1 /* 2 * Single-precision log10 function. 3 * 4 * Copyright (c) 2022-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include <math.h> 9 #include <stdint.h> 10 11 #include "math_config.h" 12 #include "pl_sig.h" 13 #include "pl_test.h" 14 15 /* Data associated to logf: 16 17 LOGF_TABLE_BITS = 4 18 LOGF_POLY_ORDER = 4 19 20 ULP error: 0.818 (nearest rounding.) 21 Relative error: 1.957 * 2^-26 (before rounding.). */ 22 23 #define T __logf_data.tab 24 #define A __logf_data.poly 25 #define Ln2 __logf_data.ln2 26 #define InvLn10 __logf_data.invln10 27 #define N (1 << LOGF_TABLE_BITS) 28 #define OFF 0x3f330000 29 30 /* This naive implementation of log10f mimics that of log 31 then simply scales the result by 1/log(10) to switch from base e to 32 base 10. Hence, most computations are carried out in double precision. 33 Scaling before rounding to single precision is both faster and more accurate. 34 35 ULP error: 0.797 ulp (nearest rounding.). */ 36 float 37 log10f (float x) 38 { 39 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 40 double_t z, r, r2, y, y0, invc, logc; 41 uint32_t ix, iz, tmp; 42 int k, i; 43 44 ix = asuint (x); 45 #if WANT_ROUNDING 46 /* Fix sign of zero with downward rounding when x==1. */ 47 if (unlikely (ix == 0x3f800000)) 48 return 0; 49 #endif 50 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000)) 51 { 52 /* x < 0x1p-126 or inf or nan. */ 53 if (ix * 2 == 0) 54 return __math_divzerof (1); 55 if (ix == 0x7f800000) /* log(inf) == inf. */ 56 return x; 57 if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 58 return __math_invalidf (x); 59 /* x is subnormal, normalize it. */ 60 ix = asuint (x * 0x1p23f); 61 ix -= 23 << 23; 62 } 63 64 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. 65 The range is split into N subintervals. 66 The ith subinterval contains z and c is near its center. */ 67 tmp = ix - OFF; 68 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N; 69 k = (int32_t) tmp >> 23; /* arithmetic shift. */ 70 iz = ix - (tmp & 0xff800000); 71 invc = T[i].invc; 72 logc = T[i].logc; 73 z = (double_t) asfloat (iz); 74 75 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ 76 r = z * invc - 1; 77 y0 = logc + (double_t) k * Ln2; 78 79 /* Pipelined polynomial evaluation to approximate log1p(r). */ 80 r2 = r * r; 81 y = A[1] * r + A[2]; 82 y = A[0] * r2 + y; 83 y = y * r2 + (y0 + r); 84 85 /* Multiply by 1/log(10). */ 86 y = y * InvLn10; 87 88 return eval_as_float (y); 89 } 90 91 PL_SIG (S, F, 1, log10, 0.01, 11.1) 92 PL_TEST_ULP (log10f, 0.30) 93 PL_TEST_INTERVAL (log10f, 0, 0xffff0000, 10000) 94 PL_TEST_INTERVAL (log10f, 0x1p-127, 0x1p-26, 50000) 95 PL_TEST_INTERVAL (log10f, 0x1p-26, 0x1p3, 50000) 96 PL_TEST_INTERVAL (log10f, 0x1p-4, 0x1p4, 50000) 97 PL_TEST_INTERVAL (log10f, 0, inf, 50000) 98