/*  LibMImplB.c  */
/*   NFS   */

/* cabs(), hypot(), cbrt(), floor(), ceil(), rint()  */

asm ("        export Libm");

mesa double LibmSupport_copysign(), LibmSupport_scalb();
mesa double LibmSupport_drem(), LibmSupport_logb(), Libm_sqrt();
mesa int LibmSupport_finite();
mesa double Libm_modf();

#define copysign(x,y) (LibmSupport_copysign(x,y))
#define scalb(x,n)  (LibmSupport_scalb(x,n))
#define logb(x)  (LibmSupport_logb(x))
#define finite(x) (LibmSupport_finite(x))
#define drem(x,p) (LibmSupport_drem(x,p))
#define sqrt(x)  (Libm_sqrt(x))

/* 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) .
 */

asm ("        exportproc _cabs, Libm");
double cabs(z)
struct { double x, y;} z;
{
	double hypot();
	return(hypot(z.x,z.y));
}


/* 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.
 */


static double
r2p1hi =  2.4142135623730949234E0     , /*Hex  2^1     *  1.3504F333F9DE6 */
r2p1lo =  1.2537167179050217666E-16   , /*Hex  2^-53   *  1.21165F626CDD5 */
sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */

asm ("        exportproc _hypot, Libm");
double hypot(x,y)
double x, y;
{
	static double zero=0, one=1, 
		      small=1.0E-18;	/* fl(1+small)==1 */
	static ibig=30;	/* fl(1+2**(2*ibig))==1 */
	double LibmSupport_copysign(),
	       LibmSupport_scalb(),
	       LibmSupport_logb(),
	       Libm_sqrt(),t,r;
	int LibmSupport_finite(), 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 */
	else if(y!=y) return(y);  /* x and y is NaN */
	else return(copysign(y,one));   /* y is INF */
}

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


/*  CBRT   */
/* kahan's cube root (53 bits IEEE double precision)
 * for IEEE machines only
 * coded in C by K.C. Ng, 4/30/85
 *
 * Accuracy:
 *	better than 0.667 ulps according to an error analysis. Maximum
 * error observed was 0.666 ulps in an 1,000,000 random arguments test.
 *
 * Warning: this code is semi machine dependent; the ordering of words in
 * a floating point number must be known in advance. I assume that the
 * long interger at the address of a floating point number will be the
 * leading 32 bits of that floating point number (i.e., sign, exponent,
 * and the 20 most significant bits).
 * On a National machine, it has different ordering; therefore, this code 
 * must be compiled with flag -DNATIONAL. 
 */

static unsigned long B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
	             B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
static double
	    C= 19./35.,
	    D= -864./1225.,
	    E= 99./70.,
	    F= 45./28.,
	    G= 5./14.;

asm ("        exportproc _cbrt, Libm");
double cbrt(x) 
double x;
{
	double r,s,t=0.0,w;
	unsigned long *px = (unsigned long *) &x,
	              *pt = (unsigned long *) &t,
		      mexp,sign;


	int n0=0,n1=1;

	mexp=px[n0]&0x7ff00000;
	if(mexp==0x7ff00000) return(x); /* cbrt(NaN,INF) is itself */
	if(x==0.0) return(x);		/* cbrt(0) is itself */

	sign=px[n0]&0x80000000; /* sign= sign(x) */
	px[n0] ^= sign;		/* x=|x| */


    /* rough cbrt to 5 bits */
	if(mexp==0) 		/* subnormal number */
	  {pt[n0]=0x43500000; 	/* set t= 2**54 */
	   t*=x; pt[n0]=pt[n0]/3+B2;
	  }
	else
	  pt[n0]=px[n0]/3+B1;	


    /* new cbrt to 23 bits, may be implemented in single precision */
	r=t*t/x;
	s=C+r*t;
	t*=G+F/(s+E+D/s);	

    /* chopped to 20 bits and make it larger than cbrt(x) */ 
	pt[n1]=0; pt[n0]+=0x00000001;


    /* one step newton iteration to 53 bits with error less than 0.667 ulps */
	s=t*t;		/* t*t is exact */
	r=x/s;
	w=t+t;
	r=(r-t)/(w+r);	/* r-s is exact */
	t=t+t*r;


    /* retore the sign bit */
	pt[n0] |= sign;
	return(t);
}

/*	@(#)floor.c	4.2	9/11/85 */

/* 
 * floor and ceil-- greatest integer <= arg
 * (resp least >=)
 */

double	Libm_modf();

asm ("        exportproc _floor, Libm");
double
floor(d)
double d;
{
	double fract;

	if (d<0.0) {
		d = -d;
		fract = Libm_modf(d, &d);
		if (fract != 0.0)
			d += 1;
		d = -d;
	} else
		Libm_modf(d, &d);
	return(d);
}

asm ("        exportproc _ceil, Libm");
double
ceil(d)
double d;
{
	return(-floor(-d));
}

/*
 * algorithm for rint(x) in pseudo-pascal form ...
 *
 * real rint(x): real x;
 *	... delivers integer nearest x in direction of prevailing rounding
 *	... mode
 * const	L = (last consecutive integer)/2
 * 	  = 2**55; for VAX D
 * 	  = 2**52; for IEEE 754 Double
 * real	s,t;
 * begin
 * 	if x != x then return x;		... NaN
 * 	if |x| >= L then return x;		... already an integer
 * 	s := copysign(L,x);
 * 	t := x + s;				... = (x+s) rounded to integer
 * 	return t - s
 * end;
 *
 * Note: Inexact will be signaled if x is not an integer, as is
 *	customary for IEEE 754.  No other signal can be emitted.
 */

asm ("        exportproc _rint, Libm");
static double L = 4503599627370496.0E0;		/* 2**52 */
double
rint(x)
double x;
{
	double s,t,one = 1.0,LibmSupport_copysign();
	if (x != x)				/* NaN */
		return (x);
	if (copysign(x,one) >= L)		/* already an integer */
	    return (x);
	s = copysign(L,x);
	t = x + s;				/* x+s rounded to integer */
	return (t - s);
}