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