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 #include <sys/cdefs.h>
13 /* long double version of hypot().  See e_hypot.c for most comments. */
14 
15 #include "namespace.h"
16 
17 
18 #include <float.h>
19 #include <math.h>
20 
21 #include <machine/ieee.h>
22 
23 __weak_alias(hypotl, _hypotl)
24 
25 #ifdef __HAVE_LONG_DOUBLE
26 #include "math.h"
27 #include "math_private.h"
28 
29 #ifdef LDBL_IMPLICIT_NBIT
30 #define   LDBL_NBIT 0
31 #endif
32 
33 #define   GET_LDBL_MAN(h, l, v) do {    \
34           union ieee_ext_u uv;                    \
35                                                   \
36           uv.extu_ld = v;                         \
37           h = uv.extu_frach;            \
38           l = uv.extu_fracl;            \
39 } while (0)
40 
41 #undef GET_HIGH_WORD
42 #define   GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v)
43 #undef SET_HIGH_WORD
44 #define   SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i)
45 
46 #define   DESW(exp) (exp)               /* delta expsign word */
47 #define   ESW(exp)  (MAX_EXP - 1 + (exp))         /* expsign word */
48 #define   MANT_DIG  LDBL_MANT_DIG
49 #define   MAX_EXP             LDBL_MAX_EXP
50 
51 #if EXT_FRACLBITS > 32
52 typedef   uint64_t man_t;
53 #else
54 typedef   uint32_t man_t;
55 #endif
56 
57 long double
hypotl(long double x,long double y)58 hypotl(long double x, long double y)
59 {
60           long double a=x,b=y,t1,t2,y1,y2,w;
61           int32_t j,k,ha,hb;
62 
63           GET_HIGH_WORD(ha,x);
64           ha &= 0x7fff;
65           GET_HIGH_WORD(hb,y);
66           hb &= 0x7fff;
67           if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
68           a = fabsl(a);
69           b = fabsl(b);
70           if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
71           k=0;
72           if(ha > ESW(MAX_EXP/2-12)) {  /* a>2**(MAX_EXP/2-12) */
73              if(ha >= ESW(MAX_EXP)) {   /* Inf or NaN */
74                  man_t manh, manl;
75                  /* Use original arg order iff result is NaN; quieten sNaNs. */
76                  w = fabsl(x+0.0L)-fabsl(y+0);
77                  GET_LDBL_MAN(manh,manl,a);
78                  if (manh == LDBL_NBIT && manl == 0) w = a;
79                  GET_LDBL_MAN(manh,manl,b);
80                  if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
81                  return w;
82              }
83              /* scale a and b by 2**-(MAX_EXP/2+88) */
84              ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
85              k += MAX_EXP/2+88;
86              SET_HIGH_WORD(a,ha);
87              SET_HIGH_WORD(b,hb);
88           }
89           if(hb < ESW(-(MAX_EXP/2-12))) {         /* b < 2**-(MAX_EXP/2-12) */
90               if(hb <= 0) {             /* subnormal b or 0 */
91                   man_t manh, manl;
92                     GET_LDBL_MAN(manh,manl,b);
93                     if((manh|manl)==0) return a;
94                     t1=1;
95                     SET_HIGH_WORD(t1,ESW(MAX_EXP-2));       /* t1=2^(MAX_EXP-2) */
96                     b *= t1;
97                     a *= t1;
98                     k -= MAX_EXP-2;
99               } else {                  /* scale a and b by 2^(MAX_EXP/2+88) */
100                     ha += DESW(MAX_EXP/2+88);
101                     hb += DESW(MAX_EXP/2+88);
102                     k -= MAX_EXP/2+88;
103                     SET_HIGH_WORD(a,ha);
104                     SET_HIGH_WORD(b,hb);
105               }
106           }
107     /* medium size a and b */
108           w = a-b;
109           if (w>b) {
110               t1 = a;
111               union ieee_ext_u uv;
112               uv.extu_ld = t1; uv.extu_fracl = 0; t1 = uv.extu_ld;
113               t2 = a-t1;
114               w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
115           } else {
116               a  = a+a;
117               y1 = b;
118               union ieee_ext_u uv;
119               uv.extu_ld = y1; uv.extu_fracl = 0; y1 = uv.extu_ld;
120               y2 = b - y1;
121               t1 = a;
122               uv.extu_ld = t1; uv.extu_fracl = 0; t1 = uv.extu_ld;
123               t2 = a - t1;
124               w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
125           }
126           if(k!=0) {
127               u_int32_t high;
128               t1 = 1.0;
129               GET_HIGH_WORD(high,t1);
130               SET_HIGH_WORD(t1,high+DESW(k));
131               return t1*w;
132           } else return w;
133 }
134 #else
135 #include "math.h"
136 
137 long double
138 hypotl(long double x, long double y)
139 {
140           return hypot(x, y);
141 }
142 #endif
143