uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 461 insertions, 0 deletions

diff --git a/libm/double/cmplx.c b/libm/double/cmplx.c
new file mode 100644
index 000000000..dcd972bea
--- /dev/null
+++ b/libm/double/cmplx.c
@@ -0,0 +1,461 @@
+/*							cmplx.c
+ *
+ *	Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ *      double r;     real part
+ *      double i;     imaginary part
+ *     }cmplx;
+ *
+ * cmplx *a, *b, *c;
+ *
+ * cadd( a, b, c );     c = b + a
+ * csub( a, b, c );     c = b - a
+ * cmul( a, b, c );     c = b * a
+ * cdiv( a, b, c );     c = b / a
+ * cneg( c );           c = -c
+ * cmov( b, c );        c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ *    c.r  =  b.r + a.r
+ *    c.i  =  b.i + a.i
+ *
+ * Subtraction:
+ *    c.r  =  b.r - a.r
+ *    c.i  =  b.i - a.i
+ *
+ * Multiplication:
+ *    c.r  =  b.r * a.r  -  b.i * a.i
+ *    c.i  =  b.r * a.i  +  b.i * a.r
+ *
+ * Division:
+ *    d    =  a.r * a.r  +  a.i * a.i
+ *    c.r  = (b.r * a.r  + b.i * a.i)/d
+ *    c.i  = (b.i * a.r  -  b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17.  The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ *                      Relative error:
+ * arithmetic   function  # trials      peak         rms
+ *    DEC        cadd       10000       1.4e-17     3.4e-18
+ *    IEEE       cadd      100000       1.1e-16     2.7e-17
+ *    DEC        csub       10000       1.4e-17     4.5e-18
+ *    IEEE       csub      100000       1.1e-16     3.4e-17
+ *    DEC        cmul        3000       2.3e-17     8.7e-18
+ *    IEEE       cmul      100000       2.1e-16     6.9e-17
+ *    DEC        cdiv       18000       4.9e-17     1.3e-17
+ *    IEEE       cdiv      100000       3.7e-16     1.1e-16
+ */
+/*				cmplx.c
+ * complex number arithmetic
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double cabs ( cmplx * );
+extern double sqrt ( double );
+extern double atan2 ( double, double );
+extern double cos ( double );
+extern double sin ( double );
+extern double sqrt ( double );
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+int isnan ( double );
+void cdiv ( cmplx *, cmplx *, cmplx * );
+void cadd ( cmplx *, cmplx *, cmplx * );
+#else
+double fabs(), cabs(), sqrt(), atan2(), cos(), sin();
+double sqrt(), frexp(), ldexp();
+int isnan();
+void cdiv(), cadd();
+#endif
+
+extern double MAXNUM, MACHEP, PI, PIO2, INFINITY, NAN;
+/*
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+*/
+cmplx czero = {0.0, 0.0};
+extern cmplx czero;
+cmplx cone = {1.0, 0.0};
+extern cmplx cone;
+
+/*	c = b + a	*/
+
+void cadd( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+
+c->r = b->r + a->r;
+c->i = b->i + a->i;
+}
+
+
+/*	c = b - a	*/
+
+void csub( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+
+c->r = b->r - a->r;
+c->i = b->i - a->i;
+}
+
+/*	c = b * a */
+
+void cmul( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+double y;
+
+y    = b->r * a->r  -  b->i * a->i;
+c->i = b->r * a->i  +  b->i * a->r;
+c->r = y;
+}
+
+
+
+/*	c = b / a */
+
+void cdiv( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+double y, p, q, w;
+
+
+y = a->r * a->r  +  a->i * a->i;
+p = b->r * a->r  +  b->i * a->i;
+q = b->i * a->r  -  b->r * a->i;
+
+if( y < 1.0 )
+	{
+	w = MAXNUM * y;
+	if( (fabs(p) > w) || (fabs(q) > w) || (y == 0.0) )
+		{
+		c->r = MAXNUM;
+		c->i = MAXNUM;
+		mtherr( "cdiv", OVERFLOW );
+		return;
+		}
+	}
+c->r = p/y;
+c->i = q/y;
+}
+
+
+/*	b = a
+   Caution, a `short' is assumed to be 16 bits wide.  */
+
+void cmov( a, b )
+void *a, *b;
+{
+register short *pa, *pb;
+int i;
+
+pa = (short *) a;
+pb = (short *) b;
+i = 8;
+do
+	*pb++ = *pa++;
+while( --i );
+}
+
+
+void cneg( a )
+register cmplx *a;
+{
+
+a->r = -a->r;
+a->i = -a->i;
+}
+
+/*							cabs()
+ *
+ *	Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double cabs();
+ * cmplx z;
+ * double a;
+ *
+ * a = cabs( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ *       a = sqrt( x**2 + y**2 ).
+ * 
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring.  If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -30,+30     30000       3.2e-17     9.2e-18
+ *    IEEE      -10,+10    100000       2.7e-16     6.9e-17
+ */
+
+
+/*
+Cephes Math Library Release 2.1:  January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/*
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+*/
+
+#ifdef UNK
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+#ifdef DEC
+#define PREC 29
+#define MAXEXP 128
+#define MINEXP -128
+#endif
+#ifdef IBMPC
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+#ifdef MIEEE
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+
+
+double cabs( z )
+register cmplx *z;
+{
+double x, y, b, re, im;
+int ex, ey, e;
+
+#ifdef INFINITIES
+/* Note, cabs(INFINITY,NAN) = INFINITY. */
+if( z->r == INFINITY || z->i == INFINITY
+   || z->r == -INFINITY || z->i == -INFINITY )
+  return( INFINITY );
+#endif
+
+#ifdef NANS
+if( isnan(z->r) )
+  return(z->r);
+if( isnan(z->i) )
+  return(z->i);
+#endif
+
+re = fabs( z->r );
+im = fabs( z->i );
+
+if( re == 0.0 )
+	return( im );
+if( im == 0.0 )
+	return( re );
+
+/* Get the exponents of the numbers */
+x = frexp( re, &ex );
+y = frexp( im, &ey );
+
+/* Check if one number is tiny compared to the other */
+e = ex - ey;
+if( e > PREC )
+	return( re );
+if( e < -PREC )
+	return( im );
+
+/* Find approximate exponent e of the geometric mean. */
+e = (ex + ey) >> 1;
+
+/* Rescale so mean is about 1 */
+x = ldexp( re, -e );
+y = ldexp( im, -e );
+		
+/* Hypotenuse of the right triangle */
+b = sqrt( x * x  +  y * y );
+
+/* Compute the exponent of the answer. */
+y = frexp( b, &ey );
+ey = e + ey;
+
+/* Check it for overflow and underflow. */
+if( ey > MAXEXP )
+	{
+	mtherr( "cabs", OVERFLOW );
+	return( INFINITY );
+	}
+if( ey < MINEXP )
+	return(0.0);
+
+/* Undo the scaling */
+b = ldexp( b, e );
+return( b );
+}
+/*							csqrt()
+ *
+ *	Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrt();
+ * cmplx z, w;
+ *
+ * csqrt( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy,  r = |z|, then
+ *
+ *                       1/2
+ * Im w  =  [ (r - x)/2 ]   ,
+ *
+ * Re w  =  y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z.  The root chosen
+ * is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    DEC       -10,+10     25000       3.2e-17     9.6e-18
+ *    IEEE      -10,+10    100000       3.2e-16     7.7e-17
+ *
+ *                        2
+ * Also tested by csqrt( z ) = z, and tested by arguments
+ * close to the real axis.
+ */
+
+
+void csqrt( z, w )
+cmplx *z, *w;
+{
+cmplx q, s;
+double x, y, r, t;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0 )
+	{
+	if( x < 0.0 )
+		{
+		w->r = 0.0;
+		w->i = sqrt(-x);
+		return;
+		}
+	else
+		{
+		w->r = sqrt(x);
+		w->i = 0.0;
+		return;
+		}
+	}
+
+
+if( x == 0.0 )
+	{
+	r = fabs(y);
+	r = sqrt(0.5*r);
+	if( y > 0 )
+		w->r = r;
+	else
+		w->r = -r;
+	w->i = r;
+	return;
+	}
+
+/* Approximate  sqrt(x^2+y^2) - x  =  y^2/2x - y^4/24x^3 + ... .
+ * The relative error in the first term is approximately y^2/12x^2 .
+ */
+if( (fabs(y) < 2.e-4 * fabs(x))
+   && (x > 0) )
+	{
+	t = 0.25*y*(y/x);
+	}
+else
+	{
+	r = cabs(z);
+	t = 0.5*(r - x);
+	}
+
+r = sqrt(t);
+q.i = r;
+q.r = y/(2.0*r);
+/* Heron iteration in complex arithmetic */
+cdiv( &q, z, &s );
+cadd( &q, &s, w );
+w->r *= 0.5;
+w->i *= 0.5;
+}
+
+
+double hypot( x, y )
+double x, y;
+{
+cmplx z;
+
+z.r = x;
+z.i = y;
+return( cabs(&z) );
+}