1 /* 2 * Single-precision SVE log10 function. 3 * 4 * Copyright (c) 2022-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 #if SV_SUPPORTED 13 14 #define SpecialCaseMin 0x00800000 15 #define SpecialCaseMax 0x7f800000 16 #define Offset 0x3f2aaaab /* 0.666667. */ 17 #define Mask 0x007fffff 18 #define Ln2 0x1.62e43p-1f /* 0x3f317218. */ 19 #define InvLn10 0x1.bcb7b2p-2f 20 21 #define P(i) __v_log10f_poly[i] 22 23 static NOINLINE sv_f32_t 24 special_case (sv_f32_t x, sv_f32_t y, svbool_t special) 25 { 26 return sv_call_f32 (log10f, x, y, special); 27 } 28 29 /* Optimised implementation of SVE log10f using the same algorithm and 30 polynomial as v_log10f. Maximum error is 3.31ulps: 31 __sv_log10f(0x1.555c16p+0) got 0x1.ffe2fap-4 32 want 0x1.ffe2f4p-4. */ 33 sv_f32_t 34 __sv_log10f_x (sv_f32_t x, const svbool_t pg) 35 { 36 sv_u32_t ix = sv_as_u32_f32 (x); 37 svbool_t special_cases 38 = svcmpge_n_u32 (pg, svsub_n_u32_x (pg, ix, SpecialCaseMin), 39 SpecialCaseMax - SpecialCaseMin); 40 41 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */ 42 ix = svsub_n_u32_x (pg, ix, Offset); 43 sv_f32_t n = sv_to_f32_s32_x (pg, svasr_n_s32_x (pg, sv_as_s32_u32 (ix), 44 23)); /* signextend. */ 45 ix = svand_n_u32_x (pg, ix, Mask); 46 ix = svadd_n_u32_x (pg, ix, Offset); 47 sv_f32_t r = svsub_n_f32_x (pg, sv_as_f32_u32 (ix), 1.0f); 48 49 /* y = log10(1+r) + n*log10(2) 50 log10(1+r) ~ r * InvLn(10) + P(r) 51 where P(r) is a polynomial. Use order 9 for log10(1+x), i.e. order 8 for 52 log10(1+x)/x, with x in [-1/3, 1/3] (offset=2/3) 53 54 P(r) = r2 * (Q01 + r2 * (Q23 + r2 * (Q45 + r2 * Q67))) 55 and Qij = Pi + r * Pj. */ 56 sv_f32_t q12 = sv_fma_n_f32_x (pg, P (1), r, sv_f32 (P (0))); 57 sv_f32_t q34 = sv_fma_n_f32_x (pg, P (3), r, sv_f32 (P (2))); 58 sv_f32_t q56 = sv_fma_n_f32_x (pg, P (5), r, sv_f32 (P (4))); 59 sv_f32_t q78 = sv_fma_n_f32_x (pg, P (7), r, sv_f32 (P (6))); 60 61 sv_f32_t r2 = svmul_f32_x (pg, r, r); 62 sv_f32_t y = sv_fma_f32_x (pg, q78, r2, q56); 63 y = sv_fma_f32_x (pg, y, r2, q34); 64 y = sv_fma_f32_x (pg, y, r2, q12); 65 66 /* Using p = Log10(2)*n + r*InvLn(10) is slightly faster but less 67 accurate. */ 68 sv_f32_t p = sv_fma_n_f32_x (pg, Ln2, n, r); 69 y = sv_fma_f32_x (pg, y, r2, svmul_n_f32_x (pg, p, InvLn10)); 70 71 if (unlikely (svptest_any (pg, special_cases))) 72 { 73 return special_case (x, y, special_cases); 74 } 75 return y; 76 } 77 78 PL_ALIAS (__sv_log10f_x, _ZGVsMxv_log10f) 79 80 PL_SIG (SV, F, 1, log10, 0.01, 11.1) 81 PL_TEST_ULP (__sv_log10f, 2.82) 82 PL_TEST_INTERVAL (__sv_log10f, -0.0, -0x1p126, 100) 83 PL_TEST_INTERVAL (__sv_log10f, 0x1p-149, 0x1p-126, 4000) 84 PL_TEST_INTERVAL (__sv_log10f, 0x1p-126, 0x1p-23, 50000) 85 PL_TEST_INTERVAL (__sv_log10f, 0x1p-23, 1.0, 50000) 86 PL_TEST_INTERVAL (__sv_log10f, 1.0, 100, 50000) 87 PL_TEST_INTERVAL (__sv_log10f, 100, inf, 50000) 88 #endif 89