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/* From: @(#)e_hypot.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/* long double version of hypot(). See e_hypot.c for most comments. */
#include <float.h>
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
#define GET_LDBL_EXPSIGN(i, v) do { \
union IEEEl2bits uv; \
\
uv.e = v; \
i = uv.xbits.expsign; \
} while (0)
#define GET_LDBL_MAN(h, l, v) do { \
union IEEEl2bits uv; \
\
uv.e = v; \
h = uv.bits.manh; \
l = uv.bits.manl; \
} while (0)
#define SET_LDBL_EXPSIGN(v, i) do { \
union IEEEl2bits uv; \
\
uv.e = v; \
uv.xbits.expsign = i; \
v = uv.e; \
} while (0)
#undef GET_HIGH_WORD
#define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v)
#undef SET_HIGH_WORD
#define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i)
#define DESW(exp) (exp) /* delta expsign word */
#define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */
#define MANT_DIG LDBL_MANT_DIG
#define MAX_EXP LDBL_MAX_EXP
#if LDBL_MANL_SIZE > 32
typedef uint64_t man_t;
#else
typedef uint32_t man_t;
#endif
long double
hypotl(long double x, long double y)
{
long double a=x,b=y,t1,t2,y1,y2,w;
int32_t j,k,ha,hb;
GET_HIGH_WORD(ha,x);
ha &= 0x7fff;
GET_HIGH_WORD(hb,y);
hb &= 0x7fff;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
a = fabsl(a);
b = fabsl(b);
if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
k=0;
if(ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */
if(ha >= ESW(MAX_EXP)) { /* Inf or NaN */
man_t manh, manl;
/* Use original arg order iff result is NaN; quieten sNaNs. */
w = fabsl(x+0.0)-fabsl(y+0.0);
GET_LDBL_MAN(manh,manl,a);
if (manh == LDBL_NBIT && manl == 0) w = a;
GET_LDBL_MAN(manh,manl,b);
if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
return w;
}
/* scale a and b by 2**-(MAX_EXP/2+88) */
ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
k += MAX_EXP/2+88;
SET_HIGH_WORD(a,ha);
SET_HIGH_WORD(b,hb);
}
if(hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */
if(hb <= 0) { /* subnormal b or 0 */
man_t manh, manl;
GET_LDBL_MAN(manh,manl,b);
if((manh|manl)==0) return a;
t1=0;
SET_HIGH_WORD(t1,ESW(MAX_EXP-2)); /* t1=2^(MAX_EXP-2) */
b *= t1;
a *= t1;
k -= MAX_EXP-2;
} else { /* scale a and b by 2^(MAX_EXP/2+88) */
ha += DESW(MAX_EXP/2+88);
hb += DESW(MAX_EXP/2+88);
k -= MAX_EXP/2+88;
SET_HIGH_WORD(a,ha);
SET_HIGH_WORD(b,hb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = a;
union IEEEl2bits uv;
uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
t2 = a-t1;
w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
y1 = b;
union IEEEl2bits uv;
uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
y2 = b - y1;
t1 = a;
uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
t2 = a - t1;
w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int32_t high;
t1 = 1.0;
GET_HIGH_WORD(high,t1);
SET_HIGH_WORD(t1,high+DESW(k));
return t1*w;
} else return w;
}
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