lib/libm/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  * FreeBSD SVN: 226412 (2011-10-16)
  13  */
  14
  15 /* long double version of hypot().  See e_hypot.c for most comments. */
  16
  17 #include <float.h>
  18
  19 #include "fpmath.h"
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 #define GET_LDBL_MAN(h, l, v) do {      \
  24         union IEEEl2bits uv;            \
  25                                         \
  26         uv.e = v;                       \
  27         h = uv.bits.manh;               \
  28         l = uv.bits.manl;               \
  29 } while (0)
  30
  31 #undef GET_HIGH_WORD
  32 #define GET_HIGH_WORD(i, v)     GET_LDBL_EXPSIGN(i, v)
  33 #undef SET_HIGH_WORD
  34 #define SET_HIGH_WORD(v, i)     SET_LDBL_EXPSIGN(v, i)
  35
  36 #define DESW(exp)       (exp)           /* delta expsign word */
  37 #define ESW(exp)        (MAX_EXP - 1 + (exp))   /* expsign word */
  38 #define MANT_DIG        LDBL_MANT_DIG
  39 #define MAX_EXP         LDBL_MAX_EXP
  40
  41 #if LDBL_MANL_SIZE > 32
  42 typedef uint64_t man_t;
  43 #else
  44 typedef uint32_t man_t;
  45 #endif
  46
  47 long double
  48 hypotl(long double x, long double y)
  49 {
  50         long double a=x,b=y,t1,t2,y1,y2,w;
  51         int32_t j,k,ha,hb;
  52
  53         GET_HIGH_WORD(ha,x);
  54         ha &= 0x7fff;
  55         GET_HIGH_WORD(hb,y);
  56         hb &= 0x7fff;
  57         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  58         a = fabsl(a);
  59         b = fabsl(b);
  60         if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
  61         k=0;
  62         if(ha > ESW(MAX_EXP/2-12)) {    /* a>2**(MAX_EXP/2-12) */
  63            if(ha >= ESW(MAX_EXP)) {     /* Inf or NaN */
  64                man_t manh, manl;
  65                /* Use original arg order iff result is NaN; quieten sNaNs. */
  66                w = fabsl(x+0.0)-fabsl(y+0.0);
  67                GET_LDBL_MAN(manh,manl,a);
  68                if (manh == LDBL_NBIT && manl == 0) w = a;
  69                GET_LDBL_MAN(manh,manl,b);
  70                if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
  71                return w;
  72            }
  73            /* scale a and b by 2**-(MAX_EXP/2+88) */
  74            ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
  75            k += MAX_EXP/2+88;
  76            SET_HIGH_WORD(a,ha);
  77            SET_HIGH_WORD(b,hb);
  78         }
  79         if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */
  80             if(hb <= 0) {               /* subnormal b or 0 */
  81                 man_t manh, manl;
  82                 GET_LDBL_MAN(manh,manl,b);
  83                 if((manh|manl)==0) return a;
  84                 t1=0;
  85                 SET_HIGH_WORD(t1,ESW(MAX_EXP-2));       /* t1=2^(MAX_EXP-2) */
  86                 b *= t1;
  87                 a *= t1;
  88                 k -= MAX_EXP-2;
  89             } else {            /* scale a and b by 2^(MAX_EXP/2+88) */
  90                 ha += DESW(MAX_EXP/2+88);
  91                 hb += DESW(MAX_EXP/2+88);
  92                 k -= MAX_EXP/2+88;
  93                 SET_HIGH_WORD(a,ha);
  94                 SET_HIGH_WORD(b,hb);
  95             }
  96         }
  97     /* medium size a and b */
  98         w = a-b;
  99         if (w>b) {
 100             t1 = a;
 101             union IEEEl2bits uv;
 102             uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
 103             t2 = a-t1;
 104             w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
 105         } else {
 106             a  = a+a;
 107             y1 = b;
 108             union IEEEl2bits uv;
 109             uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
 110             y2 = b - y1;
 111             t1 = a;
 112             uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
 113             t2 = a - t1;
 114             w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 115         }
 116         if(k!=0) {
 117             u_int32_t high;
 118             t1 = 1.0;
 119             GET_HIGH_WORD(high,t1);
 120             SET_HIGH_WORD(t1,high+DESW(k));
 121             return t1*w;
 122         } else return w;
 123 }