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