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 static const struct data 13 { 14 float poly_0246[4]; 15 float poly_1357[4]; 16 float ln2, inv_ln10; 17 } data = { 18 .poly_1357 = { 19 /* Coefficients copied from the AdvSIMD routine, then rearranged so that coeffs 20 1, 3, 5 and 7 can be loaded as a single quad-word, hence used with _lane 21 variant of MLA intrinsic. */ 22 0x1.2879c8p-3f, 0x1.6408f8p-4f, 0x1.f0e514p-5f, 0x1.f5f76ap-5f 23 }, 24 .poly_0246 = { -0x1.bcb79cp-3f, -0x1.bcd472p-4f, -0x1.246f8p-4f, 25 -0x1.0fc92cp-4f }, 26 .ln2 = 0x1.62e43p-1f, 27 .inv_ln10 = 0x1.bcb7b2p-2f, 28 }; 29 30 #define Min 0x00800000 31 #define Max 0x7f800000 32 #define Thres 0x7f000000 /* Max - Min. */ 33 #define Offset 0x3f2aaaab /* 0.666667. */ 34 #define MantissaMask 0x007fffff 35 36 static svfloat32_t NOINLINE 37 special_case (svfloat32_t x, svfloat32_t y, svbool_t special) 38 { 39 return sv_call_f32 (log10f, x, y, special); 40 } 41 42 /* Optimised implementation of SVE log10f using the same algorithm and 43 polynomial as AdvSIMD log10f. 44 Maximum error is 3.31ulps: 45 SV_NAME_F1 (log10)(0x1.555c16p+0) got 0x1.ffe2fap-4 46 want 0x1.ffe2f4p-4. */ 47 svfloat32_t SV_NAME_F1 (log10) (svfloat32_t x, const svbool_t pg) 48 { 49 const struct data *d = ptr_barrier (&data); 50 svuint32_t ix = svreinterpret_u32 (x); 51 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres); 52 53 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */ 54 ix = svsub_x (pg, ix, Offset); 55 svfloat32_t n = svcvt_f32_x ( 56 pg, svasr_x (pg, svreinterpret_s32 (ix), 23)); /* signextend. */ 57 ix = svand_x (pg, ix, MantissaMask); 58 ix = svadd_x (pg, ix, Offset); 59 svfloat32_t r = svsub_x (pg, svreinterpret_f32 (ix), 1.0f); 60 61 /* y = log10(1+r) + n*log10(2) 62 log10(1+r) ~ r * InvLn(10) + P(r) 63 where P(r) is a polynomial. Use order 9 for log10(1+x), i.e. order 8 for 64 log10(1+x)/x, with x in [-1/3, 1/3] (offset=2/3). */ 65 svfloat32_t r2 = svmul_x (pg, r, r); 66 svfloat32_t r4 = svmul_x (pg, r2, r2); 67 svfloat32_t p_1357 = svld1rq (svptrue_b32 (), &d->poly_1357[0]); 68 svfloat32_t q_01 = svmla_lane (sv_f32 (d->poly_0246[0]), r, p_1357, 0); 69 svfloat32_t q_23 = svmla_lane (sv_f32 (d->poly_0246[1]), r, p_1357, 1); 70 svfloat32_t q_45 = svmla_lane (sv_f32 (d->poly_0246[2]), r, p_1357, 2); 71 svfloat32_t q_67 = svmla_lane (sv_f32 (d->poly_0246[3]), r, p_1357, 3); 72 svfloat32_t q_47 = svmla_x (pg, q_45, r2, q_67); 73 svfloat32_t q_03 = svmla_x (pg, q_01, r2, q_23); 74 svfloat32_t y = svmla_x (pg, q_03, r4, q_47); 75 76 /* Using hi = Log10(2)*n + r*InvLn(10) is faster but less accurate. */ 77 svfloat32_t hi = svmla_x (pg, r, n, d->ln2); 78 hi = svmul_x (pg, hi, d->inv_ln10); 79 80 if (unlikely (svptest_any (pg, special))) 81 return special_case (x, svmla_x (svnot_z (pg, special), hi, r2, y), 82 special); 83 return svmla_x (pg, hi, r2, y); 84 } 85 86 PL_SIG (SV, F, 1, log10, 0.01, 11.1) 87 PL_TEST_ULP (SV_NAME_F1 (log10), 2.82) 88 PL_TEST_INTERVAL (SV_NAME_F1 (log10), -0.0, -0x1p126, 100) 89 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 0x1p-149, 0x1p-126, 4000) 90 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 0x1p-126, 0x1p-23, 50000) 91 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 0x1p-23, 1.0, 50000) 92 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 1.0, 100, 50000) 93 PL_TEST_INTERVAL (SV_NAME_F1 (log10), 100, inf, 50000) 94