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src/java.base/share/classes/java/lang/FdLibm.java
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*** 1,32 ****
! /*
! * Copyright (c) 1998, 2004, Oracle and/or its affiliates. All rights reserved.
! * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
! *
! * This code is free software; you can redistribute it and/or modify it
! * under the terms of the GNU General Public License version 2 only, as
! * published by the Free Software Foundation. Oracle designates this
! * particular file as subject to the "Classpath" exception as provided
! * by Oracle in the LICENSE file that accompanied this code.
! *
! * This code is distributed in the hope that it will be useful, but WITHOUT
! * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
! * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
! * version 2 for more details (a copy is included in the LICENSE file that
! * accompanied this code).
! *
! * You should have received a copy of the GNU General Public License version
! * 2 along with this work; if not, write to the Free Software Foundation,
! * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
! *
! * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
! * or visit www.oracle.com if you need additional information or have any
! * questions.
*/
! /* __ieee754_pow(x,y) return x**y
*
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
--- 1,44 ----
+ package java.lang;
! /**
! * Port of the "Freely Distributable Math Library", version 4.3, from C to Java.
! */
! class FdLibm {
! /**
! * Return the low-order 32 bits of the double argument as an int.
! */
! private static int __LO(double x) {
! long transducer = Double.doubleToLongBits(x);
! return (int)transducer;
! }
!
! /**
! * Return the a double with its low-order bits reset.
! */
! private static double __LO(double x, int low) {
! long transX = Double.doubleToLongBits(x);
! return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low );
! }
!
! /**
! * Return the high-order 32 bits of the double argument as an int.
*/
+ private static int __HI(double x) {
+ long transducer = Double.doubleToLongBits(x);
+ return (int)(transducer >> 32);
+ }
+ /**
+ * Return the a double with its high-order bits reset.
+ */
+ private static double __HI(double x, int high) {
+ long transX = Double.doubleToLongBits(x);
+ return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
+ }
! /**
! * Return x**y
*
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
*** 66,320 ****
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
!
! #include "fdlibm.h"
!
! #ifdef __STDC__
! static const double
! #else
! static double
! #endif
! bp[] = {1.0, 1.5,},
! dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
! dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
! zero = 0.0,
! one = 1.0,
! two = 2.0,
! two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
! huge = 1.0e300,
! tiny = 1.0e-300,
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
! L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
! L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
! L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
! L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
! L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
! L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
! P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
! P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
! P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
! P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
! P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
! lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
! lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
! lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
! ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
! cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
! cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
! cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
! ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
! ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
! ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
!
! #ifdef __STDC__
! double __ieee754_pow(double x, double y)
! #else
! double __ieee754_pow(x,y)
! double x, y;
! #endif
! {
! double z,ax,z_h,z_l,p_h,p_l;
! double y1,t1,t2,r,s,t,u,v,w;
! int i0,i1,i,j,k,yisint,n;
! int hx,hy,ix,iy;
! unsigned lx,ly;
!
! i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
! hx = __HI(x); lx = __LO(x);
! hy = __HI(y); ly = __LO(y);
! ix = hx&0x7fffffff; iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
! if((iy|ly)==0) return one;
/* +-NaN return x+y */
! if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
! iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
! return x+y;
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
! if(hx<0) {
! if(iy>=0x43400000) yisint = 2; /* even integer y */
! else if(iy>=0x3ff00000) {
! k = (iy>>20)-0x3ff; /* exponent */
! if(k>20) {
! j = ly>>(52-k);
! if((j<<(52-k))==ly) yisint = 2-(j&1);
! } else if(ly==0) {
! j = iy>>(20-k);
! if((j<<(20-k))==iy) yisint = 2-(j&1);
}
}
}
/* special value of y */
! if(ly==0) {
! if (iy==0x7ff00000) { /* y is +-inf */
! if(((ix-0x3ff00000)|lx)==0)
return y - y; /* inf**+-1 is NaN */
! else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
! return (hy>=0)? y: zero;
! else /* (|x|<1)**-,+inf = inf,0 */
! return (hy<0)?-y: zero;
! }
! if(iy==0x3ff00000) { /* y is +-1 */
! if(hy<0) return one/x; else return x;
! }
! if(hy==0x40000000) return x*x; /* y is 2 */
! if(hy==0x3fe00000) { /* y is 0.5 */
! if(hx>=0) /* x >= +0 */
! return sqrt(x);
}
}
! ax = fabs(x);
/* special value of x */
! if(lx==0) {
! if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
z = ax; /*x is +-0,+-inf,+-1*/
! if(hy<0) z = one/z; /* z = (1/|x|) */
! if(hx<0) {
! if(((ix-0x3ff00000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
! } else if(yisint==1)
z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
! n = (hx>>31)+1;
/* (x<0)**(non-int) is NaN */
! if((n|yisint)==0) return (x-x)/(x-x);
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
! if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
/* |y| is huge */
! if(iy>0x41e00000) { /* if |y| > 2**31 */
! if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
! if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
! if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
}
/* over/underflow if x is not close to one */
! if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
! if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = ax-one; /* t has 20 trailing zeros */
! w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
! u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
v = t*ivln2_l-w*ivln2;
! t1 = u+v;
! __LO(t1) = 0;
t2 = v-(t1-u);
} else {
! double ss,s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
! if(ix<0x00100000)
! {ax *= two53; n -= 53; ix = __HI(ax); }
! n += ((ix)>>20)-0x3ff;
! j = ix&0x000fffff;
/* determine interval */
! ix = j|0x3ff00000; /* normalize ix */
! if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
! else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
! else {k=0;n+=1;ix -= 0x00100000;}
! __HI(ax) = ix;
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
! u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
! v = one/(ax+bp[k]);
! ss = u*v;
s_h = ss;
! __LO(s_h) = 0;
/* t_h=ax+bp[k] High */
t_h = zero;
! __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
! t_l = ax - (t_h-bp[k]);
! s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
! s2 = ss*ss;
! r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
! r += s_l*(s_h+ss);
! s2 = s_h*s_h;
! t_h = 3.0+s2+r;
! __LO(t_h) = 0;
! t_l = r-((t_h-3.0)-s2);
/* u+v = ss*(1+...) */
! u = s_h*t_h;
! v = s_l*t_h+t_l*ss;
/* 2/(3log2)*(ss+...) */
! p_h = u+v;
! __LO(p_h) = 0;
p_l = v-(p_h-u);
! z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
! z_l = cp_l*p_h+p_l*cp+dp_l[k];
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double)n;
! t1 = (((z_h+z_l)+dp_h[k])+t);
! __LO(t1) = 0;
! t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
! __LO(y1) = 0;
! p_l = (y-y1)*t1+y*t2;
! p_h = y1*t1;
! z = p_l+p_h;
j = __HI(z);
i = __LO(z);
! if (j>=0x40900000) { /* z >= 1024 */
! if(((j-0x40900000)|i)!=0) /* if z > 1024 */
return s*huge*huge; /* overflow */
else {
! if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
}
! } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
! if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
return s*tiny*tiny; /* underflow */
else {
! if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
! i = j&0x7fffffff;
! k = (i>>20)-0x3ff;
n = 0;
! if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
! n = j+(0x00100000>>(k+1));
! k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
t = zero;
! __HI(t) = (n&~(0x000fffff>>k));
! n = ((n&0x000fffff)|0x00100000)>>(20-k);
! if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
! __LO(t) = 0;
! u = t*lg2_h;
! v = (p_l-(t-p_h))*lg2+t*lg2_l;
! z = u+v;
w = v-(z-u);
! t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-two)-(w+z*w);
! z = one-(r-z);
j = __HI(z);
! j += (n<<20);
! if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
! else __HI(z) += (n<<20);
! return s*z;
}
--- 78,355 ----
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
! public static class Pow {
! static final double bp[] = {1.0, 1.5,};
! static final double dp_h[] = { 0.0, 0x1.2b8034p-1,}; // 5.84962487220764160156e-01
! static final double dp_l[] = { 0.0, 0x1.cfdeb43cfd006p-27,}; // 1.35003920212974897128e-08
! static final double zero = 0.0;
! static final double one = 1.0;
! static final double two = 2.0;
! static final double two53 = 0x1.0p53; // 9007199254740992.0
! static final double huge = 1.0e300;
! static final double tiny = 1.0e-300;
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
! static final double L1 = 0x1.3333333333303p-1; // 5.99999999999994648725e-01
! static final double L2 = 0x1.b6db6db6fabffp-2; // 4.28571428578550184252e-01
! static final double L3 = 0x1.55555518f264dp-2; // 3.33333329818377432918e-01
! static final double L4 = 0x1.17460a91d4101p-2; // 2.72728123808534006489e-01
! static final double L5 = 0x1.d864a93c9db65p-3; // 2.30660745775561754067e-01
! static final double L6 = 0x1.a7e284a454eefp-3; // 2.06975017800338417784e-01
! static final double P1 = 0x1.555555555553ep-3; // 1.66666666666666019037e-01
! static final double P2 = -0x1.6c16c16bebd93p-9; // -2.77777777770155933842e-03
! static final double P3 = 0x1.1566aaf25de2cp-14; // 6.61375632143793436117e-05
! static final double P4 = -0x1.bbd41c5d26bf1p-20; // -1.65339022054652515390e-06
! static final double P5 = 0x1.6376972bea4d0p-25; // 4.13813679705723846039e-08
! static final double lg2 = 0x1.62e42fefa39efp-1; // 6.93147180559945286227e-01
! static final double lg2_h = 0x1.62e43p-1; // 6.93147182464599609375e-01
! static final double lg2_l = -0x1.05c610ca86c39p-29; // -1.90465429995776804525e-09
! static final double ovt = 8.0085662595372944372e-0017; // -(1024-log2(ovfl+.5ulp))
! static final double cp = 0x1.ec709dc3a03fdp-1; // 9.61796693925975554329e-01 = 2/(3ln2)
! static final double cp_h = 0x1.ec709ep-1; // 9.61796700954437255859e-01 = (float)cp
! static final double cp_l = -0x1.e2fe0145b01f5p-28; // -7.02846165095275826516e-09 = tail of cp_h
! static final double ivln2 = 0x1.71547652b82fep0; // 1.44269504088896338700e+00 = 1/ln2
! static final double ivln2_h = 0x1.715476p0; // 1.44269502162933349609e+00 = 24 bits of 1/ln2
! static final double ivln2_l = 0x1.4ae0bf85ddf44p-26; // 1.92596299112661746887e-08 = 1/ln2 tail
!
! public static double pow(double x, double y) {
! double z, ax, z_h, z_l, p_h, p_l;
! double y1, t1, t2, r, s, t, u, v, w;
! int i, j, k, yisint, n;
! int hx, hy, ix, iy;
! /*unsigned*/ int lx, ly;
!
! hx = __HI(x);
! lx = __LO(x);
! hy = __HI(y);
! ly = __LO(y);
! ix = hx & 0x7fffffff;
! iy = hy & 0x7fffffff;
/* y==zero: x**0 = 1 */
! if (y == 0.0)
! return 1.0;
/* +-NaN return x+y */
! if (Double.isNaN(x) || Double.isNaN(y))
! return x + y;
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
! if (hx < 0) {
! if (iy >= 0x43400000)
! yisint = 2; /* even integer y */
! else if (iy >= 0x3ff00000) {
! k = (iy >> 20) - 0x3ff; /* exponent */
! if (k > 20) {
! j = ly >> (52-k);
! if ((j << (52-k) )==ly)
! yisint = 2 - (j&1);
! } else if (ly == 0) {
! j = iy >> (20-k);
! if ((j << (20-k))==iy) {
! yisint = 2-(j & 1);
! }
}
}
}
/* special value of y */
! if ( ly == 0 ) {
! if (iy == 0x7ff00000) { /* y is +-inf */
! if (((ix - 0x3ff00000) | lx) == 0)
return y - y; /* inf**+-1 is NaN */
! else if (ix >= 0x3ff00000) /* (|x| > 1)**+-inf = inf,0 */
! return (hy >= 0) ? y: zero;
! else /* (|x| < 1)**-,+inf = inf,0 */
! return (hy < 0) ? -y: zero;
! }
! if (iy == 0x3ff00000) { /* y is +-1 */
! if (hy < 0)
! return one/x;
! else
! return x;
! }
! if (hy == 0x40000000)
! return x*x; /* y is 2 */
! if (hy == 0x3fe00000) { /* y is 0.5 */
! if (hx >= 0) /* x >= +0 */
! return Math.sqrt(x);
}
}
! ax = Math.abs(x);
/* special value of x */
! if (lx == 0) {
! if (ix == 0x7ff00000 || ix==0 || ix == 0x3ff00000){
z = ax; /*x is +-0,+-inf,+-1*/
! if (hy < 0)
! z = one/z; /* z = (1/|x|) */
! if (hx < 0) {
! if (((ix - 0x3ff00000) | yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
! } else if (yisint == 1)
z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
! n = (hx >> 31)+1;
/* (x<0)**(non-int) is NaN */
! if ((n | yisint) == 0)
! return (x-x)/(x-x);
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
! if ( (n | (yisint-1)) == 0)
! s = -one;/* (-ve)**(odd int) */
/* |y| is huge */
! if(iy > 0x41e00000) { /* if |y| > 2**31 */
! if(iy > 0x43f00000){ /* if |y| > 2**64, must o/uflow */
! if (ix <= 0x3fefffff)
! return (hy < 0) ? huge*huge : tiny*tiny;
! if (ix >= 0x3ff00000)
! return (hy > 0) ? huge*huge : tiny*tiny;
}
/* over/underflow if x is not close to one */
! if (ix < 0x3fefffff)
! return (hy < 0) ? s*huge*huge : s*tiny*tiny;
! if (ix > 0x3ff00000)
! return (hy > 0) ? s*huge*huge : s*tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = ax-one; /* t has 20 trailing zeros */
! w = (t*t) * (0.5-t*(0.3333333333333333333333-t*0.25));
! u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
v = t*ivln2_l-w*ivln2;
! t1 = u + v;
! t1 =__LO(t1, 0);
t2 = v-(t1-u);
} else {
! double ss, s2, s_h, s_l, t_h, t_l;
n = 0;
/* take care subnormal number */
! if (ix < 0x00100000) {
! ax *= two53;
! n -= 53;
! ix = __HI(ax);
! }
! n += ((ix) >> 20) - 0x3ff;
! j = ix & 0x000fffff;
/* determine interval */
! ix = j | 0x3ff00000; /* normalize ix */
! if(j <= 0x3988E)
! k=0; /* |x| <sqrt(3/2) */
! else if (j < 0xBB67A)
! k=1; /* |x| <sqrt(3) */
! else {
! k = 0;
! n += 1;
! ix -= 0x00100000;
! }
! ax = __HI(ax, ix);
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
! u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
! v = one / (ax + bp[k]);
! ss = u * v;
s_h = ss;
! s_h = __LO(s_h, 0);
/* t_h=ax+bp[k] High */
t_h = zero;
! t_h = __HI(t_h, ((ix >> 1)|0x20000000)+0x00080000+(k << 18) );
! t_l = ax - (t_h - bp[k]);
! s_l = v * ((u- s_h * t_h) - s_h * t_l);
/* compute log(ax) */
! s2 = ss * ss;
! r = s2 * s2* (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
! r += s_l * (s_h + ss);
! s2 = s_h * s_h;
! t_h = 3.0 + s2 + r;
! t_h = __LO(t_h, 0);
! t_l = r-((t_h - 3.0)-s2);
/* u+v = ss*(1+...) */
! u = s_h * t_h;
! v = s_l * t_h + t_l * ss;
/* 2/(3log2)*(ss+...) */
! p_h = u + v;
! p_h = __LO(p_h, 0);
p_l = v-(p_h-u);
! z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
! z_l = cp_l * p_h + p_l * cp + dp_l[k];
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double)n;
! t1 = (((z_h + z_l) + dp_h[k]) + t);
! t1 = __LO(t1, 0);
! t2 = z_l - (((t1-t)-dp_h[k])-z_h);
}
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
y1 = y;
! y1 = __LO(y1, 0);
! p_l = (y-y1) * t1 + y *t2;
! p_h = y1 * t1;
! z = p_l + p_h;
j = __HI(z);
i = __LO(z);
! if (j >= 0x40900000) { /* z >= 1024 */
! if (((j - 0x40900000) | i)!=0) /* if z > 1024 */
return s*huge*huge; /* overflow */
else {
! if (p_l+ovt>z-p_h)
! return s*huge*huge; /* overflow */
}
! } else if ((j & 0x7fffffff) >= 0x4090cc00 ) { /* z <= -1075 */
! if (((j-0xc090cc00)|i)!=0) /* z < -1075 */
return s*tiny*tiny; /* underflow */
else {
! if(p_l<=z-p_h)
! return s*tiny*tiny; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
! i = j & 0x7fffffff;
! k = (i >> 20)-0x3ff;
n = 0;
! if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
! n = j + (0x00100000 >> (k+1));
! k = ((n & 0x7fffffff) >> 20)-0x3ff; /* new k for n */
t = zero;
! t = __HI(t, (n & ~(0x000fffff >> k)) );
! n = ((n & 0x000fffff)|0x00100000) >> (20-k);
! if (j < 0)
! n = -n;
p_h -= t;
}
t = p_l+p_h;
! t = __LO(t, 0);
! u = t * lg2_h;
! v = (p_l-(t-p_h))* lg2 + t * lg2_l;
! z = u + v;
w = v-(z-u);
! t = z * z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-two)-(w+z*w);
! z = one - (r-z);
j = __HI(z);
! j += (n << 20);
! if ((j >> 20) <= 0)
! z = Math.scalb(z, n); /* subnormal output */
! else {
! int z_hi = __HI(z);
! z_hi += (n << 20);
! z = __HI(z, z_hi);
! }
! return s * z;
! }
! }
}
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