782 lines
15 KiB
C
782 lines
15 KiB
C
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/* 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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*/
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/*
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Modified for mingw
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2002-09-27 Danny Smith <dannysmith@users.sourceforge.net>
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*/
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#ifdef __MINGW32__
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#include "cephes_mconf.h"
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#else
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#include "mconf.h"
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static char fname[] = {"pow"};
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#endif
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#ifndef _SET_ERRNO
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#define _SET_ERRNO(x)
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#endif
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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 const 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 const 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 const 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 const 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 const 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,
|
|||
|
|
0xbc8b,0xdd34,0x13b2,0x6456,
|
|||
|
|
0x3c6d,0x4397,0xafec,0x42e2,
|
|||
|
|
0x3c76,0xf46a,0xd231,0x82e4,
|
|||
|
|
0xbc71,0x9041,0xb9d7,0x8a76,
|
|||
|
|
0x0000,0x0000,0x0000,0x0000
|
|||
|
|
};
|
|||
|
|
static unsigned short R[] = {
|
|||
|
|
0x3eef,0x6307,0xd7f2,0x937f,
|
|||
|
|
0x3f24,0x2fbe,0x60fc,0x9259,
|
|||
|
|
0x3f55,0xd87e,0xc84a,0xef1d,
|
|||
|
|
0x3f83,0xb2ab,0x6ef1,0x33b7,
|
|||
|
|
0x3fac,0x6b08,0xd704,0x1a92,
|
|||
|
|
0x3fce,0xbfbd,0xff82,0xc56d,
|
|||
|
|
0x3fe6,0x2e42,0xfefa,0x39ef
|
|||
|
|
};
|
|||
|
|
|
|||
|
|
#define douba(k) (*(double *)&A[(k)<<2])
|
|||
|
|
#define doubb(k) (*(double *)&B[(k)<<2])
|
|||
|
|
#define MEXP 16383.0
|
|||
|
|
#ifdef DENORMAL
|
|||
|
|
#define MNEXP -17183.0
|
|||
|
|
#else
|
|||
|
|
#define MNEXP -16383.0
|
|||
|
|
#endif
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
/* log2(e) - 1 */
|
|||
|
|
#define LOG2EA 0.44269504088896340736
|
|||
|
|
|
|||
|
|
#define F W
|
|||
|
|
#define Fa Wa
|
|||
|
|
#define Fb Wb
|
|||
|
|
#define G W
|
|||
|
|
#define Ga Wa
|
|||
|
|
#define Gb u
|
|||
|
|
#define H W
|
|||
|
|
#define Ha Wb
|
|||
|
|
#define Hb Wb
|
|||
|
|
|
|||
|
|
#ifdef __MINGW32__
|
|||
|
|
static __inline__ double reduc( double );
|
|||
|
|
extern double __powi ( double, int );
|
|||
|
|
extern double pow ( double x, double y);
|
|||
|
|
|
|||
|
|
#else /* __MINGW32__ */
|
|||
|
|
|
|||
|
|
#ifdef ANSIPROT
|
|||
|
|
extern double floor ( double );
|
|||
|
|
extern double fabs ( double );
|
|||
|
|
extern double frexp ( double, int * );
|
|||
|
|
extern double ldexp ( double, int );
|
|||
|
|
extern double polevl ( double, void *, int );
|
|||
|
|
extern double p1evl ( double, void *, int );
|
|||
|
|
extern double __powi ( double, int );
|
|||
|
|
extern int signbit ( double );
|
|||
|
|
extern int isnan ( double );
|
|||
|
|
extern int isfinite ( double );
|
|||
|
|
static double reduc ( double );
|
|||
|
|
#else
|
|||
|
|
double floor(), fabs(), frexp(), ldexp();
|
|||
|
|
double polevl(), p1evl(), __powi();
|
|||
|
|
int signbit(), isnan(), isfinite();
|
|||
|
|
static double reduc();
|
|||
|
|
#endif
|
|||
|
|
extern double MAXNUM;
|
|||
|
|
#ifdef INFINITIES
|
|||
|
|
extern double INFINITY;
|
|||
|
|
#endif
|
|||
|
|
#ifdef NANS
|
|||
|
|
extern double NAN;
|
|||
|
|
#endif
|
|||
|
|
#ifdef MINUSZERO
|
|||
|
|
extern double NEGZERO;
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
#endif /* __MINGW32__ */
|
|||
|
|
|
|||
|
|
double pow( x, y )
|
|||
|
|
double x, y;
|
|||
|
|
{
|
|||
|
|
double w, z, W, Wa, Wb, ya, yb, u;
|
|||
|
|
/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
|
|||
|
|
double aw, ay, wy;
|
|||
|
|
int e, i, nflg, iyflg, yoddint;
|
|||
|
|
|
|||
|
|
if( y == 0.0 )
|
|||
|
|
return( 1.0 );
|
|||
|
|
#ifdef NANS
|
|||
|
|
if( isnan(x) || isnan(y) )
|
|||
|
|
{
|
|||
|
|
_SET_ERRNO (EDOM);
|
|||
|
|
return( x + y );
|
|||
|
|
}
|
|||
|
|
#endif
|
|||
|
|
if( y == 1.0 )
|
|||
|
|
return( x );
|
|||
|
|
|
|||
|
|
|
|||
|
|
#ifdef INFINITIES
|
|||
|
|
if( !isfinite(y) && (x == 1.0 || x == -1.0) )
|
|||
|
|
{
|
|||
|
|
mtherr( "pow", DOMAIN );
|
|||
|
|
#ifdef NANS
|
|||
|
|
return( NAN );
|
|||
|
|
#else
|
|||
|
|
return( INFINITY );
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
#endif
|
|||
|
|
|
|||
|
|
if( x == 1.0 )
|
|||
|
|
return( 1.0 );
|
|||
|
|
|
|||
|
|
if( y >= MAXNUM )
|
|||
|
|
{
|
|||
|
|
_SET_ERRNO (ERANGE);
|
|||
|
|
#ifdef INFINITIES
|
|||
|
|
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 )
|
|||
|
|
{
|
|||
|
|
_SET_ERRNO (ERANGE);
|
|||
|
|
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 );
|
|||
|
|
_SET_ERRNO (EDOM);
|
|||
|
|
#ifdef NANS
|
|||
|
|
return(NAN);
|
|||
|
|
#else
|
|||
|
|
return(0.0L);
|
|||
|
|
#endif
|
|||
|
|
}
|
|||
|
|
nflg = 1;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/* Integer power of an integer. */
|
|||
|
|
|
|||
|
|
if( iyflg )
|
|||
|
|
{
|
|||
|
|
i = w;
|
|||
|
|
w = floor(x);
|
|||
|
|
if( (w == x) && (fabs(y) < 32768.0) )
|
|||
|
|
{
|
|||
|
|
w = __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 = 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 __inline__ double reduc(x)
|
|||
|
|
double x;
|
|||
|
|
{
|
|||
|
|
double t;
|
|||
|
|
|
|||
|
|
t = ldexp( x, 4 );
|
|||
|
|
t = floor( t );
|
|||
|
|
t = ldexp( t, -4 );
|
|||
|
|
return(t);
|
|||
|
|
}
|