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The Cephes Mathematical Library author Steve Moshier has released the Cephes Mathematical Library under the BSD license. This patch patch replaces the cephes license with the BSD license for all Cephes Mathematical Library code. See also: https://bugs.gentoo.org/687276 See also: https://lists.debian.org/debian-legal/2004/12/msg00295.html See also: https://github.com/deepmind/torch-cephes/blob/master/LICENSE.txt See also: https://github.com/nearform/node-cephes/blob/master/LICENSE
780 lines
16 KiB
C
780 lines
16 KiB
C
/* pow.c
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*
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* Power function
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, z, pow();
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*
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* z = pow( x, y );
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*
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*
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*
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* DESCRIPTION:
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*
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* Computes x raised to the yth power. Analytically,
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*
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* x**y = exp( y log(x) ).
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*
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* Following Cody and Waite, this program uses a lookup table
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* of 2**-i/16 and pseudo extended precision arithmetic to
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* obtain an extra three bits of accuracy in both the logarithm
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* and the exponential.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -26,26 30000 4.2e-16 7.7e-17
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* DEC -26,26 60000 4.8e-17 9.1e-18
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* 1/26 < x < 26, with log(x) uniformly distributed.
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* -26 < y < 26, y uniformly distributed.
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* IEEE 0,8700 30000 1.5e-14 2.1e-15
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* 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* pow overflow x**y > MAXNUM INFINITY
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* pow underflow x**y < 1/MAXNUM 0.0
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* pow domain x<0 and y noninteger 0.0
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*
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*/
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1995, 2000 by Stephen L. Moshier
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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1. Redistributions of source code must retain the above copyright notice,
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this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. Neither the name of the <ORGANIZATION> nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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*/
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#include "mconf.h"
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static char fname[] = {"pow"};
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#define SQRTH 0.70710678118654752440
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#ifdef UNK
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static double P[] = {
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4.97778295871696322025E-1,
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3.73336776063286838734E0,
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7.69994162726912503298E0,
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4.66651806774358464979E0
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};
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static double Q[] = {
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/* 1.00000000000000000000E0, */
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9.33340916416696166113E0,
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2.79999886606328401649E1,
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3.35994905342304405431E1,
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1.39995542032307539578E1
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};
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/* 2^(-i/16), IEEE precision */
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static double A[] = {
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1.00000000000000000000E0,
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9.57603280698573700036E-1,
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9.17004043204671215328E-1,
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8.78126080186649726755E-1,
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8.40896415253714502036E-1,
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8.05245165974627141736E-1,
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7.71105412703970372057E-1,
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7.38413072969749673113E-1,
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7.07106781186547572737E-1,
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6.77127773468446325644E-1,
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6.48419777325504820276E-1,
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6.20928906036742001007E-1,
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5.94603557501360513449E-1,
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5.69394317378345782288E-1,
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5.45253866332628844837E-1,
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5.22136891213706877402E-1,
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5.00000000000000000000E-1
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};
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static double B[] = {
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0.00000000000000000000E0,
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1.64155361212281360176E-17,
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4.09950501029074826006E-17,
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3.97491740484881042808E-17,
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-4.83364665672645672553E-17,
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1.26912513974441574796E-17,
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1.99100761573282305549E-17,
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-1.52339103990623557348E-17,
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0.00000000000000000000E0
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};
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static double R[] = {
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1.49664108433729301083E-5,
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1.54010762792771901396E-4,
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1.33335476964097721140E-3,
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9.61812908476554225149E-3,
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5.55041086645832347466E-2,
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2.40226506959099779976E-1,
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6.93147180559945308821E-1
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};
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#define douba(k) A[k]
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#define doubb(k) B[k]
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#define MEXP 16383.0
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#ifdef DENORMAL
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#define MNEXP -17183.0
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#else
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#define MNEXP -16383.0
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#endif
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#endif
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#ifdef DEC
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static unsigned short P[] = {
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0037776,0156313,0175332,0163602,
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0040556,0167577,0052366,0174245,
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0040766,0062753,0175707,0055564,
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0040625,0052035,0131344,0155636,
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0041025,0052644,0154404,0105155,
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0041337,0177772,0007016,0047646,
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0041406,0062740,0154273,0020020,
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0041137,0177054,0106127,0044555,
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};
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static unsigned short A[] = {
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0040200,0000000,0000000,0000000,
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0040165,0022575,0012444,0103314,
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0040152,0140306,0163735,0022071,
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0040140,0146336,0166052,0112341,
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0040127,0042374,0145326,0116553,
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0040116,0022214,0012437,0102201,
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0040105,0063452,0010525,0003333,
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0040075,0004243,0117530,0006067,
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0040065,0002363,0031771,0157145,
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0040055,0054076,0165102,0120513,
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0040045,0177326,0124661,0050471,
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0040036,0172462,0060221,0120422,
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0040030,0033760,0050615,0134251,
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0040021,0141723,0071653,0010703,
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0040013,0112701,0161752,0105727,
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0040005,0125303,0063714,0044173,
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0040000,0000000,0000000,0000000
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};
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static unsigned short B[] = {
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0000000,0000000,0000000,0000000,
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0021473,0040265,0153315,0140671,
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0121074,0062627,0042146,0176454,
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0121413,0003524,0136332,0066212,
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0121767,0046404,0166231,0012553,
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0121257,0015024,0002357,0043574,
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0021736,0106532,0043060,0056206,
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0121310,0020334,0165705,0035326,
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0000000,0000000,0000000,0000000
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};
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static unsigned short R[] = {
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0034173,0014076,0137624,0115771,
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0035041,0076763,0003744,0111311,
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0035656,0141766,0041127,0074351,
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0036435,0112533,0073611,0116664,
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0037143,0054106,0134040,0152223,
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0037565,0176757,0176026,0025551,
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0040061,0071027,0173721,0147572
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};
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/*
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static double R[] = {
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0.14928852680595608186e-4,
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0.15400290440989764601e-3,
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0.13333541313585784703e-2,
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0.96181290595172416964e-2,
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0.55504108664085595326e-1,
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0.24022650695909537056e0,
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0.69314718055994529629e0
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};
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*/
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#define douba(k) (*(double *)&A[(k)<<2])
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#define doubb(k) (*(double *)&B[(k)<<2])
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#define MEXP 2031.0
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#define MNEXP -2031.0
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#endif
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#ifdef IBMPC
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static unsigned short P[] = {
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0x5cf0,0x7f5b,0xdb99,0x3fdf,
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0xdf15,0xea9e,0xddef,0x400d,
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0xeb6f,0x7f78,0xccbd,0x401e,
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0x9b74,0xb65c,0xaa83,0x4012,
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0x914e,0x9b20,0xaab4,0x4022,
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0xc9f5,0x41c1,0xffff,0x403b,
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0x6402,0x1b17,0xccbc,0x4040,
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0xe92e,0x918a,0xffc5,0x402b,
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};
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static unsigned short A[] = {
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0x0000,0x0000,0x0000,0x3ff0,
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0x90da,0xa2a4,0xa4af,0x3fee,
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0xa487,0xdcfb,0x5818,0x3fed,
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0x529c,0xdd85,0x199b,0x3fec,
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0xd3ad,0x995a,0xe89f,0x3fea,
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0xf090,0x82a3,0xc491,0x3fe9,
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0xa0db,0x422a,0xace5,0x3fe8,
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0x0187,0x73eb,0xa114,0x3fe7,
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0x3bcd,0x667f,0xa09e,0x3fe6,
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0x5429,0xdd48,0xab07,0x3fe5,
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0x2a27,0xd536,0xbfda,0x3fe4,
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0x3422,0x4c12,0xdea6,0x3fe3,
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0xb715,0x0a31,0x06fe,0x3fe3,
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0x6238,0x6e75,0x387a,0x3fe2,
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0x517b,0x3c7d,0x72b8,0x3fe1,
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0x890f,0x6cf9,0xb558,0x3fe0,
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0x0000,0x0000,0x0000,0x3fe0
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};
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static unsigned short B[] = {
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0x0000,0x0000,0x0000,0x0000,
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0x3707,0xd75b,0xed02,0x3c72,
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0xcc81,0x345d,0xa1cd,0x3c87,
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0x4b27,0x5686,0xe9f1,0x3c86,
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0x6456,0x13b2,0xdd34,0xbc8b,
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0x42e2,0xafec,0x4397,0x3c6d,
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0x82e4,0xd231,0xf46a,0x3c76,
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0x8a76,0xb9d7,0x9041,0xbc71,
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0x0000,0x0000,0x0000,0x0000
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};
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static unsigned short R[] = {
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0x937f,0xd7f2,0x6307,0x3eef,
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0x9259,0x60fc,0x2fbe,0x3f24,
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0xef1d,0xc84a,0xd87e,0x3f55,
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0x33b7,0x6ef1,0xb2ab,0x3f83,
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0x1a92,0xd704,0x6b08,0x3fac,
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0xc56d,0xff82,0xbfbd,0x3fce,
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0x39ef,0xfefa,0x2e42,0x3fe6
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};
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#define douba(k) (*(double *)&A[(k)<<2])
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#define doubb(k) (*(double *)&B[(k)<<2])
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#define MEXP 16383.0
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#ifdef DENORMAL
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#define MNEXP -17183.0
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#else
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#define MNEXP -16383.0
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#endif
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#endif
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#ifdef MIEEE
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static unsigned short P[] = {
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0x3fdf,0xdb99,0x7f5b,0x5cf0,
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0x400d,0xddef,0xea9e,0xdf15,
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0x401e,0xccbd,0x7f78,0xeb6f,
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0x4012,0xaa83,0xb65c,0x9b74
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};
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static unsigned short Q[] = {
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0x4022,0xaab4,0x9b20,0x914e,
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0x403b,0xffff,0x41c1,0xc9f5,
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0x4040,0xccbc,0x1b17,0x6402,
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0x402b,0xffc5,0x918a,0xe92e
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};
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static unsigned short A[] = {
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0x3ff0,0x0000,0x0000,0x0000,
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0x3fee,0xa4af,0xa2a4,0x90da,
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0x3fed,0x5818,0xdcfb,0xa487,
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0x3fec,0x199b,0xdd85,0x529c,
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0x3fea,0xe89f,0x995a,0xd3ad,
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0x3fe9,0xc491,0x82a3,0xf090,
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0x3fe8,0xace5,0x422a,0xa0db,
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0x3fe7,0xa114,0x73eb,0x0187,
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0x3fe6,0xa09e,0x667f,0x3bcd,
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0x3fe5,0xab07,0xdd48,0x5429,
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0x3fe4,0xbfda,0xd536,0x2a27,
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0x3fe3,0xdea6,0x4c12,0x3422,
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0x3fe3,0x06fe,0x0a31,0xb715,
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0x3fe2,0x387a,0x6e75,0x6238,
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0x3fe1,0x72b8,0x3c7d,0x517b,
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0x3fe0,0xb558,0x6cf9,0x890f,
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0x3fe0,0x0000,0x0000,0x0000
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};
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static unsigned short B[] = {
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0x0000,0x0000,0x0000,0x0000,
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0x3c72,0xed02,0xd75b,0x3707,
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0x3c87,0xa1cd,0x345d,0xcc81,
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0x3c86,0xe9f1,0x5686,0x4b27,
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0xbc8b,0xdd34,0x13b2,0x6456,
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0x3c6d,0x4397,0xafec,0x42e2,
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0x3c76,0xf46a,0xd231,0x82e4,
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0xbc71,0x9041,0xb9d7,0x8a76,
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0x0000,0x0000,0x0000,0x0000
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};
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static unsigned short R[] = {
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0x3eef,0x6307,0xd7f2,0x937f,
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0x3f24,0x2fbe,0x60fc,0x9259,
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0x3f55,0xd87e,0xc84a,0xef1d,
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0x3f83,0xb2ab,0x6ef1,0x33b7,
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0x3fac,0x6b08,0xd704,0x1a92,
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0x3fce,0xbfbd,0xff82,0xc56d,
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0x3fe6,0x2e42,0xfefa,0x39ef
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};
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#define douba(k) (*(double *)&A[(k)<<2])
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#define doubb(k) (*(double *)&B[(k)<<2])
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#define MEXP 16383.0
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#ifdef DENORMAL
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#define MNEXP -17183.0
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#else
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#define MNEXP -16383.0
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#endif
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#endif
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/* log2(e) - 1 */
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#define LOG2EA 0.44269504088896340736
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#define F W
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#define Fa Wa
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#define Fb Wb
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#define G W
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#define Ga Wa
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#define Gb u
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#define H W
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#define Ha Wb
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#define Hb Wb
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#ifdef ANSIPROT
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extern double floor ( double );
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extern double fabs ( double );
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extern double frexp ( double, int * );
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extern double ldexp ( double, int );
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern double c_powi ( double, int );
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extern int signbit ( double );
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extern int isnan ( double );
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extern int isfinite ( double );
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static double reduc ( double );
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#else
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double floor(), fabs(), frexp(), ldexp();
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double polevl(), p1evl(), c_powi();
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int signbit(), isnan(), isfinite();
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static double reduc();
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#endif
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extern double MAXNUM;
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#ifdef INFINITIES
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extern double INFINITY;
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#endif
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#ifdef NANS
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extern double NAN;
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#endif
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#ifdef MINUSZERO
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extern double NEGZERO;
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#endif
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double c_pow( x, y )
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double x, y;
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{
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double w, z, W, Wa, Wb, ya, yb, u;
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/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
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double aw, ay, wy;
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int e, i, nflg, iyflg, yoddint;
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if( y == 0.0 )
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return( 1.0 );
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#ifdef NANS
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if( isnan(x) )
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return( x );
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if( isnan(y) )
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return( y );
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#endif
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if( y == 1.0 )
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return( x );
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#ifdef INFINITIES
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if( !isfinite(y) && (x == 1.0 || x == -1.0) )
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{
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mtherr( "pow", DOMAIN );
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#ifdef NANS
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return( NAN );
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#else
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return( INFINITY );
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#endif
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}
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#endif
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if( x == 1.0 )
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return( 1.0 );
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if( y >= MAXNUM )
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{
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#ifdef INFINITIES
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if( x > 1.0 )
|
||
return( INFINITY );
|
||
#else
|
||
if( x > 1.0 )
|
||
return( MAXNUM );
|
||
#endif
|
||
if( x > 0.0 && x < 1.0 )
|
||
return( 0.0);
|
||
if( x < -1.0 )
|
||
{
|
||
#ifdef INFINITIES
|
||
return( INFINITY );
|
||
#else
|
||
return( MAXNUM );
|
||
#endif
|
||
}
|
||
if( x > -1.0 && x < 0.0 )
|
||
return( 0.0 );
|
||
}
|
||
if( y <= -MAXNUM )
|
||
{
|
||
if( x > 1.0 )
|
||
return( 0.0 );
|
||
#ifdef INFINITIES
|
||
if( x > 0.0 && x < 1.0 )
|
||
return( INFINITY );
|
||
#else
|
||
if( x > 0.0 && x < 1.0 )
|
||
return( MAXNUM );
|
||
#endif
|
||
if( x < -1.0 )
|
||
return( 0.0 );
|
||
#ifdef INFINITIES
|
||
if( x > -1.0 && x < 0.0 )
|
||
return( INFINITY );
|
||
#else
|
||
if( x > -1.0 && x < 0.0 )
|
||
return( MAXNUM );
|
||
#endif
|
||
}
|
||
if( x >= MAXNUM )
|
||
{
|
||
#if INFINITIES
|
||
if( y > 0.0 )
|
||
return( INFINITY );
|
||
#else
|
||
if( y > 0.0 )
|
||
return( MAXNUM );
|
||
#endif
|
||
return(0.0);
|
||
}
|
||
/* Set iyflg to 1 if y is an integer. */
|
||
iyflg = 0;
|
||
w = floor(y);
|
||
if( w == y )
|
||
iyflg = 1;
|
||
|
||
/* Test for odd integer y. */
|
||
yoddint = 0;
|
||
if( iyflg )
|
||
{
|
||
ya = fabs(y);
|
||
ya = floor(0.5 * ya);
|
||
yb = 0.5 * fabs(w);
|
||
if( ya != yb )
|
||
yoddint = 1;
|
||
}
|
||
|
||
if( x <= -MAXNUM )
|
||
{
|
||
if( y > 0.0 )
|
||
{
|
||
#ifdef INFINITIES
|
||
if( yoddint )
|
||
return( -INFINITY );
|
||
return( INFINITY );
|
||
#else
|
||
if( yoddint )
|
||
return( -MAXNUM );
|
||
return( MAXNUM );
|
||
#endif
|
||
}
|
||
if( y < 0.0 )
|
||
{
|
||
#ifdef MINUSZERO
|
||
if( yoddint )
|
||
return( NEGZERO );
|
||
#endif
|
||
return( 0.0 );
|
||
}
|
||
}
|
||
|
||
nflg = 0; /* flag = 1 if x<0 raised to integer power */
|
||
if( x <= 0.0 )
|
||
{
|
||
if( x == 0.0 )
|
||
{
|
||
if( y < 0.0 )
|
||
{
|
||
#ifdef MINUSZERO
|
||
if( signbit(x) && yoddint )
|
||
return( -INFINITY );
|
||
#endif
|
||
#ifdef INFINITIES
|
||
return( INFINITY );
|
||
#else
|
||
return( MAXNUM );
|
||
#endif
|
||
}
|
||
if( y > 0.0 )
|
||
{
|
||
#ifdef MINUSZERO
|
||
if( signbit(x) && yoddint )
|
||
return( NEGZERO );
|
||
#endif
|
||
return( 0.0 );
|
||
}
|
||
return( 1.0 );
|
||
}
|
||
else
|
||
{
|
||
if( iyflg == 0 )
|
||
{ /* noninteger power of negative number */
|
||
mtherr( fname, DOMAIN );
|
||
#ifdef NANS
|
||
return(NAN);
|
||
#else
|
||
return(0.0L);
|
||
#endif
|
||
}
|
||
nflg = 1;
|
||
}
|
||
}
|
||
|
||
/* Integer power of an integer. */
|
||
|
||
if( iyflg )
|
||
{
|
||
i = (int)w;
|
||
w = floor(x);
|
||
if( (w == x) && (fabs(y) < 32768.0) )
|
||
{
|
||
w = c_powi( x, (int) y );
|
||
return( w );
|
||
}
|
||
}
|
||
|
||
if( nflg )
|
||
x = fabs(x);
|
||
|
||
/* For results close to 1, use a series expansion. */
|
||
w = x - 1.0;
|
||
aw = fabs(w);
|
||
ay = fabs(y);
|
||
wy = w * y;
|
||
ya = fabs(wy);
|
||
if((aw <= 1.0e-3 && ay <= 1.0)
|
||
|| (ya <= 1.0e-3 && ay >= 1.0))
|
||
{
|
||
z = (((((w*(y-5.)/720. + 1./120.)*w*(y-4.) + 1./24.)*w*(y-3.)
|
||
+ 1./6.)*w*(y-2.) + 0.5)*w*(y-1.) )*wy + wy + 1.;
|
||
goto done;
|
||
}
|
||
/* These are probably too much trouble. */
|
||
#if 0
|
||
w = y * log(x);
|
||
if (aw > 1.0e-3 && fabs(w) < 1.0e-3)
|
||
{
|
||
z = ((((((
|
||
w/7. + 1.)*w/6. + 1.)*w/5. + 1.)*w/4. + 1.)*w/3. + 1.)*w/2. + 1.)*w + 1.;
|
||
goto done;
|
||
}
|
||
|
||
if(ya <= 1.0e-3 && aw <= 1.0e-4)
|
||
{
|
||
z = (((((
|
||
wy*1./720.
|
||
+ (-w*1./48. + 1./120.) )*wy
|
||
+ ((w*17./144. - 1./12.)*w + 1./24.) )*wy
|
||
+ (((-w*5./16. + 7./24.)*w - 1./4.)*w + 1./6.) )*wy
|
||
+ ((((w*137./360. - 5./12.)*w + 11./24.)*w - 1./2.)*w + 1./2.) )*wy
|
||
+ (((((-w*1./6. + 1./5.)*w - 1./4)*w + 1./3.)*w -1./2.)*w ) )*wy
|
||
+ wy + 1.0;
|
||
goto done;
|
||
}
|
||
#endif
|
||
|
||
/* separate significand from exponent */
|
||
x = frexp( x, &e );
|
||
|
||
#if 0
|
||
/* For debugging, check for gross overflow. */
|
||
if( (e * y) > (MEXP + 1024) )
|
||
goto overflow;
|
||
#endif
|
||
|
||
/* Find significand of x in antilog table A[]. */
|
||
i = 1;
|
||
if( x <= douba(9) )
|
||
i = 9;
|
||
if( x <= douba(i+4) )
|
||
i += 4;
|
||
if( x <= douba(i+2) )
|
||
i += 2;
|
||
if( x >= douba(1) )
|
||
i = -1;
|
||
i += 1;
|
||
|
||
|
||
/* Find (x - A[i])/A[i]
|
||
* in order to compute log(x/A[i]):
|
||
*
|
||
* log(x) = log( a x/a ) = log(a) + log(x/a)
|
||
*
|
||
* log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
|
||
*/
|
||
x -= douba(i);
|
||
x -= doubb(i/2);
|
||
x /= douba(i);
|
||
|
||
|
||
/* rational approximation for log(1+v):
|
||
*
|
||
* log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
|
||
*/
|
||
z = x*x;
|
||
w = x * ( z * polevl( x, P, 3 ) / p1evl( x, Q, 4 ) );
|
||
w = w - ldexp( z, -1 ); /* w - 0.5 * z */
|
||
|
||
/* Convert to base 2 logarithm:
|
||
* multiply by log2(e)
|
||
*/
|
||
w = w + LOG2EA * w;
|
||
/* Note x was not yet added in
|
||
* to above rational approximation,
|
||
* so do it now, while multiplying
|
||
* by log2(e).
|
||
*/
|
||
z = w + LOG2EA * x;
|
||
z = z + x;
|
||
|
||
/* Compute exponent term of the base 2 logarithm. */
|
||
w = -i;
|
||
w = ldexp( w, -4 ); /* divide by 16 */
|
||
w += e;
|
||
/* Now base 2 log of x is w + z. */
|
||
|
||
/* Multiply base 2 log by y, in extended precision. */
|
||
|
||
/* separate y into large part ya
|
||
* and small part yb less than 1/16
|
||
*/
|
||
ya = reduc(y);
|
||
yb = y - ya;
|
||
|
||
|
||
F = z * y + w * yb;
|
||
Fa = reduc(F);
|
||
Fb = F - Fa;
|
||
|
||
G = Fa + w * ya;
|
||
Ga = reduc(G);
|
||
Gb = G - Ga;
|
||
|
||
H = Fb + Gb;
|
||
Ha = reduc(H);
|
||
w = ldexp( Ga+Ha, 4 );
|
||
|
||
/* Test the power of 2 for overflow */
|
||
if( w > MEXP )
|
||
{
|
||
#ifndef INFINITIES
|
||
mtherr( fname, OVERFLOW );
|
||
#endif
|
||
#ifdef INFINITIES
|
||
if( nflg && yoddint )
|
||
return( -INFINITY );
|
||
return( INFINITY );
|
||
#else
|
||
if( nflg && yoddint )
|
||
return( -MAXNUM );
|
||
return( MAXNUM );
|
||
#endif
|
||
}
|
||
|
||
if( w < (MNEXP - 1) )
|
||
{
|
||
#ifndef DENORMAL
|
||
mtherr( fname, UNDERFLOW );
|
||
#endif
|
||
#ifdef MINUSZERO
|
||
if( nflg && yoddint )
|
||
return( NEGZERO );
|
||
#endif
|
||
return( 0.0 );
|
||
}
|
||
|
||
e = (int)w;
|
||
Hb = H - Ha;
|
||
|
||
if( Hb > 0.0 )
|
||
{
|
||
e += 1;
|
||
Hb -= 0.0625;
|
||
}
|
||
|
||
/* Now the product y * log2(x) = Hb + e/16.0.
|
||
*
|
||
* Compute base 2 exponential of Hb,
|
||
* where -0.0625 <= Hb <= 0.
|
||
*/
|
||
z = Hb * polevl( Hb, R, 6 ); /* z = 2**Hb - 1 */
|
||
|
||
/* Express e/16 as an integer plus a negative number of 16ths.
|
||
* Find lookup table entry for the fractional power of 2.
|
||
*/
|
||
if( e < 0 )
|
||
i = 0;
|
||
else
|
||
i = 1;
|
||
i = e/16 + i;
|
||
e = 16*i - e;
|
||
w = douba( e );
|
||
z = w + w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
|
||
z = ldexp( z, i ); /* multiply by integer power of 2 */
|
||
|
||
done:
|
||
|
||
/* Negate if odd integer power of negative number */
|
||
if( nflg && yoddint )
|
||
{
|
||
#ifdef MINUSZERO
|
||
if( z == 0.0 )
|
||
z = NEGZERO;
|
||
else
|
||
#endif
|
||
z = -z;
|
||
}
|
||
return( z );
|
||
}
|
||
|
||
|
||
/* Find a multiple of 1/16 that is within 1/16 of x. */
|
||
static double reduc(x)
|
||
double x;
|
||
{
|
||
double t;
|
||
|
||
t = ldexp( x, 4 );
|
||
t = floor( t );
|
||
t = ldexp( t, -4 );
|
||
return(t);
|
||
}
|