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, 720 deletions

diff --git a/libm/ldouble/clogl.c b/libm/ldouble/clogl.c
deleted file mode 100644
index b3e6b25fb..000000000
--- a/libm/ldouble/clogl.c
+++ /dev/null
@@ -1,720 +0,0 @@
-/*							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;
-}