lib/msun/src/e_hypotl.c

   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
  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 }