1 /* 2 * Single-precision log2 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 "log2f_data.h" 12 13 /* 14 LOG2F_TABLE_BITS = 4 15 LOG2F_POLY_ORDER = 4 16 17 ULP error: 0.752 (nearest rounding.) 18 Relative error: 1.9 * 2^-26 (before rounding.) 19 */ 20 21 #define N (1 << LOG2F_TABLE_BITS) 22 #define T __log2f_data.tab 23 #define A __log2f_data.poly 24 #define OFF 0x3f330000 25 26 float log2f(float x) 27 { 28 double_t z, r, r2, p, y, y0, invc, logc; 29 uint32_t ix, iz, top, tmp; 30 int k, i; 31 32 ix = asuint(x); 33 /* Fix sign of zero with downward rounding when x==1. */ 34 if (WANT_ROUNDING && predict_false(ix == 0x3f800000)) 35 return 0; 36 if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) { 37 /* x < 0x1p-126 or inf or nan. */ 38 if (ix * 2 == 0) 39 return __math_divzerof(1); 40 if (ix == 0x7f800000) /* log2(inf) == inf. */ 41 return x; 42 if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 43 return __math_invalidf(x); 44 /* x is subnormal, normalize it. */ 45 ix = asuint(x * 0x1p23f); 46 ix -= 23 << 23; 47 } 48 49 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. 50 The range is split into N subintervals. 51 The ith subinterval contains z and c is near its center. */ 52 tmp = ix - OFF; 53 i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N; 54 top = tmp & 0xff800000; 55 iz = ix - top; 56 k = (int32_t)tmp >> 23; /* arithmetic shift */ 57 invc = T[i].invc; 58 logc = T[i].logc; 59 z = (double_t)asfloat(iz); 60 61 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ 62 r = z * invc - 1; 63 y0 = logc + (double_t)k; 64 65 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ 66 r2 = r * r; 67 y = A[1] * r + A[2]; 68 y = A[0] * r2 + y; 69 p = A[3] * r + y0; 70 y = y * r2 + p; 71 return eval_as_float(y); 72 } 73