uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 720 insertions, 0 deletions

diff --git a/libm/ldouble/clogl.c b/libm/ldouble/clogl.c
new file mode 100644
index 000000000..b3e6b25fb
--- /dev/null
+++ b/libm/ldouble/clogl.c
@@ -0,0 +1,720 @@
+/*							clogl.c
+ *
+ *	Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clogl();
+ * cmplxl z, w;
+ *
+ * clogl( &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.
+ */
+
+#include <math.h>
+#ifdef ANSIPROT
+static void cchshl ( long double x, long double *c, long double *s );
+static long double redupil ( long double x );
+static long double ctansl ( cmplxl *z );
+long double cabsl ( cmplxl *x );
+void csqrtl ( cmplxl *x, cmplxl *y );
+void caddl ( cmplxl *x, cmplxl *y, cmplxl *z );
+extern long double fabsl ( long double );
+extern long double sqrtl ( long double );
+extern long double logl ( long double );
+extern long double expl ( long double );
+extern long double atan2l ( long double, long double );
+extern long double coshl ( long double );
+extern long double sinhl ( long double );
+extern long double asinl ( long double );
+extern long double sinl ( long double );
+extern long double cosl ( long double );
+void clogl ( cmplxl *, cmplxl *);
+void casinl ( cmplxl *, cmplxl *);
+#else
+static void cchshl();
+static long double redupil();
+static long double ctansl();
+long double cabsl(), fabsl(), sqrtl();
+lnog double logl(), expl(), atan2l(), coshl(), sinhl();
+long double asinl(), sinl(), cosl();
+void caddl(), csqrtl(), clogl(), casinl();
+#endif
+
+extern long double MAXNUML, MACHEPL, PIL, PIO2L;
+
+void clogl( z, w )
+register cmplxl *z, *w;
+{
+long double p, rr;
+
+/*rr = sqrt( z->r * z->r  +  z->i * z->i );*/
+rr = cabsl(z);
+p = logl(rr);
+#if ANSIC
+rr = atan2l( z->i, z->r );
+#else
+rr = atan2l( z->r, z->i );
+if( rr > PIL )
+	rr -= PIL + PIL;
+#endif
+w->i = rr;
+w->r = p;
+}
+/*							cexpl()
+ *
+ *	Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexpl();
+ * cmplxl z, w;
+ *
+ * cexpl( &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 cexpl( z, w )
+register cmplxl *z, *w;
+{
+long double r;
+
+r = expl( z->r );
+w->r = r * cosl( z->i );
+w->i = r * sinl( z->i );
+}
+/*							csinl()
+ *
+ *	Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinl();
+ * cmplxl z, w;
+ *
+ * csinl( &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 csinl( z, w )
+register cmplxl *z, *w;
+{
+long double ch, sh;
+
+cchshl( z->i, &ch, &sh );
+w->r = sinl( z->r ) * ch;
+w->i = cosl( z->r ) * sh;
+}
+
+
+
+/* calculate cosh and sinh */
+
+static void cchshl( x, c, s )
+long double x, *c, *s;
+{
+long double e, ei;
+
+if( fabsl(x) <= 0.5L )
+	{
+	*c = coshl(x);
+	*s = sinhl(x);
+	}
+else
+	{
+	e = expl(x);
+	ei = 0.5L/e;
+	e = 0.5L * e;
+	*s = e - ei;
+	*c = e + ei;
+	}
+}
+
+/*							ccosl()
+ *
+ *	Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosl();
+ * cmplxl z, w;
+ *
+ * ccosl( &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 ccosl( z, w )
+register cmplxl *z, *w;
+{
+long double ch, sh;
+
+cchshl( z->i, &ch, &sh );
+w->r = cosl( z->r ) * ch;
+w->i = -sinl( z->r ) * sh;
+}
+/*							ctanl()
+ *
+ *	Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanl();
+ * cmplxl z, w;
+ *
+ * ctanl( &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 ctanl( z, w )
+register cmplxl *z, *w;
+{
+long double d;
+
+d = cosl( 2.0L * z->r ) + coshl( 2.0L * z->i );
+
+if( fabsl(d) < 0.25L )
+	d = ctansl(z);
+
+if( d == 0.0L )
+	{
+	mtherr( "ctan", OVERFLOW );
+	w->r = MAXNUML;
+	w->i = MAXNUML;
+	return;
+	}
+
+w->r = sinl( 2.0L * z->r ) / d;
+w->i = sinhl( 2.0L * z->i ) / d;
+}
+/*							ccotl()
+ *
+ *	Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccotl();
+ * cmplxl z, w;
+ *
+ * ccotl( &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 ccotl( z, w )
+register cmplxl *z, *w;
+{
+long double d;
+
+d = coshl(2.0L * z->i) - cosl(2.0L * z->r);
+
+if( fabsl(d) < 0.25L )
+	d = ctansl(z);
+
+if( d == 0.0L )
+	{
+	mtherr( "ccot", OVERFLOW );
+	w->r = MAXNUML;
+	w->i = MAXNUML;
+	return;
+	}
+
+w->r = sinl( 2.0L * z->r ) / d;
+w->i = -sinhl( 2.0L * 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 long double redupil(x)
+long double x;
+{
+long double t;
+long i;
+
+t = x/PIL;
+if( t >= 0.0L )
+	t += 0.5L;
+else
+	t -= 0.5L;
+
+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 long double ctansl(z)
+cmplxl *z;
+{
+long double f, x, x2, y, y2, rn, t;
+long double d;
+
+x = fabsl( 2.0L * z->r );
+y = fabsl( 2.0L * z->i );
+
+x = redupil(x);
+
+x = x * x;
+y = y * y;
+x2 = 1.0L;
+y2 = 1.0L;
+f = 1.0L;
+rn = 0.0;
+d = 0.0;
+do
+	{
+	rn += 1.0L;
+	f *= rn;
+	rn += 1.0L;
+	f *= rn;
+	x2 *= x;
+	y2 *= y;
+	t = y2 + x2;
+	t /= f;
+	d += t;
+
+	rn += 1.0L;
+	f *= rn;
+	rn += 1.0L;
+	f *= rn;
+	x2 *= x;
+	y2 *= y;
+	t = y2 - x2;
+	t /= f;
+	d += t;
+	}
+while( fabsl(t/d) > MACHEPL );
+return(d);
+}
+/*							casinl()
+ *
+ *	Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinl();
+ * cmplxl z, w;
+ *
+ * casinl( &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 casinl( z, w )
+cmplxl *z, *w;
+{
+static cmplxl ca, ct, zz, z2;
+long double x, y;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0L )
+	{
+	if( fabsl(x) > 1.0L )
+		{
+		w->r = PIO2L;
+		w->i = 0.0L;
+		mtherr( "casinl", DOMAIN );
+		}
+	else
+		{
+		w->r = asinl(x);
+		w->i = 0.0L;
+		}
+	return;
+	}
+
+/* Power series expansion */
+/*
+b = cabsl(z);
+if( b < 0.125L )
+{
+z2.r = (x - y) * (x + y);
+z2.i = 2.0L * x * y;
+
+cn = 1.0L;
+n = 1.0L;
+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 += 1.0L;
+	cn /= n;
+	n += 1.0L;
+	b = cn/n;
+
+	ct.r *= b;
+	ct.i *= b;
+	sum.r += ct.r;
+	sum.i += ct.i;
+	b = fabsl(ct.r) + fabs(ct.i);
+	}
+while( b > MACHEPL );
+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 = 2.0L * ca.r * ca.i;
+
+zz.r = 1.0L - zz.r;
+zz.i = -zz.i;
+csqrtl( &zz, &z2 );
+
+caddl( &z2, &ct, &zz );
+clogl( &zz, &zz );
+w->r = zz.i;	/* mult by 1/i = -i */
+w->i = -zz.r;
+return;
+}
+/*							cacosl()
+ *
+ *	Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosl();
+ * cmplxl z, w;
+ *
+ * cacosl( &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 cacosl( z, w )
+cmplxl *z, *w;
+{
+
+casinl( z, w );
+w->r = PIO2L  -  w->r;
+w->i = -w->i;
+}
+/*							catanl()
+ *
+ *	Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catanl();
+ * cmplxl z, w;
+ *
+ * catanl( &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 catanl( z, w )
+cmplxl *z, *w;
+{
+long double a, t, x, x2, y;
+
+x = z->r;
+y = z->i;
+
+if( (x == 0.0L) && (y > 1.0L) )
+	goto ovrf;
+
+x2 = x * x;
+a = 1.0L - x2 - (y * y);
+if( a == 0.0L )
+	goto ovrf;
+
+#if ANSIC
+t = atan2l( 2.0L * x, a ) * 0.5L;
+#else
+t = atan2l( a, 2.0 * x ) * 0.5L;
+#endif
+w->r = redupil( t );
+
+t = y - 1.0L;
+a = x2 + (t * t);
+if( a == 0.0L )
+	goto ovrf;
+
+t = y + 1.0L;
+a = (x2 + (t * t))/a;
+w->i = logl(a)/4.0;
+return;
+
+ovrf:
+mtherr( "catanl", OVERFLOW );
+w->r = MAXNUML;
+w->i = MAXNUML;
+}