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diff --git a/libm/double/pow.c b/libm/double/pow.c
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+/* 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 2024-11-09 23:10:07 +0000