/*
* 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;
}
}