uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 1043 insertions, 0 deletions

diff --git a/libm/double/clog.c b/libm/double/clog.c
new file mode 100644
index 000000000..70a318a50
--- /dev/null
+++ b/libm/double/clog.c
@@ -0,0 +1,1043 @@
+/*							clog.c
+ *
+ *	Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clog();
+ * cmplx z, w;
+ *
+ * clog( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ *       w = log(r) + i arctan(y/x).
+ * 
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      7000       8.5e-17     1.9e-17
+ *    IEEE      -10,+10     30000       5.0e-15     1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#ifdef ANSIPROT
+static void cchsh ( double x, double *c, double *s );
+static double redupi ( double x );
+static double ctans ( cmplx *z );
+/* These are supposed to be in some standard place. */
+double fabs (double);
+double sqrt (double);
+double pow (double, double);
+double log (double);
+double exp (double);
+double atan2 (double, double);
+double cosh (double);
+double sinh (double);
+double asin (double);
+double sin (double);
+double cos (double);
+double cabs (cmplx *);
+void cadd ( cmplx *, cmplx *, cmplx * );
+void cmul ( cmplx *, cmplx *, cmplx * );
+void csqrt ( cmplx *, cmplx * );
+static void cchsh ( double, double *, double * );
+static double redupi ( double );
+static double ctans ( cmplx * );
+void clog ( cmplx *, cmplx * );
+void casin ( cmplx *, cmplx * );
+void cacos ( cmplx *, cmplx * );
+void catan ( cmplx *, cmplx * );
+#else
+static void cchsh();
+static double redupi();
+static double ctans();
+double cabs(), fabs(), sqrt(), pow();
+double log(), exp(), atan2(), cosh(), sinh();
+double asin(), sin(), cos();
+void cadd(), cmul(), csqrt();
+void clog(), casin(), cacos(), catan();
+#endif
+
+
+extern double MAXNUM, MACHEP, PI, PIO2;
+
+void clog( z, w )
+register cmplx *z, *w;
+{
+double p, rr;
+
+/*rr = sqrt( z->r * z->r  +  z->i * z->i );*/
+rr = cabs(z);
+p = log(rr);
+#if ANSIC
+rr = atan2( z->i, z->r );
+#else
+rr = atan2( z->r, z->i );
+if( rr > PI )
+	rr -= PI + PI;
+#endif
+w->i = rr;
+w->r = p;
+}
+/*							cexp()
+ *
+ *	Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexp();
+ * cmplx z, w;
+ *
+ * cexp( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ *     z = x + iy,
+ *     r = exp(x),
+ *
+ * then
+ *
+ *     w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8700       3.7e-17     1.1e-17
+ *    IEEE      -10,+10     30000       3.0e-16     8.7e-17
+ *
+ */
+
+void cexp( z, w )
+register cmplx *z, *w;
+{
+double r;
+
+r = exp( z->r );
+w->r = r * cos( z->i );
+w->i = r * sin( z->i );
+}
+/*							csin()
+ *
+ *	Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csin();
+ * cmplx z, w;
+ *
+ * csin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *     w = sin x  cosh y  +  i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8400       5.3e-17     1.3e-17
+ *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+
+void csin( z, w )
+register cmplx *z, *w;
+{
+double ch, sh;
+
+cchsh( z->i, &ch, &sh );
+w->r = sin( z->r ) * ch;
+w->i = cos( z->r ) * sh;
+}
+
+
+
+/* calculate cosh and sinh */
+
+static void cchsh( x, c, s )
+double x, *c, *s;
+{
+double e, ei;
+
+if( fabs(x) <= 0.5 )
+	{
+	*c = cosh(x);
+	*s = sinh(x);
+	}
+else
+	{
+	e = exp(x);
+	ei = 0.5/e;
+	e = 0.5 * e;
+	*s = e - ei;
+	*c = e + ei;
+	}
+}
+
+/*							ccos()
+ *
+ *	Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccos();
+ * cmplx z, w;
+ *
+ * ccos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *     w = cos x  cosh y  -  i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      8400       4.5e-17     1.3e-17
+ *    IEEE      -10,+10     30000       3.8e-16     1.0e-16
+ */
+
+void ccos( z, w )
+register cmplx *z, *w;
+{
+double ch, sh;
+
+cchsh( z->i, &ch, &sh );
+w->r = cos( z->r ) * ch;
+w->i = -sin( z->r ) * sh;
+}
+/*							ctan()
+ *
+ *	Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctan();
+ * cmplx z, w;
+ *
+ * ctan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *           sin 2x  +  i sinh 2y
+ *     w  =  --------------------.
+ *            cos 2x  +  cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2.  The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5200       7.1e-17     1.6e-17
+ *    IEEE      -10,+10     30000       7.2e-16     1.2e-16
+ * Also tested by ctan * ccot = 1 and catan(ctan(z))  =  z.
+ */
+
+void ctan( z, w )
+register cmplx *z, *w;
+{
+double d;
+
+d = cos( 2.0 * z->r ) + cosh( 2.0 * z->i );
+
+if( fabs(d) < 0.25 )
+	d = ctans(z);
+
+if( d == 0.0 )
+	{
+	mtherr( "ctan", OVERFLOW );
+	w->r = MAXNUM;
+	w->i = MAXNUM;
+	return;
+	}
+
+w->r = sin( 2.0 * z->r ) / d;
+w->i = sinh( 2.0 * z->i ) / d;
+}
+/*							ccot()
+ *
+ *	Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccot();
+ * cmplx z, w;
+ *
+ * ccot( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *
+ *           sin 2x  -  i sinh 2y
+ *     w  =  --------------------.
+ *            cosh 2y  -  cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2.  Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      3000       6.5e-17     1.6e-17
+ *    IEEE      -10,+10     30000       9.2e-16     1.2e-16
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+
+void ccot( z, w )
+register cmplx *z, *w;
+{
+double d;
+
+d = cosh(2.0 * z->i) - cos(2.0 * z->r);
+
+if( fabs(d) < 0.25 )
+	d = ctans(z);
+
+if( d == 0.0 )
+	{
+	mtherr( "ccot", OVERFLOW );
+	w->r = MAXNUM;
+	w->i = MAXNUM;
+	return;
+	}
+
+w->r = sin( 2.0 * z->r ) / d;
+w->i = -sinh( 2.0 * z->i ) / d;
+}
+
+/* Program to subtract nearest integer multiple of PI */
+/* extended precision value of PI: */
+#ifdef UNK
+static double DP1 = 3.14159265160560607910E0;
+static double DP2 = 1.98418714791870343106E-9;
+static double DP3 = 1.14423774522196636802E-17;
+#endif
+
+#ifdef DEC
+static unsigned short P1[] = {0040511,0007732,0120000,0000000,};
+static unsigned short P2[] = {0031010,0055060,0100000,0000000,};
+static unsigned short P3[] = {0022123,0011431,0105056,0001560,};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef IBMPC
+static unsigned short P1[] = {0x0000,0x5400,0x21fb,0x4009};
+static unsigned short P2[] = {0x0000,0x1000,0x0b46,0x3e21};
+static unsigned short P3[] = {0xc06e,0x3145,0x6263,0x3c6a};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef MIEEE
+static unsigned short P1[] = {
+0x4009,0x21fb,0x5400,0x0000
+};
+static unsigned short P2[] = {
+0x3e21,0x0b46,0x1000,0x0000
+};
+static unsigned short P3[] = {
+0x3c6a,0x6263,0x3145,0xc06e
+};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+static double redupi(x)
+double x;
+{
+double t;
+long i;
+
+t = x/PI;
+if( t >= 0.0 )
+	t += 0.5;
+else
+	t -= 0.5;
+
+i = t;	/* the multiple */
+t = i;
+t = ((x - t * DP1) - t * DP2) - t * DP3;
+return(t);
+}
+
+/*  Taylor series expansion for cosh(2y) - cos(2x)	*/
+
+static double ctans(z)
+cmplx *z;
+{
+double f, x, x2, y, y2, rn, t;
+double d;
+
+x = fabs( 2.0 * z->r );
+y = fabs( 2.0 * z->i );
+
+x = redupi(x);
+
+x = x * x;
+y = y * y;
+x2 = 1.0;
+y2 = 1.0;
+f = 1.0;
+rn = 0.0;
+d = 0.0;
+do
+	{
+	rn += 1.0;
+	f *= rn;
+	rn += 1.0;
+	f *= rn;
+	x2 *= x;
+	y2 *= y;
+	t = y2 + x2;
+	t /= f;
+	d += t;
+
+	rn += 1.0;
+	f *= rn;
+	rn += 1.0;
+	f *= rn;
+	x2 *= x;
+	y2 *= y;
+	t = y2 - x2;
+	t /= f;
+	d += t;
+	}
+while( fabs(t/d) > MACHEP );
+return(d);
+}
+/*							casin()
+ *
+ *	Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casin();
+ * cmplx z, w;
+ *
+ * casin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ *                               2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10     10100       2.1e-15     3.4e-16
+ *    IEEE      -10,+10     30000       2.2e-14     2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+
+void casin( z, w )
+cmplx *z, *w;
+{
+static cmplx ca, ct, zz, z2;
+double x, y;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0 )
+	{
+	if( fabs(x) > 1.0 )
+		{
+		w->r = PIO2;
+		w->i = 0.0;
+		mtherr( "casin", DOMAIN );
+		}
+	else
+		{
+		w->r = asin(x);
+		w->i = 0.0;
+		}
+	return;
+	}
+
+/* Power series expansion */
+/*
+b = cabs(z);
+if( b < 0.125 )
+{
+z2.r = (x - y) * (x + y);
+z2.i = 2.0 * x * y;
+
+cn = 1.0;
+n = 1.0;
+ca.r = x;
+ca.i = y;
+sum.r = x;
+sum.i = y;
+do
+	{
+	ct.r = z2.r * ca.r  -  z2.i * ca.i;
+	ct.i = z2.r * ca.i  +  z2.i * ca.r;
+	ca.r = ct.r;
+	ca.i = ct.i;
+
+	cn *= n;
+	n += 1.0;
+	cn /= n;
+	n += 1.0;
+	b = cn/n;
+
+	ct.r *= b;
+	ct.i *= b;
+	sum.r += ct.r;
+	sum.i += ct.i;
+	b = fabs(ct.r) + fabs(ct.i);
+	}
+while( b > MACHEP );
+w->r = sum.r;
+w->i = sum.i;
+return;
+}
+*/
+
+
+ca.r = x;
+ca.i = y;
+
+ct.r = -ca.i;	/* iz */
+ct.i = ca.r;
+
+	/* sqrt( 1 - z*z) */
+/* cmul( &ca, &ca, &zz ) */
+zz.r = (ca.r - ca.i) * (ca.r + ca.i);	/*x * x  -  y * y */
+zz.i = 2.0 * ca.r * ca.i;
+
+zz.r = 1.0 - zz.r;
+zz.i = -zz.i;
+csqrt( &zz, &z2 );
+
+cadd( &z2, &ct, &zz );
+clog( &zz, &zz );
+w->r = zz.i;	/* mult by 1/i = -i */
+w->i = -zz.r;
+return;
+}
+/*							cacos()
+ *
+ *	Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacos();
+ * cmplx z, w;
+ *
+ * cacos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z  =  PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5200      1.6e-15      2.8e-16
+ *    IEEE      -10,+10     30000      1.8e-14      2.2e-15
+ */
+
+void cacos( z, w )
+cmplx *z, *w;
+{
+
+casin( z, w );
+w->r = PIO2  -  w->r;
+w->i = -w->i;
+}
+/*							catan()
+ *
+ *	Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catan();
+ * cmplx z, w;
+ *
+ * catan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *     z = x + iy,
+ *
+ * then
+ *          1       (    2x     )
+ * Re w  =  - arctan(-----------)  +  k PI
+ *          2       (     2    2)
+ *                  (1 - x  - y )
+ *
+ *               ( 2         2)
+ *          1    (x  +  (y+1) )
+ * Im w  =  - log(------------)
+ *          4    ( 2         2)
+ *               (x  +  (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10      5900       1.3e-16     7.8e-18
+ *    IEEE      -10,+10     30000       2.3e-15     8.5e-17
+ * The check catan( ctan(z) )  =  z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17.  See also clog().
+ */
+
+void catan( z, w )
+cmplx *z, *w;
+{
+double a, t, x, x2, y;
+
+x = z->r;
+y = z->i;
+
+if( (x == 0.0) && (y > 1.0) )
+	goto ovrf;
+
+x2 = x * x;
+a = 1.0 - x2 - (y * y);
+if( a == 0.0 )
+	goto ovrf;
+
+#if ANSIC
+t = atan2( 2.0 * x, a )/2.0;
+#else
+t = atan2( a, 2.0 * x )/2.0;
+#endif
+w->r = redupi( t );
+
+t = y - 1.0;
+a = x2 + (t * t);
+if( a == 0.0 )
+	goto ovrf;
+
+t = y + 1.0;
+a = (x2 + (t * t))/a;
+w->i = log(a)/4.0;
+return;
+
+ovrf:
+mtherr( "catan", OVERFLOW );
+w->r = MAXNUM;
+w->i = MAXNUM;
+}
+
+
+/*							csinh
+ *
+ *	Complex hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinh();
+ * cmplx z, w;
+ *
+ * csinh( &z, &w );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * csinh z = (cexp(z) - cexp(-z))/2
+ *         = sinh x * cos y  +  i cosh x * sin y .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       3.1e-16     8.2e-17
+ *
+ */
+
+void
+csinh (z, w)
+     cmplx *z, *w;
+{
+  double x, y;
+
+  x = z->r;
+  y = z->i;
+  w->r = sinh (x) * cos (y);
+  w->i = cosh (x) * sin (y);
+}
+
+
+/*							casinh
+ *
+ *	Complex inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinh();
+ * cmplx z, w;
+ *
+ * casinh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * casinh z = -i casin iz .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       1.8e-14     2.6e-15
+ *
+ */
+
+void
+casinh (z, w)
+     cmplx *z, *w;
+{
+  cmplx u;
+
+  u.r = 0.0;
+  u.i = 1.0;
+  cmul( z, &u, &u );
+  casin( &u, w );
+  u.r = 0.0;
+  u.i = -1.0;
+  cmul( &u, w, w );
+}
+
+/*							ccosh
+ *
+ *	Complex hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosh();
+ * cmplx z, w;
+ *
+ * ccosh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * ccosh(z) = cosh x  cos y + i sinh x sin y .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       2.9e-16     8.1e-17
+ *
+ */
+
+void
+ccosh (z, w)
+     cmplx *z, *w;
+{
+  double x, y;
+
+  x = z->r;
+  y = z->i;
+  w->r = cosh (x) * cos (y);
+  w->i = sinh (x) * sin (y);
+}
+
+
+/*							cacosh
+ *
+ *	Complex inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosh();
+ * cmplx z, w;
+ *
+ * cacosh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * acosh z = i acos z .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       1.6e-14     2.1e-15
+ *
+ */
+
+void
+cacosh (z, w)
+     cmplx *z, *w;
+{
+  cmplx u;
+
+  cacos( z, w );
+  u.r = 0.0;
+  u.i = 1.0;
+  cmul( &u, w, w );
+}
+
+
+/*							ctanh
+ *
+ *	Complex hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanh();
+ * cmplx z, w;
+ *
+ * ctanh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * tanh z = (sinh 2x  +  i sin 2y) / (cosh 2x + cos 2y) .
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       1.7e-14     2.4e-16
+ *
+ */
+
+/* 5.253E-02,1.550E+00 1.643E+01,6.553E+00 1.729E-14  21355  */
+
+void
+ctanh (z, w)
+     cmplx *z, *w;
+{
+  double x, y, d;
+
+  x = z->r;
+  y = z->i;
+  d = cosh (2.0 * x) + cos (2.0 * y);
+  w->r = sinh (2.0 * x) / d;
+  w->i = sin (2.0 * y) / d;
+  return;
+}
+
+
+/*							catanh
+ *
+ *	Complex inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catanh();
+ * cmplx z, w;
+ *
+ * catanh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse tanh, equal to  -i catan (iz);
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       2.3e-16     6.2e-17
+ *
+ */
+
+void
+catanh (z, w)
+     cmplx *z, *w;
+{
+  cmplx u;
+
+  u.r = 0.0;
+  u.i = 1.0;
+  cmul (z, &u, &u);  /* i z */
+  catan (&u, w);
+  u.r = 0.0;
+  u.i = -1.0;
+  cmul (&u, w, w);  /* -i catan iz */
+  return;
+}
+
+
+/*							cpow
+ *
+ *	Complex power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cpow();
+ * cmplx a, z, w;
+ *
+ * cpow (&a, &z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Raises complex A to the complex Zth power.
+ * Definition is per AMS55 # 4.2.8,
+ * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      -10,+10     30000       9.4e-15     1.5e-15
+ *
+ */
+
+
+void
+cpow (a, z, w)
+     cmplx *a, *z, *w;
+{
+  double x, y, r, theta, absa, arga;
+
+  x = z->r;
+  y = z->i;
+  absa = cabs (a);
+  if (absa == 0.0)
+    {
+      w->r = 0.0;
+      w->i = 0.0;
+      return;
+    }
+  arga = atan2 (a->i, a->r);
+  r = pow (absa, x);
+  theta = x * arga;
+  if (y != 0.0)
+    {
+      r = r * exp (-y * arga);
+      theta = theta + y * log (absa);
+    }
+  w->r = r * cos (theta);
+  w->i = r * sin (theta);
+  return;
+}