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/* origin: FreeBSD /usr/src/lib/msun/src/e_hypotl.c */
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* ====================================================
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/* long double version of hypot(). See comments in hypot.c. */
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#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
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#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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#define GET_LDBL_EXPSIGN(i, v) do { \
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union IEEEl2bits uv; \
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i = uv.xbits.expsign; \
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#define GET_LDBL_MAN(h, l, v) do { \
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union IEEEl2bits uv; \
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#define SET_LDBL_EXPSIGN(v, i) do { \
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union IEEEl2bits uv; \
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uv.xbits.expsign = i; \
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#define GET_HIGH_WORD(i, v) GET_LDBL_EXPSIGN(i, v)
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#define SET_HIGH_WORD(v, i) SET_LDBL_EXPSIGN(v, i)
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#define DESW(exp) (exp) /* delta expsign word */
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#define ESW(exp) (MAX_EXP - 1 + (exp)) /* expsign word */
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#define MANT_DIG LDBL_MANT_DIG
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#define MAX_EXP LDBL_MAX_EXP
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#if LDBL_MANL_SIZE > 32
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typedef uint64_t man_t;
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typedef uint32_t man_t;
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#if LDBL_MANT_DIG == 64
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#define SPLIT (0x1p32L+1)
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#elif LDBL_MANT_DIG == 113
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#define SPLIT (0x1p57L+1)
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static void sq(long double *hi, long double *lo, long double x)
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long double xh, xl, xc;
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*lo = xh*xh - *hi + 2*xh*xl + xl*xl;
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long double hypotl(long double x, long double y)
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long double a=x,b=y,t1,t2,y1,y2,w;
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if (ha - hb > DESW(MANT_DIG+7)) /* x/y > 2**(MANT_DIG+7) */
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if (ha > ESW(MAX_EXP/2-12)) { /* a>2**(MAX_EXP/2-12) */
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if (ha >= ESW(MAX_EXP)) { /* Inf or NaN */
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/* Use original arg order iff result is NaN; quieten sNaNs. */
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w = fabsl(x+0.0)-fabsl(y+0.0);
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GET_LDBL_MAN(manh,manl,a);
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if (manh == LDBL_NBIT && manl == 0) w = a;
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GET_LDBL_MAN(manh,manl,b);
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if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
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/* scale a and b by 2**-(MAX_EXP/2+88) */
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ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
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if (hb < ESW(-(MAX_EXP/2-12))) { /* b < 2**-(MAX_EXP/2-12) */
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if (hb <= 0) { /* subnormal b or 0 */
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GET_LDBL_MAN(manh,manl,b);
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if ((manh|manl) == 0)
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SET_HIGH_WORD(t1, ESW(MAX_EXP-2)); /* t1 = 2^(MAX_EXP-2) */
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} else { /* scale a and b by 2^(MAX_EXP/2+88) */
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ha += DESW(MAX_EXP/2+88);
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hb += DESW(MAX_EXP/2+88);
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SET_HIGH_WORD(a, ha);
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SET_HIGH_WORD(b, hb);
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/* medium size a and b */
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uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
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w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
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uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
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uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
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w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
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GET_HIGH_WORD(high, t1);
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SET_HIGH_WORD(t1, high+DESW(k));
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union ldshape ux = {x}, uy = {y};
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long double hx, lx, hy, ly, z;
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if (ux.i.se < uy.i.se) {
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if (ex == 0x7fff && isinf(y))
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if (ex == 0x7fff || y == 0)
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if (ex - ey > LDBL_MANT_DIG)
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if (ex > 0x3fff+8000) {
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} else if (ey < 0x3fff-8000) {
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return z*sqrtl(ly+lx+hy+hx);