--- /dev/null 2015-10-02 10:10:00.970447879 -0700 +++ new/test/java/lang/StrictMath/FdlibmTranslit.java 2015-10-02 19:19:38.892032440 -0700 @@ -0,0 +1,192 @@ +/* + * 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. + */ + +/** + * A transliteration of the "Freely Distributable Math Library" + * algorithms from C into Java. That is, this port of the algorithms + * is as close to the C originals as possible while still being + * readable legal Java. + */ +public class FdlibmTranslit { + private FdlibmTranslit() { + throw new UnsupportedOperationException("No FdLibmTranslit instances for you."); + } + + /** + * Return the low-order 32 bits of the double argument as an int. + */ + private static int __LO(double x) { + long transducer = Double.doubleToRawLongBits(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.doubleToRawLongBits(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.doubleToRawLongBits(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.doubleToRawLongBits(x); + return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 ); + } + + public static double hypot(double x, double y) { + return Hypot.compute(x, y); + } + + /** + * hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z = x*x + y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x + y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x > y > 0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1 + (y*y + (x2*(x + x1))) for x*x + y*y + * where x1 = x with lower 32 bits cleared, x2 = x - x1; else + * 2. if x <= 2y use + * t1*y1 + ((x-y) * (x-y) + (t1*y2 + t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x - t1, + * y1= y with lower 32 bits chopped, y2 = y - y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2 + y^2) with error less + * than 1 ulps (units in the last place) + */ + static class Hypot { + public static double compute(double x, double y) { + double a = x; + double b = y; + double t1, t2, y1, y2, w; + int j, k, ha, hb; + + ha = __HI(x) & 0x7fffffff; // high word of x + hb = __HI(y) & 0x7fffffff; // high word of y + if(hb > ha) { + a = y; + b = x; + j = ha; + ha = hb; + hb = j; + } else { + a = x; + b = y; + } + a = __HI(a, ha); // a <- |a| + b = __HI(b, hb); // b <- |b| + if ((ha - hb) > 0x3c00000) { + return a + b; // x / y > 2**60 + } + k=0; + if (ha > 0x5f300000) { // a>2**500 + if (ha >= 0x7ff00000) { // Inf or NaN + w = a + b; // for sNaN + if (((ha & 0xfffff) | __LO(a)) == 0) + w = a; + if (((hb ^ 0x7ff00000) | __LO(b)) == 0) + w = b; + return w; + } + // scale a and b by 2**-600 + ha -= 0x25800000; + hb -= 0x25800000; + k += 600; + a = __HI(a, ha); + b = __HI(b, hb); + } + if (hb < 0x20b00000) { // b < 2**-500 + if (hb <= 0x000fffff) { // subnormal b or 0 */ + if ((hb | (__LO(b))) == 0) + return a; + t1 = 0; + t1 = __HI(t1, 0x7fd00000); // t1=2^1022 + b *= t1; + a *= t1; + k -= 1022; + } else { // scale a and b by 2^600 + ha += 0x25800000; // a *= 2^600 + hb += 0x25800000; // b *= 2^600 + k -= 600; + a = __HI(a, ha); + b = __HI(b, hb); + } + } + // medium size a and b + w = a - b; + if (w > b) { + t1 = 0; + t1 = __HI(t1, ha); + t2 = a - t1; + w = Math.sqrt(t1*t1 - (b*(-b) - t2 * (a + t1))); + } else { + a = a + a; + y1 = 0; + y1 = __HI(y1, hb); + y2 = b - y1; + t1 = 0; + t1 = __HI(t1, ha + 0x00100000); + t2 = a - t1; + w = Math.sqrt(t1*y1 - (w*(-w) - (t1*y2 + t2*b))); + } + if (k != 0) { + t1 = 1.0; + int t1_hi = __HI(t1); + t1_hi += (k << 20); + t1 = __HI(t1, t1_hi); + return t1 * w; + } else + return w; + } + } +}