96 TEST_ULP (SV_NAME_F1 (exp10), 0.52) 97 TEST_DISABLE_FENV (SV_NAME_F1 (exp10)) 98 TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), 0, Thres, 50000) 99 TEST_SYM_INTERVAL (SV_NAME_F1 (exp10), Thres, inf, 50000) 100 #endif 101 CLOSE_SVE_ATTR 102