1 /* 2 * Single-precision log2 function. 3 * 4 * Copyright (c) 2017-2018, 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 #include "math_config.h" 11 12 /* 13 LOG2F_TABLE_BITS = 4 14 LOG2F_POLY_ORDER = 4 15 16 ULP error: 0.752 (nearest rounding.) 17 Relative error: 1.9 * 2^-26 (before rounding.) 18 */ 19 20 #define N (1 << LOG2F_TABLE_BITS) 21 #define T __log2f_data.tab 22 #define A __log2f_data.poly 23 #define OFF 0x3f330000 24 25 float 26 log2f (float x) 27 { 28 /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 29 double_t z, r, r2, p, y, y0, invc, logc; 30 uint32_t ix, iz, top, tmp; 31 int k, i; 32 33 ix = asuint (x); 34 #if WANT_ROUNDING 35 /* Fix sign of zero with downward rounding when x==1. */ 36 if (unlikely (ix == 0x3f800000)) 37 return 0; 38 #endif 39 if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000)) 40 { 41 /* x < 0x1p-126 or inf or nan. */ 42 if (ix * 2 == 0) 43 return __math_divzerof (1); 44 if (ix == 0x7f800000) /* log2(inf) == inf. */ 45 return x; 46 if ((ix & 0x80000000) || ix * 2 >= 0xff000000) 47 return __math_invalidf (x); 48 /* x is subnormal, normalize it. */ 49 ix = asuint (x * 0x1p23f); 50 ix -= 23 << 23; 51 } 52 53 /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. 54 The range is split into N subintervals. 55 The ith subinterval contains z and c is near its center. */ 56 tmp = ix - OFF; 57 i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N; 58 top = tmp & 0xff800000; 59 iz = ix - top; 60 k = (int32_t) tmp >> 23; /* arithmetic shift */ 61 invc = T[i].invc; 62 logc = T[i].logc; 63 z = (double_t) asfloat (iz); 64 65 /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ 66 r = z * invc - 1; 67 y0 = logc + (double_t) k; 68 69 /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ 70 r2 = r * r; 71 y = A[1] * r + A[2]; 72 y = A[0] * r2 + y; 73 p = A[3] * r + y0; 74 y = y * r2 + p; 75 return eval_as_float (y); 76 } 77 #if USE_GLIBC_ABI 78 strong_alias (log2f, __log2f_finite) 79 hidden_alias (log2f, __ieee754_log2f) 80 #endif 81