Totally rework the math library, this time based on the MacOs X

math library (which is itself based on the math lib from FreeBSD).
 -Erik

1 files changed, 0 insertions, 461 deletions

diff --git a/libm/ldouble/cmplxl.c b/libm/ldouble/cmplxl.c
deleted file mode 100644
index ef130618d..000000000
--- a/libm/ldouble/cmplxl.c
+++ /dev/null
@@ -1,461 +0,0 @@
-/*							cmplxl.c
- *
- *	Complex number arithmetic
- *
- *
- *
- * SYNOPSIS:
- *
- * typedef struct {
- *      long double r;     real part
- *      long double i;     imaginary part
- *     }cmplxl;
- *
- * cmplxl *a, *b, *c;
- *
- * caddl( a, b, c );     c = b + a
- * csubl( a, b, c );     c = b - a
- * cmull( a, b, c );     c = b * a
- * cdivl( a, b, c );     c = b / a
- * cnegl( c );           c = -c
- * cmovl( 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 2.3:  March, 1995
-Copyright 1984, 1995 by Stephen L. Moshier
-*/
-
-
-#include <math.h>
-
-/*
-typedef struct
-	{
-	long double r;
-	long double i;
-	}cmplxl;
-*/
-
-#ifdef ANSIPROT
-extern long double fabsl ( long double );
-extern long double cabsl ( cmplxl * );
-extern long double sqrtl ( long double );
-extern long double atan2l ( long double, long double );
-extern long double cosl ( long double );
-extern long double sinl ( long double );
-extern long double frexpl ( long double, int * );
-extern long double ldexpl ( long double, int );
-extern int isnanl ( long double );
-void cdivl ( cmplxl *, cmplxl *, cmplxl * );
-void caddl ( cmplxl *, cmplxl *, cmplxl * );
-#else
-long double fabsl(), cabsl(), sqrtl(), atan2l(), cosl(), sinl();
-long double frexpl(), ldexpl();
-int isnanl();
-void cdivl(), caddl();
-#endif
-
-
-extern double MAXNUML, MACHEPL, PIL, PIO2L, INFINITYL, NANL;
-cmplx czerol = {0.0L, 0.0L};
-cmplx conel = {1.0L, 0.0L};
-
-
-/*	c = b + a	*/
-
-void caddl( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-
-c->r = b->r + a->r;
-c->i = b->i + a->i;
-}
-
-
-/*	c = b - a	*/
-
-void csubl( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-
-c->r = b->r - a->r;
-c->i = b->i - a->i;
-}
-
-/*	c = b * a */
-
-void cmull( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-long 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 cdivl( a, b, c )
-register cmplxl *a, *b;
-cmplxl *c;
-{
-long 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 < 1.0L )
-	{
-	w = MAXNUML * y;
-	if( (fabsl(p) > w) || (fabsl(q) > w) || (y == 0.0L) )
-		{
-		c->r = INFINITYL;
-		c->i = INFINITYL;
-		mtherr( "cdivl", OVERFLOW );
-		return;
-		}
-	}
-c->r = p/y;
-c->i = q/y;
-}
-
-
-/*	b = a
-   Caution, a `short' is assumed to be 16 bits wide.  */
-
-void cmovl( a, b )
-void *a, *b;
-{
-register short *pa, *pb;
-int i;
-
-pa = (short *) a;
-pb = (short *) b;
-i = 16;
-do
-	*pb++ = *pa++;
-while( --i );
-}
-
-
-void cnegl( a )
-register cmplxl *a;
-{
-
-a->r = -a->r;
-a->i = -a->i;
-}
-
-/*							cabsl()
- *
- *	Complex absolute value
- *
- *
- *
- * SYNOPSIS:
- *
- * long double cabsl();
- * cmplxl z;
- * long 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
-	{
-	long double r;
-	long double i;
-	}cmplxl;
-*/
-
-#ifdef UNK
-#define PRECL 32
-#define MAXEXPL 16384
-#define MINEXPL -16384
-#endif
-#ifdef IBMPC
-#define PRECL 32
-#define MAXEXPL 16384
-#define MINEXPL -16384
-#endif
-#ifdef MIEEE
-#define PRECL 32
-#define MAXEXPL 16384
-#define MINEXPL -16384
-#endif
-
-
-long double cabsl( z )
-register cmplxl *z;
-{
-long double x, y, b, re, im;
-int ex, ey, e;
-
-#ifdef INFINITIES
-/* Note, cabs(INFINITY,NAN) = INFINITY. */
-if( z->r == INFINITYL || z->i == INFINITYL
-   || z->r == -INFINITYL || z->i == -INFINITYL )
-  return( INFINITYL );
-#endif
-
-#ifdef NANS
-if( isnanl(z->r) )
-  return(z->r);
-if( isnanl(z->i) )
-  return(z->i);
-#endif
-
-re = fabsl( z->r );
-im = fabsl( z->i );
-
-if( re == 0.0 )
-	return( im );
-if( im == 0.0 )
-	return( re );
-
-/* Get the exponents of the numbers */
-x = frexpl( re, &ex );
-y = frexpl( im, &ey );
-
-/* Check if one number is tiny compared to the other */
-e = ex - ey;
-if( e > PRECL )
-	return( re );
-if( e < -PRECL )
-	return( im );
-
-/* Find approximate exponent e of the geometric mean. */
-e = (ex + ey) >> 1;
-
-/* Rescale so mean is about 1 */
-x = ldexpl( re, -e );
-y = ldexpl( im, -e );
-		
-/* Hypotenuse of the right triangle */
-b = sqrtl( x * x  +  y * y );
-
-/* Compute the exponent of the answer. */
-y = frexpl( b, &ey );
-ey = e + ey;
-
-/* Check it for overflow and underflow. */
-if( ey > MAXEXPL )
-	{
-	mtherr( "cabsl", OVERFLOW );
-	return( INFINITYL );
-	}
-if( ey < MINEXPL )
-	return(0.0L);
-
-/* Undo the scaling */
-b = ldexpl( b, e );
-return( b );
-}
-/*							csqrtl()
- *
- *	Complex square root
- *
- *
- *
- * SYNOPSIS:
- *
- * void csqrtl();
- * cmplxl z, w;
- *
- * csqrtl( &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 csqrtl( z, w )
-cmplxl *z, *w;
-{
-cmplxl q, s;
-long double x, y, r, t;
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0L )
-	{
-	if( x < 0.0L )
-		{
-		w->r = 0.0L;
-		w->i = sqrtl(-x);
-		return;
-		}
-	else
-		{
-		w->r = sqrtl(x);
-		w->i = 0.0L;
-		return;
-		}
-	}
-
-
-if( x == 0.0L )
-	{
-	r = fabsl(y);
-	r = sqrtl(0.5L*r);
-	if( y > 0.0L )
-		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( (fabsl(y) < 2.e-4L * fabsl(x))
-   && (x > 0) )
-	{
-	t = 0.25L*y*(y/x);
-	}
-else
-	{
-	r = cabsl(z);
-	t = 0.5L*(r - x);
-	}
-
-r = sqrtl(t);
-q.i = r;
-q.r = y/(2.0L*r);
-/* Heron iteration in complex arithmetic */
-cdivl( &q, z, &s );
-caddl( &q, &s, w );
-w->r *= 0.5L;
-w->i *= 0.5L;
-
-cdivl( &q, z, &s );
-caddl( &q, &s, w );
-w->r *= 0.5L;
-w->i *= 0.5L;
-}
-
-
-long double hypotl( x, y )
-long double x, y;
-{
-cmplxl z;
-
-z.r = x;
-z.i = y;
-return( cabsl(&z) );
-}