| /* |
| * 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. |
| * <p> |
| * 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. |
| * <p> |
| * The methods in this class are specified using the "Freely Distributable Math |
| * Library" (fdlibm), version 5.3. |
| * <p> |
| * <a href="http://www.netlib.org/fdlibm/">http://www.netlib.org/fdlibm/</a> |
| */ |
| public final class StrictMath { |
| /** |
| * The double value closest to e, the base of the natural logarithm. |
| */ |
| public final static double E = Math.E; |
| |
| /** |
| * The double value closest to pi, the ratio of a circle's circumference to |
| * its diameter. |
| */ |
| public final static double PI = Math.PI; |
| |
| private static java.util.Random random; |
| |
| /** |
| * Prevents this class from being instantiated. |
| */ |
| private StrictMath() { |
| } |
| |
| /** |
| * Returns the absolute value of the argument. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code abs(-0.0) = +0.0}</li> |
| * <li>{@code abs(+infinity) = +infinity}</li> |
| * <li>{@code abs(-infinity) = +infinity}</li> |
| * <li>{@code abs(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @param d |
| * the value whose absolute value has to be computed. |
| * @return the absolute value of the argument. |
| */ |
| public static double abs(double d) { |
| return Math.abs(d); |
| } |
| |
| /** |
| * Returns the absolute value of the argument. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code abs(-0.0) = +0.0}</li> |
| * <li>{@code abs(+infinity) = +infinity}</li> |
| * <li>{@code abs(-infinity) = +infinity}</li> |
| * <li>{@code abs(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @param f |
| * the value whose absolute value has to be computed. |
| * @return the argument if it is positive, otherwise the negation of the |
| * argument. |
| */ |
| public static float abs(float f) { |
| return Math.abs(f); |
| } |
| |
| /** |
| * Returns the absolute value of the argument. |
| * <p> |
| * If the argument is {@code Integer.MIN_VALUE}, {@code Integer.MIN_VALUE} |
| * is returned. |
| * |
| * @param i |
| * the value whose absolute value has to be computed. |
| * @return the argument if it is positive, otherwise the negation of the |
| * argument. |
| */ |
| public static int abs(int i) { |
| return Math.abs(i); |
| } |
| |
| /** |
| * Returns the absolute value of the argument. |
| * <p> |
| * If the argument is {@code Long.MIN_VALUE}, {@code Long.MIN_VALUE} is |
| * returned. |
| * |
| * @param l |
| * the value whose absolute value has to be computed. |
| * @return the argument if it is positive, otherwise the negation of the |
| * argument. |
| */ |
| 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]}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code acos((anything > 1) = NaN}</li> |
| * <li>{@code acos((anything < -1) = NaN}</li> |
| * <li>{@code acos(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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]}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code asin((anything > 1)) = NaN}</li> |
| * <li>{@code asin((anything < -1)) = NaN}</li> |
| * <li>{@code asin(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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]}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code atan(+0.0) = +0.0}</li> |
| * <li>{@code atan(-0.0) = -0.0}</li> |
| * <li>{@code atan(+infinity) = +pi/2}</li> |
| * <li>{@code atan(-infinity) = -pi/2}</li> |
| * <li>{@code atan(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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). |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code atan2((anything), NaN ) = NaN;}</li> |
| * <li>{@code atan2(NaN , (anything) ) = NaN;}</li> |
| * <li>{@code atan2(+0.0, +(anything but NaN)) = +0.0}</li> |
| * <li>{@code atan2(-0.0, +(anything but NaN)) = -0.0}</li> |
| * <li>{@code atan2(+0.0, -(anything but NaN)) = +pi}</li> |
| * <li>{@code atan2(-0.0, -(anything but NaN)) = -pi}</li> |
| * <li>{@code atan2(+(anything but 0 and NaN), 0) = +pi/2}</li> |
| * <li>{@code atan2(-(anything but 0 and NaN), 0) = -pi/2}</li> |
| * <li>{@code atan2(+(anything but infinity and NaN), +infinity)} {@code =} |
| * {@code +0.0}</li> |
| * <li>{@code atan2(-(anything but infinity and NaN), +infinity)} {@code =} |
| * {@code -0.0}</li> |
| * <li>{@code atan2(+(anything but infinity and NaN), -infinity) = +pi}</li> |
| * <li>{@code atan2(-(anything but infinity and NaN), -infinity) = -pi}</li> |
| * <li>{@code atan2(+infinity, +infinity ) = +pi/4}</li> |
| * <li>{@code atan2(-infinity, +infinity ) = -pi/4}</li> |
| * <li>{@code atan2(+infinity, -infinity ) = +3pi/4}</li> |
| * <li>{@code atan2(-infinity, -infinity ) = -3pi/4}</li> |
| * <li>{@code atan2(+infinity, (anything but,0, NaN, and infinity))} |
| * {@code =} {@code +pi/2}</li> |
| * <li>{@code atan2(-infinity, (anything but,0, NaN, and infinity))} |
| * {@code =} {@code -pi/2}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code cbrt(+0.0) = +0.0}</li> |
| * <li>{@code cbrt(-0.0) = -0.0}</li> |
| * <li>{@code cbrt(+infinity) = +infinity}</li> |
| * <li>{@code cbrt(-infinity) = -infinity}</li> |
| * <li>{@code cbrt(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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 which is greater than the argument. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code ceil(+0.0) = +0.0}</li> |
| * <li>{@code ceil(-0.0) = -0.0}</li> |
| * <li>{@code ceil((anything in range (-1,0)) = -0.0}</li> |
| * <li>{@code ceil(+infinity) = +infinity}</li> |
| * <li>{@code ceil(-infinity) = -infinity}</li> |
| * <li>{@code ceil(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @param d |
| * the value whose closest integer value has to be computed. |
| * @return the ceiling of the argument. |
| */ |
| public static native double ceil(double d); |
| |
| |
| /** |
| * Returns the closest double approximation of the hyperbolic cosine of the |
| * argument. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code cosh(+infinity) = +infinity}</li> |
| * <li>{@code cosh(-infinity) = +infinity}</li> |
| * <li>{@code cosh(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code cos(+infinity) = NaN}</li> |
| * <li>{@code cos(-infinity) = NaN}</li> |
| * <li>{@code cos(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code exp(+infinity) = +infinity}</li> |
| * <li>{@code exp(-infinity) = +0.0}</li> |
| * <li>{@code exp(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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 <i>{@code e}</i><sup> |
| * {@code d}</sup>{@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). |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code expm1(+0.0) = +0.0}</li> |
| * <li>{@code expm1(-0.0) = -0.0}</li> |
| * <li>{@code expm1(+infinity) = +infinity}</li> |
| * <li>{@code expm1(-infinity) = -1.0}</li> |
| * <li>{@code expm1(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @param d |
| * the value to compute the <i>{@code e}</i><sup>{@code d}</sup> |
| * {@code - 1} of. |
| * @return the <i>{@code e}</i><sup>{@code d}</sup>{@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 value which is less than the argument. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code floor(+0.0) = +0.0}</li> |
| * <li>{@code floor(-0.0) = -0.0}</li> |
| * <li>{@code floor(+infinity) = +infinity}</li> |
| * <li>{@code floor(-infinity) = -infinity}</li> |
| * <li>{@code floor(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @param d the value whose closest integer value has to be computed. |
| * @return the floor of the argument. |
| */ |
| public static native double floor(double d); |
| |
| /** |
| * Returns {@code sqrt(}<i>{@code x}</i><sup>{@code 2}</sup>{@code +} |
| * <i> {@code y}</i><sup>{@code 2}</sup>{@code )}. The final result is |
| * without medium underflow or overflow. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code hypot(+infinity, (anything including NaN)) = +infinity}</li> |
| * <li>{@code hypot(-infinity, (anything including NaN)) = +infinity}</li> |
| * <li>{@code hypot((anything including NaN), +infinity) = +infinity}</li> |
| * <li>{@code hypot((anything including NaN), -infinity) = +infinity}</li> |
| * <li>{@code hypot(NaN, NaN) = NaN}</li> |
| * </ul> |
| * |
| * @param x |
| * a double number. |
| * @param y |
| * a double number. |
| * @return the {@code sqrt(}<i>{@code x}</i><sup>{@code 2}</sup>{@code +} |
| * <i> {@code y}</i><sup>{@code 2}</sup>{@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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code IEEEremainder((anything), 0) = NaN}</li> |
| * <li>{@code IEEEremainder(+infinity, (anything)) = NaN}</li> |
| * <li>{@code IEEEremainder(-infinity, (anything)) = NaN}</li> |
| * <li>{@code IEEEremainder(NaN, (anything)) = NaN}</li> |
| * <li>{@code IEEEremainder((anything), NaN) = NaN}</li> |
| * <li>{@code IEEEremainder(x, +infinity) = x } where x is anything but |
| * +/-infinity</li> |
| * <li>{@code IEEEremainder(x, -infinity) = x } where x is anything but |
| * +/-infinity</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code log(+0.0) = -infinity}</li> |
| * <li>{@code log(-0.0) = -infinity}</li> |
| * <li>{@code log((anything < 0) = NaN}</li> |
| * <li>{@code log(+infinity) = +infinity}</li> |
| * <li>{@code log(-infinity) = NaN}</li> |
| * <li>{@code log(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code log10(+0.0) = -infinity}</li> |
| * <li>{@code log10(-0.0) = -infinity}</li> |
| * <li>{@code log10((anything < 0) = NaN}</li> |
| * <li>{@code log10(+infinity) = +infinity}</li> |
| * <li>{@code log10(-infinity) = NaN}</li> |
| * <li>{@code log10(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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). |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code log1p(+0.0) = +0.0}</li> |
| * <li>{@code log1p(-0.0) = -0.0}</li> |
| * <li>{@code log1p((anything < 1)) = NaN}</li> |
| * <li>{@code log1p(-1.0) = -infinity}</li> |
| * <li>{@code log1p(+infinity) = +infinity}</li> |
| * <li>{@code log1p(-infinity) = NaN}</li> |
| * <li>{@code log1p(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code max(NaN, (anything)) = NaN}</li> |
| * <li>{@code max((anything), NaN) = NaN}</li> |
| * <li>{@code max(+0.0, -0.0) = +0.0}</li> |
| * <li>{@code max(-0.0, +0.0) = +0.0}</li> |
| * </ul> |
| * |
| * @param d1 |
| * the first argument. |
| * @param d2 |
| * the second argument. |
| * @return the larger of {@code d1} and {@code d2}. |
| */ |
| 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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code max(NaN, (anything)) = NaN}</li> |
| * <li>{@code max((anything), NaN) = NaN}</li> |
| * <li>{@code max(+0.0, -0.0) = +0.0}</li> |
| * <li>{@code max(-0.0, +0.0) = +0.0}</li> |
| * </ul> |
| * |
| * @param f1 |
| * the first argument. |
| * @param f2 |
| * the second argument. |
| * @return the larger of {@code f1} and {@code f2}. |
| */ |
| 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. |
| * |
| * @param i1 |
| * the first argument. |
| * @param i2 |
| * the second argument. |
| * @return the larger of {@code i1} and {@code i2}. |
| */ |
| 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. |
| * |
| * @param l1 |
| * the first argument. |
| * @param l2 |
| * the second argument. |
| * @return the larger of {@code l1} and {@code l2}. |
| */ |
| public static long max(long l1, long l2) { |
| return Math.max(l1, l2); |
| } |
| |
| /** |
| * Returns the most negative (closest to negative infinity) of the two |
| * arguments. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code min(NaN, (anything)) = NaN}</li> |
| * <li>{@code min((anything), NaN) = NaN}</li> |
| * <li>{@code min(+0.0, -0.0) = -0.0}</li> |
| * <li>{@code min(-0.0, +0.0) = -0.0}</li> |
| * </ul> |
| * |
| * @param d1 |
| * the first argument. |
| * @param d2 |
| * the second argument. |
| * @return the smaller of {@code d1} and {@code d2}. |
| */ |
| 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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code min(NaN, (anything)) = NaN}</li> |
| * <li>{@code min((anything), NaN) = NaN}</li> |
| * <li>{@code min(+0.0, -0.0) = -0.0}</li> |
| * <li>{@code min(-0.0, +0.0) = -0.0}</li> |
| * </ul> |
| * |
| * @param f1 |
| * the first argument. |
| * @param f2 |
| * the second argument. |
| * @return the smaller of {@code f1} and {@code f2}. |
| */ |
| 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. |
| * |
| * @param i1 |
| * the first argument. |
| * @param i2 |
| * the second argument. |
| * @return the smaller of {@code i1} and {@code i2}. |
| */ |
| 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. |
| * |
| * @param l1 |
| * the first argument. |
| * @param l2 |
| * the second argument. |
| * @return the smaller of {@code l1} and {@code l2}. |
| */ |
| public static long min(long l1, long l2) { |
| return Math.min(l1, l2); |
| } |
| |
| /** |
| * Returns the closest double approximation of the result of raising |
| * {@code x} to the power of {@code y}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code pow((anything), +0.0) = 1.0}</li> |
| * <li>{@code pow((anything), -0.0) = 1.0}</li> |
| * <li>{@code pow(x, 1.0) = x}</li> |
| * <li>{@code pow((anything), NaN) = NaN}</li> |
| * <li>{@code pow(NaN, (anything except 0)) = NaN}</li> |
| * <li>{@code pow(+/-(|x| > 1), +infinity) = +infinity}</li> |
| * <li>{@code pow(+/-(|x| > 1), -infinity) = +0.0}</li> |
| * <li>{@code pow(+/-(|x| < 1), +infinity) = +0.0}</li> |
| * <li>{@code pow(+/-(|x| < 1), -infinity) = +infinity}</li> |
| * <li>{@code pow(+/-1.0 , +infinity) = NaN}</li> |
| * <li>{@code pow(+/-1.0 , -infinity) = NaN}</li> |
| * <li>{@code pow(+0.0, (+anything except 0, NaN)) = +0.0}</li> |
| * <li>{@code pow(-0.0, (+anything except 0, NaN, odd integer)) = +0.0}</li> |
| * <li>{@code pow(+0.0, (-anything except 0, NaN)) = +infinity}</li> |
| * <li>{@code pow(-0.0, (-anything except 0, NAN, odd integer))} {@code =} |
| * {@code +infinity}</li> |
| * <li>{@code pow(-0.0, (odd integer)) = -pow( +0 , (odd integer) )}</li> |
| * <li>{@code pow(+infinity, (+anything except 0, NaN)) = +infinity}</li> |
| * <li>{@code pow(+infinity, (-anything except 0, NaN)) = +0.0}</li> |
| * <li>{@code pow(-infinity, (anything)) = -pow(0, (-anything))}</li> |
| * <li>{@code pow((-anything), (integer))} {@code =} |
| * {@code pow(-1,(integer))*pow(+anything,integer)}</li> |
| * <li>{@code pow((-anything except 0 and infinity), (non-integer))} |
| * {@code =} {@code NAN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code rint(+0.0) = +0.0}</li> |
| * <li>{@code rint(-0.0) = -0.0}</li> |
| * <li>{@code rint(+infinity) = +infinity}</li> |
| * <li>{@code rint(-infinity) = -infinity}</li> |
| * <li>{@code rint(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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)}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code round(+0.0) = +0.0}</li> |
| * <li>{@code round(-0.0) = +0.0}</li> |
| * <li>{@code round((anything > Long.MAX_VALUE) = Long.MAX_VALUE}</li> |
| * <li>{@code round((anything < Long.MIN_VALUE) = Long.MIN_VALUE}</li> |
| * <li>{@code round(+infinity) = Long.MAX_VALUE}</li> |
| * <li>{@code round(-infinity) = Long.MIN_VALUE}</li> |
| * <li>{@code round(NaN) = +0.0}</li> |
| * </ul> |
| * |
| * @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)}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code round(+0.0) = +0.0}</li> |
| * <li>{@code round(-0.0) = +0.0}</li> |
| * <li>{@code round((anything > Integer.MAX_VALUE) = Integer.MAX_VALUE}</li> |
| * <li>{@code round((anything < Integer.MIN_VALUE) = Integer.MIN_VALUE}</li> |
| * <li>{@code round(+infinity) = Integer.MAX_VALUE}</li> |
| * <li>{@code round(-infinity) = Integer.MIN_VALUE}</li> |
| * <li>{@code round(NaN) = +0.0}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code signum(+0.0) = +0.0}</li> |
| * <li>{@code signum(-0.0) = -0.0}</li> |
| * <li>{@code signum(+infinity) = +1.0}</li> |
| * <li>{@code signum(-infinity) = -1.0}</li> |
| * <li>{@code signum(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code signum(+0.0) = +0.0}</li> |
| * <li>{@code signum(-0.0) = -0.0}</li> |
| * <li>{@code signum(+infinity) = +1.0}</li> |
| * <li>{@code signum(-infinity) = -1.0}</li> |
| * <li>{@code signum(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code sinh(+0.0) = +0.0}</li> |
| * <li>{@code sinh(-0.0) = -0.0}</li> |
| * <li>{@code sinh(+infinity) = +infinity}</li> |
| * <li>{@code sinh(-infinity) = -infinity}</li> |
| * <li>{@code sinh(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code sin(+0.0) = +0.0}</li> |
| * <li>{@code sin(-0.0) = -0.0}</li> |
| * <li>{@code sin(+infinity) = NaN}</li> |
| * <li>{@code sin(-infinity) = NaN}</li> |
| * <li>{@code sin(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code sqrt(+0.0) = +0.0}</li> |
| * <li>{@code sqrt(-0.0) = -0.0}</li> |
| * <li>{@code sqrt( (anything < 0) ) = NaN}</li> |
| * <li>{@code sqrt(+infinity) = +infinity}</li> |
| * <li>{@code sqrt(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @param d |
| * the value whose square root has to be computed. |
| * @return the square root of the argument. |
| */ |
| public static native double sqrt(double d); |
| |
| /** |
| * Returns the closest double approximation of the tangent of the argument. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code tan(+0.0) = +0.0}</li> |
| * <li>{@code tan(-0.0) = -0.0}</li> |
| * <li>{@code tan(+infinity) = NaN}</li> |
| * <li>{@code tan(-infinity) = NaN}</li> |
| * <li>{@code tan(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code tanh(+0.0) = +0.0}</li> |
| * <li>{@code tanh(-0.0) = -0.0}</li> |
| * <li>{@code tanh(+infinity) = +1.0}</li> |
| * <li>{@code tanh(-infinity) = -1.0}</li> |
| * <li>{@code tanh(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code toDegrees(+0.0) = +0.0}</li> |
| * <li>{@code toDegrees(-0.0) = -0.0}</li> |
| * <li>{@code toDegrees(+infinity) = +infinity}</li> |
| * <li>{@code toDegrees(-infinity) = -infinity}</li> |
| * <li>{@code toDegrees(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code toRadians(+0.0) = +0.0}</li> |
| * <li>{@code toRadians(-0.0) = -0.0}</li> |
| * <li>{@code toRadians(+infinity) = +infinity}</li> |
| * <li>{@code toRadians(-infinity) = -infinity}</li> |
| * <li>{@code toRadians(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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)}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code ulp(+0.0) = Double.MIN_VALUE}</li> |
| * <li>{@code ulp(-0.0) = Double.MIN_VALUE}</li> |
| * <li>{@code ulp(+infinity) = infinity}</li> |
| * <li>{@code ulp(-infinity) = infinity}</li> |
| * <li>{@code ulp(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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)}. |
| * <p> |
| * Special cases: |
| * <ul> |
| * <li>{@code ulp(+0.0) = Float.MIN_VALUE}</li> |
| * <li>{@code ulp(-0.0) = Float.MIN_VALUE}</li> |
| * <li>{@code ulp(+infinity) = infinity}</li> |
| * <li>{@code ulp(-infinity) = infinity}</li> |
| * <li>{@code ulp(NaN) = NaN}</li> |
| * </ul> |
| * |
| * @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) { |
| // special cases |
| if (Float.isNaN(f)) { |
| return Float.NaN; |
| } else if (Float.isInfinite(f)) { |
| return Float.POSITIVE_INFINITY; |
| } else if (f == Float.MAX_VALUE || f == -Float.MAX_VALUE) { |
| return (float) pow(2, 104); |
| } |
| f = Math.abs(f); |
| return nextafterf(f, Float.MAX_VALUE) - f; |
| } |
| |
| private native static double nextafter(double x, double y); |
| |
| private native static float nextafterf(float x, float 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; |
| } |
| } |
