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-rw-r--r--libm/double/pow.c756
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diff --git a/libm/double/pow.c b/libm/double/pow.c
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--- a/libm/double/pow.c
+++ /dev/null
@@ -1,756 +0,0 @@
-/* pow.c
- *
- * Power function
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, z, pow();
- *
- * z = pow( x, y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes x raised to the yth power. Analytically,
- *
- * x**y = exp( y log(x) ).
- *
- * Following Cody and Waite, this program uses a lookup table
- * of 2**-i/16 and pseudo extended precision arithmetic to
- * obtain an extra three bits of accuracy in both the logarithm
- * and the exponential.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -26,26 30000 4.2e-16 7.7e-17
- * DEC -26,26 60000 4.8e-17 9.1e-18
- * 1/26 < x < 26, with log(x) uniformly distributed.
- * -26 < y < 26, y uniformly distributed.
- * IEEE 0,8700 30000 1.5e-14 2.1e-15
- * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * pow overflow x**y > MAXNUM INFINITY
- * pow underflow x**y < 1/MAXNUM 0.0
- * pow domain x<0 and y noninteger 0.0
- *
- */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1995, 2000 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-static char fname[] = {"pow"};
-
-#define SQRTH 0.70710678118654752440
-
-#ifdef UNK
-static double P[] = {
- 4.97778295871696322025E-1,
- 3.73336776063286838734E0,
- 7.69994162726912503298E0,
- 4.66651806774358464979E0
-};
-static double Q[] = {
-/* 1.00000000000000000000E0, */
- 9.33340916416696166113E0,
- 2.79999886606328401649E1,
- 3.35994905342304405431E1,
- 1.39995542032307539578E1
-};
-/* 2^(-i/16), IEEE precision */
-static double A[] = {
- 1.00000000000000000000E0,
- 9.57603280698573700036E-1,
- 9.17004043204671215328E-1,
- 8.78126080186649726755E-1,
- 8.40896415253714502036E-1,
- 8.05245165974627141736E-1,
- 7.71105412703970372057E-1,
- 7.38413072969749673113E-1,
- 7.07106781186547572737E-1,
- 6.77127773468446325644E-1,
- 6.48419777325504820276E-1,
- 6.20928906036742001007E-1,
- 5.94603557501360513449E-1,
- 5.69394317378345782288E-1,
- 5.45253866332628844837E-1,
- 5.22136891213706877402E-1,
- 5.00000000000000000000E-1
-};
-static double B[] = {
- 0.00000000000000000000E0,
- 1.64155361212281360176E-17,
- 4.09950501029074826006E-17,
- 3.97491740484881042808E-17,
--4.83364665672645672553E-17,
- 1.26912513974441574796E-17,
- 1.99100761573282305549E-17,
--1.52339103990623557348E-17,
- 0.00000000000000000000E0
-};
-static double R[] = {
- 1.49664108433729301083E-5,
- 1.54010762792771901396E-4,
- 1.33335476964097721140E-3,
- 9.61812908476554225149E-3,
- 5.55041086645832347466E-2,
- 2.40226506959099779976E-1,
- 6.93147180559945308821E-1
-};
-
-#define douba(k) A[k]
-#define doubb(k) B[k]
-#define MEXP 16383.0
-#ifdef DENORMAL
-#define MNEXP -17183.0
-#else
-#define MNEXP -16383.0
-#endif
-#endif
-
-#ifdef DEC
-static unsigned short P[] = {
-0037776,0156313,0175332,0163602,
-0040556,0167577,0052366,0174245,
-0040766,0062753,0175707,0055564,
-0040625,0052035,0131344,0155636,
-};
-static unsigned short Q[] = {
-/*0040200,0000000,0000000,0000000,*/
-0041025,0052644,0154404,0105155,
-0041337,0177772,0007016,0047646,
-0041406,0062740,0154273,0020020,
-0041137,0177054,0106127,0044555,
-};
-static unsigned short A[] = {
-0040200,0000000,0000000,0000000,
-0040165,0022575,0012444,0103314,
-0040152,0140306,0163735,0022071,
-0040140,0146336,0166052,0112341,
-0040127,0042374,0145326,0116553,
-0040116,0022214,0012437,0102201,
-0040105,0063452,0010525,0003333,
-0040075,0004243,0117530,0006067,
-0040065,0002363,0031771,0157145,
-0040055,0054076,0165102,0120513,
-0040045,0177326,0124661,0050471,
-0040036,0172462,0060221,0120422,
-0040030,0033760,0050615,0134251,
-0040021,0141723,0071653,0010703,
-0040013,0112701,0161752,0105727,
-0040005,0125303,0063714,0044173,
-0040000,0000000,0000000,0000000
-};
-static unsigned short B[] = {
-0000000,0000000,0000000,0000000,
-0021473,0040265,0153315,0140671,
-0121074,0062627,0042146,0176454,
-0121413,0003524,0136332,0066212,
-0121767,0046404,0166231,0012553,
-0121257,0015024,0002357,0043574,
-0021736,0106532,0043060,0056206,
-0121310,0020334,0165705,0035326,
-0000000,0000000,0000000,0000000
-};
-
-static unsigned short R[] = {
-0034173,0014076,0137624,0115771,
-0035041,0076763,0003744,0111311,
-0035656,0141766,0041127,0074351,
-0036435,0112533,0073611,0116664,
-0037143,0054106,0134040,0152223,
-0037565,0176757,0176026,0025551,
-0040061,0071027,0173721,0147572
-};
-
-/*
-static double R[] = {
-0.14928852680595608186e-4,
-0.15400290440989764601e-3,
-0.13333541313585784703e-2,
-0.96181290595172416964e-2,
-0.55504108664085595326e-1,
-0.24022650695909537056e0,
-0.69314718055994529629e0
-};
-*/
-#define douba(k) (*(double *)&A[(k)<<2])
-#define doubb(k) (*(double *)&B[(k)<<2])
-#define MEXP 2031.0
-#define MNEXP -2031.0
-#endif
-
-#ifdef IBMPC
-static unsigned short P[] = {
-0x5cf0,0x7f5b,0xdb99,0x3fdf,
-0xdf15,0xea9e,0xddef,0x400d,
-0xeb6f,0x7f78,0xccbd,0x401e,
-0x9b74,0xb65c,0xaa83,0x4012,
-};
-static unsigned short Q[] = {
-/*0x0000,0x0000,0x0000,0x3ff0,*/
-0x914e,0x9b20,0xaab4,0x4022,
-0xc9f5,0x41c1,0xffff,0x403b,
-0x6402,0x1b17,0xccbc,0x4040,
-0xe92e,0x918a,0xffc5,0x402b,
-};
-static unsigned short A[] = {
-0x0000,0x0000,0x0000,0x3ff0,
-0x90da,0xa2a4,0xa4af,0x3fee,
-0xa487,0xdcfb,0x5818,0x3fed,
-0x529c,0xdd85,0x199b,0x3fec,
-0xd3ad,0x995a,0xe89f,0x3fea,
-0xf090,0x82a3,0xc491,0x3fe9,
-0xa0db,0x422a,0xace5,0x3fe8,
-0x0187,0x73eb,0xa114,0x3fe7,
-0x3bcd,0x667f,0xa09e,0x3fe6,
-0x5429,0xdd48,0xab07,0x3fe5,
-0x2a27,0xd536,0xbfda,0x3fe4,
-0x3422,0x4c12,0xdea6,0x3fe3,
-0xb715,0x0a31,0x06fe,0x3fe3,
-0x6238,0x6e75,0x387a,0x3fe2,
-0x517b,0x3c7d,0x72b8,0x3fe1,
-0x890f,0x6cf9,0xb558,0x3fe0,
-0x0000,0x0000,0x0000,0x3fe0
-};
-static unsigned short B[] = {
-0x0000,0x0000,0x0000,0x0000,
-0x3707,0xd75b,0xed02,0x3c72,
-0xcc81,0x345d,0xa1cd,0x3c87,
-0x4b27,0x5686,0xe9f1,0x3c86,
-0x6456,0x13b2,0xdd34,0xbc8b,
-0x42e2,0xafec,0x4397,0x3c6d,
-0x82e4,0xd231,0xf46a,0x3c76,
-0x8a76,0xb9d7,0x9041,0xbc71,
-0x0000,0x0000,0x0000,0x0000
-};
-static unsigned short R[] = {
-0x937f,0xd7f2,0x6307,0x3eef,
-0x9259,0x60fc,0x2fbe,0x3f24,
-0xef1d,0xc84a,0xd87e,0x3f55,
-0x33b7,0x6ef1,0xb2ab,0x3f83,
-0x1a92,0xd704,0x6b08,0x3fac,
-0xc56d,0xff82,0xbfbd,0x3fce,
-0x39ef,0xfefa,0x2e42,0x3fe6
-};
-
-#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
-
-#ifdef MIEEE
-static unsigned short P[] = {
-0x3fdf,0xdb99,0x7f5b,0x5cf0,
-0x400d,0xddef,0xea9e,0xdf15,
-0x401e,0xccbd,0x7f78,0xeb6f,
-0x4012,0xaa83,0xb65c,0x9b74
-};
-static unsigned short Q[] = {
-0x4022,0xaab4,0x9b20,0x914e,
-0x403b,0xffff,0x41c1,0xc9f5,
-0x4040,0xccbc,0x1b17,0x6402,
-0x402b,0xffc5,0x918a,0xe92e
-};
-static unsigned short A[] = {
-0x3ff0,0x0000,0x0000,0x0000,
-0x3fee,0xa4af,0xa2a4,0x90da,
-0x3fed,0x5818,0xdcfb,0xa487,
-0x3fec,0x199b,0xdd85,0x529c,
-0x3fea,0xe89f,0x995a,0xd3ad,
-0x3fe9,0xc491,0x82a3,0xf090,
-0x3fe8,0xace5,0x422a,0xa0db,
-0x3fe7,0xa114,0x73eb,0x0187,
-0x3fe6,0xa09e,0x667f,0x3bcd,
-0x3fe5,0xab07,0xdd48,0x5429,
-0x3fe4,0xbfda,0xd536,0x2a27,
-0x3fe3,0xdea6,0x4c12,0x3422,
-0x3fe3,0x06fe,0x0a31,0xb715,
-0x3fe2,0x387a,0x6e75,0x6238,
-0x3fe1,0x72b8,0x3c7d,0x517b,
-0x3fe0,0xb558,0x6cf9,0x890f,
-0x3fe0,0x0000,0x0000,0x0000
-};
-static unsigned short B[] = {
-0x0000,0x0000,0x0000,0x0000,
-0x3c72,0xed02,0xd75b,0x3707,
-0x3c87,0xa1cd,0x345d,0xcc81,
-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 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
-
-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) )
- return( x );
-if( isnan(y) )
- return( 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 )
- {
-#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 )
- {
- 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 = 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 double reduc(x)
-double x;
-{
-double t;
-
-t = ldexp( x, 4 );
-t = floor( t );
-t = ldexp( t, -4 );
-return(t);
-}
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-02 08:20:20 +0000