1/* Copyright JS Foundation and other contributors, http://js.foundation 2 * 3 * Licensed under the Apache License, Version 2.0 (the "License"); 4 * you may not use this file except in compliance with the License. 5 * You may obtain a copy of the License at 6 * 7 * http://www.apache.org/licenses/LICENSE-2.0 8 * 9 * Unless required by applicable law or agreed to in writing, software 10 * distributed under the License is distributed on an "AS IS" BASIS 11 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 * See the License for the specific language governing permissions and 13 * limitations under the License. 14 * 15 * This file is based on work under the following copyright and permission 16 * notice: 17 * 18 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 19 * 20 * Developed at SunSoft, a Sun Microsystems, Inc. business. 21 * Permission to use, copy, modify, and distribute this 22 * software is freely granted, provided that this notice 23 * is preserved. 24 * 25 * @(#)e_log2.c 1.3 95/01/18 26 */ 27 28#include "jerry-libm-internal.h" 29 30/* log2(x) 31 * Return the base 2 logarithm of x. See e_log.c and k_log.h for most 32 * comments. 33 * 34 * This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel, 35 * then does the combining and scaling steps 36 * log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k 37 * in not-quite-routine extra precision. 38 */ 39 40#define zero 0.0 41#define two54 1.80143985094819840000e+16 /* 0x43500000, 0x00000000 */ 42#define ivln2hi 1.44269504072144627571e+00 /* 0x3FF71547, 0x65200000 */ 43#define ivln2lo 1.67517131648865118353e-10 /* 0x3DE705FC, 0x2EEFA200 */ 44#define Lg1 6.666666666666735130e-01 /* 0x3FE55555, 0x55555593 */ 45#define Lg2 3.999999999940941908e-01 /* 0x3FD99999, 0x9997FA04 */ 46#define Lg3 2.857142874366239149e-01 /* 0x3FD24924, 0x94229359 */ 47#define Lg4 2.222219843214978396e-01 /* 0x3FCC71C5, 0x1D8E78AF */ 48#define Lg5 1.818357216161805012e-01 /* 0x3FC74664, 0x96CB03DE */ 49#define Lg6 1.531383769920937332e-01 /* 0x3FC39A09, 0xD078C69F */ 50#define Lg7 1.479819860511658591e-01 /* 0x3FC2F112, 0xDF3E5244 */ 51 52double 53log2 (double x) 54{ 55 double f, hfsq, hi, lo, r, val_hi, val_lo, w, y; 56 int i, k, hx; 57 unsigned int lx; 58 double_accessor temp; 59 60 hx = __HI (x); /* high word of x */ 61 lx = __LO (x); /* low word of x */ 62 63 k = 0; 64 if (hx < 0x00100000) 65 { /* x < 2**-1022 */ 66 if (((hx & 0x7fffffff) | lx) == 0) 67 { 68 return -two54 / zero; /* log(+-0)=-inf */ 69 } 70 if (hx < 0) 71 { 72 return (x - x) / zero; /* log(-#) = NaN */ 73 } 74 k -= 54; 75 x *= two54; /* subnormal number, scale up x */ 76 hx = __HI (x); /* high word of x */ 77 } 78 if (hx >= 0x7ff00000) 79 { 80 return x + x; 81 } 82 if (hx == 0x3ff00000 && lx == 0) 83 { 84 return zero; /* log(1) = +0 */ 85 } 86 k += (hx >> 20) - 1023; 87 hx &= 0x000fffff; 88 i = (hx + 0x95f64) & 0x100000; 89 temp.dbl = x; 90 temp.as_int.hi = hx | (i ^ 0x3ff00000); /* normalize x or x/2 */ 91 k += (i >> 20); 92 y = (double) k; 93 f = temp.dbl - 1.0; 94 hfsq = 0.5 * f * f; 95 double s, z, R, t1, t2; 96 97 s = f / (2.0 + f); 98 z = s * s; 99 w = z * z; 100 t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); 101 t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); 102 R = t2 + t1; 103 r = s * (hfsq + R); 104 /* 105 * f-hfsq must (for args near 1) be evaluated in extra precision 106 * to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2). 107 * This is fairly efficient since f-hfsq only depends on f, so can 108 * be evaluated in parallel with R. Not combining hfsq with R also 109 * keeps R small (though not as small as a true `lo' term would be), 110 * so that extra precision is not needed for terms involving R. 111 * 112 * Compiler bugs involving extra precision used to break Dekker's 113 * theorem for spitting f-hfsq as hi+lo, unless double_t was used 114 * or the multi-precision calculations were avoided when double_t 115 * has extra precision. These problems are now automatically 116 * avoided as a side effect of the optimization of combining the 117 * Dekker splitting step with the clear-low-bits step. 118 * 119 * y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra 120 * precision to avoid a very large cancellation when x is very near 121 * these values. Unlike the above cancellations, this problem is 122 * specific to base 2. It is strange that adding +-1 is so much 123 * harder than adding +-ln2 or +-log10_2. 124 * 125 * This uses Dekker's theorem to normalize y+val_hi, so the 126 * compiler bugs are back in some configurations, sigh. And I 127 * don't want to used double_t to avoid them, since that gives a 128 * pessimization and the support for avoiding the pessimization 129 * is not yet available. 130 * 131 * The multi-precision calculations for the multiplications are 132 * routine. 133 */ 134 hi = f - hfsq; 135 temp.dbl = hi; 136 temp.as_int.lo = 0; 137 138 lo = (f - hi) - hfsq + r; 139 val_hi = hi * ivln2hi; 140 val_lo = (lo + hi) * ivln2lo + lo * ivln2hi; 141 142 /* spadd(val_hi, val_lo, y), except for not using double_t: */ 143 w = y + val_hi; 144 val_lo += (y - w) + val_hi; 145 val_hi = w; 146 147 return val_lo + val_hi; 148} /* log2 */ 149 150#undef zero 151#undef two54 152#undef ivln2hi 153#undef ivln2lo 154#undef Lg1 155#undef Lg2 156#undef Lg3 157#undef Lg4 158#undef Lg5 159#undef Lg6 160#undef Lg7 161