254 lines
9.1 KiB
Java
254 lines
9.1 KiB
Java
/*
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* Copyright (c) 1998, 2015, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Oracle designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Oracle in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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/**
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* A transliteration of the "Freely Distributable Math Library"
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* algorithms from C into Java. That is, this port of the algorithms
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* is as close to the C originals as possible while still being
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* readable legal Java.
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*/
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public class FdlibmTranslit {
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private FdlibmTranslit() {
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throw new UnsupportedOperationException("No FdLibmTranslit instances for you.");
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}
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/**
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* Return the low-order 32 bits of the double argument as an int.
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*/
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private static int __LO(double x) {
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long transducer = Double.doubleToRawLongBits(x);
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return (int)transducer;
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}
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/**
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* Return a double with its low-order bits of the second argument
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* and the high-order bits of the first argument..
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*/
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private static double __LO(double x, int low) {
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long transX = Double.doubleToRawLongBits(x);
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return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low );
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}
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/**
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* Return the high-order 32 bits of the double argument as an int.
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*/
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private static int __HI(double x) {
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long transducer = Double.doubleToRawLongBits(x);
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return (int)(transducer >> 32);
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}
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/**
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* Return a double with its high-order bits of the second argument
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* and the low-order bits of the first argument..
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*/
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private static double __HI(double x, int high) {
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long transX = Double.doubleToRawLongBits(x);
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return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
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}
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public static double hypot(double x, double y) {
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return Hypot.compute(x, y);
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}
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/**
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* cbrt(x)
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* Return cube root of x
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*/
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public static class Cbrt {
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// unsigned
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private static final int B1 = 715094163; /* B1 = (682-0.03306235651)*2**20 */
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private static final int B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
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private static final double C = 5.42857142857142815906e-01; /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
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private static final double D = -7.05306122448979611050e-01; /* -864/1225 = 0xBFE691DE, 0x2532C834 */
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private static final double E = 1.41428571428571436819e+00; /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
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private static final double F = 1.60714285714285720630e+00; /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
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private static final double G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
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public static strictfp double compute(double x) {
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int hx;
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double r, s, t=0.0, w;
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int sign; // unsigned
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hx = __HI(x); // high word of x
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sign = hx & 0x80000000; // sign= sign(x)
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hx ^= sign;
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if (hx >= 0x7ff00000)
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return (x+x); // cbrt(NaN,INF) is itself
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if ((hx | __LO(x)) == 0)
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return(x); // cbrt(0) is itself
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x = __HI(x, hx); // x <- |x|
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// rough cbrt to 5 bits
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if (hx < 0x00100000) { // subnormal number
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t = __HI(t, 0x43500000); // set t= 2**54
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t *= x;
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t = __HI(t, __HI(t)/3+B2);
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} else {
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t = __HI(t, hx/3+B1);
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}
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// new cbrt to 23 bits, may be implemented in single precision
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r = t * t/x;
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s = C + r*t;
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t *= G + F/(s + E + D/s);
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// chopped to 20 bits and make it larger than cbrt(x)
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t = __LO(t, 0);
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t = __HI(t, __HI(t)+0x00000001);
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// one step newton iteration to 53 bits with error less than 0.667 ulps
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s = t * t; // t*t is exact
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r = x / s;
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w = t + t;
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r= (r - t)/(w + r); // r-s is exact
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t= t + t*r;
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// retore the sign bit
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t = __HI(t, __HI(t) | sign);
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return(t);
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}
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}
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/**
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* hypot(x,y)
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*
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* Method :
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* If (assume round-to-nearest) z = x*x + y*y
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* has error less than sqrt(2)/2 ulp, than
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* sqrt(z) has error less than 1 ulp (exercise).
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*
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* So, compute sqrt(x*x + y*y) with some care as
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* follows to get the error below 1 ulp:
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*
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* Assume x > y > 0;
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* (if possible, set rounding to round-to-nearest)
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* 1. if x > 2y use
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* x1*x1 + (y*y + (x2*(x + x1))) for x*x + y*y
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* where x1 = x with lower 32 bits cleared, x2 = x - x1; else
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* 2. if x <= 2y use
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* t1*y1 + ((x-y) * (x-y) + (t1*y2 + t2*y))
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x - t1,
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* y1= y with lower 32 bits chopped, y2 = y - y1.
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*
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* NOTE: scaling may be necessary if some argument is too
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* large or too tiny
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*
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* Special cases:
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* hypot(x,y) is INF if x or y is +INF or -INF; else
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* hypot(x,y) is NAN if x or y is NAN.
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*
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* Accuracy:
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* hypot(x,y) returns sqrt(x^2 + y^2) with error less
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* than 1 ulps (units in the last place)
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*/
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static class Hypot {
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public static double compute(double x, double y) {
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double a = x;
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double b = y;
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double t1, t2, y1, y2, w;
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int j, k, ha, hb;
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ha = __HI(x) & 0x7fffffff; // high word of x
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hb = __HI(y) & 0x7fffffff; // high word of y
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if(hb > ha) {
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a = y;
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b = x;
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j = ha;
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ha = hb;
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hb = j;
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} else {
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a = x;
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b = y;
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}
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a = __HI(a, ha); // a <- |a|
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b = __HI(b, hb); // b <- |b|
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if ((ha - hb) > 0x3c00000) {
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return a + b; // x / y > 2**60
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}
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k=0;
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if (ha > 0x5f300000) { // a>2**500
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if (ha >= 0x7ff00000) { // Inf or NaN
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w = a + b; // for sNaN
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if (((ha & 0xfffff) | __LO(a)) == 0)
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w = a;
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if (((hb ^ 0x7ff00000) | __LO(b)) == 0)
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w = b;
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return w;
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}
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// scale a and b by 2**-600
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ha -= 0x25800000;
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hb -= 0x25800000;
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k += 600;
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a = __HI(a, ha);
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b = __HI(b, hb);
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}
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if (hb < 0x20b00000) { // b < 2**-500
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if (hb <= 0x000fffff) { // subnormal b or 0 */
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if ((hb | (__LO(b))) == 0)
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return a;
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t1 = 0;
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t1 = __HI(t1, 0x7fd00000); // t1=2^1022
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b *= t1;
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a *= t1;
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k -= 1022;
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} else { // scale a and b by 2^600
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ha += 0x25800000; // a *= 2^600
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hb += 0x25800000; // b *= 2^600
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k -= 600;
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a = __HI(a, ha);
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b = __HI(b, hb);
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}
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}
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// medium size a and b
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w = a - b;
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if (w > b) {
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t1 = 0;
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t1 = __HI(t1, ha);
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t2 = a - t1;
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w = Math.sqrt(t1*t1 - (b*(-b) - t2 * (a + t1)));
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} else {
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a = a + a;
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y1 = 0;
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y1 = __HI(y1, hb);
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y2 = b - y1;
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t1 = 0;
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t1 = __HI(t1, ha + 0x00100000);
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t2 = a - t1;
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w = Math.sqrt(t1*y1 - (w*(-w) - (t1*y2 + t2*b)));
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}
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if (k != 0) {
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t1 = 1.0;
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int t1_hi = __HI(t1);
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t1_hi += (k << 20);
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t1 = __HI(t1, t1_hi);
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return t1 * w;
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} else
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return w;
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}
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}
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}
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