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src/java.base/share/classes/java/lang/FdLibm.java
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*** 1,8 ****
-
/*
! * 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
--- 1,7 ----
/*
! * Copyright (c) 1998, 2015, 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
*** 22,40 ****
* 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,
! * where w1 has 53-24 = 29 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
! * arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
--- 21,102 ----
* 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.
*/
! package java.lang;
!
! /**
! * Port of the "Freely Distributable Math Library", version 5.3, from C to Java.
! *
! * <p>The C version of fdlibm relied on the idiom of pointer aliasing
! * a 64-bit double floating-point value as a two-element array of
! * 32-bit integers and reading and writing the two halves of the
! * double independently. This coding pattern was problematic to C
! * optimizers and not directly expressible in Java. Therefore, rather
! * than a memory level overlay, if portions of a double need to be
! * operated on as integer values, the standard library methods for
! * bitwise floating-point to integer conversion are directly or
! * indirectly used, Double.longBitsToDouble and
! * Double.doubleToLongBits.
*
+ * <p>The C version of fdlibm also took some pains to signal the
+ * correct IEEE 754 exceptional conditions divide by zero, invalid,
+ * overflow and underflow. For example, overflow would be signaled by
+ * {@code huge * huge} where {@code huge} was a large constant that
+ * would overflow when squared. Since IEEE floating-point exceptional
+ * handling is not supported natively in the JVM, such coding patterns
+ * have been omitted from this port. For example, rather than {@code
+ * return huge * huge}, this port will use {@code return INFINITY}.
+ */
+ class FdLibm {
+ // Constants used by multiple algorithms
+ private static final double INFINITY= Double.POSITIVE_INFINITY;
+
+ /**
+ * 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 a double with its low-order bits of the second argument
+ * and the high-order bits of the first argument..
+ */
+ 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 a double with its high-order bits of the second argument
+ * and the low-order bits of the first argument..
+ */
+ private static double __HI(double x, int high) {
+ long transX = Double.doubleToLongBits(x);
+ return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
+ }
+
+ /**
+ * Compute x**y
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
! * where w1 has 53 - 24 = 29 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
! * arithmetic, where |y'| <= 0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
*** 59,320 ****
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
* pow(integer,integer)
* always returns the correct integer provided it is
* representable.
- *
- * Constants :
- * 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;
}
--- 121,379 ----
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
* pow(integer,integer)
* always returns the correct integer provided it is
* representable.
*/
+ public static class Pow {
+ public static strictfp double compute(final double x, final double y) {
+ double z;
+ double r, s, t, u, v, w;
+ int i, j, k, n;
+
+ // y == zero: x**0 = 1
+ if (y == 0.0)
+ return 1.0;
+
+ // +/-NaN return x + y to propagate NaN significands
+ if (Double.isNaN(x) || Double.isNaN(y))
+ return x + y;
+
+ final double y_abs = Math.abs(y);
+ double x_abs = Math.abs(x);
+ // Special values of y
+ if (y == 2.0) {
+ return x * x;
+ } else if (y == 0.5) {
+ if (x >= -Double.MAX_VALUE) // Handle x == -infinity later
+ return Math.sqrt(x + 0.0); // Add 0.0 to properly handle x == -0.0
+ } else if (y_abs == 1.0) { // y is +/-1
+ return (y == 1.0) ? x : 1.0 / x;
+ } else if (y_abs == INFINITY) { // y is +/-infinity
+ if (x_abs == 1.0)
+ return y - y; // inf**+/-1 is NaN
+ else if (x_abs > 1.0) // (|x| > 1)**+/-inf = inf, 0
+ return (y >= 0) ? y : 0.0;
+ else // (|x| < 1)**-/+inf = inf, 0
+ return (y < 0) ? -y : 0.0;
+ }
! final int hx = __HI(x);
! int ix = hx & 0x7fffffff;
! /*
! * When x < 0, determine if y is an odd integer:
! * y_is_int = 0 ... y is not an integer
! * y_is_int = 1 ... y is an odd int
! * y_is_int = 2 ... y is an even int
*/
! int y_is_int = 0;
! if (hx < 0) {
! if (y_abs >= 0x1.0p53) // |y| >= 2^53 = 9.007199254740992E15
! y_is_int = 2; // y is an even integer since ulp(2^53) = 2.0
! else if (y_abs >= 1.0) { // |y| >= 1.0
! long y_abs_as_long = (long) y_abs;
! if ( ((double) y_abs_as_long) == y_abs) {
! y_is_int = 2 - (int)(y_abs_as_long & 0x1L);
}
}
}
! // Special value of x
! if (x_abs == 0.0 ||
! x_abs == INFINITY ||
! x_abs == 1.0) {
! z = x_abs; // x is +/-0, +/-inf, +/-1
! if (y < 0.0)
! z = 1.0/z; // z = (1/|x|)
! if (hx < 0) {
! if (((ix - 0x3ff00000) | y_is_int) == 0) {
! z = (z-z)/(z-z); // (-1)**non-int is NaN
! } else if (y_is_int == 1)
! z = -1.0 * z; // (x < 0)**odd = -(|x|**odd)
}
return z;
}
! n = (hx >> 31) + 1;
! // (x < 0)**(non-int) is NaN
! if ((n | y_is_int) == 0)
! return (x-x)/(x-x);
!
! s = 1.0; // s (sign of result -ve**odd) = -1 else = 1
! if ( (n | (y_is_int - 1)) == 0)
! s = -1.0; // (-ve)**(odd int)
!
! double p_h, p_l, t1, t2;
! // |y| is huge
! if (y_abs > 0x1.0p31) { // if |y| > 2**31
! final double INV_LN2 = 0x1.7154_7652_b82fep0; // 1.44269504088896338700e+00 = 1/ln2
! final double INV_LN2_H = 0x1.715476p0; // 1.44269502162933349609e+00 = 24 bits of 1/ln2
! final double INV_LN2_L = 0x1.4ae0_bf85_ddf44p-26; // 1.92596299112661746887e-08 = 1/ln2 tail
!
! // Over/underflow if x is not close to one
! if (x_abs < 0x1.fffffp-1) // |x| < 0.9999995231628418
! return (y < 0.0) ? s * INFINITY : s * 0.0;
! if (x_abs > 1.0) // |x| > 1.0
! return (y > 0.0) ? s * INFINITY : s * 0.0;
! /*
! * now |1-x| is tiny <= 2**-20, sufficient to compute
! * log(x) by x - x^2/2 + x^3/3 - x^4/4
! */
! t = x_abs - 1.0; // t has 20 trailing zeros
! w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
! u = INV_LN2_H * t; // INV_LN2_H has 21 sig. bits
! v = t * INV_LN2_L - w * INV_LN2;
! t1 = u + v;
! t1 =__LO(t1, 0);
! t2 = v - (t1 - u);
} else {
! final double CP = 0x1.ec70_9dc3_a03fdp-1; // 9.61796693925975554329e-01 = 2/(3ln2)
! final double CP_H = 0x1.ec709ep-1; // 9.61796700954437255859e-01 = (float)cp
! final double CP_L = -0x1.e2fe_0145_b01f5p-28; // -7.02846165095275826516e-09 = tail of CP_H
!
! double z_h, z_l, ss, s2, s_h, s_l, t_h, t_l;
n = 0;
! // Take care of subnormal numbers
! if (ix < 0x00100000) {
! x_abs *= 0x1.0p53; // 2^53 = 9007199254740992.0
! n -= 53;
! ix = __HI(x_abs);
! }
! 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;
! }
! x_abs = __HI(x_abs, ix);
!
! // Compute ss = s_h + s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)
!
! final double BP[] = {1.0,
! 1.5};
! final double DP_H[] = {0.0,
! 0x1.2b80_34p-1}; // 5.84962487220764160156e-01
! final double DP_L[] = {0.0,
! 0x1.cfde_b43c_fd006p-27};// 1.35003920212974897128e-08
!
! // Poly coefs for (3/2)*(log(x)-2s-2/3*s**3
! final double L1 = 0x1.3333_3333_33303p-1; // 5.99999999999994648725e-01
! final double L2 = 0x1.b6db_6db6_fabffp-2; // 4.28571428578550184252e-01
! final double L3 = 0x1.5555_5518_f264dp-2; // 3.33333329818377432918e-01
! final double L4 = 0x1.1746_0a91_d4101p-2; // 2.72728123808534006489e-01
! final double L5 = 0x1.d864_a93c_9db65p-3; // 2.30660745775561754067e-01
! final double L6 = 0x1.a7e2_84a4_54eefp-3; // 2.06975017800338417784e-01
! u = x_abs - BP[k]; // BP[0]=1.0, BP[1]=1.5
! v = 1.0 / (x_abs + BP[k]);
! ss = u * v;
s_h = ss;
! s_h = __LO(s_h, 0);
! // t_h=x_abs + BP[k] High
! t_h = 0.0;
! t_h = __HI(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18) );
! t_l = x_abs - (t_h - BP[k]);
! s_l = v * ((u - s_h * t_h) - s_h * t_l);
! // Compute log(x_abs)
! 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(x_abs) = (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)
! double 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 * INFINITY; // Overflow
else {
! final double OVT = 8.0085662595372944372e-0017; // -(1024-log2(ovfl+.5ulp))
! if (p_l + OVT > z - p_h)
! return s * INFINITY; // Overflow
! }
! } else if ((j & 0x7fffffff) >= 0x4090cc00 ) { // z <= -1075
! if (((j - 0xc090cc00) | i)!=0) // z < -1075
! return s * 0.0; // Underflow
else {
! if (p_l <= z - p_h)
! return s * 0.0; // Underflow
}
}
/*
! * Compute 2**(p_h+p_l)
*/
! // Poly coefs for (3/2)*(log(x)-2s-2/3*s**3
! final double P1 = 0x1.5555_5555_5553ep-3; // 1.66666666666666019037e-01
! final double P2 = -0x1.6c16_c16b_ebd93p-9; // -2.77777777770155933842e-03
! final double P3 = 0x1.1566_aaf2_5de2cp-14; // 6.61375632143793436117e-05
! final double P4 = -0x1.bbd4_1c5d_26bf1p-20; // -1.65339022054652515390e-06
! final double P5 = 0x1.6376_972b_ea4d0p-25; // 4.13813679705723846039e-08
! final double LG2 = 0x1.62e4_2fef_a39efp-1; // 6.93147180559945286227e-01
! final double LG2_H = 0x1.62e43p-1; // 6.93147182464599609375e-01
! final double LG2_L = -0x1.05c6_10ca_86c39p-29; // -1.90465429995776804525e-09
! 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 = 0.0;
! 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 - 2.0) - (w + z * w);
! z = 1.0 - (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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