1 /* 2 * Double-precision SVE log(x) function. 3 * 4 * Copyright (c) 2020-2023, 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 #define P(i) sv_f64 (__v_log_data.poly[i]) 13 #define N (1 << V_LOG_TABLE_BITS) 14 #define Off (0x3fe6900900000000) 15 #define MaxTop (0x7ff) 16 #define MinTop (0x001) 17 #define ThreshTop (0x7fe) /* MaxTop - MinTop. */ 18 19 static svfloat64_t NOINLINE 20 special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp) 21 { 22 return sv_call_f64 (log, x, y, cmp); 23 } 24 25 /* SVE port of AdvSIMD log algorithm. 26 Maximum measured error is 2.17 ulp: 27 SV_NAME_D1 (log)(0x1.a6129884398a3p+0) got 0x1.ffffff1cca043p-2 28 want 0x1.ffffff1cca045p-2. */ 29 svfloat64_t SV_NAME_D1 (log) (svfloat64_t x, const svbool_t pg) 30 { 31 svuint64_t ix = svreinterpret_u64 (x); 32 svuint64_t top = svlsr_x (pg, ix, 52); 33 svbool_t cmp = svcmpge (pg, svsub_x (pg, top, MinTop), sv_u64 (ThreshTop)); 34 35 /* x = 2^k z; where z is in range [Off,2*Off) and exact. 36 The range is split into N subintervals. 37 The ith subinterval contains z and c is near its center. */ 38 svuint64_t tmp = svsub_x (pg, ix, Off); 39 /* Calculate table index = (tmp >> (52 - V_LOG_TABLE_BITS)) % N. 40 The actual value of i is double this due to table layout. */ 41 svuint64_t i 42 = svand_x (pg, svlsr_x (pg, tmp, (51 - V_LOG_TABLE_BITS)), (N - 1) << 1); 43 svint64_t k 44 = svasr_x (pg, svreinterpret_s64 (tmp), 52); /* Arithmetic shift. */ 45 svuint64_t iz = svsub_x (pg, ix, svand_x (pg, tmp, 0xfffULL << 52)); 46 svfloat64_t z = svreinterpret_f64 (iz); 47 /* Lookup in 2 global lists (length N). */ 48 svfloat64_t invc = svld1_gather_index (pg, &__v_log_data.table[0].invc, i); 49 svfloat64_t logc = svld1_gather_index (pg, &__v_log_data.table[0].logc, i); 50 51 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 52 svfloat64_t r = svmad_x (pg, invc, z, -1); 53 svfloat64_t kd = svcvt_f64_x (pg, k); 54 /* hi = r + log(c) + k*Ln2. */ 55 svfloat64_t hi = svmla_x (pg, svadd_x (pg, logc, r), kd, __v_log_data.ln2); 56 /* y = r2*(A0 + r*A1 + r2*(A2 + r*A3 + r2*A4)) + hi. */ 57 svfloat64_t r2 = svmul_x (pg, r, r); 58 svfloat64_t y = svmla_x (pg, P (2), r, P (3)); 59 svfloat64_t p = svmla_x (pg, P (0), r, P (1)); 60 y = svmla_x (pg, y, r2, P (4)); 61 y = svmla_x (pg, p, r2, y); 62 63 if (unlikely (svptest_any (pg, cmp))) 64 return special_case (x, svmla_x (svnot_z (pg, cmp), hi, r2, y), cmp); 65 return svmla_x (pg, hi, r2, y); 66 } 67 68 PL_SIG (SV, D, 1, log, 0.01, 11.1) 69 PL_TEST_ULP (SV_NAME_D1 (log), 1.68) 70 PL_TEST_INTERVAL (SV_NAME_D1 (log), -0.0, -inf, 1000) 71 PL_TEST_INTERVAL (SV_NAME_D1 (log), 0, 0x1p-149, 1000) 72 PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-149, 0x1p-126, 4000) 73 PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-126, 0x1p-23, 50000) 74 PL_TEST_INTERVAL (SV_NAME_D1 (log), 0x1p-23, 1.0, 50000) 75 PL_TEST_INTERVAL (SV_NAME_D1 (log), 1.0, 100, 50000) 76 PL_TEST_INTERVAL (SV_NAME_D1 (log), 100, inf, 50000) 77