1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Single-precision log10 function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include <math.h> 9*f3087befSAndrew Turner #include <stdint.h> 10*f3087befSAndrew Turner 11*f3087befSAndrew Turner #include "math_config.h" 12*f3087befSAndrew Turner #include "test_sig.h" 13*f3087befSAndrew Turner #include "test_defs.h" 14*f3087befSAndrew Turner 15*f3087befSAndrew Turner /* Data associated to logf: 16*f3087befSAndrew Turner 17*f3087befSAndrew Turner LOGF_TABLE_BITS = 4 18*f3087befSAndrew Turner LOGF_POLY_ORDER = 4 19*f3087befSAndrew Turner 20*f3087befSAndrew Turner ULP error: 0.818 (nearest rounding.) 21*f3087befSAndrew Turner Relative error: 1.957 * 2^-26 (before rounding.). */ 22*f3087befSAndrew Turner 23*f3087befSAndrew Turner #define T __logf_data.tab 24*f3087befSAndrew Turner #define A __logf_data.poly 25*f3087befSAndrew Turner #define Ln2 __logf_data.ln2 26*f3087befSAndrew Turner #define InvLn10 __logf_data.invln10 27*f3087befSAndrew Turner #define N (1 << LOGF_TABLE_BITS) 28*f3087befSAndrew Turner #define OFF 0x3f330000 29*f3087befSAndrew Turner 30*f3087befSAndrew Turner /* This naive implementation of log10f mimics that of log 31*f3087befSAndrew Turner then simply scales the result by 1/log(10) to switch from base e to 32*f3087befSAndrew Turner base 10. Hence, most computations are carried out in double precision. 33*f3087befSAndrew Turner Scaling before rounding to single precision is both faster and more 34*f3087befSAndrew Turner accurate. 35*f3087befSAndrew Turner 36*f3087befSAndrew Turner ULP error: 0.797 ulp (nearest rounding.). */ 37*f3087befSAndrew Turner float 38*f3087befSAndrew Turner log10f (float x) 39*f3087befSAndrew Turner { 40*f3087befSAndrew Turner /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 41*f3087befSAndrew Turner double_t z, r, r2, y, y0, invc, logc; 42*f3087befSAndrew Turner uint32_t ix, iz, tmp; 43*f3087befSAndrew Turner int k, i; 44*f3087befSAndrew Turner 45*f3087befSAndrew Turner ix = asuint (x); 46*f3087befSAndrew Turner #if WANT_ROUNDING 47*f3087befSAndrew Turner /* Fix sign of zero with downward rounding when x==1. */ 48*f3087befSAndrew Turner if (unlikely (ix == 0x3f800000)) 49*f3087befSAndrew Turner return 0; 50*f3087befSAndrew Turner #endif 51*f3087befSAndrew Turner if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000)) 52*f3087befSAndrew Turner { 53*f3087befSAndrew Turner /* x < 0x1p-126 or inf or nan. */ 54*f3087befSAndrew Turner if (ix * 2 == 0) 55*f3087befSAndrew Turner return __math_divzerof (1); 56*f3087befSAndrew Turner if (ix == 0x7f800000) /* log(inf) == inf. */ 57*f3087befSAndrew Turner return x; 58*f3087befSAndrew Turner if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 59*f3087befSAndrew Turner return __math_invalidf (x); 60*f3087befSAndrew Turner /* x is subnormal, normalize it. */ 61*f3087befSAndrew Turner ix = asuint (x * 0x1p23f); 62*f3087befSAndrew Turner ix -= 23 << 23; 63*f3087befSAndrew Turner } 64*f3087befSAndrew Turner 65*f3087befSAndrew Turner /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. 66*f3087befSAndrew Turner The range is split into N subintervals. 67*f3087befSAndrew Turner The ith subinterval contains z and c is near its center. */ 68*f3087befSAndrew Turner tmp = ix - OFF; 69*f3087befSAndrew Turner i = (tmp >> (23 - LOGF_TABLE_BITS)) % N; 70*f3087befSAndrew Turner k = (int32_t) tmp >> 23; /* arithmetic shift. */ 71*f3087befSAndrew Turner iz = ix - (tmp & 0xff800000); 72*f3087befSAndrew Turner invc = T[i].invc; 73*f3087befSAndrew Turner logc = T[i].logc; 74*f3087befSAndrew Turner z = (double_t) asfloat (iz); 75*f3087befSAndrew Turner 76*f3087befSAndrew Turner /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 77*f3087befSAndrew Turner r = z * invc - 1; 78*f3087befSAndrew Turner y0 = logc + (double_t) k * Ln2; 79*f3087befSAndrew Turner 80*f3087befSAndrew Turner /* Pipelined polynomial evaluation to approximate log1p(r). */ 81*f3087befSAndrew Turner r2 = r * r; 82*f3087befSAndrew Turner y = A[1] * r + A[2]; 83*f3087befSAndrew Turner y = A[0] * r2 + y; 84*f3087befSAndrew Turner y = y * r2 + (y0 + r); 85*f3087befSAndrew Turner 86*f3087befSAndrew Turner /* Multiply by 1/log(10). */ 87*f3087befSAndrew Turner y = y * InvLn10; 88*f3087befSAndrew Turner 89*f3087befSAndrew Turner return eval_as_float (y); 90*f3087befSAndrew Turner } 91*f3087befSAndrew Turner 92*f3087befSAndrew Turner TEST_SIG (S, F, 1, log10, 0.01, 11.1) 93*f3087befSAndrew Turner TEST_ULP (log10f, 0.30) 94*f3087befSAndrew Turner TEST_ULP_NONNEAREST (log10f, 0.5) 95*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0, 0xffff0000, 10000) 96*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0x1p-127, 0x1p-26, 50000) 97*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0x1p-26, 0x1p3, 50000) 98*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0x1p-4, 0x1p4, 50000) 99*f3087befSAndrew Turner TEST_INTERVAL (log10f, 0, inf, 50000) 100