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/*
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* Copyright 2003 Sun Microsystems, Inc. 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. Sun designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
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* CA 95054 USA or visit www.sun.com if you need additional information or
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* have any questions.
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*/
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package sun.misc;
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import sun.misc.FloatConsts;
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import sun.misc.DoubleConsts;
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/**
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* The class <code>FpUtils</code> contains static utility methods for
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* manipulating and inspecting <code>float</code> and
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* <code>double</code> floating-point numbers. These methods include
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* functionality recommended or required by the IEEE 754
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* floating-point standard.
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*
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* @author Joseph D. Darcy
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*/
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public class FpUtils {
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/*
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* The methods in this class are reasonably implemented using
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* direct or indirect bit-level manipulation of floating-point
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* values. However, having access to the IEEE 754 recommended
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* functions would obviate the need for most programmers to engage
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* in floating-point bit-twiddling.
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*
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* An IEEE 754 number has three fields, from most significant bit
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* to to least significant, sign, exponent, and significand.
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*
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* msb lsb
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* [sign|exponent| fractional_significand]
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*
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* Using some encoding cleverness, explained below, the high order
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* bit of the logical significand does not need to be explicitly
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* stored, thus "fractional_significand" instead of simply
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* "significand" in the figure above.
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*
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* For finite normal numbers, the numerical value encoded is
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*
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* (-1)^sign * 2^(exponent)*(1.fractional_significand)
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*
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* Most finite floating-point numbers are normalized; the exponent
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* value is reduced until the leading significand bit is 1.
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* Therefore, the leading 1 is redundant and is not explicitly
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* stored. If a numerical value is so small it cannot be
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* normalized, it has a subnormal representation. Subnormal
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* numbers don't have a leading 1 in their significand; subnormals
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* are encoding using a special exponent value. In other words,
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* the high-order bit of the logical significand can be elided in
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* from the representation in either case since the bit's value is
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* implicit from the exponent value.
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*
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* The exponent field uses a biased representation; if the bits of
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* the exponent are interpreted as a unsigned integer E, the
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* exponent represented is E - E_bias where E_bias depends on the
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* floating-point format. E can range between E_min and E_max,
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* constants which depend on the floating-point format. E_min and
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* E_max are -126 and +127 for float, -1022 and +1023 for double.
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*
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* The 32-bit float format has 1 sign bit, 8 exponent bits, and 23
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* bits for the significand (which is logically 24 bits wide
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* because of the implicit bit). The 64-bit double format has 1
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* sign bit, 11 exponent bits, and 52 bits for the significand
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* (logically 53 bits).
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*
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* Subnormal numbers and zero have the special exponent value
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* E_min -1; the numerical value represented by a subnormal is:
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*
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* (-1)^sign * 2^(E_min)*(0.fractional_significand)
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*
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* Zero is represented by all zero bits in the exponent and all
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* zero bits in the significand; zero can have either sign.
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*
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* Infinity and NaN are encoded using the exponent value E_max +
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* 1. Signed infinities have all significand bits zero; NaNs have
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* at least one non-zero significand bit.
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*
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* The details of IEEE 754 floating-point encoding will be used in
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* the methods below without further comment. For further
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* exposition on IEEE 754 numbers, see "IEEE Standard for Binary
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* Floating-Point Arithmetic" ANSI/IEEE Std 754-1985 or William
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* Kahan's "Lecture Notes on the Status of IEEE Standard 754 for
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* Binary Floating-Point Arithmetic",
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* http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps.
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*
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* Many of this class's methods are members of the set of IEEE 754
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* recommended functions or similar functions recommended or
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* required by IEEE 754R. Discussion of various implementation
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* techniques for these functions have occurred in:
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*
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* W.J. Cody and Jerome T. Coonen, "Algorithm 772 Functions to
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* Support the IEEE Standard for Binary Floating-Point
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* Arithmetic," ACM Transactions on Mathematical Software,
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* vol. 19, no. 4, December 1993, pp. 443-451.
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*
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* Joseph D. Darcy, "Writing robust IEEE recommended functions in
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* ``100% Pure Java''(TM)," University of California, Berkeley
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* technical report UCB//CSD-98-1009.
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*/
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/**
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* Don't let anyone instantiate this class.
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*/
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private FpUtils() {}
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// Constants used in scalb
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static double twoToTheDoubleScaleUp = powerOfTwoD(512);
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static double twoToTheDoubleScaleDown = powerOfTwoD(-512);
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// Helper Methods
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// The following helper methods are used in the implementation of
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// the public recommended functions; they generally omit certain
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// tests for exception cases.
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/**
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* Returns unbiased exponent of a <code>double</code>.
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*/
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public static int getExponent(double d){
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/*
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* Bitwise convert d to long, mask out exponent bits, shift
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* to the right and then subtract out double's bias adjust to
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* get true exponent value.
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*/
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return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>
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(DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);
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}
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/**
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* Returns unbiased exponent of a <code>float</code>.
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*/
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public static int getExponent(float f){
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/*
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* Bitwise convert f to integer, mask out exponent bits, shift
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* to the right and then subtract out float's bias adjust to
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* get true exponent value
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*/
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return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>
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(FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;
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}
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/**
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* Returns a floating-point power of two in the normal range.
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*/
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static double powerOfTwoD(int n) {
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assert(n >= DoubleConsts.MIN_EXPONENT && n <= DoubleConsts.MAX_EXPONENT);
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return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<
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(DoubleConsts.SIGNIFICAND_WIDTH-1))
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& DoubleConsts.EXP_BIT_MASK);
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}
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/**
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* Returns a floating-point power of two in the normal range.
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*/
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static float powerOfTwoF(int n) {
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assert(n >= FloatConsts.MIN_EXPONENT && n <= FloatConsts.MAX_EXPONENT);
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return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<
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(FloatConsts.SIGNIFICAND_WIDTH-1))
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& FloatConsts.EXP_BIT_MASK);
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}
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/**
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* Returns the first floating-point argument with the sign of the
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* second floating-point argument. Note that unlike the {@link
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* FpUtils#copySign(double, double) copySign} method, this method
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* does not require NaN <code>sign</code> arguments to be treated
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* as positive values; implementations are permitted to treat some
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* NaN arguments as positive and other NaN arguments as negative
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* to allow greater performance.
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*
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* @param magnitude the parameter providing the magnitude of the result
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* @param sign the parameter providing the sign of the result
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* @return a value with the magnitude of <code>magnitude</code>
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* and the sign of <code>sign</code>.
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* @author Joseph D. Darcy
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*/
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public static double rawCopySign(double magnitude, double sign) {
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return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &
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(DoubleConsts.SIGN_BIT_MASK)) |
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(Double.doubleToRawLongBits(magnitude) &
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(DoubleConsts.EXP_BIT_MASK |
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DoubleConsts.SIGNIF_BIT_MASK)));
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}
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/**
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* Returns the first floating-point argument with the sign of the
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* second floating-point argument. Note that unlike the {@link
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* FpUtils#copySign(float, float) copySign} method, this method
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* does not require NaN <code>sign</code> arguments to be treated
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* as positive values; implementations are permitted to treat some
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* NaN arguments as positive and other NaN arguments as negative
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* to allow greater performance.
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*
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* @param magnitude the parameter providing the magnitude of the result
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* @param sign the parameter providing the sign of the result
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* @return a value with the magnitude of <code>magnitude</code>
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* and the sign of <code>sign</code>.
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* @author Joseph D. Darcy
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*/
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public static float rawCopySign(float magnitude, float sign) {
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return Float.intBitsToFloat((Float.floatToRawIntBits(sign) &
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(FloatConsts.SIGN_BIT_MASK)) |
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(Float.floatToRawIntBits(magnitude) &
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(FloatConsts.EXP_BIT_MASK |
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FloatConsts.SIGNIF_BIT_MASK)));
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}
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/* ***************************************************************** */
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/**
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* Returns <code>true</code> if the argument is a finite
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* floating-point value; returns <code>false</code> otherwise (for
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* NaN and infinity arguments).
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*
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* @param d the <code>double</code> value to be tested
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* @return <code>true</code> if the argument is a finite
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* floating-point value, <code>false</code> otherwise.
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*/
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public static boolean isFinite(double d) {
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return Math.abs(d) <= DoubleConsts.MAX_VALUE;
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}
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/**
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* Returns <code>true</code> if the argument is a finite
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* floating-point value; returns <code>false</code> otherwise (for
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* NaN and infinity arguments).
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*
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* @param f the <code>float</code> value to be tested
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* @return <code>true</code> if the argument is a finite
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* floating-point value, <code>false</code> otherwise.
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*/
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public static boolean isFinite(float f) {
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return Math.abs(f) <= FloatConsts.MAX_VALUE;
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}
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/**
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* Returns <code>true</code> if the specified number is infinitely
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* large in magnitude, <code>false</code> otherwise.
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*
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* <p>Note that this method is equivalent to the {@link
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* Double#isInfinite(double) Double.isInfinite} method; the
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* functionality is included in this class for convenience.
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*
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* @param d the value to be tested.
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* @return <code>true</code> if the value of the argument is positive
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* infinity or negative infinity; <code>false</code> otherwise.
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*/
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public static boolean isInfinite(double d) {
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return Double.isInfinite(d);
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}
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/**
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* Returns <code>true</code> if the specified number is infinitely
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* large in magnitude, <code>false</code> otherwise.
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*
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* <p>Note that this method is equivalent to the {@link
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* Float#isInfinite(float) Float.isInfinite} method; the
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* functionality is included in this class for convenience.
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*
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* @param f the value to be tested.
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* @return <code>true</code> if the argument is positive infinity or
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* negative infinity; <code>false</code> otherwise.
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*/
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public static boolean isInfinite(float f) {
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return Float.isInfinite(f);
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}
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/**
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* Returns <code>true</code> if the specified number is a
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* Not-a-Number (NaN) value, <code>false</code> otherwise.
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*
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* <p>Note that this method is equivalent to the {@link
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* Double#isNaN(double) Double.isNaN} method; the functionality is
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* included in this class for convenience.
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*
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* @param d the value to be tested.
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* @return <code>true</code> if the value of the argument is NaN;
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* <code>false</code> otherwise.
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*/
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public static boolean isNaN(double d) {
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return Double.isNaN(d);
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}
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/**
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* Returns <code>true</code> if the specified number is a
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* Not-a-Number (NaN) value, <code>false</code> otherwise.
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*
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* <p>Note that this method is equivalent to the {@link
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* Float#isNaN(float) Float.isNaN} method; the functionality is
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* included in this class for convenience.
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*
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* @param f the value to be tested.
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* @return <code>true</code> if the argument is NaN;
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* <code>false</code> otherwise.
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*/
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public static boolean isNaN(float f) {
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return Float.isNaN(f);
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}
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/**
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* Returns <code>true</code> if the unordered relation holds
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* between the two arguments. When two floating-point values are
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* unordered, one value is neither less than, equal to, nor
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* greater than the other. For the unordered relation to be true,
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* at least one argument must be a <code>NaN</code>.
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*
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* @param arg1 the first argument
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* @param arg2 the second argument
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* @return <code>true</code> if at least one argument is a NaN,
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* <code>false</code> otherwise.
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*/
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public static boolean isUnordered(double arg1, double arg2) {
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return isNaN(arg1) || isNaN(arg2);
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}
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/**
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* Returns <code>true</code> if the unordered relation holds
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* between the two arguments. When two floating-point values are
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* unordered, one value is neither less than, equal to, nor
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* greater than the other. For the unordered relation to be true,
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* at least one argument must be a <code>NaN</code>.
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*
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* @param arg1 the first argument
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* @param arg2 the second argument
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* @return <code>true</code> if at least one argument is a NaN,
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* <code>false</code> otherwise.
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*/
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public static boolean isUnordered(float arg1, float arg2) {
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return isNaN(arg1) || isNaN(arg2);
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}
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/**
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* Returns unbiased exponent of a <code>double</code>; for
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* subnormal values, the number is treated as if it were
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* normalized. That is for all finite, non-zero, positive numbers
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* <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is
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* always in the range [1, 2).
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* <p>
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* Special cases:
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* <ul>
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* <li> If the argument is NaN, then the result is 2<sup>30</sup>.
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* <li> If the argument is infinite, then the result is 2<sup>28</sup>.
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* <li> If the argument is zero, then the result is -(2<sup>28</sup>).
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* </ul>
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*
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* @param d floating-point number whose exponent is to be extracted
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* @return unbiased exponent of the argument.
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* @author Joseph D. Darcy
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*/
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public static int ilogb(double d) {
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int exponent = getExponent(d);
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switch (exponent) {
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case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity
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if( isNaN(d) )
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return (1<<30); // 2^30
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else // infinite value
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return (1<<28); // 2^28
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// break;
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case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal
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if(d == 0.0) {
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|
385 |
return -(1<<28); // -(2^28)
|
|
386 |
}
|
|
387 |
else {
|
|
388 |
long transducer = Double.doubleToRawLongBits(d);
|
|
389 |
|
|
390 |
/*
|
|
391 |
* To avoid causing slow arithmetic on subnormals,
|
|
392 |
* the scaling to determine when d's significand
|
|
393 |
* is normalized is done in integer arithmetic.
|
|
394 |
* (there must be at least one "1" bit in the
|
|
395 |
* significand since zero has been screened out.
|
|
396 |
*/
|
|
397 |
|
|
398 |
// isolate significand bits
|
|
399 |
transducer &= DoubleConsts.SIGNIF_BIT_MASK;
|
|
400 |
assert(transducer != 0L);
|
|
401 |
|
|
402 |
// This loop is simple and functional. We might be
|
|
403 |
// able to do something more clever that was faster;
|
|
404 |
// e.g. number of leading zero detection on
|
|
405 |
// (transducer << (# exponent and sign bits).
|
|
406 |
while (transducer <
|
|
407 |
(1L << (DoubleConsts.SIGNIFICAND_WIDTH - 1))) {
|
|
408 |
transducer *= 2;
|
|
409 |
exponent--;
|
|
410 |
}
|
|
411 |
exponent++;
|
|
412 |
assert( exponent >=
|
|
413 |
DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1) &&
|
|
414 |
exponent < DoubleConsts.MIN_EXPONENT);
|
|
415 |
return exponent;
|
|
416 |
}
|
|
417 |
// break;
|
|
418 |
|
|
419 |
default:
|
|
420 |
assert( exponent >= DoubleConsts.MIN_EXPONENT &&
|
|
421 |
exponent <= DoubleConsts.MAX_EXPONENT);
|
|
422 |
return exponent;
|
|
423 |
// break;
|
|
424 |
}
|
|
425 |
}
|
|
426 |
|
|
427 |
/**
|
|
428 |
* Returns unbiased exponent of a <code>float</code>; for
|
|
429 |
* subnormal values, the number is treated as if it were
|
|
430 |
* normalized. That is for all finite, non-zero, positive numbers
|
|
431 |
* <i>x</i>, <code>scalb(<i>x</i>, -ilogb(<i>x</i>))</code> is
|
|
432 |
* always in the range [1, 2).
|
|
433 |
* <p>
|
|
434 |
* Special cases:
|
|
435 |
* <ul>
|
|
436 |
* <li> If the argument is NaN, then the result is 2<sup>30</sup>.
|
|
437 |
* <li> If the argument is infinite, then the result is 2<sup>28</sup>.
|
|
438 |
* <li> If the argument is zero, then the result is -(2<sup>28</sup>).
|
|
439 |
* </ul>
|
|
440 |
*
|
|
441 |
* @param f floating-point number whose exponent is to be extracted
|
|
442 |
* @return unbiased exponent of the argument.
|
|
443 |
* @author Joseph D. Darcy
|
|
444 |
*/
|
|
445 |
public static int ilogb(float f) {
|
|
446 |
int exponent = getExponent(f);
|
|
447 |
|
|
448 |
switch (exponent) {
|
|
449 |
case FloatConsts.MAX_EXPONENT+1: // NaN or infinity
|
|
450 |
if( isNaN(f) )
|
|
451 |
return (1<<30); // 2^30
|
|
452 |
else // infinite value
|
|
453 |
return (1<<28); // 2^28
|
|
454 |
// break;
|
|
455 |
|
|
456 |
case FloatConsts.MIN_EXPONENT-1: // zero or subnormal
|
|
457 |
if(f == 0.0f) {
|
|
458 |
return -(1<<28); // -(2^28)
|
|
459 |
}
|
|
460 |
else {
|
|
461 |
int transducer = Float.floatToRawIntBits(f);
|
|
462 |
|
|
463 |
/*
|
|
464 |
* To avoid causing slow arithmetic on subnormals,
|
|
465 |
* the scaling to determine when f's significand
|
|
466 |
* is normalized is done in integer arithmetic.
|
|
467 |
* (there must be at least one "1" bit in the
|
|
468 |
* significand since zero has been screened out.
|
|
469 |
*/
|
|
470 |
|
|
471 |
// isolate significand bits
|
|
472 |
transducer &= FloatConsts.SIGNIF_BIT_MASK;
|
|
473 |
assert(transducer != 0);
|
|
474 |
|
|
475 |
// This loop is simple and functional. We might be
|
|
476 |
// able to do something more clever that was faster;
|
|
477 |
// e.g. number of leading zero detection on
|
|
478 |
// (transducer << (# exponent and sign bits).
|
|
479 |
while (transducer <
|
|
480 |
(1 << (FloatConsts.SIGNIFICAND_WIDTH - 1))) {
|
|
481 |
transducer *= 2;
|
|
482 |
exponent--;
|
|
483 |
}
|
|
484 |
exponent++;
|
|
485 |
assert( exponent >=
|
|
486 |
FloatConsts.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1) &&
|
|
487 |
exponent < FloatConsts.MIN_EXPONENT);
|
|
488 |
return exponent;
|
|
489 |
}
|
|
490 |
// break;
|
|
491 |
|
|
492 |
default:
|
|
493 |
assert( exponent >= FloatConsts.MIN_EXPONENT &&
|
|
494 |
exponent <= FloatConsts.MAX_EXPONENT);
|
|
495 |
return exponent;
|
|
496 |
// break;
|
|
497 |
}
|
|
498 |
}
|
|
499 |
|
|
500 |
|
|
501 |
/*
|
|
502 |
* The scalb operation should be reasonably fast; however, there
|
|
503 |
* are tradeoffs in writing a method to minimize the worst case
|
|
504 |
* performance and writing a method to minimize the time for
|
|
505 |
* expected common inputs. Some processors operate very slowly on
|
|
506 |
* subnormal operands, taking hundreds or thousands of cycles for
|
|
507 |
* one floating-point add or multiply as opposed to, say, four
|
|
508 |
* cycles for normal operands. For processors with very slow
|
|
509 |
* subnormal execution, scalb would be fastest if written entirely
|
|
510 |
* with integer operations; in other words, scalb would need to
|
|
511 |
* include the logic of performing correct rounding of subnormal
|
|
512 |
* values. This could be reasonably done in at most a few hundred
|
|
513 |
* cycles. However, this approach may penalize normal operations
|
|
514 |
* since at least the exponent of the floating-point argument must
|
|
515 |
* be examined.
|
|
516 |
*
|
|
517 |
* The approach taken in this implementation is a compromise.
|
|
518 |
* Floating-point multiplication is used to do most of the work;
|
|
519 |
* but knowingly multiplying by a subnormal scaling factor is
|
|
520 |
* avoided. However, the floating-point argument is not examined
|
|
521 |
* to see whether or not it is subnormal since subnormal inputs
|
|
522 |
* are assumed to be rare. At most three multiplies are needed to
|
|
523 |
* scale from the largest to smallest exponent ranges (scaling
|
|
524 |
* down, at most two multiplies are needed if subnormal scaling
|
|
525 |
* factors are allowed). However, in this implementation an
|
|
526 |
* expensive integer remainder operation is avoided at the cost of
|
|
527 |
* requiring five floating-point multiplies in the worst case,
|
|
528 |
* which should still be a performance win.
|
|
529 |
*
|
|
530 |
* If scaling of entire arrays is a concern, it would probably be
|
|
531 |
* more efficient to provide a double[] scalb(double[], int)
|
|
532 |
* version of scalb to avoid having to recompute the needed
|
|
533 |
* scaling factors for each floating-point value.
|
|
534 |
*/
|
|
535 |
|
|
536 |
/**
|
|
537 |
* Return <code>d</code> ×
|
|
538 |
* 2<sup><code>scale_factor</code></sup> rounded as if performed
|
|
539 |
* by a single correctly rounded floating-point multiply to a
|
|
540 |
* member of the double value set. See <a
|
|
541 |
* href="http://java.sun.com/docs/books/jls/second_edition/html/typesValues.doc.html#9208">§4.2.3</a>
|
|
542 |
* of the <a href="http://java.sun.com/docs/books/jls/html/">Java
|
|
543 |
* Language Specification</a> for a discussion of floating-point
|
|
544 |
* value sets. If the exponent of the result is between the
|
|
545 |
* <code>double</code>'s minimum exponent and maximum exponent,
|
|
546 |
* the answer is calculated exactly. If the exponent of the
|
|
547 |
* result would be larger than <code>doubles</code>'s maximum
|
|
548 |
* exponent, an infinity is returned. Note that if the result is
|
|
549 |
* subnormal, precision may be lost; that is, when <code>scalb(x,
|
|
550 |
* n)</code> is subnormal, <code>scalb(scalb(x, n), -n)</code> may
|
|
551 |
* not equal <i>x</i>. When the result is non-NaN, the result has
|
|
552 |
* the same sign as <code>d</code>.
|
|
553 |
*
|
|
554 |
*<p>
|
|
555 |
* Special cases:
|
|
556 |
* <ul>
|
|
557 |
* <li> If the first argument is NaN, NaN is returned.
|
|
558 |
* <li> If the first argument is infinite, then an infinity of the
|
|
559 |
* same sign is returned.
|
|
560 |
* <li> If the first argument is zero, then a zero of the same
|
|
561 |
* sign is returned.
|
|
562 |
* </ul>
|
|
563 |
*
|
|
564 |
* @param d number to be scaled by a power of two.
|
|
565 |
* @param scale_factor power of 2 used to scale <code>d</code>
|
|
566 |
* @return <code>d * </code>2<sup><code>scale_factor</code></sup>
|
|
567 |
* @author Joseph D. Darcy
|
|
568 |
*/
|
|
569 |
public static double scalb(double d, int scale_factor) {
|
|
570 |
/*
|
|
571 |
* This method does not need to be declared strictfp to
|
|
572 |
* compute the same correct result on all platforms. When
|
|
573 |
* scaling up, it does not matter what order the
|
|
574 |
* multiply-store operations are done; the result will be
|
|
575 |
* finite or overflow regardless of the operation ordering.
|
|
576 |
* However, to get the correct result when scaling down, a
|
|
577 |
* particular ordering must be used.
|
|
578 |
*
|
|
579 |
* When scaling down, the multiply-store operations are
|
|
580 |
* sequenced so that it is not possible for two consecutive
|
|
581 |
* multiply-stores to return subnormal results. If one
|
|
582 |
* multiply-store result is subnormal, the next multiply will
|
|
583 |
* round it away to zero. This is done by first multiplying
|
|
584 |
* by 2 ^ (scale_factor % n) and then multiplying several
|
|
585 |
* times by by 2^n as needed where n is the exponent of number
|
|
586 |
* that is a covenient power of two. In this way, at most one
|
|
587 |
* real rounding error occurs. If the double value set is
|
|
588 |
* being used exclusively, the rounding will occur on a
|
|
589 |
* multiply. If the double-extended-exponent value set is
|
|
590 |
* being used, the products will (perhaps) be exact but the
|
|
591 |
* stores to d are guaranteed to round to the double value
|
|
592 |
* set.
|
|
593 |
*
|
|
594 |
* It is _not_ a valid implementation to first multiply d by
|
|
595 |
* 2^MIN_EXPONENT and then by 2 ^ (scale_factor %
|
|
596 |
* MIN_EXPONENT) since even in a strictfp program double
|
|
597 |
* rounding on underflow could occur; e.g. if the scale_factor
|
|
598 |
* argument was (MIN_EXPONENT - n) and the exponent of d was a
|
|
599 |
* little less than -(MIN_EXPONENT - n), meaning the final
|
|
600 |
* result would be subnormal.
|
|
601 |
*
|
|
602 |
* Since exact reproducibility of this method can be achieved
|
|
603 |
* without any undue performance burden, there is no
|
|
604 |
* compelling reason to allow double rounding on underflow in
|
|
605 |
* scalb.
|
|
606 |
*/
|
|
607 |
|
|
608 |
// magnitude of a power of two so large that scaling a finite
|
|
609 |
// nonzero value by it would be guaranteed to over or
|
|
610 |
// underflow; due to rounding, scaling down takes takes an
|
|
611 |
// additional power of two which is reflected here
|
|
612 |
final int MAX_SCALE = DoubleConsts.MAX_EXPONENT + -DoubleConsts.MIN_EXPONENT +
|
|
613 |
DoubleConsts.SIGNIFICAND_WIDTH + 1;
|
|
614 |
int exp_adjust = 0;
|
|
615 |
int scale_increment = 0;
|
|
616 |
double exp_delta = Double.NaN;
|
|
617 |
|
|
618 |
// Make sure scaling factor is in a reasonable range
|
|
619 |
|
|
620 |
if(scale_factor < 0) {
|
|
621 |
scale_factor = Math.max(scale_factor, -MAX_SCALE);
|
|
622 |
scale_increment = -512;
|
|
623 |
exp_delta = twoToTheDoubleScaleDown;
|
|
624 |
}
|
|
625 |
else {
|
|
626 |
scale_factor = Math.min(scale_factor, MAX_SCALE);
|
|
627 |
scale_increment = 512;
|
|
628 |
exp_delta = twoToTheDoubleScaleUp;
|
|
629 |
}
|
|
630 |
|
|
631 |
// Calculate (scale_factor % +/-512), 512 = 2^9, using
|
|
632 |
// technique from "Hacker's Delight" section 10-2.
|
|
633 |
int t = (scale_factor >> 9-1) >>> 32 - 9;
|
|
634 |
exp_adjust = ((scale_factor + t) & (512 -1)) - t;
|
|
635 |
|
|
636 |
d *= powerOfTwoD(exp_adjust);
|
|
637 |
scale_factor -= exp_adjust;
|
|
638 |
|
|
639 |
while(scale_factor != 0) {
|
|
640 |
d *= exp_delta;
|
|
641 |
scale_factor -= scale_increment;
|
|
642 |
}
|
|
643 |
return d;
|
|
644 |
}
|
|
645 |
|
|
646 |
/**
|
|
647 |
* Return <code>f </code>×
|
|
648 |
* 2<sup><code>scale_factor</code></sup> rounded as if performed
|
|
649 |
* by a single correctly rounded floating-point multiply to a
|
|
650 |
* member of the float value set. See <a
|
|
651 |
* href="http://java.sun.com/docs/books/jls/second_edition/html/typesValues.doc.html#9208">§4.2.3</a>
|
|
652 |
* of the <a href="http://java.sun.com/docs/books/jls/html/">Java
|
|
653 |
* Language Specification</a> for a discussion of floating-point
|
|
654 |
* value set. If the exponent of the result is between the
|
|
655 |
* <code>float</code>'s minimum exponent and maximum exponent, the
|
|
656 |
* answer is calculated exactly. If the exponent of the result
|
|
657 |
* would be larger than <code>float</code>'s maximum exponent, an
|
|
658 |
* infinity is returned. Note that if the result is subnormal,
|
|
659 |
* precision may be lost; that is, when <code>scalb(x, n)</code>
|
|
660 |
* is subnormal, <code>scalb(scalb(x, n), -n)</code> may not equal
|
|
661 |
* <i>x</i>. When the result is non-NaN, the result has the same
|
|
662 |
* sign as <code>f</code>.
|
|
663 |
*
|
|
664 |
*<p>
|
|
665 |
* Special cases:
|
|
666 |
* <ul>
|
|
667 |
* <li> If the first argument is NaN, NaN is returned.
|
|
668 |
* <li> If the first argument is infinite, then an infinity of the
|
|
669 |
* same sign is returned.
|
|
670 |
* <li> If the first argument is zero, then a zero of the same
|
|
671 |
* sign is returned.
|
|
672 |
* </ul>
|
|
673 |
*
|
|
674 |
* @param f number to be scaled by a power of two.
|
|
675 |
* @param scale_factor power of 2 used to scale <code>f</code>
|
|
676 |
* @return <code>f * </code>2<sup><code>scale_factor</code></sup>
|
|
677 |
* @author Joseph D. Darcy
|
|
678 |
*/
|
|
679 |
public static float scalb(float f, int scale_factor) {
|
|
680 |
// magnitude of a power of two so large that scaling a finite
|
|
681 |
// nonzero value by it would be guaranteed to over or
|
|
682 |
// underflow; due to rounding, scaling down takes takes an
|
|
683 |
// additional power of two which is reflected here
|
|
684 |
final int MAX_SCALE = FloatConsts.MAX_EXPONENT + -FloatConsts.MIN_EXPONENT +
|
|
685 |
FloatConsts.SIGNIFICAND_WIDTH + 1;
|
|
686 |
|
|
687 |
// Make sure scaling factor is in a reasonable range
|
|
688 |
scale_factor = Math.max(Math.min(scale_factor, MAX_SCALE), -MAX_SCALE);
|
|
689 |
|
|
690 |
/*
|
|
691 |
* Since + MAX_SCALE for float fits well within the double
|
|
692 |
* exponent range and + float -> double conversion is exact
|
|
693 |
* the multiplication below will be exact. Therefore, the
|
|
694 |
* rounding that occurs when the double product is cast to
|
|
695 |
* float will be the correctly rounded float result. Since
|
|
696 |
* all operations other than the final multiply will be exact,
|
|
697 |
* it is not necessary to declare this method strictfp.
|
|
698 |
*/
|
|
699 |
return (float)((double)f*powerOfTwoD(scale_factor));
|
|
700 |
}
|
|
701 |
|
|
702 |
/**
|
|
703 |
* Returns the floating-point number adjacent to the first
|
|
704 |
* argument in the direction of the second argument. If both
|
|
705 |
* arguments compare as equal the second argument is returned.
|
|
706 |
*
|
|
707 |
* <p>
|
|
708 |
* Special cases:
|
|
709 |
* <ul>
|
|
710 |
* <li> If either argument is a NaN, then NaN is returned.
|
|
711 |
*
|
|
712 |
* <li> If both arguments are signed zeros, <code>direction</code>
|
|
713 |
* is returned unchanged (as implied by the requirement of
|
|
714 |
* returning the second argument if the arguments compare as
|
|
715 |
* equal).
|
|
716 |
*
|
|
717 |
* <li> If <code>start</code> is
|
|
718 |
* ±<code>Double.MIN_VALUE</code> and <code>direction</code>
|
|
719 |
* has a value such that the result should have a smaller
|
|
720 |
* magnitude, then a zero with the same sign as <code>start</code>
|
|
721 |
* is returned.
|
|
722 |
*
|
|
723 |
* <li> If <code>start</code> is infinite and
|
|
724 |
* <code>direction</code> has a value such that the result should
|
|
725 |
* have a smaller magnitude, <code>Double.MAX_VALUE</code> with the
|
|
726 |
* same sign as <code>start</code> is returned.
|
|
727 |
*
|
|
728 |
* <li> If <code>start</code> is equal to ±
|
|
729 |
* <code>Double.MAX_VALUE</code> and <code>direction</code> has a
|
|
730 |
* value such that the result should have a larger magnitude, an
|
|
731 |
* infinity with same sign as <code>start</code> is returned.
|
|
732 |
* </ul>
|
|
733 |
*
|
|
734 |
* @param start starting floating-point value
|
|
735 |
* @param direction value indicating which of
|
|
736 |
* <code>start</code>'s neighbors or <code>start</code> should
|
|
737 |
* be returned
|
|
738 |
* @return The floating-point number adjacent to <code>start</code> in the
|
|
739 |
* direction of <code>direction</code>.
|
|
740 |
* @author Joseph D. Darcy
|
|
741 |
*/
|
|
742 |
public static double nextAfter(double start, double direction) {
|
|
743 |
/*
|
|
744 |
* The cases:
|
|
745 |
*
|
|
746 |
* nextAfter(+infinity, 0) == MAX_VALUE
|
|
747 |
* nextAfter(+infinity, +infinity) == +infinity
|
|
748 |
* nextAfter(-infinity, 0) == -MAX_VALUE
|
|
749 |
* nextAfter(-infinity, -infinity) == -infinity
|
|
750 |
*
|
|
751 |
* are naturally handled without any additional testing
|
|
752 |
*/
|
|
753 |
|
|
754 |
// First check for NaN values
|
|
755 |
if (isNaN(start) || isNaN(direction)) {
|
|
756 |
// return a NaN derived from the input NaN(s)
|
|
757 |
return start + direction;
|
|
758 |
} else if (start == direction) {
|
|
759 |
return direction;
|
|
760 |
} else { // start > direction or start < direction
|
|
761 |
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
|
|
762 |
// then bitwise convert start to integer.
|
|
763 |
long transducer = Double.doubleToRawLongBits(start + 0.0d);
|
|
764 |
|
|
765 |
/*
|
|
766 |
* IEEE 754 floating-point numbers are lexicographically
|
|
767 |
* ordered if treated as signed- magnitude integers .
|
|
768 |
* Since Java's integers are two's complement,
|
|
769 |
* incrementing" the two's complement representation of a
|
|
770 |
* logically negative floating-point value *decrements*
|
|
771 |
* the signed-magnitude representation. Therefore, when
|
|
772 |
* the integer representation of a floating-point values
|
|
773 |
* is less than zero, the adjustment to the representation
|
|
774 |
* is in the opposite direction than would be expected at
|
|
775 |
* first .
|
|
776 |
*/
|
|
777 |
if (direction > start) { // Calculate next greater value
|
|
778 |
transducer = transducer + (transducer >= 0L ? 1L:-1L);
|
|
779 |
} else { // Calculate next lesser value
|
|
780 |
assert direction < start;
|
|
781 |
if (transducer > 0L)
|
|
782 |
--transducer;
|
|
783 |
else
|
|
784 |
if (transducer < 0L )
|
|
785 |
++transducer;
|
|
786 |
/*
|
|
787 |
* transducer==0, the result is -MIN_VALUE
|
|
788 |
*
|
|
789 |
* The transition from zero (implicitly
|
|
790 |
* positive) to the smallest negative
|
|
791 |
* signed magnitude value must be done
|
|
792 |
* explicitly.
|
|
793 |
*/
|
|
794 |
else
|
|
795 |
transducer = DoubleConsts.SIGN_BIT_MASK | 1L;
|
|
796 |
}
|
|
797 |
|
|
798 |
return Double.longBitsToDouble(transducer);
|
|
799 |
}
|
|
800 |
}
|
|
801 |
|
|
802 |
/**
|
|
803 |
* Returns the floating-point number adjacent to the first
|
|
804 |
* argument in the direction of the second argument. If both
|
|
805 |
* arguments compare as equal, the second argument is returned.
|
|
806 |
*
|
|
807 |
* <p>
|
|
808 |
* Special cases:
|
|
809 |
* <ul>
|
|
810 |
* <li> If either argument is a NaN, then NaN is returned.
|
|
811 |
*
|
|
812 |
* <li> If both arguments are signed zeros, a <code>float</code>
|
|
813 |
* zero with the same sign as <code>direction</code> is returned
|
|
814 |
* (as implied by the requirement of returning the second argument
|
|
815 |
* if the arguments compare as equal).
|
|
816 |
*
|
|
817 |
* <li> If <code>start</code> is
|
|
818 |
* ±<code>Float.MIN_VALUE</code> and <code>direction</code>
|
|
819 |
* has a value such that the result should have a smaller
|
|
820 |
* magnitude, then a zero with the same sign as <code>start</code>
|
|
821 |
* is returned.
|
|
822 |
*
|
|
823 |
* <li> If <code>start</code> is infinite and
|
|
824 |
* <code>direction</code> has a value such that the result should
|
|
825 |
* have a smaller magnitude, <code>Float.MAX_VALUE</code> with the
|
|
826 |
* same sign as <code>start</code> is returned.
|
|
827 |
*
|
|
828 |
* <li> If <code>start</code> is equal to ±
|
|
829 |
* <code>Float.MAX_VALUE</code> and <code>direction</code> has a
|
|
830 |
* value such that the result should have a larger magnitude, an
|
|
831 |
* infinity with same sign as <code>start</code> is returned.
|
|
832 |
* </ul>
|
|
833 |
*
|
|
834 |
* @param start starting floating-point value
|
|
835 |
* @param direction value indicating which of
|
|
836 |
* <code>start</code>'s neighbors or <code>start</code> should
|
|
837 |
* be returned
|
|
838 |
* @return The floating-point number adjacent to <code>start</code> in the
|
|
839 |
* direction of <code>direction</code>.
|
|
840 |
* @author Joseph D. Darcy
|
|
841 |
*/
|
|
842 |
public static float nextAfter(float start, double direction) {
|
|
843 |
/*
|
|
844 |
* The cases:
|
|
845 |
*
|
|
846 |
* nextAfter(+infinity, 0) == MAX_VALUE
|
|
847 |
* nextAfter(+infinity, +infinity) == +infinity
|
|
848 |
* nextAfter(-infinity, 0) == -MAX_VALUE
|
|
849 |
* nextAfter(-infinity, -infinity) == -infinity
|
|
850 |
*
|
|
851 |
* are naturally handled without any additional testing
|
|
852 |
*/
|
|
853 |
|
|
854 |
// First check for NaN values
|
|
855 |
if (isNaN(start) || isNaN(direction)) {
|
|
856 |
// return a NaN derived from the input NaN(s)
|
|
857 |
return start + (float)direction;
|
|
858 |
} else if (start == direction) {
|
|
859 |
return (float)direction;
|
|
860 |
} else { // start > direction or start < direction
|
|
861 |
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
|
|
862 |
// then bitwise convert start to integer.
|
|
863 |
int transducer = Float.floatToRawIntBits(start + 0.0f);
|
|
864 |
|
|
865 |
/*
|
|
866 |
* IEEE 754 floating-point numbers are lexicographically
|
|
867 |
* ordered if treated as signed- magnitude integers .
|
|
868 |
* Since Java's integers are two's complement,
|
|
869 |
* incrementing" the two's complement representation of a
|
|
870 |
* logically negative floating-point value *decrements*
|
|
871 |
* the signed-magnitude representation. Therefore, when
|
|
872 |
* the integer representation of a floating-point values
|
|
873 |
* is less than zero, the adjustment to the representation
|
|
874 |
* is in the opposite direction than would be expected at
|
|
875 |
* first.
|
|
876 |
*/
|
|
877 |
if (direction > start) {// Calculate next greater value
|
|
878 |
transducer = transducer + (transducer >= 0 ? 1:-1);
|
|
879 |
} else { // Calculate next lesser value
|
|
880 |
assert direction < start;
|
|
881 |
if (transducer > 0)
|
|
882 |
--transducer;
|
|
883 |
else
|
|
884 |
if (transducer < 0 )
|
|
885 |
++transducer;
|
|
886 |
/*
|
|
887 |
* transducer==0, the result is -MIN_VALUE
|
|
888 |
*
|
|
889 |
* The transition from zero (implicitly
|
|
890 |
* positive) to the smallest negative
|
|
891 |
* signed magnitude value must be done
|
|
892 |
* explicitly.
|
|
893 |
*/
|
|
894 |
else
|
|
895 |
transducer = FloatConsts.SIGN_BIT_MASK | 1;
|
|
896 |
}
|
|
897 |
|
|
898 |
return Float.intBitsToFloat(transducer);
|
|
899 |
}
|
|
900 |
}
|
|
901 |
|
|
902 |
/**
|
|
903 |
* Returns the floating-point value adjacent to <code>d</code> in
|
|
904 |
* the direction of positive infinity. This method is
|
|
905 |
* semantically equivalent to <code>nextAfter(d,
|
|
906 |
* Double.POSITIVE_INFINITY)</code>; however, a <code>nextUp</code>
|
|
907 |
* implementation may run faster than its equivalent
|
|
908 |
* <code>nextAfter</code> call.
|
|
909 |
*
|
|
910 |
* <p>Special Cases:
|
|
911 |
* <ul>
|
|
912 |
* <li> If the argument is NaN, the result is NaN.
|
|
913 |
*
|
|
914 |
* <li> If the argument is positive infinity, the result is
|
|
915 |
* positive infinity.
|
|
916 |
*
|
|
917 |
* <li> If the argument is zero, the result is
|
|
918 |
* <code>Double.MIN_VALUE</code>
|
|
919 |
*
|
|
920 |
* </ul>
|
|
921 |
*
|
|
922 |
* @param d starting floating-point value
|
|
923 |
* @return The adjacent floating-point value closer to positive
|
|
924 |
* infinity.
|
|
925 |
* @author Joseph D. Darcy
|
|
926 |
*/
|
|
927 |
public static double nextUp(double d) {
|
|
928 |
if( isNaN(d) || d == Double.POSITIVE_INFINITY)
|
|
929 |
return d;
|
|
930 |
else {
|
|
931 |
d += 0.0d;
|
|
932 |
return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
|
|
933 |
((d >= 0.0d)?+1L:-1L));
|
|
934 |
}
|
|
935 |
}
|
|
936 |
|
|
937 |
/**
|
|
938 |
* Returns the floating-point value adjacent to <code>f</code> in
|
|
939 |
* the direction of positive infinity. This method is
|
|
940 |
* semantically equivalent to <code>nextAfter(f,
|
|
941 |
* Double.POSITIVE_INFINITY)</code>; however, a <code>nextUp</code>
|
|
942 |
* implementation may run faster than its equivalent
|
|
943 |
* <code>nextAfter</code> call.
|
|
944 |
*
|
|
945 |
* <p>Special Cases:
|
|
946 |
* <ul>
|
|
947 |
* <li> If the argument is NaN, the result is NaN.
|
|
948 |
*
|
|
949 |
* <li> If the argument is positive infinity, the result is
|
|
950 |
* positive infinity.
|
|
951 |
*
|
|
952 |
* <li> If the argument is zero, the result is
|
|
953 |
* <code>Float.MIN_VALUE</code>
|
|
954 |
*
|
|
955 |
* </ul>
|
|
956 |
*
|
|
957 |
* @param f starting floating-point value
|
|
958 |
* @return The adjacent floating-point value closer to positive
|
|
959 |
* infinity.
|
|
960 |
* @author Joseph D. Darcy
|
|
961 |
*/
|
|
962 |
public static float nextUp(float f) {
|
|
963 |
if( isNaN(f) || f == FloatConsts.POSITIVE_INFINITY)
|
|
964 |
return f;
|
|
965 |
else {
|
|
966 |
f += 0.0f;
|
|
967 |
return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
|
|
968 |
((f >= 0.0f)?+1:-1));
|
|
969 |
}
|
|
970 |
}
|
|
971 |
|
|
972 |
/**
|
|
973 |
* Returns the floating-point value adjacent to <code>d</code> in
|
|
974 |
* the direction of negative infinity. This method is
|
|
975 |
* semantically equivalent to <code>nextAfter(d,
|
|
976 |
* Double.NEGATIVE_INFINITY)</code>; however, a
|
|
977 |
* <code>nextDown</code> implementation may run faster than its
|
|
978 |
* equivalent <code>nextAfter</code> call.
|
|
979 |
*
|
|
980 |
* <p>Special Cases:
|
|
981 |
* <ul>
|
|
982 |
* <li> If the argument is NaN, the result is NaN.
|
|
983 |
*
|
|
984 |
* <li> If the argument is negative infinity, the result is
|
|
985 |
* negative infinity.
|
|
986 |
*
|
|
987 |
* <li> If the argument is zero, the result is
|
|
988 |
* <code>-Double.MIN_VALUE</code>
|
|
989 |
*
|
|
990 |
* </ul>
|
|
991 |
*
|
|
992 |
* @param d starting floating-point value
|
|
993 |
* @return The adjacent floating-point value closer to negative
|
|
994 |
* infinity.
|
|
995 |
* @author Joseph D. Darcy
|
|
996 |
*/
|
|
997 |
public static double nextDown(double d) {
|
|
998 |
if( isNaN(d) || d == Double.NEGATIVE_INFINITY)
|
|
999 |
return d;
|
|
1000 |
else {
|
|
1001 |
if (d == 0.0)
|
|
1002 |
return -Double.MIN_VALUE;
|
|
1003 |
else
|
|
1004 |
return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
|
|
1005 |
((d > 0.0d)?-1L:+1L));
|
|
1006 |
}
|
|
1007 |
}
|
|
1008 |
|
|
1009 |
/**
|
|
1010 |
* Returns the floating-point value adjacent to <code>f</code> in
|
|
1011 |
* the direction of negative infinity. This method is
|
|
1012 |
* semantically equivalent to <code>nextAfter(f,
|
|
1013 |
* Float.NEGATIVE_INFINITY)</code>; however, a
|
|
1014 |
* <code>nextDown</code> implementation may run faster than its
|
|
1015 |
* equivalent <code>nextAfter</code> call.
|
|
1016 |
*
|
|
1017 |
* <p>Special Cases:
|
|
1018 |
* <ul>
|
|
1019 |
* <li> If the argument is NaN, the result is NaN.
|
|
1020 |
*
|
|
1021 |
* <li> If the argument is negative infinity, the result is
|
|
1022 |
* negative infinity.
|
|
1023 |
*
|
|
1024 |
* <li> If the argument is zero, the result is
|
|
1025 |
* <code>-Float.MIN_VALUE</code>
|
|
1026 |
*
|
|
1027 |
* </ul>
|
|
1028 |
*
|
|
1029 |
* @param f starting floating-point value
|
|
1030 |
* @return The adjacent floating-point value closer to negative
|
|
1031 |
* infinity.
|
|
1032 |
* @author Joseph D. Darcy
|
|
1033 |
*/
|
|
1034 |
public static double nextDown(float f) {
|
|
1035 |
if( isNaN(f) || f == Float.NEGATIVE_INFINITY)
|
|
1036 |
return f;
|
|
1037 |
else {
|
|
1038 |
if (f == 0.0f)
|
|
1039 |
return -Float.MIN_VALUE;
|
|
1040 |
else
|
|
1041 |
return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
|
|
1042 |
((f > 0.0f)?-1:+1));
|
|
1043 |
}
|
|
1044 |
}
|
|
1045 |
|
|
1046 |
/**
|
|
1047 |
* Returns the first floating-point argument with the sign of the
|
|
1048 |
* second floating-point argument. For this method, a NaN
|
|
1049 |
* <code>sign</code> argument is always treated as if it were
|
|
1050 |
* positive.
|
|
1051 |
*
|
|
1052 |
* @param magnitude the parameter providing the magnitude of the result
|
|
1053 |
* @param sign the parameter providing the sign of the result
|
|
1054 |
* @return a value with the magnitude of <code>magnitude</code>
|
|
1055 |
* and the sign of <code>sign</code>.
|
|
1056 |
* @author Joseph D. Darcy
|
|
1057 |
* @since 1.5
|
|
1058 |
*/
|
|
1059 |
public static double copySign(double magnitude, double sign) {
|
|
1060 |
return rawCopySign(magnitude, (isNaN(sign)?1.0d:sign));
|
|
1061 |
}
|
|
1062 |
|
|
1063 |
/**
|
|
1064 |
* Returns the first floating-point argument with the sign of the
|
|
1065 |
* second floating-point argument. For this method, a NaN
|
|
1066 |
* <code>sign</code> argument is always treated as if it were
|
|
1067 |
* positive.
|
|
1068 |
*
|
|
1069 |
* @param magnitude the parameter providing the magnitude of the result
|
|
1070 |
* @param sign the parameter providing the sign of the result
|
|
1071 |
* @return a value with the magnitude of <code>magnitude</code>
|
|
1072 |
* and the sign of <code>sign</code>.
|
|
1073 |
* @author Joseph D. Darcy
|
|
1074 |
*/
|
|
1075 |
public static float copySign(float magnitude, float sign) {
|
|
1076 |
return rawCopySign(magnitude, (isNaN(sign)?1.0f:sign));
|
|
1077 |
}
|
|
1078 |
|
|
1079 |
/**
|
|
1080 |
* Returns the size of an ulp of the argument. An ulp of a
|
|
1081 |
* <code>double</code> value is the positive distance between this
|
|
1082 |
* floating-point value and the <code>double</code> value next
|
|
1083 |
* larger in magnitude. Note that for non-NaN <i>x</i>,
|
|
1084 |
* <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
|
|
1085 |
*
|
|
1086 |
* <p>Special Cases:
|
|
1087 |
* <ul>
|
|
1088 |
* <li> If the argument is NaN, then the result is NaN.
|
|
1089 |
* <li> If the argument is positive or negative infinity, then the
|
|
1090 |
* result is positive infinity.
|
|
1091 |
* <li> If the argument is positive or negative zero, then the result is
|
|
1092 |
* <code>Double.MIN_VALUE</code>.
|
|
1093 |
* <li> If the argument is ±<code>Double.MAX_VALUE</code>, then
|
|
1094 |
* the result is equal to 2<sup>971</sup>.
|
|
1095 |
* </ul>
|
|
1096 |
*
|
|
1097 |
* @param d the floating-point value whose ulp is to be returned
|
|
1098 |
* @return the size of an ulp of the argument
|
|
1099 |
* @author Joseph D. Darcy
|
|
1100 |
* @since 1.5
|
|
1101 |
*/
|
|
1102 |
public static double ulp(double d) {
|
|
1103 |
int exp = getExponent(d);
|
|
1104 |
|
|
1105 |
switch(exp) {
|
|
1106 |
case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity
|
|
1107 |
return Math.abs(d);
|
|
1108 |
// break;
|
|
1109 |
|
|
1110 |
case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal
|
|
1111 |
return Double.MIN_VALUE;
|
|
1112 |
// break
|
|
1113 |
|
|
1114 |
default:
|
|
1115 |
assert exp <= DoubleConsts.MAX_EXPONENT && exp >= DoubleConsts.MIN_EXPONENT;
|
|
1116 |
|
|
1117 |
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
|
|
1118 |
exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1);
|
|
1119 |
if (exp >= DoubleConsts.MIN_EXPONENT) {
|
|
1120 |
return powerOfTwoD(exp);
|
|
1121 |
}
|
|
1122 |
else {
|
|
1123 |
// return a subnormal result; left shift integer
|
|
1124 |
// representation of Double.MIN_VALUE appropriate
|
|
1125 |
// number of positions
|
|
1126 |
return Double.longBitsToDouble(1L <<
|
|
1127 |
(exp - (DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));
|
|
1128 |
}
|
|
1129 |
// break
|
|
1130 |
}
|
|
1131 |
}
|
|
1132 |
|
|
1133 |
/**
|
|
1134 |
* Returns the size of an ulp of the argument. An ulp of a
|
|
1135 |
* <code>float</code> value is the positive distance between this
|
|
1136 |
* floating-point value and the <code>float</code> value next
|
|
1137 |
* larger in magnitude. Note that for non-NaN <i>x</i>,
|
|
1138 |
* <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
|
|
1139 |
*
|
|
1140 |
* <p>Special Cases:
|
|
1141 |
* <ul>
|
|
1142 |
* <li> If the argument is NaN, then the result is NaN.
|
|
1143 |
* <li> If the argument is positive or negative infinity, then the
|
|
1144 |
* result is positive infinity.
|
|
1145 |
* <li> If the argument is positive or negative zero, then the result is
|
|
1146 |
* <code>Float.MIN_VALUE</code>.
|
|
1147 |
* <li> If the argument is ±<code>Float.MAX_VALUE</code>, then
|
|
1148 |
* the result is equal to 2<sup>104</sup>.
|
|
1149 |
* </ul>
|
|
1150 |
*
|
|
1151 |
* @param f the floating-point value whose ulp is to be returned
|
|
1152 |
* @return the size of an ulp of the argument
|
|
1153 |
* @author Joseph D. Darcy
|
|
1154 |
* @since 1.5
|
|
1155 |
*/
|
|
1156 |
public static float ulp(float f) {
|
|
1157 |
int exp = getExponent(f);
|
|
1158 |
|
|
1159 |
switch(exp) {
|
|
1160 |
case FloatConsts.MAX_EXPONENT+1: // NaN or infinity
|
|
1161 |
return Math.abs(f);
|
|
1162 |
// break;
|
|
1163 |
|
|
1164 |
case FloatConsts.MIN_EXPONENT-1: // zero or subnormal
|
|
1165 |
return FloatConsts.MIN_VALUE;
|
|
1166 |
// break
|
|
1167 |
|
|
1168 |
default:
|
|
1169 |
assert exp <= FloatConsts.MAX_EXPONENT && exp >= FloatConsts.MIN_EXPONENT;
|
|
1170 |
|
|
1171 |
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
|
|
1172 |
exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1);
|
|
1173 |
if (exp >= FloatConsts.MIN_EXPONENT) {
|
|
1174 |
return powerOfTwoF(exp);
|
|
1175 |
}
|
|
1176 |
else {
|
|
1177 |
// return a subnormal result; left shift integer
|
|
1178 |
// representation of FloatConsts.MIN_VALUE appropriate
|
|
1179 |
// number of positions
|
|
1180 |
return Float.intBitsToFloat(1 <<
|
|
1181 |
(exp - (FloatConsts.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));
|
|
1182 |
}
|
|
1183 |
// break
|
|
1184 |
}
|
|
1185 |
}
|
|
1186 |
|
|
1187 |
/**
|
|
1188 |
* Returns the signum function of the argument; zero if the argument
|
|
1189 |
* is zero, 1.0 if the argument is greater than zero, -1.0 if the
|
|
1190 |
* argument is less than zero.
|
|
1191 |
*
|
|
1192 |
* <p>Special Cases:
|
|
1193 |
* <ul>
|
|
1194 |
* <li> If the argument is NaN, then the result is NaN.
|
|
1195 |
* <li> If the argument is positive zero or negative zero, then the
|
|
1196 |
* result is the same as the argument.
|
|
1197 |
* </ul>
|
|
1198 |
*
|
|
1199 |
* @param d the floating-point value whose signum is to be returned
|
|
1200 |
* @return the signum function of the argument
|
|
1201 |
* @author Joseph D. Darcy
|
|
1202 |
* @since 1.5
|
|
1203 |
*/
|
|
1204 |
public static double signum(double d) {
|
|
1205 |
return (d == 0.0 || isNaN(d))?d:copySign(1.0, d);
|
|
1206 |
}
|
|
1207 |
|
|
1208 |
/**
|
|
1209 |
* Returns the signum function of the argument; zero if the argument
|
|
1210 |
* is zero, 1.0f if the argument is greater than zero, -1.0f if the
|
|
1211 |
* argument is less than zero.
|
|
1212 |
*
|
|
1213 |
* <p>Special Cases:
|
|
1214 |
* <ul>
|
|
1215 |
* <li> If the argument is NaN, then the result is NaN.
|
|
1216 |
* <li> If the argument is positive zero or negative zero, then the
|
|
1217 |
* result is the same as the argument.
|
|
1218 |
* </ul>
|
|
1219 |
*
|
|
1220 |
* @param f the floating-point value whose signum is to be returned
|
|
1221 |
* @return the signum function of the argument
|
|
1222 |
* @author Joseph D. Darcy
|
|
1223 |
* @since 1.5
|
|
1224 |
*/
|
|
1225 |
public static float signum(float f) {
|
|
1226 |
return (f == 0.0f || isNaN(f))?f:copySign(1.0f, f);
|
|
1227 |
}
|
|
1228 |
|
|
1229 |
}
|