--- old/src/java.base/share/native/libfdlibm/e_pow.c 2015-09-14 21:46:12.708502600 -0700 +++ /dev/null 2015-08-18 14:49:49.949180963 -0700 @@ -1,320 +0,0 @@ - -/* - * 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, - * 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 - * 3. (anything) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. +-1 ** +-INF is NAN - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF - * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) - * 15. +INF ** (+anything except 0,NAN) is +INF - * 16. +INF ** (-anything except 0,NAN) is +0 - * 17. -INF ** (anything) = -0 ** (-anything) - * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 19. (-anything except 0 and inf) ** (non-integer) is NAN - * - * 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|>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; -} --- /dev/null 2015-08-18 14:49:49.949180963 -0700 +++ new/src/java.base/share/classes/java/lang/FdLibm.java 2015-09-14 21:46:12.296502589 -0700 @@ -0,0 +1,379 @@ +/* + * 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 + * 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. + */ + +package java.lang; + +/** + * Port of the "Freely Distributable Math Library", version 5.3, from C to Java. + * + *

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. + * + *

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 + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * 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| > 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; + } + } +}