1 /* 2 * Single-precision log function. 3 * 4 * Copyright (c) 2017-2019, Arm Limited. 5 * SPDX-License-Identifier: MIT 6 */ 7 8 #include <math.h> 9 #include <stdint.h> 10 #include "math_config.h" 11 12 /* 13 LOGF_TABLE_BITS = 4 14 LOGF_POLY_ORDER = 4 15 16 ULP error: 0.818 (nearest rounding.) 17 Relative error: 1.957 * 2^-26 (before rounding.) 18 */ 19 20 #define T __logf_data.tab 21 #define A __logf_data.poly 22 #define Ln2 __logf_data.ln2 23 #define N (1 << LOGF_TABLE_BITS) 24 #define OFF 0x3f330000 25 26 float 27 logf (float x) 28 { 29 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 30 double_t z, r, r2, y, y0, invc, logc; 31 uint32_t ix, iz, tmp; 32 int k, i; 33 34 ix = asuint (x); 35 #if WANT_ROUNDING 36 /* Fix sign of zero with downward rounding when x==1. */ 37 if (unlikely (ix == 0x3f800000)) 38 return 0; 39 #endif 40 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000)) 41 { 42 /* x < 0x1p-126 or inf or nan. */ 43 if (ix * 2 == 0) 44 return __math_divzerof (1); 45 if (ix == 0x7f800000) /* log(inf) == inf. */ 46 return x; 47 if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 48 return __math_invalidf (x); 49 /* x is subnormal, normalize it. */ 50 ix = asuint (x * 0x1p23f); 51 ix -= 23 << 23; 52 } 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 tmp = ix - OFF; 58 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N; 59 k = (int32_t) tmp >> 23; /* arithmetic shift */ 60 iz = ix - (tmp & 0x1ff << 23); 61 invc = T[i].invc; 62 logc = T[i].logc; 63 z = (double_t) asfloat (iz); 64 65 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */ 66 r = z * invc - 1; 67 y0 = logc + (double_t) k * Ln2; 68 69 /* Pipelined polynomial evaluation to approximate log1p(r). */ 70 r2 = r * r; 71 y = A[1] * r + A[2]; 72 y = A[0] * r2 + y; 73 y = y * r2 + (y0 + r); 74 return eval_as_float (y); 75 } 76 #if USE_GLIBC_ABI 77 strong_alias (logf, __logf_finite) 78 hidden_alias (logf, __ieee754_logf) 79 #endif 80