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, 669 deletions

diff --git a/libm/float/clogf.c b/libm/float/clogf.c
deleted file mode 100644
index 5f4944eba..000000000
--- a/libm/float/clogf.c
+++ /dev/null
@@ -1,669 +0,0 @@
-/*							clogf.c
- *
- *	Complex natural logarithm
- *
- *
- *
- * SYNOPSIS:
- *
- * void clogf();
- * cmplxf z, w;
- *
- * clogf( &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
- *    IEEE      -10,+10     30000       1.9e-6       6.2e-8
- *
- * Larger relative error can be observed for z near 1 +i0.
- * In IEEE arithmetic the peak absolute error is 3.1e-7.
- *
- */
-
-#include <math.h>
-extern float MAXNUMF, MACHEPF, PIF, PIO2F;
-#ifdef ANSIC
-float cabsf(cmplxf *), sqrtf(float), logf(float), atan2f(float, float);
-float expf(float), sinf(float), cosf(float);
-float coshf(float), sinhf(float), asinf(float);
-float ctansf(cmplxf *), redupif(float);
-void cchshf( float, float *, float * );
-void caddf( cmplxf *, cmplxf *, cmplxf * );
-void csqrtf( cmplxf *, cmplxf * );
-#else
-float cabsf(), sqrtf(), logf(), atan2f();
-float expf(), sinf(), cosf();
-float coshf(), sinhf(), asinf();
-float ctansf(), redupif();
-void cchshf(), csqrtf(), caddf();
-#endif
-
-#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
-
-void clogf( z, w )
-register cmplxf *z, *w;
-{
-float p, rr;
-
-/*rr = sqrtf( z->r * z->r  +  z->i * z->i );*/
-rr = cabsf(z);
-p = logf(rr);
-#if ANSIC
-rr = atan2f( z->i, z->r );
-#else
-rr = atan2f( z->r, z->i );
-if( rr > PIF )
-	rr -= PIF + PIF;
-#endif
-w->i = rr;
-w->r = p;
-}
-/*							cexpf()
- *
- *	Complex exponential function
- *
- *
- *
- * SYNOPSIS:
- *
- * void cexpf();
- * cmplxf z, w;
- *
- * cexpf( &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
- *    IEEE      -10,+10     30000       1.4e-7      4.5e-8
- *
- */
-
-void cexpf( z, w )
-register cmplxf *z, *w;
-{
-float r;
-
-r = expf( z->r );
-w->r = r * cosf( z->i );
-w->i = r * sinf( z->i );
-}
-/*							csinf()
- *
- *	Complex circular sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void csinf();
- * cmplxf z, w;
- *
- * csinf( &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
- *    IEEE      -10,+10     30000       1.9e-7      5.5e-8
- *
- */
-
-void csinf( z, w )
-register cmplxf *z, *w;
-{
-float ch, sh;
-
-cchshf( z->i, &ch, &sh );
-w->r = sinf( z->r ) * ch;
-w->i = cosf( z->r ) * sh;
-}
-
-
-
-/* calculate cosh and sinh */
-
-void cchshf( float xx, float *c, float *s )
-{
-float x, e, ei;
-
-x = xx;
-if( fabsf(x) <= 0.5f )
-	{
-	*c = coshf(x);
-	*s = sinhf(x);
-	}
-else
-	{
-	e = expf(x);
-	ei = 0.5f/e;
-	e = 0.5f * e;
-	*s = e - ei;
-	*c = e + ei;
-	}
-}
-
-/*							ccosf()
- *
- *	Complex circular cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccosf();
- * cmplxf z, w;
- *
- * ccosf( &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
- *    IEEE      -10,+10     30000       1.8e-7       5.5e-8
- */
-
-void ccosf( z, w )
-register cmplxf *z, *w;
-{
-float ch, sh;
-
-cchshf( z->i, &ch, &sh );
-w->r = cosf( z->r ) * ch;
-w->i = -sinf( z->r ) * sh;
-}
-/*							ctanf()
- *
- *	Complex circular tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ctanf();
- * cmplxf z, w;
- *
- * ctanf( &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
- *    IEEE      -10,+10     30000       3.3e-7       5.1e-8
- */
-
-void ctanf( z, w )
-register cmplxf *z, *w;
-{
-float d;
-
-d = cosf( 2.0f * z->r ) + coshf( 2.0f * z->i );
-
-if( fabsf(d) < 0.25f )
-	d = ctansf(z);
-
-if( d == 0.0f )
-	{
-	mtherr( "ctanf", OVERFLOW );
-	w->r = MAXNUMF;
-	w->i = MAXNUMF;
-	return;
-	}
-
-w->r = sinf( 2.0f * z->r ) / d;
-w->i = sinhf( 2.0f * z->i ) / d;
-}
-/*							ccotf()
- *
- *	Complex circular cotangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void ccotf();
- * cmplxf z, w;
- *
- * ccotf( &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
- *    IEEE      -10,+10     30000       3.6e-7       5.7e-8
- * Also tested by ctan * ccot = 1 + i0.
- */
-
-void ccotf( z, w )
-register cmplxf *z, *w;
-{
-float d;
-
-
-d = coshf(2.0f * z->i) - cosf(2.0f * z->r);
-
-if( fabsf(d) < 0.25f )
-	d = ctansf(z);
-
-if( d == 0.0f )
-	{
-	mtherr( "ccotf", OVERFLOW );
-	w->r = MAXNUMF;
-	w->i = MAXNUMF;
-	return;
-	}
-
-d = 1.0f/d;
-w->r = sinf( 2.0f * z->r ) * d;
-w->i = -sinhf( 2.0f * z->i ) * d;
-}
-
-/* Program to subtract nearest integer multiple of PI */
-/* extended precision value of PI: */
-
-static float DP1 =  3.140625;
-static float DP2 =  9.67502593994140625E-4;
-static float DP3 =  1.509957990978376432E-7;
-
-
-float redupif(float xx)
-{
-float x, t;
-long i;
-
-x = xx;
-t = x/PIF;
-if( t >= 0.0f )
-	t += 0.5f;
-else
-	t -= 0.5f;
-
-i = t;	/* the multiple */
-t = i;
-t = ((x - t * DP1) - t * DP2) - t * DP3;
-return(t);
-}
-
-/*  Taylor series expansion for cosh(2y) - cos(2x)	*/
-
-float ctansf(z)
-cmplxf *z;
-{
-float f, x, x2, y, y2, rn, t, d;
-
-x = fabsf( 2.0f * z->r );
-y = fabsf( 2.0f * z->i );
-
-x = redupif(x);
-
-x = x * x;
-y = y * y;
-x2 = 1.0f;
-y2 = 1.0f;
-f = 1.0f;
-rn = 0.0f;
-d = 0.0f;
-do
-	{
-	rn += 1.0f;
-	f *= rn;
-	rn += 1.0f;
-	f *= rn;
-	x2 *= x;
-	y2 *= y;
-	t = y2 + x2;
-	t /= f;
-	d += t;
-
-	rn += 1.0f;
-	f *= rn;
-	rn += 1.0f;
-	f *= rn;
-	x2 *= x;
-	y2 *= y;
-	t = y2 - x2;
-	t /= f;
-	d += t;
-	}
-while( fabsf(t/d) > MACHEPF );
-return(d);
-}
-/*							casinf()
- *
- *	Complex circular arc sine
- *
- *
- *
- * SYNOPSIS:
- *
- * void casinf();
- * cmplxf z, w;
- *
- * casinf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- * Inverse complex sine:
- *
- *                               2
- * w = -i clog( iz + csqrt( 1 - z ) ).
- *
- *
- * ACCURACY:
- *
- *                      Relative error:
- * arithmetic   domain     # trials      peak         rms
- *    IEEE      -10,+10     30000       1.1e-5      1.5e-6
- * Larger relative error can be observed for z near zero.
- *
- */
-
-void casinf( z, w )
-cmplxf *z, *w;
-{
-float x, y;
-static cmplxf ca, ct, zz, z2;
-/*
-float cn, n;
-static float a, b, s, t, u, v, y2;
-static cmplxf sum;
-*/
-
-x = z->r;
-y = z->i;
-
-if( y == 0.0f )
-	{
-	if( fabsf(x) > 1.0f )
-		{
-		w->r = PIO2F;
-		w->i = 0.0f;
-		mtherr( "casinf", DOMAIN );
-		}
-	else
-		{
-		w->r = asinf(x);
-		w->i = 0.0f;
-		}
-	return;
-	}
-
-/* Power series expansion */
-/*
-b = cabsf(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 = fabsf(ct.r) + fabsf(ct.i);
-	}
-while( b > MACHEPF );
-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 = 2.0f * ca.r * ca.i;
-
-zz.r = 1.0f - zz.r;
-zz.i = -zz.i;
-csqrtf( &zz, &z2 );
-
-caddf( &z2, &ct, &zz );
-clogf( &zz, &zz );
-w->r = zz.i;	/* mult by 1/i = -i */
-w->i = -zz.r;
-return;
-}
-/*							cacosf()
- *
- *	Complex circular arc cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * void cacosf();
- * cmplxf z, w;
- *
- * cacosf( &z, &w );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- * w = arccos z  =  PI/2 - arcsin z.
- *
- *
- *
- *
- * ACCURACY:
- *
- *                      Relative error:
- * arithmetic   domain     # trials      peak         rms
- *    IEEE      -10,+10     30000       9.2e-6       1.2e-6
- *
- */
-
-void cacosf( z, w )
-cmplxf *z, *w;
-{
-
-casinf( z, w );
-w->r = PIO2F  -  w->r;
-w->i = -w->i;
-}
-/*							catan()
- *
- *	Complex circular arc tangent
- *
- *
- *
- * SYNOPSIS:
- *
- * void catan();
- * cmplxf 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
- *    IEEE      -10,+10     30000        2.3e-6      5.2e-8
- *
- */
-
-void catanf( z, w )
-cmplxf *z, *w;
-{
-float a, t, x, x2, y;
-
-x = z->r;
-y = z->i;
-
-if( (x == 0.0f) && (y > 1.0f) )
-	goto ovrf;
-
-x2 = x * x;
-a = 1.0f - x2 - (y * y);
-if( a == 0.0f )
-	goto ovrf;
-
-#if ANSIC
-t = 0.5f * atan2f( 2.0f * x, a );
-#else
-t = 0.5f * atan2f( a, 2.0f * x );
-#endif
-w->r = redupif( t );
-
-t = y - 1.0f;
-a = x2 + (t * t);
-if( a == 0.0f )
-	goto ovrf;
-
-t = y + 1.0f;
-a = (x2 + (t * t))/a;
-w->i = 0.25f*logf(a);
-return;
-
-ovrf:
-mtherr( "catanf", OVERFLOW );
-w->r = MAXNUMF;
-w->i = MAXNUMF;
-}