1 /* From: @(#)e_hypot.c 1.3 95/01/18 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 #include <sys/cdefs.h>
14 __FBSDID("$FreeBSD$");
15
16 /* long double version of hypot(). See e_hypot.c for most comments. */
17
18 #include <float.h>
19
20 #include "fpmath.h"
21 #include "math.h"
22 #include "math_private.h"
23
24 #define GET_LDBL_MAN(h, l, v) do { \
25 union IEEEl2bits uv; \
26 \
27 uv.e = v; \
28 h = uv.bits.manh; \
29 l = uv.bits.manl; \
30 } while (0)
31
32 #undef GET_HIGH_WORD
33 #define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v)
34 #undef SET_HIGH_WORD
35 #define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i)
36
37 #define DESW(exp) (exp) /* delta expsign word */
38 #define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */
39 #define MANT_DIG LDBL_MANT_DIG
40 #define MAX_EXP LDBL_MAX_EXP
41
42 #if LDBL_MANL_SIZE > 32
43 typedef uint64_t man_t;
44 #else
45 typedef uint32_t man_t;
46 #endif
47
48 long double
hypotl(long double x,long double y)49 hypotl(long double x, long double y)
50 {
51 long double a=x,b=y,t1,t2,y1,y2,w;
52 int32_t j,k,ha,hb;
53
54 GET_HIGH_WORD(ha,x);
55 ha &= 0x7fff;
56 GET_HIGH_WORD(hb,y);
57 hb &= 0x7fff;
58 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
59 a = fabsl(a);
60 b = fabsl(b);
61 if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
62 k=0;
63 if(ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */
64 if(ha >= ESW(MAX_EXP)) { /* Inf or NaN */
65 man_t manh, manl;
66 /* Use original arg order iff result is NaN; quieten sNaNs. */
67 w = fabsl(x+0.0)-fabsl(y+0.0);
68 GET_LDBL_MAN(manh,manl,a);
69 if (manh == LDBL_NBIT && manl == 0) w = a;
70 GET_LDBL_MAN(manh,manl,b);
71 if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
72 return w;
73 }
74 /* scale a and b by 2**-(MAX_EXP/2+88) */
75 ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
76 k += MAX_EXP/2+88;
77 SET_HIGH_WORD(a,ha);
78 SET_HIGH_WORD(b,hb);
79 }
80 if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */
81 if(hb <= 0) { /* subnormal b or 0 */
82 man_t manh, manl;
83 GET_LDBL_MAN(manh,manl,b);
84 if((manh|manl)==0) return a;
85 t1=0;
86 SET_HIGH_WORD(t1,ESW(MAX_EXP-2)); /* t1=2^(MAX_EXP-2) */
87 b *= t1;
88 a *= t1;
89 k -= MAX_EXP-2;
90 } else { /* scale a and b by 2^(MAX_EXP/2+88) */
91 ha += DESW(MAX_EXP/2+88);
92 hb += DESW(MAX_EXP/2+88);
93 k -= MAX_EXP/2+88;
94 SET_HIGH_WORD(a,ha);
95 SET_HIGH_WORD(b,hb);
96 }
97 }
98 /* medium size a and b */
99 w = a-b;
100 if (w>b) {
101 t1 = a;
102 union IEEEl2bits uv;
103 uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
104 t2 = a-t1;
105 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
106 } else {
107 a = a+a;
108 y1 = b;
109 union IEEEl2bits uv;
110 uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
111 y2 = b - y1;
112 t1 = a;
113 uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
114 t2 = a - t1;
115 w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
116 }
117 if(k!=0) {
118 u_int32_t high;
119 t1 = 1.0;
120 GET_HIGH_WORD(high,t1);
121 SET_HIGH_WORD(t1,high+DESW(k));
122 return t1*w;
123 } else return w;
124 }
125