1 /* 2 * Double-precision SVE log10(x) function. 3 * 4 * Copyright (c) 2022-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "test_sig.h" 10 #include "test_defs.h" 11 12 #define Min 0x0010000000000000 13 #define Max 0x7ff0000000000000 14 #define Thres 0x7fe0000000000000 /* Max - Min. */ 15 #define N (1 << V_LOG10_TABLE_BITS) 16 17 static const struct data 18 { 19 double c0, c2; 20 double c1, c3; 21 double invln10, log10_2; 22 double c4; 23 uint64_t off; 24 } data = { 25 .c0 = -0x1.bcb7b1526e506p-3, 26 .c1 = 0x1.287a7636be1d1p-3, 27 .c2 = -0x1.bcb7b158af938p-4, 28 .c3 = 0x1.63c78734e6d07p-4, 29 .c4 = -0x1.287461742fee4p-4, 30 .invln10 = 0x1.bcb7b1526e50ep-2, 31 .log10_2 = 0x1.34413509f79ffp-2, 32 .off = 0x3fe6900900000000, 33 }; 34 35 static svfloat64_t NOINLINE 36 special_case (svfloat64_t hi, svuint64_t tmp, svfloat64_t y, svfloat64_t r2, 37 svbool_t special, const struct data *d) 38 { 39 svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off)); 40 return sv_call_f64 (log10, x, svmla_x (svptrue_b64 (), hi, r2, y), special); 41 } 42 43 /* Double-precision SVE log10 routine. 44 Maximum measured error is 2.46 ulps. 45 SV_NAME_D1 (log10)(0x1.131956cd4b627p+0) got 0x1.fffbdf6eaa669p-6 46 want 0x1.fffbdf6eaa667p-6. */ 47 svfloat64_t SV_NAME_D1 (log10) (svfloat64_t x, const svbool_t pg) 48 { 49 const struct data *d = ptr_barrier (&data); 50 51 svuint64_t ix = svreinterpret_u64 (x); 52 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thres); 53 54 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 55 The range is split into N subintervals. 56 The ith subinterval contains z and c is near its center. */ 57 svuint64_t tmp = svsub_x (pg, ix, d->off); 58 svuint64_t i = svlsr_x (pg, tmp, 51 - V_LOG10_TABLE_BITS); 59 i = svand_x (pg, i, (N - 1) << 1); 60 svfloat64_t k = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52)); 61 svfloat64_t z = svreinterpret_f64 ( 62 svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52))); 63 64 /* log(x) = k*log(2) + log(c) + log(z/c). */ 65 svfloat64_t invc = svld1_gather_index (pg, &__v_log10_data.table[0].invc, i); 66 svfloat64_t logc 67 = svld1_gather_index (pg, &__v_log10_data.table[0].log10c, i); 68 69 /* We approximate log(z/c) with a polynomial P(x) ~= log(x + 1): 70 r = z/c - 1 (we look up precomputed 1/c) 71 log(z/c) ~= P(r). */ 72 svfloat64_t r = svmad_x (pg, invc, z, -1.0); 73 74 /* hi = log(c) + k*log(2). */ 75 svfloat64_t invln10_log10_2 = svld1rq_f64 (svptrue_b64 (), &d->invln10); 76 svfloat64_t w = svmla_lane_f64 (logc, r, invln10_log10_2, 0); 77 svfloat64_t hi = svmla_lane_f64 (w, k, invln10_log10_2, 1); 78 79 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 80 svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1); 81 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r); 82 svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1); 83 svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0); 84 y = svmla_x (pg, y, r2, d->c4); 85 y = svmla_x (pg, p, r2, y); 86 87 if (unlikely (svptest_any (pg, special))) 88 return special_case (hi, tmp, y, r2, special, d); 89 return svmla_x (pg, hi, r2, y); 90 } 91 92 TEST_SIG (SV, D, 1, log10, 0.01, 11.1) 93 TEST_ULP (SV_NAME_D1 (log10), 1.97) 94 TEST_DISABLE_FENV (SV_NAME_D1 (log10)) 95 TEST_INTERVAL (SV_NAME_D1 (log10), -0.0, -0x1p126, 100) 96 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-149, 0x1p-126, 4000) 97 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-126, 0x1p-23, 50000) 98 TEST_INTERVAL (SV_NAME_D1 (log10), 0x1p-23, 1.0, 50000) 99 TEST_INTERVAL (SV_NAME_D1 (log10), 1.0, 100, 50000) 100 TEST_INTERVAL (SV_NAME_D1 (log10), 100, inf, 50000) 101 CLOSE_SVE_ATTR 102