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/*
 *  Licensed to the Apache Software Foundation (ASF) under one or more
 *  contributor license agreements.  See the NOTICE file distributed with
 *  this work for additional information regarding copyright ownership.
 *  The ASF licenses this file to You under the Apache License, Version 2.0
 *  (the "License"); you may not use this file except in compliance with
 *  the License.  You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

package java.lang;

/**
 * Class StrictMath provides basic math constants and operations such as
 * trigonometric functions, hyperbolic functions, exponential, logarithms, etc.
 * 

* In contrast to class {@link Math}, the methods in this class return exactly * the same results on all platforms. Algorithms based on these methods thus * behave the same (e.g. regarding numerical convergence) on all platforms, * complying with the slogan "write once, run everywhere". On the other side, * the implementation of class StrictMath may be less efficient than that of * class Math, as class StrictMath cannot utilize platform specific features * such as an extended precision math co-processors. *

* The methods in this class are specified using the "Freely Distributable Math * Library" (fdlibm), version 5.3. *

* http://www.netlib.org/fdlibm/ */ public final class StrictMath { /** * The double value closest to e, the base of the natural logarithm. */ public static final double E = Math.E; /** * The double value closest to pi, the ratio of a circle's circumference to * its diameter. */ public static final double PI = Math.PI; /** * Prevents this class from being instantiated. */ private StrictMath() { } /** * Returns the absolute value of the argument. *

* Special cases: *

    *
  • {@code abs(-0.0) = +0.0}
  • *
  • {@code abs(+infinity) = +infinity}
  • *
  • {@code abs(-infinity) = +infinity}
  • *
  • {@code abs(NaN) = NaN}
  • *
*/ public static double abs(double d) { return Math.abs(d); } /** * Returns the absolute value of the argument. *

* Special cases: *

    *
  • {@code abs(-0.0) = +0.0}
  • *
  • {@code abs(+infinity) = +infinity}
  • *
  • {@code abs(-infinity) = +infinity}
  • *
  • {@code abs(NaN) = NaN}
  • *
*/ public static float abs(float f) { return Math.abs(f); } /** * Returns the absolute value of the argument. *

* If the argument is {@code Integer.MIN_VALUE}, {@code Integer.MIN_VALUE} * is returned. */ public static int abs(int i) { return Math.abs(i); } /** * Returns the absolute value of the argument. *

* If the argument is {@code Long.MIN_VALUE}, {@code Long.MIN_VALUE} is * returned. */ public static long abs(long l) { return Math.abs(l); } /** * Returns the closest double approximation of the arc cosine of the * argument within the range {@code [0..pi]}. *

* Special cases: *

    *
  • {@code acos((anything > 1) = NaN}
  • *
  • {@code acos((anything < -1) = NaN}
  • *
  • {@code acos(NaN) = NaN}
  • *
* * @param d * the value to compute arc cosine of. * @return the arc cosine of the argument. */ public static native double acos(double d); /** * Returns the closest double approximation of the arc sine of the argument * within the range {@code [-pi/2..pi/2]}. *

* Special cases: *

    *
  • {@code asin((anything > 1)) = NaN}
  • *
  • {@code asin((anything < -1)) = NaN}
  • *
  • {@code asin(NaN) = NaN}
  • *
* * @param d * the value whose arc sine has to be computed. * @return the arc sine of the argument. */ public static native double asin(double d); /** * Returns the closest double approximation of the arc tangent of the * argument within the range {@code [-pi/2..pi/2]}. *

* Special cases: *

    *
  • {@code atan(+0.0) = +0.0}
  • *
  • {@code atan(-0.0) = -0.0}
  • *
  • {@code atan(+infinity) = +pi/2}
  • *
  • {@code atan(-infinity) = -pi/2}
  • *
  • {@code atan(NaN) = NaN}
  • *
* * @param d * the value whose arc tangent has to be computed. * @return the arc tangent of the argument. */ public static native double atan(double d); /** * Returns the closest double approximation of the arc tangent of * {@code y/x} within the range {@code [-pi..pi]}. This is the angle of the * polar representation of the rectangular coordinates (x,y). *

* Special cases: *

    *
  • {@code atan2((anything), NaN ) = NaN;}
  • *
  • {@code atan2(NaN , (anything) ) = NaN;}
  • *
  • {@code atan2(+0.0, +(anything but NaN)) = +0.0}
  • *
  • {@code atan2(-0.0, +(anything but NaN)) = -0.0}
  • *
  • {@code atan2(+0.0, -(anything but NaN)) = +pi}
  • *
  • {@code atan2(-0.0, -(anything but NaN)) = -pi}
  • *
  • {@code atan2(+(anything but 0 and NaN), 0) = +pi/2}
  • *
  • {@code atan2(-(anything but 0 and NaN), 0) = -pi/2}
  • *
  • {@code atan2(+(anything but infinity and NaN), +infinity)} {@code =} * {@code +0.0}
  • *
  • {@code atan2(-(anything but infinity and NaN), +infinity)} {@code =} * {@code -0.0}
  • *
  • {@code atan2(+(anything but infinity and NaN), -infinity) = +pi}
  • *
  • {@code atan2(-(anything but infinity and NaN), -infinity) = -pi}
  • *
  • {@code atan2(+infinity, +infinity ) = +pi/4}
  • *
  • {@code atan2(-infinity, +infinity ) = -pi/4}
  • *
  • {@code atan2(+infinity, -infinity ) = +3pi/4}
  • *
  • {@code atan2(-infinity, -infinity ) = -3pi/4}
  • *
  • {@code atan2(+infinity, (anything but,0, NaN, and infinity))} * {@code =} {@code +pi/2}
  • *
  • {@code atan2(-infinity, (anything but,0, NaN, and infinity))} * {@code =} {@code -pi/2}
  • *
* * @param y * the numerator of the value whose atan has to be computed. * @param x * the denominator of the value whose atan has to be computed. * @return the arc tangent of {@code y/x}. */ public static native double atan2(double y, double x); /** * Returns the closest double approximation of the cube root of the * argument. *

* Special cases: *

    *
  • {@code cbrt(+0.0) = +0.0}
  • *
  • {@code cbrt(-0.0) = -0.0}
  • *
  • {@code cbrt(+infinity) = +infinity}
  • *
  • {@code cbrt(-infinity) = -infinity}
  • *
  • {@code cbrt(NaN) = NaN}
  • *
* * @param d * the value whose cube root has to be computed. * @return the cube root of the argument. */ public static native double cbrt(double d); /** * Returns the double conversion of the most negative (closest to negative * infinity) integer value greater than or equal to the argument. *

* Special cases: *

    *
  • {@code ceil(+0.0) = +0.0}
  • *
  • {@code ceil(-0.0) = -0.0}
  • *
  • {@code ceil((anything in range (-1,0)) = -0.0}
  • *
  • {@code ceil(+infinity) = +infinity}
  • *
  • {@code ceil(-infinity) = -infinity}
  • *
  • {@code ceil(NaN) = NaN}
  • *
*/ public static native double ceil(double d); /** * Returns the closest double approximation of the hyperbolic cosine of the * argument. *

* Special cases: *

    *
  • {@code cosh(+infinity) = +infinity}
  • *
  • {@code cosh(-infinity) = +infinity}
  • *
  • {@code cosh(NaN) = NaN}
  • *
* * @param d * the value whose hyperbolic cosine has to be computed. * @return the hyperbolic cosine of the argument. */ public static native double cosh(double d); /** * Returns the closest double approximation of the cosine of the argument. *

* Special cases: *

    *
  • {@code cos(+infinity) = NaN}
  • *
  • {@code cos(-infinity) = NaN}
  • *
  • {@code cos(NaN) = NaN}
  • *
* * @param d * the angle whose cosine has to be computed, in radians. * @return the cosine of the argument. */ public static native double cos(double d); /** * Returns the closest double approximation of the raising "e" to the power * of the argument. *

* Special cases: *

    *
  • {@code exp(+infinity) = +infinity}
  • *
  • {@code exp(-infinity) = +0.0}
  • *
  • {@code exp(NaN) = NaN}
  • *
* * @param d * the value whose exponential has to be computed. * @return the exponential of the argument. */ public static native double exp(double d); /** * Returns the closest double approximation of {@code e} * {@code d}{@code - 1}. If the argument is very close to 0, it is * much more accurate to use {@code expm1(d)+1} than {@code exp(d)} (due to * cancellation of significant digits). *

* Special cases: *

    *
  • {@code expm1(+0.0) = +0.0}
  • *
  • {@code expm1(-0.0) = -0.0}
  • *
  • {@code expm1(+infinity) = +infinity}
  • *
  • {@code expm1(-infinity) = -1.0}
  • *
  • {@code expm1(NaN) = NaN}
  • *
* * @param d * the value to compute the {@code e}{@code d} * {@code - 1} of. * @return the {@code e}{@code d}{@code - 1} value * of the argument. */ public static native double expm1(double d); /** * Returns the double conversion of the most positive (closest to * positive infinity) integer less than or equal to the argument. *

* Special cases: *

    *
  • {@code floor(+0.0) = +0.0}
  • *
  • {@code floor(-0.0) = -0.0}
  • *
  • {@code floor(+infinity) = +infinity}
  • *
  • {@code floor(-infinity) = -infinity}
  • *
  • {@code floor(NaN) = NaN}
  • *
*/ public static native double floor(double d); /** * Returns {@code sqrt(}{@code x}{@code 2}{@code +} * {@code y}{@code 2}{@code )}. The final result is * without medium underflow or overflow. *

* Special cases: *

    *
  • {@code hypot(+infinity, (anything including NaN)) = +infinity}
  • *
  • {@code hypot(-infinity, (anything including NaN)) = +infinity}
  • *
  • {@code hypot((anything including NaN), +infinity) = +infinity}
  • *
  • {@code hypot((anything including NaN), -infinity) = +infinity}
  • *
  • {@code hypot(NaN, NaN) = NaN}
  • *
* * @param x * a double number. * @param y * a double number. * @return the {@code sqrt(}{@code x}{@code 2}{@code +} * {@code y}{@code 2}{@code )} value of the * arguments. */ public static native double hypot(double x, double y); /** * Returns the remainder of dividing {@code x} by {@code y} using the IEEE * 754 rules. The result is {@code x-round(x/p)*p} where {@code round(x/p)} * is the nearest integer (rounded to even), but without numerical * cancellation problems. *

* Special cases: *

    *
  • {@code IEEEremainder((anything), 0) = NaN}
  • *
  • {@code IEEEremainder(+infinity, (anything)) = NaN}
  • *
  • {@code IEEEremainder(-infinity, (anything)) = NaN}
  • *
  • {@code IEEEremainder(NaN, (anything)) = NaN}
  • *
  • {@code IEEEremainder((anything), NaN) = NaN}
  • *
  • {@code IEEEremainder(x, +infinity) = x } where x is anything but * +/-infinity
  • *
  • {@code IEEEremainder(x, -infinity) = x } where x is anything but * +/-infinity
  • *
* * @param x * the numerator of the operation. * @param y * the denominator of the operation. * @return the IEEE754 floating point reminder of of {@code x/y}. */ public static native double IEEEremainder(double x, double y); /** * Returns the closest double approximation of the natural logarithm of the * argument. *

* Special cases: *

    *
  • {@code log(+0.0) = -infinity}
  • *
  • {@code log(-0.0) = -infinity}
  • *
  • {@code log((anything < 0) = NaN}
  • *
  • {@code log(+infinity) = +infinity}
  • *
  • {@code log(-infinity) = NaN}
  • *
  • {@code log(NaN) = NaN}
  • *
* * @param d * the value whose log has to be computed. * @return the natural logarithm of the argument. */ public static native double log(double d); /** * Returns the closest double approximation of the base 10 logarithm of the * argument. *

* Special cases: *

    *
  • {@code log10(+0.0) = -infinity}
  • *
  • {@code log10(-0.0) = -infinity}
  • *
  • {@code log10((anything < 0) = NaN}
  • *
  • {@code log10(+infinity) = +infinity}
  • *
  • {@code log10(-infinity) = NaN}
  • *
  • {@code log10(NaN) = NaN}
  • *
* * @param d * the value whose base 10 log has to be computed. * @return the natural logarithm of the argument. */ public static native double log10(double d); /** * Returns the closest double approximation of the natural logarithm of the * sum of the argument and 1. If the argument is very close to 0, it is much * more accurate to use {@code log1p(d)} than {@code log(1.0+d)} (due to * numerical cancellation). *

* Special cases: *

    *
  • {@code log1p(+0.0) = +0.0}
  • *
  • {@code log1p(-0.0) = -0.0}
  • *
  • {@code log1p((anything < 1)) = NaN}
  • *
  • {@code log1p(-1.0) = -infinity}
  • *
  • {@code log1p(+infinity) = +infinity}
  • *
  • {@code log1p(-infinity) = NaN}
  • *
  • {@code log1p(NaN) = NaN}
  • *
* * @param d * the value to compute the {@code ln(1+d)} of. * @return the natural logarithm of the sum of the argument and 1. */ public static native double log1p(double d); /** * Returns the most positive (closest to positive infinity) of the two * arguments. *

* Special cases: *

    *
  • {@code max(NaN, (anything)) = NaN}
  • *
  • {@code max((anything), NaN) = NaN}
  • *
  • {@code max(+0.0, -0.0) = +0.0}
  • *
  • {@code max(-0.0, +0.0) = +0.0}
  • *
*/ public static double max(double d1, double d2) { if (d1 > d2) return d1; if (d1 < d2) return d2; /* if either arg is NaN, return NaN */ if (d1 != d2) return Double.NaN; /* max( +0.0,-0.0) == +0.0 */ if (d1 == 0.0 && ((Double.doubleToLongBits(d1) & Double.doubleToLongBits(d2)) & 0x8000000000000000L) == 0) return 0.0; return d1; } /** * Returns the most positive (closest to positive infinity) of the two * arguments. *

* Special cases: *

    *
  • {@code max(NaN, (anything)) = NaN}
  • *
  • {@code max((anything), NaN) = NaN}
  • *
  • {@code max(+0.0, -0.0) = +0.0}
  • *
  • {@code max(-0.0, +0.0) = +0.0}
  • *
*/ public static float max(float f1, float f2) { if (f1 > f2) return f1; if (f1 < f2) return f2; /* if either arg is NaN, return NaN */ if (f1 != f2) return Float.NaN; /* max( +0.0,-0.0) == +0.0 */ if (f1 == 0.0f && ((Float.floatToIntBits(f1) & Float.floatToIntBits(f2)) & 0x80000000) == 0) return 0.0f; return f1; } /** * Returns the most positive (closest to positive infinity) of the two * arguments. */ public static int max(int i1, int i2) { return Math.max(i1, i2); } /** * Returns the most positive (closest to positive infinity) of the two * arguments. */ public static long max(long l1, long l2) { return l1 > l2 ? l1 : l2; } /** * Returns the most negative (closest to negative infinity) of the two * arguments. *

* Special cases: *

    *
  • {@code min(NaN, (anything)) = NaN}
  • *
  • {@code min((anything), NaN) = NaN}
  • *
  • {@code min(+0.0, -0.0) = -0.0}
  • *
  • {@code min(-0.0, +0.0) = -0.0}
  • *
*/ public static double min(double d1, double d2) { if (d1 > d2) return d2; if (d1 < d2) return d1; /* if either arg is NaN, return NaN */ if (d1 != d2) return Double.NaN; /* min( +0.0,-0.0) == -0.0 */ if (d1 == 0.0 && ((Double.doubleToLongBits(d1) | Double.doubleToLongBits(d2)) & 0x8000000000000000l) != 0) return 0.0 * (-1.0); return d1; } /** * Returns the most negative (closest to negative infinity) of the two * arguments. *

* Special cases: *

    *
  • {@code min(NaN, (anything)) = NaN}
  • *
  • {@code min((anything), NaN) = NaN}
  • *
  • {@code min(+0.0, -0.0) = -0.0}
  • *
  • {@code min(-0.0, +0.0) = -0.0}
  • *
*/ public static float min(float f1, float f2) { if (f1 > f2) return f2; if (f1 < f2) return f1; /* if either arg is NaN, return NaN */ if (f1 != f2) return Float.NaN; /* min( +0.0,-0.0) == -0.0 */ if (f1 == 0.0f && ((Float.floatToIntBits(f1) | Float.floatToIntBits(f2)) & 0x80000000) != 0) return 0.0f * (-1.0f); return f1; } /** * Returns the most negative (closest to negative infinity) of the two * arguments. */ public static int min(int i1, int i2) { return Math.min(i1, i2); } /** * Returns the most negative (closest to negative infinity) of the two * arguments. */ public static long min(long l1, long l2) { return l1 < l2 ? l1 : l2; } /** * Returns the closest double approximation of the result of raising * {@code x} to the power of {@code y}. *

* Special cases: *

    *
  • {@code pow((anything), +0.0) = 1.0}
  • *
  • {@code pow((anything), -0.0) = 1.0}
  • *
  • {@code pow(x, 1.0) = x}
  • *
  • {@code pow((anything), NaN) = NaN}
  • *
  • {@code pow(NaN, (anything except 0)) = NaN}
  • *
  • {@code pow(+/-(|x| > 1), +infinity) = +infinity}
  • *
  • {@code pow(+/-(|x| > 1), -infinity) = +0.0}
  • *
  • {@code pow(+/-(|x| < 1), +infinity) = +0.0}
  • *
  • {@code pow(+/-(|x| < 1), -infinity) = +infinity}
  • *
  • {@code pow(+/-1.0 , +infinity) = NaN}
  • *
  • {@code pow(+/-1.0 , -infinity) = NaN}
  • *
  • {@code pow(+0.0, (+anything except 0, NaN)) = +0.0}
  • *
  • {@code pow(-0.0, (+anything except 0, NaN, odd integer)) = +0.0}
  • *
  • {@code pow(+0.0, (-anything except 0, NaN)) = +infinity}
  • *
  • {@code pow(-0.0, (-anything except 0, NAN, odd integer))} {@code =} * {@code +infinity}
  • *
  • {@code pow(-0.0, (odd integer)) = -pow( +0 , (odd integer) )}
  • *
  • {@code pow(+infinity, (+anything except 0, NaN)) = +infinity}
  • *
  • {@code pow(+infinity, (-anything except 0, NaN)) = +0.0}
  • *
  • {@code pow(-infinity, (anything)) = -pow(0, (-anything))}
  • *
  • {@code pow((-anything), (integer))} {@code =} * {@code pow(-1,(integer))*pow(+anything,integer)}
  • *
  • {@code pow((-anything except 0 and infinity), (non-integer))} * {@code =} {@code NAN}
  • *
* * @param x * the base of the operation. * @param y * the exponent of the operation. * @return {@code x} to the power of {@code y}. */ public static native double pow(double x, double y); /** * Returns a pseudo-random number between 0.0 (inclusive) and 1.0 * (exclusive). * * @return a pseudo-random number. */ public static double random() { return Math.random(); } /** * Returns the double conversion of the result of rounding the argument to * an integer. Tie breaks are rounded towards even. *

* Special cases: *

    *
  • {@code rint(+0.0) = +0.0}
  • *
  • {@code rint(-0.0) = -0.0}
  • *
  • {@code rint(+infinity) = +infinity}
  • *
  • {@code rint(-infinity) = -infinity}
  • *
  • {@code rint(NaN) = NaN}
  • *
* * @param d * the value to be rounded. * @return the closest integer to the argument (as a double). */ public static native double rint(double d); /** * Returns the result of rounding the argument to an integer. The result is * equivalent to {@code (long) Math.floor(d+0.5)}. *

* Special cases: *

    *
  • {@code round(+0.0) = +0.0}
  • *
  • {@code round(-0.0) = +0.0}
  • *
  • {@code round((anything > Long.MAX_VALUE) = Long.MAX_VALUE}
  • *
  • {@code round((anything < Long.MIN_VALUE) = Long.MIN_VALUE}
  • *
  • {@code round(+infinity) = Long.MAX_VALUE}
  • *
  • {@code round(-infinity) = Long.MIN_VALUE}
  • *
  • {@code round(NaN) = +0.0}
  • *
* * @param d * the value to be rounded. * @return the closest integer to the argument. */ public static long round(double d) { return Math.round(d); } /** * Returns the result of rounding the argument to an integer. The result is * equivalent to {@code (int) Math.floor(f+0.5)}. *

* Special cases: *

    *
  • {@code round(+0.0) = +0.0}
  • *
  • {@code round(-0.0) = +0.0}
  • *
  • {@code round((anything > Integer.MAX_VALUE) = Integer.MAX_VALUE}
  • *
  • {@code round((anything < Integer.MIN_VALUE) = Integer.MIN_VALUE}
  • *
  • {@code round(+infinity) = Integer.MAX_VALUE}
  • *
  • {@code round(-infinity) = Integer.MIN_VALUE}
  • *
  • {@code round(NaN) = +0.0}
  • *
* * @param f * the value to be rounded. * @return the closest integer to the argument. */ public static int round(float f) { return Math.round(f); } /** * Returns the signum function of the argument. If the argument is less than * zero, it returns -1.0. If the argument is greater than zero, 1.0 is * returned. If the argument is either positive or negative zero, the * argument is returned as result. *

* Special cases: *

    *
  • {@code signum(+0.0) = +0.0}
  • *
  • {@code signum(-0.0) = -0.0}
  • *
  • {@code signum(+infinity) = +1.0}
  • *
  • {@code signum(-infinity) = -1.0}
  • *
  • {@code signum(NaN) = NaN}
  • *
* * @param d * the value whose signum has to be computed. * @return the value of the signum function. */ public static double signum(double d){ return Math.signum(d); } /** * Returns the signum function of the argument. If the argument is less than * zero, it returns -1.0. If the argument is greater than zero, 1.0 is * returned. If the argument is either positive or negative zero, the * argument is returned as result. *

* Special cases: *

    *
  • {@code signum(+0.0) = +0.0}
  • *
  • {@code signum(-0.0) = -0.0}
  • *
  • {@code signum(+infinity) = +1.0}
  • *
  • {@code signum(-infinity) = -1.0}
  • *
  • {@code signum(NaN) = NaN}
  • *
* * @param f * the value whose signum has to be computed. * @return the value of the signum function. */ public static float signum(float f){ return Math.signum(f); } /** * Returns the closest double approximation of the hyperbolic sine of the * argument. *

* Special cases: *

    *
  • {@code sinh(+0.0) = +0.0}
  • *
  • {@code sinh(-0.0) = -0.0}
  • *
  • {@code sinh(+infinity) = +infinity}
  • *
  • {@code sinh(-infinity) = -infinity}
  • *
  • {@code sinh(NaN) = NaN}
  • *
* * @param d * the value whose hyperbolic sine has to be computed. * @return the hyperbolic sine of the argument. */ public static native double sinh(double d); /** * Returns the closest double approximation of the sine of the argument. *

* Special cases: *

    *
  • {@code sin(+0.0) = +0.0}
  • *
  • {@code sin(-0.0) = -0.0}
  • *
  • {@code sin(+infinity) = NaN}
  • *
  • {@code sin(-infinity) = NaN}
  • *
  • {@code sin(NaN) = NaN}
  • *
* * @param d * the angle whose sin has to be computed, in radians. * @return the sine of the argument. */ public static native double sin(double d); /** * Returns the closest double approximation of the square root of the * argument. *

* Special cases: *

    *
  • {@code sqrt(+0.0) = +0.0}
  • *
  • {@code sqrt(-0.0) = -0.0}
  • *
  • {@code sqrt( (anything < 0) ) = NaN}
  • *
  • {@code sqrt(+infinity) = +infinity}
  • *
  • {@code sqrt(NaN) = NaN}
  • *
*/ public static native double sqrt(double d); /** * Returns the closest double approximation of the tangent of the argument. *

* Special cases: *

    *
  • {@code tan(+0.0) = +0.0}
  • *
  • {@code tan(-0.0) = -0.0}
  • *
  • {@code tan(+infinity) = NaN}
  • *
  • {@code tan(-infinity) = NaN}
  • *
  • {@code tan(NaN) = NaN}
  • *
* * @param d * the angle whose tangent has to be computed, in radians. * @return the tangent of the argument. */ public static native double tan(double d); /** * Returns the closest double approximation of the hyperbolic tangent of the * argument. The absolute value is always less than 1. *

* Special cases: *

    *
  • {@code tanh(+0.0) = +0.0}
  • *
  • {@code tanh(-0.0) = -0.0}
  • *
  • {@code tanh(+infinity) = +1.0}
  • *
  • {@code tanh(-infinity) = -1.0}
  • *
  • {@code tanh(NaN) = NaN}
  • *
* * @param d * the value whose hyperbolic tangent has to be computed. * @return the hyperbolic tangent of the argument */ public static native double tanh(double d); /** * Returns the measure in degrees of the supplied radian angle. The result * is {@code angrad * 180 / pi}. *

* Special cases: *

    *
  • {@code toDegrees(+0.0) = +0.0}
  • *
  • {@code toDegrees(-0.0) = -0.0}
  • *
  • {@code toDegrees(+infinity) = +infinity}
  • *
  • {@code toDegrees(-infinity) = -infinity}
  • *
  • {@code toDegrees(NaN) = NaN}
  • *
* * @param angrad * an angle in radians. * @return the degree measure of the angle. */ public static double toDegrees(double angrad) { return Math.toDegrees(angrad); } /** * Returns the measure in radians of the supplied degree angle. The result * is {@code angdeg / 180 * pi}. *

* Special cases: *

    *
  • {@code toRadians(+0.0) = +0.0}
  • *
  • {@code toRadians(-0.0) = -0.0}
  • *
  • {@code toRadians(+infinity) = +infinity}
  • *
  • {@code toRadians(-infinity) = -infinity}
  • *
  • {@code toRadians(NaN) = NaN}
  • *
* * @param angdeg * an angle in degrees. * @return the radian measure of the angle. */ public static double toRadians(double angdeg) { return Math.toRadians(angdeg); } /** * Returns the argument's ulp (unit in the last place). The size of a ulp of * a double value is the positive distance between this value and the double * value next larger in magnitude. For non-NaN {@code x}, * {@code ulp(-x) == ulp(x)}. *

* Special cases: *

    *
  • {@code ulp(+0.0) = Double.MIN_VALUE}
  • *
  • {@code ulp(-0.0) = Double.MIN_VALUE}
  • *
  • {@code ulp(+infinity) = infinity}
  • *
  • {@code ulp(-infinity) = infinity}
  • *
  • {@code ulp(NaN) = NaN}
  • *
* * @param d * the floating-point value to compute ulp of. * @return the size of a ulp of the argument. */ public static double ulp(double d) { // special cases if (Double.isInfinite(d)) { return Double.POSITIVE_INFINITY; } else if (d == Double.MAX_VALUE || d == -Double.MAX_VALUE) { return pow(2, 971); } d = Math.abs(d); return nextafter(d, Double.MAX_VALUE) - d; } /** * Returns the argument's ulp (unit in the last place). The size of a ulp of * a float value is the positive distance between this value and the float * value next larger in magnitude. For non-NaN {@code x}, * {@code ulp(-x) == ulp(x)}. *

* Special cases: *

    *
  • {@code ulp(+0.0) = Float.MIN_VALUE}
  • *
  • {@code ulp(-0.0) = Float.MIN_VALUE}
  • *
  • {@code ulp(+infinity) = infinity}
  • *
  • {@code ulp(-infinity) = infinity}
  • *
  • {@code ulp(NaN) = NaN}
  • *
* * @param f * the floating-point value to compute ulp of. * @return the size of a ulp of the argument. */ public static float ulp(float f) { return Math.ulp(f); } private static native double nextafter(double x, double y); /** * Returns a double with the given magnitude and the sign of {@code sign}. * If {@code sign} is NaN, the sign of the result is positive. * @since 1.6 */ public static double copySign(double magnitude, double sign) { // We manually inline Double.isNaN here because the JIT can't do it yet. // With Double.isNaN: 236.3ns // With manual inline: 141.2ns // With no check (i.e. Math's behavior): 110.0ns // (Tested on a Nexus One.) long magnitudeBits = Double.doubleToRawLongBits(magnitude); long signBits = Double.doubleToRawLongBits((sign != sign) ? 1.0 : sign); magnitudeBits = (magnitudeBits & ~Double.SIGN_MASK) | (signBits & Double.SIGN_MASK); return Double.longBitsToDouble(magnitudeBits); } /** * Returns a float with the given magnitude and the sign of {@code sign}. * If {@code sign} is NaN, the sign of the result is positive. * @since 1.6 */ public static float copySign(float magnitude, float sign) { // We manually inline Float.isNaN here because the JIT can't do it yet. // With Float.isNaN: 214.7ns // With manual inline: 112.3ns // With no check (i.e. Math's behavior): 93.1ns // (Tested on a Nexus One.) int magnitudeBits = Float.floatToRawIntBits(magnitude); int signBits = Float.floatToRawIntBits((sign != sign) ? 1.0f : sign); magnitudeBits = (magnitudeBits & ~Float.SIGN_MASK) | (signBits & Float.SIGN_MASK); return Float.intBitsToFloat(magnitudeBits); } /** * Returns the exponent of float {@code f}. * @since 1.6 */ public static int getExponent(float f) { return Math.getExponent(f); } /** * Returns the exponent of double {@code d}. * @since 1.6 */ public static int getExponent(double d){ return Math.getExponent(d); } /** * Returns the next double after {@code start} in the given {@code direction}. * @since 1.6 */ public static double nextAfter(double start, double direction) { if (start == 0 && direction == 0) { return direction; } return nextafter(start, direction); } /** * Returns the next float after {@code start} in the given {@code direction}. * @since 1.6 */ public static float nextAfter(float start, double direction) { return Math.nextAfter(start, direction); } /** * Returns the next double larger than {@code d}. * @since 1.6 */ public static double nextUp(double d) { return Math.nextUp(d); } /** * Returns the next float larger than {@code f}. * @since 1.6 */ public static float nextUp(float f) { return Math.nextUp(f); } /** * Returns {@code d} * 2^{@code scaleFactor}. The result may be rounded. * @since 1.6 */ public static double scalb(double d, int scaleFactor) { if (Double.isNaN(d) || Double.isInfinite(d) || d == 0) { return d; } // change double to long for calculation long bits = Double.doubleToLongBits(d); // the sign of the results must be the same of given d long sign = bits & Double.SIGN_MASK; // calculates the factor of the result long factor = (int) ((bits & Double.EXPONENT_MASK) >> Double.MANTISSA_BITS) - Double.EXPONENT_BIAS + scaleFactor; // calculates the factor of sub-normal values int subNormalFactor = Long.numberOfLeadingZeros(bits & ~Double.SIGN_MASK) - Double.EXPONENT_BITS; if (subNormalFactor < 0) { // not sub-normal values subNormalFactor = 0; } if (Math.abs(d) < Double.MIN_NORMAL) { factor = factor - subNormalFactor; } if (factor > Double.MAX_EXPONENT) { return (d > 0 ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY); } long result; // if result is a sub-normal if (factor < -Double.EXPONENT_BIAS) { // the number of digits that shifts long digits = factor + Double.EXPONENT_BIAS + subNormalFactor; if (Math.abs(d) < Double.MIN_NORMAL) { // origin d is already sub-normal result = shiftLongBits(bits & Double.MANTISSA_MASK, digits); } else { // origin d is not sub-normal, change mantissa to sub-normal result = shiftLongBits(bits & Double.MANTISSA_MASK | 0x0010000000000000L, digits - 1); } } else { if (Math.abs(d) >= Double.MIN_NORMAL) { // common situation result = ((factor + Double.EXPONENT_BIAS) << Double.MANTISSA_BITS) | (bits & Double.MANTISSA_MASK); } else { // origin d is sub-normal, change mantissa to normal style result = ((factor + Double.EXPONENT_BIAS) << Double.MANTISSA_BITS) | ((bits << (subNormalFactor + 1)) & Double.MANTISSA_MASK); } } return Double.longBitsToDouble(result | sign); } /** * Returns {@code d} * 2^{@code scaleFactor}. The result may be rounded. * @since 1.6 */ public static float scalb(float d, int scaleFactor) { if (Float.isNaN(d) || Float.isInfinite(d) || d == 0) { return d; } int bits = Float.floatToIntBits(d); int sign = bits & Float.SIGN_MASK; int factor = ((bits & Float.EXPONENT_MASK) >> Float.MANTISSA_BITS) - Float.EXPONENT_BIAS + scaleFactor; // calculates the factor of sub-normal values int subNormalFactor = Integer.numberOfLeadingZeros(bits & ~Float.SIGN_MASK) - Float.EXPONENT_BITS; if (subNormalFactor < 0) { // not sub-normal values subNormalFactor = 0; } if (Math.abs(d) < Float.MIN_NORMAL) { factor = factor - subNormalFactor; } if (factor > Float.MAX_EXPONENT) { return (d > 0 ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY); } int result; // if result is a sub-normal if (factor < -Float.EXPONENT_BIAS) { // the number of digits that shifts int digits = factor + Float.EXPONENT_BIAS + subNormalFactor; if (Math.abs(d) < Float.MIN_NORMAL) { // origin d is already sub-normal result = shiftIntBits(bits & Float.MANTISSA_MASK, digits); } else { // origin d is not sub-normal, change mantissa to sub-normal result = shiftIntBits(bits & Float.MANTISSA_MASK | 0x00800000, digits - 1); } } else { if (Math.abs(d) >= Float.MIN_NORMAL) { // common situation result = ((factor + Float.EXPONENT_BIAS) << Float.MANTISSA_BITS) | (bits & Float.MANTISSA_MASK); } else { // origin d is sub-normal, change mantissa to normal style result = ((factor + Float.EXPONENT_BIAS) << Float.MANTISSA_BITS) | ((bits << (subNormalFactor + 1)) & Float.MANTISSA_MASK); } } return Float.intBitsToFloat(result | sign); } // Shifts integer bits as float, if the digits is positive, left-shift; if // not, shift to right and calculate its carry. private static int shiftIntBits(int bits, int digits) { if (digits > 0) { return bits << digits; } // change it to positive int absDigits = -digits; if (Integer.numberOfLeadingZeros(bits & ~Float.SIGN_MASK) <= (32 - absDigits)) { // some bits will remain after shifting, calculates its carry if ((((bits >> (absDigits - 1)) & 0x1) == 0) || Integer.numberOfTrailingZeros(bits) == (absDigits - 1)) { return bits >> absDigits; } return ((bits >> absDigits) + 1); } return 0; } // Shifts long bits as double, if the digits is positive, left-shift; if // not, shift to right and calculate its carry. private static long shiftLongBits(long bits, long digits) { if (digits > 0) { return bits << digits; } // change it to positive long absDigits = -digits; if (Long.numberOfLeadingZeros(bits & ~Double.SIGN_MASK) <= (64 - absDigits)) { // some bits will remain after shifting, calculates its carry if ((((bits >> (absDigits - 1)) & 0x1) == 0) || Long.numberOfTrailingZeros(bits) == (absDigits - 1)) { return bits >> absDigits; } return ((bits >> absDigits) + 1); } return 0; } }




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