1 /* 2 * Single-precision log function. 3 * 4 * Copyright (c) 2017-2018, Arm Limited. 5 * SPDX-License-Identifier: MIT 6 */ 7 8 #include <math.h> 9 #include <stdint.h> 10 #include "libm.h" 11 #include "logf_data.h" 12 13 /* 14 LOGF_TABLE_BITS = 4 15 LOGF_POLY_ORDER = 4 16 17 ULP error: 0.818 (nearest rounding.) 18 Relative error: 1.957 * 2^-26 (before rounding.) 19 */ 20 21 #define T __logf_data.tab 22 #define A __logf_data.poly 23 #define Ln2 __logf_data.ln2 24 #define N (1 << LOGF_TABLE_BITS) 25 #define OFF 0x3f330000 26 27 float logf(float x) 28 { 29 double_t z, r, r2, y, y0, invc, logc; 30 uint32_t ix, iz, tmp; 31 int k, i; 32 33 ix = asuint(x); 34 /* Fix sign of zero with downward rounding when x==1. */ 35 if (WANT_ROUNDING && predict_false(ix == 0x3f800000)) 36 return 0; 37 if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) { 38 /* x < 0x1p-126 or inf or nan. */ 39 if (ix * 2 == 0) 40 return __math_divzerof(1); 41 if (ix == 0x7f800000) /* log(inf) == inf. */ 42 return x; 43 if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 44 return __math_invalidf(x); 45 /* x is subnormal, normalize it. */ 46 ix = asuint(x * 0x1p23f); 47 ix -= 23 << 23; 48 } 49 50 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. 51 The range is split into N subintervals. 52 The ith subinterval contains z and c is near its center. */ 53 tmp = ix - OFF; 54 i = (tmp >> (23 - LOGF_TABLE_BITS)) % N; 55 k = (int32_t)tmp >> 23; /* arithmetic shift */ 56 iz = ix - (tmp & 0x1ff << 23); 57 invc = T[i].invc; 58 logc = T[i].logc; 59 z = (double_t)asfloat(iz); 60 61 /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */ 62 r = z * invc - 1; 63 y0 = logc + (double_t)k * Ln2; 64 65 /* Pipelined polynomial evaluation to approximate log1p(r). */ 66 r2 = r * r; 67 y = A[1] * r + A[2]; 68 y = A[0] * r2 + y; 69 y = y * r2 + (y0 + r); 70 return eval_as_float(y); 71 } 72