summaryrefslogtreecommitdiff
path: root/sysdeps/ieee754/ldbl-96/e_hypotl.c
blob: 7cd487e8623b854503343e61d7c72f2888ac8011 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
/* e_hypotl.c -- long double version of e_hypot.c.
 * Conversion to long double by Ulrich Drepper,
 * Cygnus Support, drepper@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/* __ieee754_hypotl(x,y)
 *
 * Method :
 *	If (assume round-to-nearest) z=x*x+y*y
 *	has error less than sqrt(2)/2 ulp, than
 *	sqrt(z) has error less than 1 ulp (exercise).
 *
 *	So, compute sqrt(x*x+y*y) with some care as
 *	follows to get the error below 1 ulp:
 *
 *	Assume x>y>0;
 *	(if possible, set rounding to round-to-nearest)
 *	1. if x > 2y  use
 *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
 *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
 *	2. if x <= 2y use
 *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
 *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
 *	y1= y with lower 32 bits chopped, y2 = y-y1.
 *
 *	NOTE: scaling may be necessary if some argument is too
 *	      large or too tiny
 *
 * 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 sqrt(x^2+y^2) with error less
 *	than 1 ulps (units in the last place)
 */

#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-finite.h>

long double __ieee754_hypotl(long double x, long double y)
{
	long double a,b,t1,t2,y1,y2,w;
	uint32_t j,k,ea,eb;

	GET_LDOUBLE_EXP(ea,x);
	ea &= 0x7fff;
	GET_LDOUBLE_EXP(eb,y);
	eb &= 0x7fff;
	if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
	SET_LDOUBLE_EXP(a,ea);	/* a <- |a| */
	SET_LDOUBLE_EXP(b,eb);	/* b <- |b| */
	if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
	k=0;
	if(__builtin_expect(ea > 0x5f3f,0)) {	/* a>2**8000 */
	   if(ea == 0x7fff) {	/* Inf or NaN */
	       uint32_t exp __attribute__ ((unused));
	       uint32_t high,low;
	       w = a+b;			/* for sNaN */
	       if (issignaling (a) || issignaling (b))
		 return w;
	       GET_LDOUBLE_WORDS(exp,high,low,a);
	       if(((high&0x7fffffff)|low)==0) w = a;
	       GET_LDOUBLE_WORDS(exp,high,low,b);
	       if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
	       return w;
	   }
	   /* scale a and b by 2**-9600 */
	   ea -= 0x2580; eb -= 0x2580;	k += 9600;
	   SET_LDOUBLE_EXP(a,ea);
	   SET_LDOUBLE_EXP(b,eb);
	}
	if(__builtin_expect(eb < 0x20bf, 0)) {	/* b < 2**-8000 */
	    if(eb == 0) {	/* subnormal b or 0 */
		uint32_t exp __attribute__ ((unused));
		uint32_t high,low;
		GET_LDOUBLE_WORDS(exp,high,low,b);
		if((high|low)==0) return a;
		SET_LDOUBLE_WORDS(t1, 0x7ffd, 0x80000000, 0); /* t1=2^16382 */
		b *= t1;
		a *= t1;
		k -= 16382;
		GET_LDOUBLE_EXP (ea, a);
		GET_LDOUBLE_EXP (eb, b);
		if (eb > ea)
		  {
		    t1 = a;
		    a = b;
		    b = t1;
		    j = ea;
		    ea = eb;
		    eb = j;
		  }
	    } else {		/* scale a and b by 2^9600 */
		ea += 0x2580;	/* a *= 2^9600 */
		eb += 0x2580;	/* b *= 2^9600 */
		k -= 9600;
		SET_LDOUBLE_EXP(a,ea);
		SET_LDOUBLE_EXP(b,eb);
	    }
	}
    /* medium size a and b */
	w = a-b;
	if (w>b) {
	    uint32_t high;
	    GET_LDOUBLE_MSW(high,a);
	    SET_LDOUBLE_WORDS(t1,ea,high,0);
	    t2 = a-t1;
	    w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
	} else {
	    uint32_t high;
	    GET_LDOUBLE_MSW(high,b);
	    a  = a+a;
	    SET_LDOUBLE_WORDS(y1,eb,high,0);
	    y2 = b - y1;
	    GET_LDOUBLE_MSW(high,a);
	    SET_LDOUBLE_WORDS(t1,ea+1,high,0);
	    t2 = a - t1;
	    w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
	}
	if(k!=0) {
	    uint32_t exp;
	    t1 = 1.0;
	    GET_LDOUBLE_EXP(exp,t1);
	    SET_LDOUBLE_EXP(t1,exp+k);
	    w *= t1;
	    math_check_force_underflow_nonneg (w);
	    return w;
	} else return w;
}
libm_alias_finite (__ieee754_hypotl, __hypotl)