Automatic sources dropoff on 2020-06-10 18:32:38.095721 The change is generated with prebuilt drop tool. Change-Id: I24cbf6ba6db262a1ae1445db1427a08fee35b3b4
diff --git a/java/lang/Math.java b/java/lang/Math.java new file mode 100644 index 0000000..17cbf6d --- /dev/null +++ b/java/lang/Math.java
@@ -0,0 +1,2397 @@ +/* + * Copyright (C) 2014 The Android Open Source Project + * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. Oracle designates this + * particular file as subject to the "Classpath" exception as provided + * by Oracle in the LICENSE file that accompanied this code. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package java.lang; +import dalvik.annotation.optimization.CriticalNative; +import java.util.Random; + +import sun.misc.FloatConsts; +import sun.misc.DoubleConsts; + +// Android-note: Document that the results from Math are based on libm's behavior. +// For performance, Android implements many of the methods in this class in terms of the underlying +// OS's libm functions. libm has well-defined behavior for special cases. Where known these are +// marked with the tag above and the documentation has been modified as needed. +/** + * The class {@code Math} contains methods for performing basic + * numeric operations such as the elementary exponential, logarithm, + * square root, and trigonometric functions. + * + * <p>Unlike some of the numeric methods of class + * {@code StrictMath}, all implementations of the equivalent + * functions of class {@code Math} are not defined to return the + * bit-for-bit same results. This relaxation permits + * better-performing implementations where strict reproducibility is + * not required. + * + * <p>By default many of the {@code Math} methods simply call + * the equivalent method in {@code StrictMath} for their + * implementation. Code generators are encouraged to use + * platform-specific native libraries or microprocessor instructions, + * where available, to provide higher-performance implementations of + * {@code Math} methods. Such higher-performance + * implementations still must conform to the specification for + * {@code Math}. + * + * <p>The quality of implementation specifications concern two + * properties, accuracy of the returned result and monotonicity of the + * method. Accuracy of the floating-point {@code Math} methods is + * measured in terms of <i>ulps</i>, units in the last place. For a + * given floating-point format, an {@linkplain #ulp(double) ulp} of a + * specific real number value is the distance between the two + * floating-point values bracketing that numerical value. When + * discussing the accuracy of a method as a whole rather than at a + * specific argument, the number of ulps cited is for the worst-case + * error at any argument. If a method always has an error less than + * 0.5 ulps, the method always returns the floating-point number + * nearest the exact result; such a method is <i>correctly + * rounded</i>. A correctly rounded method is generally the best a + * floating-point approximation can be; however, it is impractical for + * many floating-point methods to be correctly rounded. Instead, for + * the {@code Math} class, a larger error bound of 1 or 2 ulps is + * allowed for certain methods. Informally, with a 1 ulp error bound, + * when the exact result is a representable number, the exact result + * should be returned as the computed result; otherwise, either of the + * two floating-point values which bracket the exact result may be + * returned. For exact results large in magnitude, one of the + * endpoints of the bracket may be infinite. Besides accuracy at + * individual arguments, maintaining proper relations between the + * method at different arguments is also important. Therefore, most + * methods with more than 0.5 ulp errors are required to be + * <i>semi-monotonic</i>: whenever the mathematical function is + * non-decreasing, so is the floating-point approximation, likewise, + * whenever the mathematical function is non-increasing, so is the + * floating-point approximation. Not all approximations that have 1 + * ulp accuracy will automatically meet the monotonicity requirements. + * + * <p> + * The platform uses signed two's complement integer arithmetic with + * int and long primitive types. The developer should choose + * the primitive type to ensure that arithmetic operations consistently + * produce correct results, which in some cases means the operations + * will not overflow the range of values of the computation. + * The best practice is to choose the primitive type and algorithm to avoid + * overflow. In cases where the size is {@code int} or {@code long} and + * overflow errors need to be detected, the methods {@code addExact}, + * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact} + * throw an {@code ArithmeticException} when the results overflow. + * For other arithmetic operations such as divide, absolute value, + * increment, decrement, and negation overflow occurs only with + * a specific minimum or maximum value and should be checked against + * the minimum or maximum as appropriate. + * + * @author unascribed + * @author Joseph D. Darcy + * @since JDK1.0 + */ + +public final class Math { + + // Android-changed: Numerous methods in this class are re-implemented in native for performance. + // Those methods are also annotated @CriticalNative. + + /** + * Don't let anyone instantiate this class. + */ + private Math() {} + + /** + * The {@code double} value that is closer than any other to + * <i>e</i>, the base of the natural logarithms. + */ + public static final double E = 2.7182818284590452354; + + /** + * The {@code double} value that is closer than any other to + * <i>pi</i>, the ratio of the circumference of a circle to its + * diameter. + */ + public static final double PI = 3.14159265358979323846; + + /** + * Returns the trigonometric sine of an angle. Special cases: + * <ul><li>If the argument is NaN or an infinity, then the + * result is NaN. + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a an angle, in radians. + * @return the sine of the argument. + */ + @CriticalNative + public static native double sin(double a); + + /** + * Returns the trigonometric cosine of an angle. Special cases: + * <ul><li>If the argument is NaN or an infinity, then the + * result is NaN.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a an angle, in radians. + * @return the cosine of the argument. + */ + @CriticalNative + public static native double cos(double a); + + /** + * Returns the trigonometric tangent of an angle. Special cases: + * <ul><li>If the argument is NaN or an infinity, then the result + * is NaN. + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a an angle, in radians. + * @return the tangent of the argument. + */ + @CriticalNative + public static native double tan(double a); + + /** + * Returns the arc sine of a value; the returned angle is in the + * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: + * <ul><li>If the argument is NaN or its absolute value is greater + * than 1, then the result is NaN. + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the value whose arc sine is to be returned. + * @return the arc sine of the argument. + */ + @CriticalNative + public static native double asin(double a); + + /** + * Returns the arc cosine of a value; the returned angle is in the + * range 0.0 through <i>pi</i>. Special case: + * <ul><li>If the argument is NaN or its absolute value is greater + * than 1, then the result is NaN.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the value whose arc cosine is to be returned. + * @return the arc cosine of the argument. + */ + @CriticalNative + public static native double acos(double a); + + /** + * Returns the arc tangent of a value; the returned angle is in the + * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: + * <ul><li>If the argument is NaN, then the result is NaN. + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the value whose arc tangent is to be returned. + * @return the arc tangent of the argument. + */ + @CriticalNative + public static native double atan(double a); + + /** + * Converts an angle measured in degrees to an approximately + * equivalent angle measured in radians. The conversion from + * degrees to radians is generally inexact. + * + * @param angdeg an angle, in degrees + * @return the measurement of the angle {@code angdeg} + * in radians. + * @since 1.2 + */ + public static double toRadians(double angdeg) { + return angdeg / 180.0 * PI; + } + + /** + * Converts an angle measured in radians to an approximately + * equivalent angle measured in degrees. The conversion from + * radians to degrees is generally inexact; users should + * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly + * equal {@code 0.0}. + * + * @param angrad an angle, in radians + * @return the measurement of the angle {@code angrad} + * in degrees. + * @since 1.2 + */ + public static double toDegrees(double angrad) { + return angrad * 180.0 / PI; + } + + /** + * Returns Euler's number <i>e</i> raised to the power of a + * {@code double} value. Special cases: + * <ul><li>If the argument is NaN, the result is NaN. + * <li>If the argument is positive infinity, then the result is + * positive infinity. + * <li>If the argument is negative infinity, then the result is + * positive zero.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the exponent to raise <i>e</i> to. + * @return the value <i>e</i><sup>{@code a}</sup>, + * where <i>e</i> is the base of the natural logarithms. + */ + @CriticalNative + public static native double exp(double a); + + /** + * Returns the natural logarithm (base <i>e</i>) of a {@code double} + * value. Special cases: + * <ul><li>If the argument is NaN or less than zero, then the result + * is NaN. + * <li>If the argument is positive infinity, then the result is + * positive infinity. + * <li>If the argument is positive zero or negative zero, then the + * result is negative infinity.</ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a a value + * @return the value ln {@code a}, the natural logarithm of + * {@code a}. + */ + @CriticalNative + public static native double log(double a); + + /** + * Returns the base 10 logarithm of a {@code double} value. + * Special cases: + * + * <ul><li>If the argument is NaN or less than zero, then the result + * is NaN. + * <li>If the argument is positive infinity, then the result is + * positive infinity. + * <li>If the argument is positive zero or negative zero, then the + * result is negative infinity. + * <li> If the argument is equal to 10<sup><i>n</i></sup> for + * integer <i>n</i>, then the result is <i>n</i>. + * </ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a a value + * @return the base 10 logarithm of {@code a}. + * @since 1.5 + */ + @CriticalNative + public static native double log10(double a); + + /** + * Returns the correctly rounded positive square root of a + * {@code double} value. + * Special cases: + * <ul><li>If the argument is NaN or less than zero, then the result + * is NaN. + * <li>If the argument is positive infinity, then the result is positive + * infinity. + * <li>If the argument is positive zero or negative zero, then the + * result is the same as the argument.</ul> + * Otherwise, the result is the {@code double} value closest to + * the true mathematical square root of the argument value. + * + * @param a a value. + * @return the positive square root of {@code a}. + * If the argument is NaN or less than zero, the result is NaN. + */ + @CriticalNative + public static native double sqrt(double a); + + + /** + * Returns the cube root of a {@code double} value. For + * positive finite {@code x}, {@code cbrt(-x) == + * -cbrt(x)}; that is, the cube root of a negative value is + * the negative of the cube root of that value's magnitude. + * + * Special cases: + * + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is infinite, then the result is an infinity + * with the same sign as the argument. + * + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument. + * + * </ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * + * @param a a value. + * @return the cube root of {@code a}. + * @since 1.5 + */ + @CriticalNative + public static native double cbrt(double a); + + /** + * Computes the remainder operation on two arguments as prescribed + * by the IEEE 754 standard. + * The remainder value is mathematically equal to + * <code>f1 - f2</code> × <i>n</i>, + * where <i>n</i> is the mathematical integer closest to the exact + * mathematical value of the quotient {@code f1/f2}, and if two + * mathematical integers are equally close to {@code f1/f2}, + * then <i>n</i> is the integer that is even. If the remainder is + * zero, its sign is the same as the sign of the first argument. + * Special cases: + * <ul><li>If either argument is NaN, or the first argument is infinite, + * or the second argument is positive zero or negative zero, then the + * result is NaN. + * <li>If the first argument is finite and the second argument is + * infinite, then the result is the same as the first argument.</ul> + * + * @param f1 the dividend. + * @param f2 the divisor. + * @return the remainder when {@code f1} is divided by + * {@code f2}. + */ + @CriticalNative + public static native double IEEEremainder(double f1, double f2); + + /** + * Returns the smallest (closest to negative infinity) + * {@code double} value that is greater than or equal to the + * argument and is equal to a mathematical integer. Special cases: + * <ul><li>If the argument value is already equal to a + * mathematical integer, then the result is the same as the + * argument. <li>If the argument is NaN or an infinity or + * positive zero or negative zero, then the result is the same as + * the argument. <li>If the argument value is less than zero but + * greater than -1.0, then the result is negative zero.</ul> Note + * that the value of {@code Math.ceil(x)} is exactly the + * value of {@code -Math.floor(-x)}. + * + * + * @param a a value. + * @return the smallest (closest to negative infinity) + * floating-point value that is greater than or equal to + * the argument and is equal to a mathematical integer. + */ + @CriticalNative + public static native double ceil(double a); + + /** + * Returns the largest (closest to positive infinity) + * {@code double} value that is less than or equal to the + * argument and is equal to a mathematical integer. Special cases: + * <ul><li>If the argument value is already equal to a + * mathematical integer, then the result is the same as the + * argument. <li>If the argument is NaN or an infinity or + * positive zero or negative zero, then the result is the same as + * the argument.</ul> + * + * @param a a value. + * @return the largest (closest to positive infinity) + * floating-point value that less than or equal to the argument + * and is equal to a mathematical integer. + */ + @CriticalNative + public static native double floor(double a); + + /** + * Returns the {@code double} value that is closest in value + * to the argument and is equal to a mathematical integer. If two + * {@code double} values that are mathematical integers are + * equally close, the result is the integer value that is + * even. Special cases: + * <ul><li>If the argument value is already equal to a mathematical + * integer, then the result is the same as the argument. + * <li>If the argument is NaN or an infinity or positive zero or negative + * zero, then the result is the same as the argument.</ul> + * + * @param a a {@code double} value. + * @return the closest floating-point value to {@code a} that is + * equal to a mathematical integer. + */ + @CriticalNative + public static native double rint(double a); + + /** + * Returns the angle <i>theta</i> from the conversion of rectangular + * coordinates ({@code x}, {@code y}) to polar + * coordinates (r, <i>theta</i>). + * This method computes the phase <i>theta</i> by computing an arc tangent + * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special + * cases: + * <ul><li>If either argument is NaN, then the result is NaN. + * <li>If the first argument is positive zero and the second argument + * is positive, or the first argument is positive and finite and the + * second argument is positive infinity, then the result is positive + * zero. + * <li>If the first argument is negative zero and the second argument + * is positive, or the first argument is negative and finite and the + * second argument is positive infinity, then the result is negative zero. + * <li>If the first argument is positive zero and the second argument + * is negative, or the first argument is positive and finite and the + * second argument is negative infinity, then the result is the + * {@code double} value closest to <i>pi</i>. + * <li>If the first argument is negative zero and the second argument + * is negative, or the first argument is negative and finite and the + * second argument is negative infinity, then the result is the + * {@code double} value closest to -<i>pi</i>. + * <li>If the first argument is positive and the second argument is + * positive zero or negative zero, or the first argument is positive + * infinity and the second argument is finite, then the result is the + * {@code double} value closest to <i>pi</i>/2. + * <li>If the first argument is negative and the second argument is + * positive zero or negative zero, or the first argument is negative + * infinity and the second argument is finite, then the result is the + * {@code double} value closest to -<i>pi</i>/2. + * <li>If both arguments are positive infinity, then the result is the + * {@code double} value closest to <i>pi</i>/4. + * <li>If the first argument is positive infinity and the second argument + * is negative infinity, then the result is the {@code double} + * value closest to 3*<i>pi</i>/4. + * <li>If the first argument is negative infinity and the second argument + * is positive infinity, then the result is the {@code double} value + * closest to -<i>pi</i>/4. + * <li>If both arguments are negative infinity, then the result is the + * {@code double} value closest to -3*<i>pi</i>/4.</ul> + * + * <p>The computed result must be within 2 ulps of the exact result. + * Results must be semi-monotonic. + * + * @param y the ordinate coordinate + * @param x the abscissa coordinate + * @return the <i>theta</i> component of the point + * (<i>r</i>, <i>theta</i>) + * in polar coordinates that corresponds to the point + * (<i>x</i>, <i>y</i>) in Cartesian coordinates. + */ + @CriticalNative + public static native double atan2(double y, double x); + + // Android-changed: Document that the results from Math are based on libm's behavior. + // The cases known to differ with libm's pow(): + // If the first argument is 1.0 then result is always 1.0 (not NaN). + // If the first argument is -1.0 and the second argument is infinite, the result is 1.0 (not + // NaN). + /** + * Returns the value of the first argument raised to the power of the + * second argument. Special cases: + * + * <ul><li>If the second argument is positive or negative zero, then the + * result is 1.0. + * <li>If the second argument is 1.0, then the result is the same as the + * first argument. + * <li>If the first argument is 1.0, then the result is 1.0. + * <li>If the second argument is NaN, then the result is NaN except where the first argument is + * 1.0. + * <li>If the first argument is NaN and the second argument is nonzero, + * then the result is NaN. + * + * <li>If + * <ul> + * <li>the absolute value of the first argument is greater than 1 + * and the second argument is positive infinity, or + * <li>the absolute value of the first argument is less than 1 and + * the second argument is negative infinity, + * </ul> + * then the result is positive infinity. + * + * <li>If + * <ul> + * <li>the absolute value of the first argument is greater than 1 and + * the second argument is negative infinity, or + * <li>the absolute value of the + * first argument is less than 1 and the second argument is positive + * infinity, + * </ul> + * then the result is positive zero. + * + * <li>If the absolute value of the first argument equals 1 and the + * second argument is infinite, then the result is 1.0. + * + * <li>If + * <ul> + * <li>the first argument is positive zero and the second argument + * is greater than zero, or + * <li>the first argument is positive infinity and the second + * argument is less than zero, + * </ul> + * then the result is positive zero. + * + * <li>If + * <ul> + * <li>the first argument is positive zero and the second argument + * is less than zero, or + * <li>the first argument is positive infinity and the second + * argument is greater than zero, + * </ul> + * then the result is positive infinity. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument + * is greater than zero but not a finite odd integer, or + * <li>the first argument is negative infinity and the second + * argument is less than zero but not a finite odd integer, + * </ul> + * then the result is positive zero. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument + * is a positive finite odd integer, or + * <li>the first argument is negative infinity and the second + * argument is a negative finite odd integer, + * </ul> + * then the result is negative zero. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument + * is less than zero but not a finite odd integer, or + * <li>the first argument is negative infinity and the second + * argument is greater than zero but not a finite odd integer, + * </ul> + * then the result is positive infinity. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument + * is a negative finite odd integer, or + * <li>the first argument is negative infinity and the second + * argument is a positive finite odd integer, + * </ul> + * then the result is negative infinity. + * + * <li>If the first argument is finite and less than zero + * <ul> + * <li> if the second argument is a finite even integer, the + * result is equal to the result of raising the absolute value of + * the first argument to the power of the second argument + * + * <li>if the second argument is a finite odd integer, the result + * is equal to the negative of the result of raising the absolute + * value of the first argument to the power of the second + * argument + * + * <li>if the second argument is finite and not an integer, then + * the result is NaN. + * </ul> + * + * <li>If both arguments are integers, then the result is exactly equal + * to the mathematical result of raising the first argument to the power + * of the second argument if that result can in fact be represented + * exactly as a {@code double} value.</ul> + * + * <p>(In the foregoing descriptions, a floating-point value is + * considered to be an integer if and only if it is finite and a + * fixed point of the method {@link #ceil ceil} or, + * equivalently, a fixed point of the method {@link #floor + * floor}. A value is a fixed point of a one-argument + * method if and only if the result of applying the method to the + * value is equal to the value.) + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param a the base. + * @param b the exponent. + * @return the value {@code a}<sup>{@code b}</sup>. + */ + @CriticalNative + public static native double pow(double a, double b); + + /** + * Returns the closest {@code int} to the argument, with ties + * rounding to positive infinity. + * + * <p> + * Special cases: + * <ul><li>If the argument is NaN, the result is 0. + * <li>If the argument is negative infinity or any value less than or + * equal to the value of {@code Integer.MIN_VALUE}, the result is + * equal to the value of {@code Integer.MIN_VALUE}. + * <li>If the argument is positive infinity or any value greater than or + * equal to the value of {@code Integer.MAX_VALUE}, the result is + * equal to the value of {@code Integer.MAX_VALUE}.</ul> + * + * @param a a floating-point value to be rounded to an integer. + * @return the value of the argument rounded to the nearest + * {@code int} value. + * @see java.lang.Integer#MAX_VALUE + * @see java.lang.Integer#MIN_VALUE + */ + public static int round(float a) { + int intBits = Float.floatToRawIntBits(a); + int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK) + >> (FloatConsts.SIGNIFICAND_WIDTH - 1); + int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2 + + FloatConsts.EXP_BIAS) - biasedExp; + if ((shift & -32) == 0) { // shift >= 0 && shift < 32 + // a is a finite number such that pow(2,-32) <= ulp(a) < 1 + int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK) + | (FloatConsts.SIGNIF_BIT_MASK + 1)); + if (intBits < 0) { + r = -r; + } + // In the comments below each Java expression evaluates to the value + // the corresponding mathematical expression: + // (r) evaluates to a / ulp(a) + // (r >> shift) evaluates to floor(a * 2) + // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) + // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) + return ((r >> shift) + 1) >> 1; + } else { + // a is either + // - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2 + // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer + // - an infinity or NaN + return (int) a; + } + } + + /** + * Returns the closest {@code long} to the argument, with ties + * rounding to positive infinity. + * + * <p>Special cases: + * <ul><li>If the argument is NaN, the result is 0. + * <li>If the argument is negative infinity or any value less than or + * equal to the value of {@code Long.MIN_VALUE}, the result is + * equal to the value of {@code Long.MIN_VALUE}. + * <li>If the argument is positive infinity or any value greater than or + * equal to the value of {@code Long.MAX_VALUE}, the result is + * equal to the value of {@code Long.MAX_VALUE}.</ul> + * + * @param a a floating-point value to be rounded to a + * {@code long}. + * @return the value of the argument rounded to the nearest + * {@code long} value. + * @see java.lang.Long#MAX_VALUE + * @see java.lang.Long#MIN_VALUE + */ + public static long round(double a) { + long longBits = Double.doubleToRawLongBits(a); + long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK) + >> (DoubleConsts.SIGNIFICAND_WIDTH - 1); + long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2 + + DoubleConsts.EXP_BIAS) - biasedExp; + if ((shift & -64) == 0) { // shift >= 0 && shift < 64 + // a is a finite number such that pow(2,-64) <= ulp(a) < 1 + long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK) + | (DoubleConsts.SIGNIF_BIT_MASK + 1)); + if (longBits < 0) { + r = -r; + } + // In the comments below each Java expression evaluates to the value + // the corresponding mathematical expression: + // (r) evaluates to a / ulp(a) + // (r >> shift) evaluates to floor(a * 2) + // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2) + // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2) + return ((r >> shift) + 1) >> 1; + } else { + // a is either + // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2 + // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer + // - an infinity or NaN + return (long) a; + } + } + + private static final class RandomNumberGeneratorHolder { + static final Random randomNumberGenerator = new Random(); + } + + /** + * Returns a {@code double} value with a positive sign, greater + * than or equal to {@code 0.0} and less than {@code 1.0}. + * Returned values are chosen pseudorandomly with (approximately) + * uniform distribution from that range. + * + * <p>When this method is first called, it creates a single new + * pseudorandom-number generator, exactly as if by the expression + * + * <blockquote>{@code new java.util.Random()}</blockquote> + * + * This new pseudorandom-number generator is used thereafter for + * all calls to this method and is used nowhere else. + * + * <p>This method is properly synchronized to allow correct use by + * more than one thread. However, if many threads need to generate + * pseudorandom numbers at a great rate, it may reduce contention + * for each thread to have its own pseudorandom-number generator. + * + * @return a pseudorandom {@code double} greater than or equal + * to {@code 0.0} and less than {@code 1.0}. + * @see Random#nextDouble() + */ + public static double random() { + return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble(); + } + + // Android-added: setRandomSeedInternal(long), called after zygote forks. + // This allows different processes to have different random seeds. + /** + * Set the seed for the pseudo random generator used by {@link #random()} + * and {@link #randomIntInternal()}. + * + * @hide for internal use only. + */ + public static void setRandomSeedInternal(long seed) { + RandomNumberGeneratorHolder.randomNumberGenerator.setSeed(seed); + } + + // Android-added: randomIntInternal() method: like random() but for int. + /** + * @hide for internal use only. + */ + public static int randomIntInternal() { + return RandomNumberGeneratorHolder.randomNumberGenerator.nextInt(); + } + + // Android-added: randomLongInternal() method: like random() but for long. + /** + * @hide for internal use only. + */ + public static long randomLongInternal() { + return RandomNumberGeneratorHolder.randomNumberGenerator.nextLong(); + } + + /** + * Returns the sum of its arguments, + * throwing an exception if the result overflows an {@code int}. + * + * @param x the first value + * @param y the second value + * @return the result + * @throws ArithmeticException if the result overflows an int + * @since 1.8 + */ + public static int addExact(int x, int y) { + int r = x + y; + // HD 2-12 Overflow iff both arguments have the opposite sign of the result + if (((x ^ r) & (y ^ r)) < 0) { + throw new ArithmeticException("integer overflow"); + } + return r; + } + + /** + * Returns the sum of its arguments, + * throwing an exception if the result overflows a {@code long}. + * + * @param x the first value + * @param y the second value + * @return the result + * @throws ArithmeticException if the result overflows a long + * @since 1.8 + */ + public static long addExact(long x, long y) { + long r = x + y; + // HD 2-12 Overflow iff both arguments have the opposite sign of the result + if (((x ^ r) & (y ^ r)) < 0) { + throw new ArithmeticException("long overflow"); + } + return r; + } + + /** + * Returns the difference of the arguments, + * throwing an exception if the result overflows an {@code int}. + * + * @param x the first value + * @param y the second value to subtract from the first + * @return the result + * @throws ArithmeticException if the result overflows an int + * @since 1.8 + */ + public static int subtractExact(int x, int y) { + int r = x - y; + // HD 2-12 Overflow iff the arguments have different signs and + // the sign of the result is different than the sign of x + if (((x ^ y) & (x ^ r)) < 0) { + throw new ArithmeticException("integer overflow"); + } + return r; + } + + /** + * Returns the difference of the arguments, + * throwing an exception if the result overflows a {@code long}. + * + * @param x the first value + * @param y the second value to subtract from the first + * @return the result + * @throws ArithmeticException if the result overflows a long + * @since 1.8 + */ + public static long subtractExact(long x, long y) { + long r = x - y; + // HD 2-12 Overflow iff the arguments have different signs and + // the sign of the result is different than the sign of x + if (((x ^ y) & (x ^ r)) < 0) { + throw new ArithmeticException("long overflow"); + } + return r; + } + + /** + * Returns the product of the arguments, + * throwing an exception if the result overflows an {@code int}. + * + * @param x the first value + * @param y the second value + * @return the result + * @throws ArithmeticException if the result overflows an int + * @since 1.8 + */ + public static int multiplyExact(int x, int y) { + long r = (long)x * (long)y; + if ((int)r != r) { + throw new ArithmeticException("integer overflow"); + } + return (int)r; + } + + /** + * Returns the product of the arguments, + * throwing an exception if the result overflows a {@code long}. + * + * @param x the first value + * @param y the second value + * @return the result + * @throws ArithmeticException if the result overflows a long + * @since 1.8 + */ + public static long multiplyExact(long x, long y) { + long r = x * y; + long ax = Math.abs(x); + long ay = Math.abs(y); + if (((ax | ay) >>> 31 != 0)) { + // Some bits greater than 2^31 that might cause overflow + // Check the result using the divide operator + // and check for the special case of Long.MIN_VALUE * -1 + if (((y != 0) && (r / y != x)) || + (x == Long.MIN_VALUE && y == -1)) { + throw new ArithmeticException("long overflow"); + } + } + return r; + } + + /** + * Returns the argument incremented by one, throwing an exception if the + * result overflows an {@code int}. + * + * @param a the value to increment + * @return the result + * @throws ArithmeticException if the result overflows an int + * @since 1.8 + */ + public static int incrementExact(int a) { + if (a == Integer.MAX_VALUE) { + throw new ArithmeticException("integer overflow"); + } + + return a + 1; + } + + /** + * Returns the argument incremented by one, throwing an exception if the + * result overflows a {@code long}. + * + * @param a the value to increment + * @return the result + * @throws ArithmeticException if the result overflows a long + * @since 1.8 + */ + public static long incrementExact(long a) { + if (a == Long.MAX_VALUE) { + throw new ArithmeticException("long overflow"); + } + + return a + 1L; + } + + /** + * Returns the argument decremented by one, throwing an exception if the + * result overflows an {@code int}. + * + * @param a the value to decrement + * @return the result + * @throws ArithmeticException if the result overflows an int + * @since 1.8 + */ + public static int decrementExact(int a) { + if (a == Integer.MIN_VALUE) { + throw new ArithmeticException("integer overflow"); + } + + return a - 1; + } + + /** + * Returns the argument decremented by one, throwing an exception if the + * result overflows a {@code long}. + * + * @param a the value to decrement + * @return the result + * @throws ArithmeticException if the result overflows a long + * @since 1.8 + */ + public static long decrementExact(long a) { + if (a == Long.MIN_VALUE) { + throw new ArithmeticException("long overflow"); + } + + return a - 1L; + } + + /** + * Returns the negation of the argument, throwing an exception if the + * result overflows an {@code int}. + * + * @param a the value to negate + * @return the result + * @throws ArithmeticException if the result overflows an int + * @since 1.8 + */ + public static int negateExact(int a) { + if (a == Integer.MIN_VALUE) { + throw new ArithmeticException("integer overflow"); + } + + return -a; + } + + /** + * Returns the negation of the argument, throwing an exception if the + * result overflows a {@code long}. + * + * @param a the value to negate + * @return the result + * @throws ArithmeticException if the result overflows a long + * @since 1.8 + */ + public static long negateExact(long a) { + if (a == Long.MIN_VALUE) { + throw new ArithmeticException("long overflow"); + } + + return -a; + } + + /** + * Returns the value of the {@code long} argument; + * throwing an exception if the value overflows an {@code int}. + * + * @param value the long value + * @return the argument as an int + * @throws ArithmeticException if the {@code argument} overflows an int + * @since 1.8 + */ + public static int toIntExact(long value) { + if ((int)value != value) { + throw new ArithmeticException("integer overflow"); + } + return (int)value; + } + + /** + * Returns the largest (closest to positive infinity) + * {@code int} value that is less than or equal to the algebraic quotient. + * There is one special case, if the dividend is the + * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1}, + * then integer overflow occurs and + * the result is equal to the {@code Integer.MIN_VALUE}. + * <p> + * Normal integer division operates under the round to zero rounding mode + * (truncation). This operation instead acts under the round toward + * negative infinity (floor) rounding mode. + * The floor rounding mode gives different results than truncation + * when the exact result is negative. + * <ul> + * <li>If the signs of the arguments are the same, the results of + * {@code floorDiv} and the {@code /} operator are the same. <br> + * For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li> + * <li>If the signs of the arguments are different, the quotient is negative and + * {@code floorDiv} returns the integer less than or equal to the quotient + * and the {@code /} operator returns the integer closest to zero.<br> + * For example, {@code floorDiv(-4, 3) == -2}, + * whereas {@code (-4 / 3) == -1}. + * </li> + * </ul> + * <p> + * + * @param x the dividend + * @param y the divisor + * @return the largest (closest to positive infinity) + * {@code int} value that is less than or equal to the algebraic quotient. + * @throws ArithmeticException if the divisor {@code y} is zero + * @see #floorMod(int, int) + * @see #floor(double) + * @since 1.8 + */ + public static int floorDiv(int x, int y) { + int r = x / y; + // if the signs are different and modulo not zero, round down + if ((x ^ y) < 0 && (r * y != x)) { + r--; + } + return r; + } + + /** + * Returns the largest (closest to positive infinity) + * {@code long} value that is less than or equal to the algebraic quotient. + * There is one special case, if the dividend is the + * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1}, + * then integer overflow occurs and + * the result is equal to the {@code Long.MIN_VALUE}. + * <p> + * Normal integer division operates under the round to zero rounding mode + * (truncation). This operation instead acts under the round toward + * negative infinity (floor) rounding mode. + * The floor rounding mode gives different results than truncation + * when the exact result is negative. + * <p> + * For examples, see {@link #floorDiv(int, int)}. + * + * @param x the dividend + * @param y the divisor + * @return the largest (closest to positive infinity) + * {@code long} value that is less than or equal to the algebraic quotient. + * @throws ArithmeticException if the divisor {@code y} is zero + * @see #floorMod(long, long) + * @see #floor(double) + * @since 1.8 + */ + public static long floorDiv(long x, long y) { + long r = x / y; + // if the signs are different and modulo not zero, round down + if ((x ^ y) < 0 && (r * y != x)) { + r--; + } + return r; + } + + /** + * Returns the floor modulus of the {@code int} arguments. + * <p> + * The floor modulus is {@code x - (floorDiv(x, y) * y)}, + * has the same sign as the divisor {@code y}, and + * is in the range of {@code -abs(y) < r < +abs(y)}. + * + * <p> + * The relationship between {@code floorDiv} and {@code floorMod} is such that: + * <ul> + * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} + * </ul> + * <p> + * The difference in values between {@code floorMod} and + * the {@code %} operator is due to the difference between + * {@code floorDiv} that returns the integer less than or equal to the quotient + * and the {@code /} operator that returns the integer closest to zero. + * <p> + * Examples: + * <ul> + * <li>If the signs of the arguments are the same, the results + * of {@code floorMod} and the {@code %} operator are the same. <br> + * <ul> + * <li>{@code floorMod(4, 3) == 1}; and {@code (4 % 3) == 1}</li> + * </ul> + * <li>If the signs of the arguments are different, the results differ from the {@code %} operator.<br> + * <ul> + * <li>{@code floorMod(+4, -3) == -2}; and {@code (+4 % -3) == +1} </li> + * <li>{@code floorMod(-4, +3) == +2}; and {@code (-4 % +3) == -1} </li> + * <li>{@code floorMod(-4, -3) == -1}; and {@code (-4 % -3) == -1 } </li> + * </ul> + * </li> + * </ul> + * <p> + * If the signs of arguments are unknown and a positive modulus + * is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}. + * + * @param x the dividend + * @param y the divisor + * @return the floor modulus {@code x - (floorDiv(x, y) * y)} + * @throws ArithmeticException if the divisor {@code y} is zero + * @see #floorDiv(int, int) + * @since 1.8 + */ + public static int floorMod(int x, int y) { + int r = x - floorDiv(x, y) * y; + return r; + } + + /** + * Returns the floor modulus of the {@code long} arguments. + * <p> + * The floor modulus is {@code x - (floorDiv(x, y) * y)}, + * has the same sign as the divisor {@code y}, and + * is in the range of {@code -abs(y) < r < +abs(y)}. + * + * <p> + * The relationship between {@code floorDiv} and {@code floorMod} is such that: + * <ul> + * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} + * </ul> + * <p> + * For examples, see {@link #floorMod(int, int)}. + * + * @param x the dividend + * @param y the divisor + * @return the floor modulus {@code x - (floorDiv(x, y) * y)} + * @throws ArithmeticException if the divisor {@code y} is zero + * @see #floorDiv(long, long) + * @since 1.8 + */ + public static long floorMod(long x, long y) { + return x - floorDiv(x, y) * y; + } + + /** + * Returns the absolute value of an {@code int} value. + * If the argument is not negative, the argument is returned. + * If the argument is negative, the negation of the argument is returned. + * + * <p>Note that if the argument is equal to the value of + * {@link Integer#MIN_VALUE}, the most negative representable + * {@code int} value, the result is that same value, which is + * negative. + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static int abs(int a) { + return (a < 0) ? -a : a; + } + + /** + * Returns the absolute value of a {@code long} value. + * If the argument is not negative, the argument is returned. + * If the argument is negative, the negation of the argument is returned. + * + * <p>Note that if the argument is equal to the value of + * {@link Long#MIN_VALUE}, the most negative representable + * {@code long} value, the result is that same value, which + * is negative. + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static long abs(long a) { + return (a < 0) ? -a : a; + } + + /** + * Returns the absolute value of a {@code float} value. + * If the argument is not negative, the argument is returned. + * If the argument is negative, the negation of the argument is returned. + * Special cases: + * <ul><li>If the argument is positive zero or negative zero, the + * result is positive zero. + * <li>If the argument is infinite, the result is positive infinity. + * <li>If the argument is NaN, the result is NaN.</ul> + * In other words, the result is the same as the value of the expression: + * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))} + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static float abs(float a) { + // Android-changed: Implementation modified to exactly match ART intrinsics behavior. + // Note, as a "quality of implementation", rather than pure "spec compliance", + // we require that Math.abs() clears the sign bit (but changes nothing else) + // for all numbers, including NaN (signaling NaN may become quiet though). + // http://b/30758343 + return Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a)); + } + + /** + * Returns the absolute value of a {@code double} value. + * If the argument is not negative, the argument is returned. + * If the argument is negative, the negation of the argument is returned. + * Special cases: + * <ul><li>If the argument is positive zero or negative zero, the result + * is positive zero. + * <li>If the argument is infinite, the result is positive infinity. + * <li>If the argument is NaN, the result is NaN.</ul> + * In other words, the result is the same as the value of the expression: + * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)} + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static double abs(double a) { + // Android-changed: Implementation modified to exactly match ART intrinsics behavior. + // Note, as a "quality of implementation", rather than pure "spec compliance", + // we require that Math.abs() clears the sign bit (but changes nothing else) + // for all numbers, including NaN (signaling NaN may become quiet though). + // http://b/30758343 + return Double.longBitsToDouble(0x7fffffffffffffffL & Double.doubleToRawLongBits(a)); + } + + /** + * Returns the greater of two {@code int} values. That is, the + * result is the argument closer to the value of + * {@link Integer#MAX_VALUE}. If the arguments have the same value, + * the result is that same value. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static int max(int a, int b) { + return (a >= b) ? a : b; + } + + /** + * Returns the greater of two {@code long} values. That is, the + * result is the argument closer to the value of + * {@link Long#MAX_VALUE}. If the arguments have the same value, + * the result is that same value. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static long max(long a, long b) { + return (a >= b) ? a : b; + } + + // Use raw bit-wise conversions on guaranteed non-NaN arguments. + private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f); + private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d); + + /** + * Returns the greater of two {@code float} values. That is, + * the result is the argument closer to positive infinity. If the + * arguments have the same value, the result is that same + * value. If either value is NaN, then the result is NaN. Unlike + * the numerical comparison operators, this method considers + * negative zero to be strictly smaller than positive zero. If one + * argument is positive zero and the other negative zero, the + * result is positive zero. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static float max(float a, float b) { + if (a != a) + return a; // a is NaN + if ((a == 0.0f) && + (b == 0.0f) && + (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) { + // Raw conversion ok since NaN can't map to -0.0. + return b; + } + return (a >= b) ? a : b; + } + + /** + * Returns the greater of two {@code double} values. That + * is, the result is the argument closer to positive infinity. If + * the arguments have the same value, the result is that same + * value. If either value is NaN, then the result is NaN. Unlike + * the numerical comparison operators, this method considers + * negative zero to be strictly smaller than positive zero. If one + * argument is positive zero and the other negative zero, the + * result is positive zero. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static double max(double a, double b) { + if (a != a) + return a; // a is NaN + if ((a == 0.0d) && + (b == 0.0d) && + (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) { + // Raw conversion ok since NaN can't map to -0.0. + return b; + } + return (a >= b) ? a : b; + } + + /** + * Returns the smaller of two {@code int} values. That is, + * the result the argument closer to the value of + * {@link Integer#MIN_VALUE}. If the arguments have the same + * value, the result is that same value. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b}. + */ + public static int min(int a, int b) { + return (a <= b) ? a : b; + } + + /** + * Returns the smaller of two {@code long} values. That is, + * the result is the argument closer to the value of + * {@link Long#MIN_VALUE}. If the arguments have the same + * value, the result is that same value. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b}. + */ + public static long min(long a, long b) { + return (a <= b) ? a : b; + } + + /** + * Returns the smaller of two {@code float} values. That is, + * the result is the value closer to negative infinity. If the + * arguments have the same value, the result is that same + * value. If either value is NaN, then the result is NaN. Unlike + * the numerical comparison operators, this method considers + * negative zero to be strictly smaller than positive zero. If + * one argument is positive zero and the other is negative zero, + * the result is negative zero. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b}. + */ + public static float min(float a, float b) { + if (a != a) + return a; // a is NaN + if ((a == 0.0f) && + (b == 0.0f) && + (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) { + // Raw conversion ok since NaN can't map to -0.0. + return b; + } + return (a <= b) ? a : b; + } + + /** + * Returns the smaller of two {@code double} values. That + * is, the result is the value closer to negative infinity. If the + * arguments have the same value, the result is that same + * value. If either value is NaN, then the result is NaN. Unlike + * the numerical comparison operators, this method considers + * negative zero to be strictly smaller than positive zero. If one + * argument is positive zero and the other is negative zero, the + * result is negative zero. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b}. + */ + public static double min(double a, double b) { + if (a != a) + return a; // a is NaN + if ((a == 0.0d) && + (b == 0.0d) && + (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) { + // Raw conversion ok since NaN can't map to -0.0. + return b; + } + return (a <= b) ? a : b; + } + + /** + * Returns the size of an ulp of the argument. An ulp, unit in + * the last place, of a {@code double} value is the positive + * distance between this floating-point value and the {@code + * double} value next larger in magnitude. Note that for non-NaN + * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, then the result is NaN. + * <li> If the argument is positive or negative infinity, then the + * result is positive infinity. + * <li> If the argument is positive or negative zero, then the result is + * {@code Double.MIN_VALUE}. + * <li> If the argument is ±{@code Double.MAX_VALUE}, then + * the result is equal to 2<sup>971</sup>. + * </ul> + * + * @param d the floating-point value whose ulp is to be returned + * @return the size of an ulp of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + public static double ulp(double d) { + int exp = getExponent(d); + + switch(exp) { + case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity + return Math.abs(d); + + case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal + return Double.MIN_VALUE; + + default: + assert exp <= DoubleConsts.MAX_EXPONENT && exp >= DoubleConsts.MIN_EXPONENT; + + // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x)) + exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1); + if (exp >= DoubleConsts.MIN_EXPONENT) { + return powerOfTwoD(exp); + } + else { + // return a subnormal result; left shift integer + // representation of Double.MIN_VALUE appropriate + // number of positions + return Double.longBitsToDouble(1L << + (exp - (DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) )); + } + } + } + + /** + * Returns the size of an ulp of the argument. An ulp, unit in + * the last place, of a {@code float} value is the positive + * distance between this floating-point value and the {@code + * float} value next larger in magnitude. Note that for non-NaN + * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, then the result is NaN. + * <li> If the argument is positive or negative infinity, then the + * result is positive infinity. + * <li> If the argument is positive or negative zero, then the result is + * {@code Float.MIN_VALUE}. + * <li> If the argument is ±{@code Float.MAX_VALUE}, then + * the result is equal to 2<sup>104</sup>. + * </ul> + * + * @param f the floating-point value whose ulp is to be returned + * @return the size of an ulp of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + public static float ulp(float f) { + int exp = getExponent(f); + + switch(exp) { + case FloatConsts.MAX_EXPONENT+1: // NaN or infinity + return Math.abs(f); + + case FloatConsts.MIN_EXPONENT-1: // zero or subnormal + return FloatConsts.MIN_VALUE; + + default: + assert exp <= FloatConsts.MAX_EXPONENT && exp >= FloatConsts.MIN_EXPONENT; + + // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x)) + exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1); + if (exp >= FloatConsts.MIN_EXPONENT) { + return powerOfTwoF(exp); + } + else { + // return a subnormal result; left shift integer + // representation of FloatConsts.MIN_VALUE appropriate + // number of positions + return Float.intBitsToFloat(1 << + (exp - (FloatConsts.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) )); + } + } + } + + /** + * Returns the signum function of the argument; zero if the argument + * is zero, 1.0 if the argument is greater than zero, -1.0 if the + * argument is less than zero. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, then the result is NaN. + * <li> If the argument is positive zero or negative zero, then the + * result is the same as the argument. + * </ul> + * + * @param d the floating-point value whose signum is to be returned + * @return the signum function of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + public static double signum(double d) { + return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, d); + } + + /** + * Returns the signum function of the argument; zero if the argument + * is zero, 1.0f if the argument is greater than zero, -1.0f if the + * argument is less than zero. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, then the result is NaN. + * <li> If the argument is positive zero or negative zero, then the + * result is the same as the argument. + * </ul> + * + * @param f the floating-point value whose signum is to be returned + * @return the signum function of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + public static float signum(float f) { + return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f); + } + + /** + * Returns the hyperbolic sine of a {@code double} value. + * The hyperbolic sine of <i>x</i> is defined to be + * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2 + * where <i>e</i> is {@linkplain Math#E Euler's number}. + * + * <p>Special cases: + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is infinite, then the result is an infinity + * with the same sign as the argument. + * + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument. + * + * </ul> + * + * <p>The computed result must be within 2.5 ulps of the exact result. + * + * @param x The number whose hyperbolic sine is to be returned. + * @return The hyperbolic sine of {@code x}. + * @since 1.5 + */ + @CriticalNative + public static native double sinh(double x); + + /** + * Returns the hyperbolic cosine of a {@code double} value. + * The hyperbolic cosine of <i>x</i> is defined to be + * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2 + * where <i>e</i> is {@linkplain Math#E Euler's number}. + * + * <p>Special cases: + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is infinite, then the result is positive + * infinity. + * + * <li>If the argument is zero, then the result is {@code 1.0}. + * + * </ul> + * + * <p>The computed result must be within 2.5 ulps of the exact result. + * + * @param x The number whose hyperbolic cosine is to be returned. + * @return The hyperbolic cosine of {@code x}. + * @since 1.5 + */ + @CriticalNative + public static native double cosh(double x); + + /** + * Returns the hyperbolic tangent of a {@code double} value. + * The hyperbolic tangent of <i>x</i> is defined to be + * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>), + * in other words, {@linkplain Math#sinh + * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note + * that the absolute value of the exact tanh is always less than + * 1. + * + * <p>Special cases: + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument. + * + * <li>If the argument is positive infinity, then the result is + * {@code +1.0}. + * + * <li>If the argument is negative infinity, then the result is + * {@code -1.0}. + * + * </ul> + * + * <p>The computed result must be within 2.5 ulps of the exact result. + * The result of {@code tanh} for any finite input must have + * an absolute value less than or equal to 1. Note that once the + * exact result of tanh is within 1/2 of an ulp of the limit value + * of ±1, correctly signed ±{@code 1.0} should + * be returned. + * + * @param x The number whose hyperbolic tangent is to be returned. + * @return The hyperbolic tangent of {@code x}. + * @since 1.5 + */ + @CriticalNative + public static native double tanh(double x); + + /** + * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) + * without intermediate overflow or underflow. + * + * <p>Special cases: + * <ul> + * + * <li> If either argument is infinite, then the result + * is positive infinity. + * + * <li> If either argument is NaN and neither argument is infinite, + * then the result is NaN. + * + * </ul> + * + * <p>The computed result must be within 1 ulp of the exact + * result. If one parameter is held constant, the results must be + * semi-monotonic in the other parameter. + * + * @param x a value + * @param y a value + * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) + * without intermediate overflow or underflow + * @since 1.5 + */ + @CriticalNative + public static native double hypot(double x, double y); + + /** + * Returns <i>e</i><sup>x</sup> -1. Note that for values of + * <i>x</i> near 0, the exact sum of + * {@code expm1(x)} + 1 is much closer to the true + * result of <i>e</i><sup>x</sup> than {@code exp(x)}. + * + * <p>Special cases: + * <ul> + * <li>If the argument is NaN, the result is NaN. + * + * <li>If the argument is positive infinity, then the result is + * positive infinity. + * + * <li>If the argument is negative infinity, then the result is + * -1.0. + * + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument. + * + * </ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. The result of + * {@code expm1} for any finite input must be greater than or + * equal to {@code -1.0}. Note that once the exact result of + * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2 + * ulp of the limit value -1, {@code -1.0} should be + * returned. + * + * @param x the exponent to raise <i>e</i> to in the computation of + * <i>e</i><sup>{@code x}</sup> -1. + * @return the value <i>e</i><sup>{@code x}</sup> - 1. + * @since 1.5 + */ + @CriticalNative + public static native double expm1(double x); + + /** + * Returns the natural logarithm of the sum of the argument and 1. + * Note that for small values {@code x}, the result of + * {@code log1p(x)} is much closer to the true result of ln(1 + * + {@code x}) than the floating-point evaluation of + * {@code log(1.0+x)}. + * + * <p>Special cases: + * + * <ul> + * + * <li>If the argument is NaN or less than -1, then the result is + * NaN. + * + * <li>If the argument is positive infinity, then the result is + * positive infinity. + * + * <li>If the argument is negative one, then the result is + * negative infinity. + * + * <li>If the argument is zero, then the result is a zero with the + * same sign as the argument. + * + * </ul> + * + * <p>The computed result must be within 1 ulp of the exact result. + * Results must be semi-monotonic. + * + * @param x a value + * @return the value ln({@code x} + 1), the natural + * log of {@code x} + 1 + * @since 1.5 + */ + @CriticalNative + public static native double log1p(double x); + + /** + * Returns the first floating-point argument with the sign of the + * second floating-point argument. Note that unlike the {@link + * StrictMath#copySign(double, double) StrictMath.copySign} + * method, this method does not require NaN {@code sign} + * arguments to be treated as positive values; implementations are + * permitted to treat some NaN arguments as positive and other NaN + * arguments as negative to allow greater performance. + * + * @param magnitude the parameter providing the magnitude of the result + * @param sign the parameter providing the sign of the result + * @return a value with the magnitude of {@code magnitude} + * and the sign of {@code sign}. + * @since 1.6 + */ + public static double copySign(double magnitude, double sign) { + return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) & + (DoubleConsts.SIGN_BIT_MASK)) | + (Double.doubleToRawLongBits(magnitude) & + (DoubleConsts.EXP_BIT_MASK | + DoubleConsts.SIGNIF_BIT_MASK))); + } + + /** + * Returns the first floating-point argument with the sign of the + * second floating-point argument. Note that unlike the {@link + * StrictMath#copySign(float, float) StrictMath.copySign} + * method, this method does not require NaN {@code sign} + * arguments to be treated as positive values; implementations are + * permitted to treat some NaN arguments as positive and other NaN + * arguments as negative to allow greater performance. + * + * @param magnitude the parameter providing the magnitude of the result + * @param sign the parameter providing the sign of the result + * @return a value with the magnitude of {@code magnitude} + * and the sign of {@code sign}. + * @since 1.6 + */ + public static float copySign(float magnitude, float sign) { + return Float.intBitsToFloat((Float.floatToRawIntBits(sign) & + (FloatConsts.SIGN_BIT_MASK)) | + (Float.floatToRawIntBits(magnitude) & + (FloatConsts.EXP_BIT_MASK | + FloatConsts.SIGNIF_BIT_MASK))); + } + + /** + * Returns the unbiased exponent used in the representation of a + * {@code float}. Special cases: + * + * <ul> + * <li>If the argument is NaN or infinite, then the result is + * {@link Float#MAX_EXPONENT} + 1. + * <li>If the argument is zero or subnormal, then the result is + * {@link Float#MIN_EXPONENT} -1. + * </ul> + * @param f a {@code float} value + * @return the unbiased exponent of the argument + * @since 1.6 + */ + public static int getExponent(float f) { + /* + * Bitwise convert f to integer, mask out exponent bits, shift + * to the right and then subtract out float's bias adjust to + * get true exponent value + */ + return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >> + (FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS; + } + + /** + * Returns the unbiased exponent used in the representation of a + * {@code double}. Special cases: + * + * <ul> + * <li>If the argument is NaN or infinite, then the result is + * {@link Double#MAX_EXPONENT} + 1. + * <li>If the argument is zero or subnormal, then the result is + * {@link Double#MIN_EXPONENT} -1. + * </ul> + * @param d a {@code double} value + * @return the unbiased exponent of the argument + * @since 1.6 + */ + public static int getExponent(double d) { + /* + * Bitwise convert d to long, mask out exponent bits, shift + * to the right and then subtract out double's bias adjust to + * get true exponent value. + */ + return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >> + (DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS); + } + + /** + * Returns the floating-point number adjacent to the first + * argument in the direction of the second argument. If both + * arguments compare as equal the second argument is returned. + * + * <p> + * Special cases: + * <ul> + * <li> If either argument is a NaN, then NaN is returned. + * + * <li> If both arguments are signed zeros, {@code direction} + * is returned unchanged (as implied by the requirement of + * returning the second argument if the arguments compare as + * equal). + * + * <li> If {@code start} is + * ±{@link Double#MIN_VALUE} and {@code direction} + * has a value such that the result should have a smaller + * magnitude, then a zero with the same sign as {@code start} + * is returned. + * + * <li> If {@code start} is infinite and + * {@code direction} has a value such that the result should + * have a smaller magnitude, {@link Double#MAX_VALUE} with the + * same sign as {@code start} is returned. + * + * <li> If {@code start} is equal to ± + * {@link Double#MAX_VALUE} and {@code direction} has a + * value such that the result should have a larger magnitude, an + * infinity with same sign as {@code start} is returned. + * </ul> + * + * @param start starting floating-point value + * @param direction value indicating which of + * {@code start}'s neighbors or {@code start} should + * be returned + * @return The floating-point number adjacent to {@code start} in the + * direction of {@code direction}. + * @since 1.6 + */ + public static double nextAfter(double start, double direction) { + /* + * The cases: + * + * nextAfter(+infinity, 0) == MAX_VALUE + * nextAfter(+infinity, +infinity) == +infinity + * nextAfter(-infinity, 0) == -MAX_VALUE + * nextAfter(-infinity, -infinity) == -infinity + * + * are naturally handled without any additional testing + */ + + // First check for NaN values + if (Double.isNaN(start) || Double.isNaN(direction)) { + // return a NaN derived from the input NaN(s) + return start + direction; + } else if (start == direction) { + return direction; + } else { // start > direction or start < direction + // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0) + // then bitwise convert start to integer. + long transducer = Double.doubleToRawLongBits(start + 0.0d); + + /* + * IEEE 754 floating-point numbers are lexicographically + * ordered if treated as signed- magnitude integers . + * Since Java's integers are two's complement, + * incrementing" the two's complement representation of a + * logically negative floating-point value *decrements* + * the signed-magnitude representation. Therefore, when + * the integer representation of a floating-point values + * is less than zero, the adjustment to the representation + * is in the opposite direction than would be expected at + * first . + */ + if (direction > start) { // Calculate next greater value + transducer = transducer + (transducer >= 0L ? 1L:-1L); + } else { // Calculate next lesser value + assert direction < start; + if (transducer > 0L) + --transducer; + else + if (transducer < 0L ) + ++transducer; + /* + * transducer==0, the result is -MIN_VALUE + * + * The transition from zero (implicitly + * positive) to the smallest negative + * signed magnitude value must be done + * explicitly. + */ + else + transducer = DoubleConsts.SIGN_BIT_MASK | 1L; + } + + return Double.longBitsToDouble(transducer); + } + } + + /** + * Returns the floating-point number adjacent to the first + * argument in the direction of the second argument. If both + * arguments compare as equal a value equivalent to the second argument + * is returned. + * + * <p> + * Special cases: + * <ul> + * <li> If either argument is a NaN, then NaN is returned. + * + * <li> If both arguments are signed zeros, a value equivalent + * to {@code direction} is returned. + * + * <li> If {@code start} is + * ±{@link Float#MIN_VALUE} and {@code direction} + * has a value such that the result should have a smaller + * magnitude, then a zero with the same sign as {@code start} + * is returned. + * + * <li> If {@code start} is infinite and + * {@code direction} has a value such that the result should + * have a smaller magnitude, {@link Float#MAX_VALUE} with the + * same sign as {@code start} is returned. + * + * <li> If {@code start} is equal to ± + * {@link Float#MAX_VALUE} and {@code direction} has a + * value such that the result should have a larger magnitude, an + * infinity with same sign as {@code start} is returned. + * </ul> + * + * @param start starting floating-point value + * @param direction value indicating which of + * {@code start}'s neighbors or {@code start} should + * be returned + * @return The floating-point number adjacent to {@code start} in the + * direction of {@code direction}. + * @since 1.6 + */ + public static float nextAfter(float start, double direction) { + /* + * The cases: + * + * nextAfter(+infinity, 0) == MAX_VALUE + * nextAfter(+infinity, +infinity) == +infinity + * nextAfter(-infinity, 0) == -MAX_VALUE + * nextAfter(-infinity, -infinity) == -infinity + * + * are naturally handled without any additional testing + */ + + // First check for NaN values + if (Float.isNaN(start) || Double.isNaN(direction)) { + // return a NaN derived from the input NaN(s) + return start + (float)direction; + } else if (start == direction) { + return (float)direction; + } else { // start > direction or start < direction + // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0) + // then bitwise convert start to integer. + int transducer = Float.floatToRawIntBits(start + 0.0f); + + /* + * IEEE 754 floating-point numbers are lexicographically + * ordered if treated as signed- magnitude integers . + * Since Java's integers are two's complement, + * incrementing" the two's complement representation of a + * logically negative floating-point value *decrements* + * the signed-magnitude representation. Therefore, when + * the integer representation of a floating-point values + * is less than zero, the adjustment to the representation + * is in the opposite direction than would be expected at + * first. + */ + if (direction > start) {// Calculate next greater value + transducer = transducer + (transducer >= 0 ? 1:-1); + } else { // Calculate next lesser value + assert direction < start; + if (transducer > 0) + --transducer; + else + if (transducer < 0 ) + ++transducer; + /* + * transducer==0, the result is -MIN_VALUE + * + * The transition from zero (implicitly + * positive) to the smallest negative + * signed magnitude value must be done + * explicitly. + */ + else + transducer = FloatConsts.SIGN_BIT_MASK | 1; + } + + return Float.intBitsToFloat(transducer); + } + } + + /** + * Returns the floating-point value adjacent to {@code d} in + * the direction of positive infinity. This method is + * semantically equivalent to {@code nextAfter(d, + * Double.POSITIVE_INFINITY)}; however, a {@code nextUp} + * implementation may run faster than its equivalent + * {@code nextAfter} call. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, the result is NaN. + * + * <li> If the argument is positive infinity, the result is + * positive infinity. + * + * <li> If the argument is zero, the result is + * {@link Double#MIN_VALUE} + * + * </ul> + * + * @param d starting floating-point value + * @return The adjacent floating-point value closer to positive + * infinity. + * @since 1.6 + */ + public static double nextUp(double d) { + if( Double.isNaN(d) || d == Double.POSITIVE_INFINITY) + return d; + else { + d += 0.0d; + return Double.longBitsToDouble(Double.doubleToRawLongBits(d) + + ((d >= 0.0d)?+1L:-1L)); + } + } + + /** + * Returns the floating-point value adjacent to {@code f} in + * the direction of positive infinity. This method is + * semantically equivalent to {@code nextAfter(f, + * Float.POSITIVE_INFINITY)}; however, a {@code nextUp} + * implementation may run faster than its equivalent + * {@code nextAfter} call. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, the result is NaN. + * + * <li> If the argument is positive infinity, the result is + * positive infinity. + * + * <li> If the argument is zero, the result is + * {@link Float#MIN_VALUE} + * + * </ul> + * + * @param f starting floating-point value + * @return The adjacent floating-point value closer to positive + * infinity. + * @since 1.6 + */ + public static float nextUp(float f) { + if( Float.isNaN(f) || f == FloatConsts.POSITIVE_INFINITY) + return f; + else { + f += 0.0f; + return Float.intBitsToFloat(Float.floatToRawIntBits(f) + + ((f >= 0.0f)?+1:-1)); + } + } + + /** + * Returns the floating-point value adjacent to {@code d} in + * the direction of negative infinity. This method is + * semantically equivalent to {@code nextAfter(d, + * Double.NEGATIVE_INFINITY)}; however, a + * {@code nextDown} implementation may run faster than its + * equivalent {@code nextAfter} call. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, the result is NaN. + * + * <li> If the argument is negative infinity, the result is + * negative infinity. + * + * <li> If the argument is zero, the result is + * {@code -Double.MIN_VALUE} + * + * </ul> + * + * @param d starting floating-point value + * @return The adjacent floating-point value closer to negative + * infinity. + * @since 1.8 + */ + public static double nextDown(double d) { + if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY) + return d; + else { + if (d == 0.0) + return -Double.MIN_VALUE; + else + return Double.longBitsToDouble(Double.doubleToRawLongBits(d) + + ((d > 0.0d)?-1L:+1L)); + } + } + + /** + * Returns the floating-point value adjacent to {@code f} in + * the direction of negative infinity. This method is + * semantically equivalent to {@code nextAfter(f, + * Float.NEGATIVE_INFINITY)}; however, a + * {@code nextDown} implementation may run faster than its + * equivalent {@code nextAfter} call. + * + * <p>Special Cases: + * <ul> + * <li> If the argument is NaN, the result is NaN. + * + * <li> If the argument is negative infinity, the result is + * negative infinity. + * + * <li> If the argument is zero, the result is + * {@code -Float.MIN_VALUE} + * + * </ul> + * + * @param f starting floating-point value + * @return The adjacent floating-point value closer to negative + * infinity. + * @since 1.8 + */ + public static float nextDown(float f) { + if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY) + return f; + else { + if (f == 0.0f) + return -Float.MIN_VALUE; + else + return Float.intBitsToFloat(Float.floatToRawIntBits(f) + + ((f > 0.0f)?-1:+1)); + } + } + + /** + * Returns {@code d} × + * 2<sup>{@code scaleFactor}</sup> rounded as if performed + * by a single correctly rounded floating-point multiply to a + * member of the double value set. See the Java + * Language Specification for a discussion of floating-point + * value sets. If the exponent of the result is between {@link + * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the + * answer is calculated exactly. If the exponent of the result + * would be larger than {@code Double.MAX_EXPONENT}, an + * infinity is returned. Note that if the result is subnormal, + * precision may be lost; that is, when {@code scalb(x, n)} + * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal + * <i>x</i>. When the result is non-NaN, the result has the same + * sign as {@code d}. + * + * <p>Special cases: + * <ul> + * <li> If the first argument is NaN, NaN is returned. + * <li> If the first argument is infinite, then an infinity of the + * same sign is returned. + * <li> If the first argument is zero, then a zero of the same + * sign is returned. + * </ul> + * + * @param d number to be scaled by a power of two. + * @param scaleFactor power of 2 used to scale {@code d} + * @return {@code d} × 2<sup>{@code scaleFactor}</sup> + * @since 1.6 + */ + public static double scalb(double d, int scaleFactor) { + /* + * This method does not need to be declared strictfp to + * compute the same correct result on all platforms. When + * scaling up, it does not matter what order the + * multiply-store operations are done; the result will be + * finite or overflow regardless of the operation ordering. + * However, to get the correct result when scaling down, a + * particular ordering must be used. + * + * When scaling down, the multiply-store operations are + * sequenced so that it is not possible for two consecutive + * multiply-stores to return subnormal results. If one + * multiply-store result is subnormal, the next multiply will + * round it away to zero. This is done by first multiplying + * by 2 ^ (scaleFactor % n) and then multiplying several + * times by by 2^n as needed where n is the exponent of number + * that is a covenient power of two. In this way, at most one + * real rounding error occurs. If the double value set is + * being used exclusively, the rounding will occur on a + * multiply. If the double-extended-exponent value set is + * being used, the products will (perhaps) be exact but the + * stores to d are guaranteed to round to the double value + * set. + * + * It is _not_ a valid implementation to first multiply d by + * 2^MIN_EXPONENT and then by 2 ^ (scaleFactor % + * MIN_EXPONENT) since even in a strictfp program double + * rounding on underflow could occur; e.g. if the scaleFactor + * argument was (MIN_EXPONENT - n) and the exponent of d was a + * little less than -(MIN_EXPONENT - n), meaning the final + * result would be subnormal. + * + * Since exact reproducibility of this method can be achieved + * without any undue performance burden, there is no + * compelling reason to allow double rounding on underflow in + * scalb. + */ + + // magnitude of a power of two so large that scaling a finite + // nonzero value by it would be guaranteed to over or + // underflow; due to rounding, scaling down takes takes an + // additional power of two which is reflected here + final int MAX_SCALE = DoubleConsts.MAX_EXPONENT + -DoubleConsts.MIN_EXPONENT + + DoubleConsts.SIGNIFICAND_WIDTH + 1; + int exp_adjust = 0; + int scale_increment = 0; + double exp_delta = Double.NaN; + + // Make sure scaling factor is in a reasonable range + + if(scaleFactor < 0) { + scaleFactor = Math.max(scaleFactor, -MAX_SCALE); + scale_increment = -512; + exp_delta = twoToTheDoubleScaleDown; + } + else { + scaleFactor = Math.min(scaleFactor, MAX_SCALE); + scale_increment = 512; + exp_delta = twoToTheDoubleScaleUp; + } + + // Calculate (scaleFactor % +/-512), 512 = 2^9, using + // technique from "Hacker's Delight" section 10-2. + int t = (scaleFactor >> 9-1) >>> 32 - 9; + exp_adjust = ((scaleFactor + t) & (512 -1)) - t; + + d *= powerOfTwoD(exp_adjust); + scaleFactor -= exp_adjust; + + while(scaleFactor != 0) { + d *= exp_delta; + scaleFactor -= scale_increment; + } + return d; + } + + /** + * Returns {@code f} × + * 2<sup>{@code scaleFactor}</sup> rounded as if performed + * by a single correctly rounded floating-point multiply to a + * member of the float value set. See the Java + * Language Specification for a discussion of floating-point + * value sets. If the exponent of the result is between {@link + * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the + * answer is calculated exactly. If the exponent of the result + * would be larger than {@code Float.MAX_EXPONENT}, an + * infinity is returned. Note that if the result is subnormal, + * precision may be lost; that is, when {@code scalb(x, n)} + * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal + * <i>x</i>. When the result is non-NaN, the result has the same + * sign as {@code f}. + * + * <p>Special cases: + * <ul> + * <li> If the first argument is NaN, NaN is returned. + * <li> If the first argument is infinite, then an infinity of the + * same sign is returned. + * <li> If the first argument is zero, then a zero of the same + * sign is returned. + * </ul> + * + * @param f number to be scaled by a power of two. + * @param scaleFactor power of 2 used to scale {@code f} + * @return {@code f} × 2<sup>{@code scaleFactor}</sup> + * @since 1.6 + */ + public static float scalb(float f, int scaleFactor) { + // magnitude of a power of two so large that scaling a finite + // nonzero value by it would be guaranteed to over or + // underflow; due to rounding, scaling down takes takes an + // additional power of two which is reflected here + final int MAX_SCALE = FloatConsts.MAX_EXPONENT + -FloatConsts.MIN_EXPONENT + + FloatConsts.SIGNIFICAND_WIDTH + 1; + + // Make sure scaling factor is in a reasonable range + scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE); + + /* + * Since + MAX_SCALE for float fits well within the double + * exponent range and + float -> double conversion is exact + * the multiplication below will be exact. Therefore, the + * rounding that occurs when the double product is cast to + * float will be the correctly rounded float result. Since + * all operations other than the final multiply will be exact, + * it is not necessary to declare this method strictfp. + */ + return (float)((double)f*powerOfTwoD(scaleFactor)); + } + + // Constants used in scalb + static double twoToTheDoubleScaleUp = powerOfTwoD(512); + static double twoToTheDoubleScaleDown = powerOfTwoD(-512); + + /** + * Returns a floating-point power of two in the normal range. + */ + static double powerOfTwoD(int n) { + assert(n >= DoubleConsts.MIN_EXPONENT && n <= DoubleConsts.MAX_EXPONENT); + return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) << + (DoubleConsts.SIGNIFICAND_WIDTH-1)) + & DoubleConsts.EXP_BIT_MASK); + } + + /** + * Returns a floating-point power of two in the normal range. + */ + static float powerOfTwoF(int n) { + assert(n >= FloatConsts.MIN_EXPONENT && n <= FloatConsts.MAX_EXPONENT); + return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) << + (FloatConsts.SIGNIFICAND_WIDTH-1)) + & FloatConsts.EXP_BIT_MASK); + } +}