1 /* 2 * Double-precision SVE log(x) function. 3 * 4 * Copyright (c) 2020-2024, 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_LOG_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 ln2, c4; 22 uint64_t off; 23 } data = { 24 .c0 = -0x1.ffffffffffff7p-2, 25 .c1 = 0x1.55555555170d4p-2, 26 .c2 = -0x1.0000000399c27p-2, 27 .c3 = 0x1.999b2e90e94cap-3, 28 .c4 = -0x1.554e550bd501ep-3, 29 .ln2 = 0x1.62e42fefa39efp-1, 30 .off = 0x3fe6900900000000, 31 }; 32 33 static svfloat64_t NOINLINE 34 special_case (svfloat64_t hi, 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 (log, x, svmla_x (svptrue_b64 (), hi, r2, y), special); 39 } 40 41 /* Double-precision SVE log routine. 42 Maximum measured error is 2.64 ulp: 43 SV_NAME_D1 (log)(0x1.95e54bc91a5e2p+184) got 0x1.fffffffe88cacp+6 44 want 0x1.fffffffe88cafp+6. */ 45 svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg) 46 { 47 const struct data *d = ptr_barrier (&data); 48 49 svuint64_t ix = svreinterpret_u64 (x); 50 svbool_t special = svcmpge (pg, svsub_x (pg, ix, Min), Thresh); 51 52 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 53 The range is split into N subintervals. 54 The ith subinterval contains z and c is near its center. */ 55 svuint64_t tmp = svsub_x (pg, ix, d->off); 56 /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N. 57 The actual value of i is double this due to table layout. */ 58 svuint64_t i 59 = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1); 60 svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)); 61 svfloat64_t z = svreinterpret_f64 (iz); 62 /* Lookup in 2 global lists (length N). */ 63 svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i); 64 svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i); 65 66 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 67 svfloat64_t kd = svcvt_f64_x (pg, svasr_x (pg, svreinterpret_s64 (tmp), 52)); 68 /* hi = r + log(c) + k*Ln2. */ 69 svfloat64_t ln2_and_c4 = svld1rq_f64 (svptrue_b64 (), &d->ln2); 70 svfloat64_t r = svmad_x (pg, invc, z, -1); 71 svfloat64_t hi = svmla_lane_f64 (logc, kd, ln2_and_c4, 0); 72 hi = svadd_x (pg, r, hi); 73 74 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 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, ln2_and_c4, 1); 80 y = svmla_x (pg, p, r2, y); 81 82 if (unlikely (svptest_any (pg, special))) 83 return special_case (hi, tmp, y, r2, special, d); 84 return svmla_x (pg, hi, r2, y); 85 } 86 87 TEST_SIG (SV, D, 1, log, 0.01, 11.1) 88 TEST_ULP (SV_NAME_D1 (log), 2.15) 89 TEST_DISABLE_FENV (SV_NAME_D1 (log)) 90 TEST_INTERVAL (SV_NAME_D1 (log), -0.0, -inf, 1000) 91 TEST_INTERVAL (SV_NAME_D1 (log), 0, 0x1p-149, 1000) 92 TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-149, 0x1p-126, 4000) 93 TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-126, 0x1p-23, 50000) 94 TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-23, 1.0, 50000) 95 TEST_INTERVAL (SV_NAME_D1 (log), 1.0, 100, 50000) 96 TEST_INTERVAL (SV_NAME_D1 (log), 100, inf, 50000) 97 CLOSE_SVE_ATTR 98