lib/libm/src/e_hypotl.c

   1 /* From: @(#)e_hypot.c 1.3 95/01/18 */
   2 /* $FreeBSD: head/lib/msun/src/e_hypotl.c 226412 2011-10-16 05:36:39Z das $ */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14 /* long double version of hypot().  See e_hypot.c for most comments. */
  15
  16 #include <float.h>
  17
  18 #include "fpmath.h"
  19 #include "math.h"
  20 #include "math_private.h"
  21
  22 #define GET_LDBL_MAN(h, l, v) do {      \
  23         union IEEEl2bits uv;            \
  24                                         \
  25         uv.e = v;                       \
  26         h = uv.bits.manh;               \
  27         l = uv.bits.manl;               \
  28 } while (0)
  29
  30 #undef GET_HIGH_WORD
  31 #define GET_HIGH_WORD(i, v)     GET_LDBL_EXPSIGN(i, v)
  32 #undef SET_HIGH_WORD
  33 #define SET_HIGH_WORD(v, i)     SET_LDBL_EXPSIGN(v, i)
  34
  35 #define DESW(exp)       (exp)           /* delta expsign word */
  36 #define ESW(exp)        (MAX_EXP - 1 + (exp))   /* expsign word */
  37 #define MANT_DIG        LDBL_MANT_DIG
  38 #define MAX_EXP         LDBL_MAX_EXP
  39
  40 #if LDBL_MANL_SIZE > 32
  41 typedef uint64_t man_t;
  42 #else
  43 typedef uint32_t man_t;
  44 #endif
  45
  46 long double
  47 hypotl(long double x, long double y)
  48 {
  49         long double a=x,b=y,t1,t2,y1,y2,w;
  50         int32_t j,k,ha,hb;
  51
  52         GET_HIGH_WORD(ha,x);
  53         ha &= 0x7fff;
  54         GET_HIGH_WORD(hb,y);
  55         hb &= 0x7fff;
  56         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  57         a = fabsl(a);
  58         b = fabsl(b);
  59         if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
  60         k=0;
  61         if(ha > ESW(MAX_EXP/2-12)) {    /* a>2**(MAX_EXP/2-12) */
  62            if(ha >= ESW(MAX_EXP)) {     /* Inf or NaN */
  63                man_t manh, manl;
  64                /* Use original arg order iff result is NaN; quieten sNaNs. */
  65                w = fabsl(x+0.0)-fabsl(y+0.0);
  66                GET_LDBL_MAN(manh,manl,a);
  67                if (manh == LDBL_NBIT && manl == 0) w = a;
  68                GET_LDBL_MAN(manh,manl,b);
  69                if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
  70                return w;
  71            }
  72            /* scale a and b by 2**-(MAX_EXP/2+88) */
  73            ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
  74            k += MAX_EXP/2+88;
  75            SET_HIGH_WORD(a,ha);
  76            SET_HIGH_WORD(b,hb);
  77         }
  78         if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */
  79             if(hb <= 0) {               /* subnormal b or 0 */
  80                 man_t manh, manl;
  81                 GET_LDBL_MAN(manh,manl,b);
  82                 if((manh|manl)==0) return a;
  83                 t1=0;
  84                 SET_HIGH_WORD(t1,ESW(MAX_EXP-2));       /* t1=2^(MAX_EXP-2) */
  85                 b *= t1;
  86                 a *= t1;
  87                 k -= MAX_EXP-2;
  88             } else {            /* scale a and b by 2^(MAX_EXP/2+88) */
  89                 ha += DESW(MAX_EXP/2+88);
  90                 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         }
  96     /* medium size a and b */
  97         w = a-b;
  98         if (w>b) {
  99             t1 = a;
 100             union IEEEl2bits uv;
 101             uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
 102             t2 = a-t1;
 103             w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
 104         } else {
 105             a  = a+a;
 106             y1 = b;
 107             union IEEEl2bits uv;
 108             uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
 109             y2 = b - y1;
 110             t1 = a;
 111             uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
 112             t2 = a - t1;
 113             w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 114         }
 115         if(k!=0) {
 116             u_int32_t high;
 117             t1 = 1.0;
 118             GET_HIGH_WORD(high,t1);
 119             SET_HIGH_WORD(t1,high+DESW(k));
 120             return t1*w;
 121         } else return w;
 122 }