[unix-history] / usr / src / lib / libm / ieee / cabs.c

/*
 * Copyright (c) 1985 Regents of the University of California.
 * All rights reserved.
 *
 * %sccs.include.redist.c%
 */

#ifndef lint
static char sccsid[] = "@(#)cabs.c	5.6 (Berkeley) %G%";
#endif /* not lint */

/* HYPOT(X,Y)
 * RETURN THE SQUARE ROOT OF X^2 + Y^2  WHERE Z=X+iY
 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 11/28/84; 
 * REVISED BY K.C. NG, 7/12/85.
 *
 * Required system supported functions :
 *	copysign(x,y)
 *	finite(x)
 *	scalb(x,N)
 *	sqrt(x)
 *
 * Method :
 *	1. replace x by |x| and y by |y|, and swap x and
 *	   y if y > x (hence x is never smaller than y).
 *	2. Hypot(x,y) is computed by:
 *	   Case I, x/y > 2
 *		
 *				       y
 *		hypot = x + -----------------------------
 *			 		    2
 *			    sqrt ( 1 + [x/y]  )  +  x/y
 *
 *	   Case II, x/y <= 2 
 *				                   y
 *		hypot = x + --------------------------------------------------
 *				          		     2 
 *				     			[x/y]   -  2
 *			   (sqrt(2)+1) + (x-y)/y + -----------------------------
 *			 		    			  2
 *			    			  sqrt ( 1 + [x/y]  )  + sqrt(2)
 *
 *
 *
 * Special cases:
 *	hypot(x,y) is INF if x or y is +INF or -INF; else
 *	hypot(x,y) is NAN if x or y is NAN.
 *
 * Accuracy:
 * 	hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
 *	in the last place). See Kahan's "Interval Arithmetic Options in the
 *	Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
 *      1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
 *	code follows in	comments.) In a test run with 500,000 random arguments
 *	on a VAX, the maximum observed error was .959 ulps.
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */
#include "mathimpl.h"

vc(r2p1hi, 2.4142135623730950345E0   ,8279,411a,ef32,99fc,   2, .9A827999FCEF32)
vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
vc(sqrt2,  1.4142135623730950622E0   ,04f3,40b5,de65,33f9,   1, .B504F333F9DE65)

ic(r2p1hi, 2.4142135623730949234E0   ,   1, 1.3504F333F9DE6)
ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
ic(sqrt2,  1.4142135623730951455E0   ,   0, 1.6A09E667F3BCD)

#ifdef vccast
#define	r2p1hi	vccast(r2p1hi)
#define	r2p1lo	vccast(r2p1lo)
#define	sqrt2	vccast(sqrt2)
#endif

double
hypot(x,y)
double x, y;
{
	static const double zero=0, one=1, 
		      small=1.0E-18;	/* fl(1+small)==1 */
	static const ibig=30;	/* fl(1+2**(2*ibig))==1 */
	double t,r;
	int exp;

	if(finite(x))
	    if(finite(y))
	    {	
		x=copysign(x,one);
		y=copysign(y,one);
		if(y > x) 
		    { t=x; x=y; y=t; }
		if(x == zero) return(zero);
		if(y == zero) return(x);
		exp= logb(x);
		if(exp-(int)logb(y) > ibig ) 	
			/* raise inexact flag and return |x| */
		   { one+small; return(x); }

	    /* start computing sqrt(x^2 + y^2) */
		r=x-y;
		if(r>y) { 	/* x/y > 2 */
		    r=x/y;
		    r=r+sqrt(one+r*r); }
		else {		/* 1 <= x/y <= 2 */
		    r/=y; t=r*(r+2.0);
		    r+=t/(sqrt2+sqrt(2.0+t));
		    r+=r2p1lo; r+=r2p1hi; }

		r=y/r;
		return(x+r);

	    }

	    else if(y==y)   	   /* y is +-INF */
		     return(copysign(y,one));
	    else 
		     return(y);	   /* y is NaN and x is finite */

	else if(x==x) 		   /* x is +-INF */
	         return (copysign(x,one));
	else if(finite(y))
	         return(x);		   /* x is NaN, y is finite */
#if !defined(vax)&&!defined(tahoe)
	else if(y!=y) return(y);  /* x and y is NaN */
#endif	/* !defined(vax)&&!defined(tahoe) */
	else return(copysign(y,one));   /* y is INF */
}

/* CABS(Z)
 * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER  Z = X + iY
 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 11/28/84.
 * REVISED BY K.C. NG, 7/12/85.
 *
 * Required kernel function :
 *	hypot(x,y)
 *
 * Method :
 *	cabs(z) = hypot(x,y) .
 */

double
cabs(z)
struct { double x, y;} z;
{
	return hypot(z.x,z.y);
}

double
z_abs(z)
struct { double x,y;} *z;
{
	return hypot(z->x,z->y);
}

/* A faster but less accurate version of cabs(x,y) */
#if 0
double hypot(x,y)
double x, y;
{
	static const double zero=0, one=1;
		      small=1.0E-18;	/* fl(1+small)==1 */
	static const ibig=30;	/* fl(1+2**(2*ibig))==1 */
	double temp;
	int exp;

	if(finite(x))
	    if(finite(y))
	    {	
		x=copysign(x,one);
		y=copysign(y,one);
		if(y > x) 
		    { temp=x; x=y; y=temp; }
		if(x == zero) return(zero);
		if(y == zero) return(x);
		exp= logb(x);
		x=scalb(x,-exp);
		if(exp-(int)logb(y) > ibig ) 
			/* raise inexact flag and return |x| */
		   { one+small; return(scalb(x,exp)); }
		else y=scalb(y,-exp);
		return(scalb(sqrt(x*x+y*y),exp));
	    }

	    else if(y==y)   	   /* y is +-INF */
		     return(copysign(y,one));
	    else 
		     return(y);	   /* y is NaN and x is finite */

	else if(x==x) 		   /* x is +-INF */
	         return (copysign(x,one));
	else if(finite(y))
	         return(x);		   /* x is NaN, y is finite */
	else if(y!=y) return(y);  	/* x and y is NaN */
	else return(copysign(y,one));   /* y is INF */
}
#endif
Commit	Line	Data
98cc7428	1	/*
f9fea09f	2	* Copyright (c) 1985 Regents of the University of California.
98cc7428 KB	3	* All rights reserved.
98cc7428 KB	4	*
7e3eac84	5	* %sccs.include.redist.c%
f9fea09f ZAL	6	*/
	7
	8	#ifndef lint
2bc65d90	9	static char sccsid[] = "@(#)cabs.c 5.6 (Berkeley) %G%";
98cc7428	10	#endif /* not lint */
f9fea09f	11
f9fea09f ZAL	12	/* HYPOT(X,Y)
	13	* RETURN THE SQUARE ROOT OF X^2 + Y^2 WHERE Z=X+iY
	14	* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
	15	* CODED IN C BY K.C. NG, 11/28/84;
	16	* REVISED BY K.C. NG, 7/12/85.
	17	*
	18	* Required system supported functions :
	19	* copysign(x,y)
	20	* finite(x)
	21	* scalb(x,N)
	22	* sqrt(x)
	23	*
	24	* Method :
	25	* 1. replace x by \|x\| and y by \|y\|, and swap x and
	26	* y if y > x (hence x is never smaller than y).
	27	* 2. Hypot(x,y) is computed by:
	28	* Case I, x/y > 2
	29	*
	30	* y
	31	* hypot = x + -----------------------------
	32	* 2
	33	* sqrt ( 1 + [x/y] ) + x/y
	34	*
	35	* Case II, x/y <= 2
	36	* y
	37	* hypot = x + --------------------------------------------------
	38	* 2
	39	* [x/y] - 2
	40	* (sqrt(2)+1) + (x-y)/y + -----------------------------
	41	* 2
	42	* sqrt ( 1 + [x/y] ) + sqrt(2)
	43	*
	44	*
	45	*
	46	* Special cases:
	47	* hypot(x,y) is INF if x or y is +INF or -INF; else
	48	* hypot(x,y) is NAN if x or y is NAN.
	49	*
	50	* Accuracy:
	51	* hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units
	52	* in the last place). See Kahan's "Interval Arithmetic Options in the
	53	* Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics
	54	* 1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate
	55	* code follows in comments.) In a test run with 500,000 random arguments
	56	* on a VAX, the maximum observed error was .959 ulps.
	57	*
	58	* Constants:
	59	* The hexadecimal values are the intended ones for the following constants.
	60	* The decimal values may be used, provided that the compiler will convert
	61	* from decimal to binary accurately enough to produce the hexadecimal values
	62	* shown.
	63	*/
9eda3584	64	#include "mathimpl.h"
f9fea09f	65
9eda3584 KB	66	vc(r2p1hi, 2.4142135623730950345E0 ,8279,411a,ef32,99fc, 2, .9A827999FCEF32)
	67	vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B)
	68	vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65)
	69
	70	ic(r2p1hi, 2.4142135623730949234E0 , 1, 1.3504F333F9DE6)
	71	ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5)
	72	ic(sqrt2, 1.4142135623730951455E0 , 0, 1.6A09E667F3BCD)
	73
	74	#ifdef vccast
	75	#define r2p1hi vccast(r2p1hi)
	76	#define r2p1lo vccast(r2p1lo)
	77	#define sqrt2 vccast(sqrt2)
	78	#endif
f9fea09f	79
74920388 ZAL	80	double
74920388 ZAL	81	hypot(x,y)
f9fea09f ZAL	82	double x, y;
f9fea09f ZAL	83	{
9eda3584	84	static const double zero=0, one=1,
f9fea09f	85	small=1.0E-18; /* fl(1+small)==1 */
9eda3584 KB	86	static const ibig=30; /* fl(1+2*(2ibig))==1 */
	87	double t,r;
	88	int exp;
f9fea09f ZAL	89
	90	if(finite(x))
	91	if(finite(y))
	92	{
	93	x=copysign(x,one);
	94	y=copysign(y,one);
	95	if(y > x)
	96	{ t=x; x=y; y=t; }
	97	if(x == zero) return(zero);
	98	if(y == zero) return(x);
	99	exp= logb(x);
	100	if(exp-(int)logb(y) > ibig )
	101	/* raise inexact flag and return \|x\| */
	102	{ one+small; return(x); }
	103
	104	/* start computing sqrt(x^2 + y^2) */
	105	r=x-y;
	106	if(r>y) { /* x/y > 2 */
	107	r=x/y;
	108	r=r+sqrt(one+r*r); }
	109	else { /* 1 <= x/y <= 2 */
	110	r/=y; t=r*(r+2.0);
	111	r+=t/(sqrt2+sqrt(2.0+t));
	112	r+=r2p1lo; r+=r2p1hi; }
	113
	114	r=y/r;
	115	return(x+r);
	116
	117	}
	118
	119	else if(y==y) /* y is +-INF */
	120	return(copysign(y,one));
	121	else
	122	return(y); /* y is NaN and x is finite */
	123
	124	else if(x==x) /* x is +-INF */
	125	return (copysign(x,one));
	126	else if(finite(y))
	127	return(x); /* x is NaN, y is finite */
859dc438	128	#if !defined(vax)&&!defined(tahoe)
f9fea09f	129	else if(y!=y) return(y); /* x and y is NaN */
859dc438	130	#endif /* !defined(vax)&&!defined(tahoe) */
f9fea09f ZAL	131	else return(copysign(y,one)); /* y is INF */
	132	}
	133
74920388 ZAL	134	/* CABS(Z)
	135	* RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER Z = X + iY
	136	* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
	137	* CODED IN C BY K.C. NG, 11/28/84.
	138	* REVISED BY K.C. NG, 7/12/85.
	139	*
	140	* Required kernel function :
	141	* hypot(x,y)
	142	*
	143	* Method :
	144	* cabs(z) = hypot(x,y) .
	145	*/
	146
	147	double
	148	cabs(z)
	149	struct { double x, y;} z;
	150	{
	151	return hypot(z.x,z.y);
	152	}
	153
	154	double
	155	z_abs(z)
	156	struct { double x,y;} *z;
	157	{
	158	return hypot(z->x,z->y);
	159	}
	160
f9fea09f ZAL	161	/* A faster but less accurate version of cabs(x,y) */
	162	#if 0
	163	double hypot(x,y)
	164	double x, y;
	165	{
9eda3584	166	static const double zero=0, one=1;
f9fea09f	167	small=1.0E-18; /* fl(1+small)==1 */
9eda3584 KB	168	static const ibig=30; /* fl(1+2*(2ibig))==1 */
	169	double temp;
	170	int exp;
f9fea09f ZAL	171
	172	if(finite(x))
	173	if(finite(y))
	174	{
	175	x=copysign(x,one);
	176	y=copysign(y,one);
	177	if(y > x)
	178	{ temp=x; x=y; y=temp; }
	179	if(x == zero) return(zero);
	180	if(y == zero) return(x);
	181	exp= logb(x);
	182	x=scalb(x,-exp);
	183	if(exp-(int)logb(y) > ibig )
	184	/* raise inexact flag and return \|x\| */
	185	{ one+small; return(scalb(x,exp)); }
	186	else y=scalb(y,-exp);
	187	return(scalb(sqrt(xx+yy),exp));
	188	}
	189
	190	else if(y==y) /* y is +-INF */
	191	return(copysign(y,one));
	192	else
	193	return(y); /* y is NaN and x is finite */
	194
	195	else if(x==x) /* x is +-INF */
	196	return (copysign(x,one));
	197	else if(finite(y))
	198	return(x); /* x is NaN, y is finite */
	199	else if(y!=y) return(y); /* x and y is NaN */
	200	else return(copysign(y,one)); /* y is INF */
	201	}
	202	#endif