forked from xuos/xiuos
161 lines
5.1 KiB
C
161 lines
5.1 KiB
C
/* Copyright JS Foundation and other contributors, http://js.foundation
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* This file is based on work under the following copyright and permission
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* notice:
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*
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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*
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* @(#)e_log2.c 1.3 95/01/18
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*/
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#include "jerry-math-internal.h"
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/* log2(x)
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* Return the base 2 logarithm of x. See e_log.c and k_log.h for most
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* comments.
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*
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* This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel,
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* then does the combining and scaling steps
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* log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k
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* in not-quite-routine extra precision.
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*/
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#define zero 0.0
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#define two54 1.80143985094819840000e+16 /* 0x43500000, 0x00000000 */
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#define ivln2hi 1.44269504072144627571e+00 /* 0x3FF71547, 0x65200000 */
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#define ivln2lo 1.67517131648865118353e-10 /* 0x3DE705FC, 0x2EEFA200 */
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#define Lg1 6.666666666666735130e-01 /* 0x3FE55555, 0x55555593 */
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#define Lg2 3.999999999940941908e-01 /* 0x3FD99999, 0x9997FA04 */
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#define Lg3 2.857142874366239149e-01 /* 0x3FD24924, 0x94229359 */
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#define Lg4 2.222219843214978396e-01 /* 0x3FCC71C5, 0x1D8E78AF */
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#define Lg5 1.818357216161805012e-01 /* 0x3FC74664, 0x96CB03DE */
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#define Lg6 1.531383769920937332e-01 /* 0x3FC39A09, 0xD078C69F */
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#define Lg7 1.479819860511658591e-01 /* 0x3FC2F112, 0xDF3E5244 */
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double
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log2 (double x)
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{
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double f, hfsq, hi, lo, r, val_hi, val_lo, w, y;
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int i, k, hx;
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unsigned int lx;
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double_accessor temp;
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hx = __HI (x); /* high word of x */
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lx = __LO (x); /* low word of x */
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k = 0;
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if (hx < 0x00100000)
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{ /* x < 2**-1022 */
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if (((hx & 0x7fffffff) | lx) == 0)
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{
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return -two54 / zero; /* log(+-0)=-inf */
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}
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if (hx < 0)
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{
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return (x - x) / zero; /* log(-#) = NaN */
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}
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k -= 54;
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x *= two54; /* subnormal number, scale up x */
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hx = __HI (x); /* high word of x */
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}
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if (hx >= 0x7ff00000)
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{
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return x + x;
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}
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if (hx == 0x3ff00000 && lx == 0)
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{
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return zero; /* log(1) = +0 */
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}
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k += (hx >> 20) - 1023;
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hx &= 0x000fffff;
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i = (hx + 0x95f64) & 0x100000;
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temp.dbl = x;
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temp.as_int.hi = hx | (i ^ 0x3ff00000); /* normalize x or x/2 */
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k += (i >> 20);
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y = (double) k;
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f = temp.dbl - 1.0;
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hfsq = 0.5 * f * f;
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double s, z, R, t1, t2;
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s = f / (2.0 + f);
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z = s * s;
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w = z * z;
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t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
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R = t2 + t1;
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r = s * (hfsq + R);
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/*
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* f-hfsq must (for args near 1) be evaluated in extra precision
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* to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
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* This is fairly efficient since f-hfsq only depends on f, so can
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* be evaluated in parallel with R. Not combining hfsq with R also
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* keeps R small (though not as small as a true `lo' term would be),
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* so that extra precision is not needed for terms involving R.
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*
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* Compiler bugs involving extra precision used to break Dekker's
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* theorem for spitting f-hfsq as hi+lo, unless double_t was used
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* or the multi-precision calculations were avoided when double_t
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* has extra precision. These problems are now automatically
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* avoided as a side effect of the optimization of combining the
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* Dekker splitting step with the clear-low-bits step.
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*
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* y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
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* precision to avoid a very large cancellation when x is very near
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* these values. Unlike the above cancellations, this problem is
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* specific to base 2. It is strange that adding +-1 is so much
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* harder than adding +-ln2 or +-log10_2.
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*
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* This uses Dekker's theorem to normalize y+val_hi, so the
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* compiler bugs are back in some configurations, sigh. And I
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* don't want to used double_t to avoid them, since that gives a
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* pessimization and the support for avoiding the pessimization
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* is not yet available.
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*
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* The multi-precision calculations for the multiplications are
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* routine.
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*/
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hi = f - hfsq;
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temp.dbl = hi;
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temp.as_int.lo = 0;
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lo = (f - hi) - hfsq + r;
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val_hi = hi * ivln2hi;
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val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
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/* spadd(val_hi, val_lo, y), except for not using double_t: */
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w = y + val_hi;
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val_lo += (y - w) + val_hi;
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val_hi = w;
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return val_lo + val_hi;
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} /* log2 */
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#undef zero
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#undef two54
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#undef ivln2hi
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#undef ivln2lo
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#undef Lg1
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#undef Lg2
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#undef Lg3
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#undef Lg4
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#undef Lg5
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#undef Lg6
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#undef Lg7
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