lib/msun/src/e_hypotl.c

   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_EXPSIGN(i, v) do {     \
  25         union IEEEl2bits uv;            \
  26                                         \
  27         uv.e = v;                       \
  28         i = uv.xbits.expsign;           \
  29 } while (0)
  30
  31 #define GET_LDBL_MAN(h, l, v) do {      \
  32         union IEEEl2bits uv;            \
  33                                         \
  34         uv.e = v;                       \
  35         h = uv.bits.manh;               \
  36         l = uv.bits.manl;               \
  37 } while (0)
  38
  39 #define SET_LDBL_EXPSIGN(v, i) do {     \
  40         union IEEEl2bits uv;            \
  41                                         \
  42         uv.e = v;                       \
  43         uv.xbits.expsign = i;           \
  44         v = uv.e;                       \
  45 } while (0)
  46
  47 #undef GET_HIGH_WORD
  48 #define GET_HIGH_WORD(i, v)     GET_LDBL_EXPSIGN(i, v)
  49 #undef SET_HIGH_WORD
  50 #define SET_HIGH_WORD(v, i)     SET_LDBL_EXPSIGN(v, i)
  51
  52 #define DESW(exp)       (exp)           /* delta expsign word */
  53 #define ESW(exp)        (MAX_EXP - 1 + (exp))   /* expsign word */
  54 #define MANT_DIG        LDBL_MANT_DIG
  55 #define MAX_EXP         LDBL_MAX_EXP
  56
  57 #if LDBL_MANL_SIZE > 32
  58 typedef uint64_t man_t;
  59 #else
  60 typedef uint32_t man_t;
  61 #endif
  62
  63 long double
  64 hypotl(long double x, long double y)
  65 {
  66         long double a=x,b=y,t1,t2,y1,y2,w;
  67         int32_t j,k,ha,hb;
  68
  69         GET_HIGH_WORD(ha,x);
  70         ha &= 0x7fff;
  71         GET_HIGH_WORD(hb,y);
  72         hb &= 0x7fff;
  73         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  74         a = fabsl(a);
  75         b = fabsl(b);
  76         if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
  77         k=0;
  78         if(ha > ESW(MAX_EXP/2-12)) {    /* a>2**(MAX_EXP/2-12) */
  79            if(ha >= ESW(MAX_EXP)) {     /* Inf or NaN */
  80                man_t manh, manl;
  81                /* Use original arg order iff result is NaN; quieten sNaNs. */
  82                w = fabsl(x+0.0)-fabsl(y+0.0);
  83                GET_LDBL_MAN(manh,manl,a);
  84                if (manh == LDBL_NBIT && manl == 0) w = a;
  85                GET_LDBL_MAN(manh,manl,b);
  86                if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
  87                return w;
  88            }
  89            /* scale a and b by 2**-(MAX_EXP/2+88) */
  90            ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
  91            k += MAX_EXP/2+88;
  92            SET_HIGH_WORD(a,ha);
  93            SET_HIGH_WORD(b,hb);
  94         }
  95         if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */
  96             if(hb <= 0) {               /* subnormal b or 0 */
  97                 man_t manh, manl;
  98                 GET_LDBL_MAN(manh,manl,b);
  99                 if((manh|manl)==0) return a;
 100                 t1=0;
 101                 SET_HIGH_WORD(t1,ESW(MAX_EXP-2));       /* t1=2^(MAX_EXP-2) */
 102                 b *= t1;
 103                 a *= t1;
 104                 k -= MAX_EXP-2;
 105             } else {            /* scale a and b by 2^(MAX_EXP/2+88) */
 106                 ha += DESW(MAX_EXP/2+88);
 107                 hb += DESW(MAX_EXP/2+88);
 108                 k -= MAX_EXP/2+88;
 109                 SET_HIGH_WORD(a,ha);
 110                 SET_HIGH_WORD(b,hb);
 111             }
 112         }
 113     /* medium size a and b */
 114         w = a-b;
 115         if (w>b) {
 116             t1 = a;
 117             union IEEEl2bits uv;
 118             uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
 119             t2 = a-t1;
 120             w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
 121         } else {
 122             a  = a+a;
 123             y1 = b;
 124             union IEEEl2bits uv;
 125             uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
 126             y2 = b - y1;
 127             t1 = a;
 128             uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
 129             t2 = a - t1;
 130             w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 131         }
 132         if(k!=0) {
 133             u_int32_t high;
 134             t1 = 1.0;
 135             GET_HIGH_WORD(high,t1);
 136             SET_HIGH_WORD(t1,high+DESW(k));
 137             return t1*w;
 138         } else return w;
 139 }