1 /* 2 * Double-precision SVE log2 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 N (1 << V_LOG2_TABLE_BITS) 13 #define Max (0x7ff0000000000000) 14 #define Min (0x0010000000000000) 15 #define Thresh (0x7fe0000000000000) /* Max - Min. */ 16 17 static const struct data 18 { 19 double c0, c2; 20 double c1, c3; 21 double invln2, c4; 22 uint64_t off; 23 } data = { 24 .c0 = -0x1.71547652b83p-1, 25 .c1 = 0x1.ec709dc340953p-2, 26 .c2 = -0x1.71547651c8f35p-2, 27 .c3 = 0x1.2777ebe12dda5p-2, 28 .c4 = -0x1.ec738d616fe26p-3, 29 .invln2 = 0x1.71547652b82fep0, 30 .off = 0x3fe6900900000000, 31 }; 32 33 static svfloat64_t NOINLINE 34 special_case (svfloat64_t w, svuint64_t tmp, svfloat64_t y, svfloat64_t r2, 35 svbool_t special, const struct data *d) 36 { 37 svfloat64_t x = svreinterpret_f64 (svadd_x (svptrue_b64 (), tmp, d->off)); 38 return sv_call_f64 (log2, x, svmla_x (svptrue_b64 (), w, r2, y), special); 39 } 40 41 /* Double-precision SVE log2 routine. 42 Implements the same algorithm as AdvSIMD log10, with coefficients and table 43 entries scaled in extended precision. 44 The maximum observed error is 2.58 ULP: 45 SV_NAME_D1 (log2)(0x1.0b556b093869bp+0) got 0x1.fffb34198d9dap-5 46 want 0x1.fffb34198d9ddp-5. */ 47 svfloat64_t SV_NAME_D1 (log2) (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), Thresh); 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_LOG2_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 svfloat64_t invc = svld1_gather_index (pg, &__v_log2_data.table[0].invc, i); 65 svfloat64_t log2c 66 = svld1_gather_index (pg, &__v_log2_data.table[0].log2c, i); 67 68 /* log2(x) = log1p(z/c-1)/log(2) + log2(c) + k. */ 69 70 svfloat64_t invln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->invln2); 71 svfloat64_t r = svmad_x (pg, invc, z, -1.0); 72 svfloat64_t w = svmla_lane_f64 (log2c, r, invln2_and_c4, 0); 73 w = svadd_x (pg, k, w); 74 75 svfloat64_t odd_coeffs = svld1rq_f64 (svptrue_b64 (), &d->c1); 76 svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r); 77 svfloat64_t y = svmla_lane_f64 (sv_f64 (d->c2), r, odd_coeffs, 1); 78 svfloat64_t p = svmla_lane_f64 (sv_f64 (d->c0), r, odd_coeffs, 0); 79 y = svmla_lane_f64 (y, r2, invln2_and_c4, 1); 80 y = svmla_x (pg, p, r2, y); 81 82 if (unlikely (svptest_any (pg, special))) 83 return special_case (w, tmp, y, r2, special, d); 84 return svmla_x (pg, w, r2, y); 85 } 86 87 TEST_SIG (SV, D, 1, log2, 0.01, 11.1) 88 TEST_ULP (SV_NAME_D1 (log2), 2.09) 89 TEST_DISABLE_FENV (SV_NAME_D1 (log2)) 90 TEST_INTERVAL (SV_NAME_D1 (log2), -0.0, -0x1p126, 1000) 91 TEST_INTERVAL (SV_NAME_D1 (log2), 0.0, 0x1p-126, 4000) 92 TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-126, 0x1p-23, 50000) 93 TEST_INTERVAL (SV_NAME_D1 (log2), 0x1p-23, 1.0, 50000) 94 TEST_INTERVAL (SV_NAME_D1 (log2), 1.0, 100, 50000) 95 TEST_INTERVAL (SV_NAME_D1 (log2), 100, inf, 50000) 96 CLOSE_SVE_ATTR 97