1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/emul/src/main/java/java/lang/StrictMath.java Sat Sep 29 11:37:46 2012 +0200
1.3 @@ -0,0 +1,1468 @@
1.4 +/*
1.5 + * Copyright (c) 1999, 2011, Oracle and/or its affiliates. All rights reserved.
1.6 + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
1.7 + *
1.8 + * This code is free software; you can redistribute it and/or modify it
1.9 + * under the terms of the GNU General Public License version 2 only, as
1.10 + * published by the Free Software Foundation. Oracle designates this
1.11 + * particular file as subject to the "Classpath" exception as provided
1.12 + * by Oracle in the LICENSE file that accompanied this code.
1.13 + *
1.14 + * This code is distributed in the hope that it will be useful, but WITHOUT
1.15 + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
1.16 + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
1.17 + * version 2 for more details (a copy is included in the LICENSE file that
1.18 + * accompanied this code).
1.19 + *
1.20 + * You should have received a copy of the GNU General Public License version
1.21 + * 2 along with this work; if not, write to the Free Software Foundation,
1.22 + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
1.23 + *
1.24 + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
1.25 + * or visit www.oracle.com if you need additional information or have any
1.26 + * questions.
1.27 + */
1.28 +
1.29 +package java.lang;
1.30 +import java.util.Random;
1.31 +import sun.misc.FpUtils;
1.32 +import sun.misc.DoubleConsts;
1.33 +
1.34 +/**
1.35 + * The class {@code StrictMath} contains methods for performing basic
1.36 + * numeric operations such as the elementary exponential, logarithm,
1.37 + * square root, and trigonometric functions.
1.38 + *
1.39 + * <p>To help ensure portability of Java programs, the definitions of
1.40 + * some of the numeric functions in this package require that they
1.41 + * produce the same results as certain published algorithms. These
1.42 + * algorithms are available from the well-known network library
1.43 + * {@code netlib} as the package "Freely Distributable Math
1.44 + * Library," <a
1.45 + * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
1.46 + * algorithms, which are written in the C programming language, are
1.47 + * then to be understood as executed with all floating-point
1.48 + * operations following the rules of Java floating-point arithmetic.
1.49 + *
1.50 + * <p>The Java math library is defined with respect to
1.51 + * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
1.52 + * more than one definition for a function (such as
1.53 + * {@code acos}), use the "IEEE 754 core function" version
1.54 + * (residing in a file whose name begins with the letter
1.55 + * {@code e}). The methods which require {@code fdlibm}
1.56 + * semantics are {@code sin}, {@code cos}, {@code tan},
1.57 + * {@code asin}, {@code acos}, {@code atan},
1.58 + * {@code exp}, {@code log}, {@code log10},
1.59 + * {@code cbrt}, {@code atan2}, {@code pow},
1.60 + * {@code sinh}, {@code cosh}, {@code tanh},
1.61 + * {@code hypot}, {@code expm1}, and {@code log1p}.
1.62 + *
1.63 + * @author unascribed
1.64 + * @author Joseph D. Darcy
1.65 + * @since 1.3
1.66 + */
1.67 +
1.68 +public final class StrictMath {
1.69 +
1.70 + /**
1.71 + * Don't let anyone instantiate this class.
1.72 + */
1.73 + private StrictMath() {}
1.74 +
1.75 + /**
1.76 + * The {@code double} value that is closer than any other to
1.77 + * <i>e</i>, the base of the natural logarithms.
1.78 + */
1.79 + public static final double E = 2.7182818284590452354;
1.80 +
1.81 + /**
1.82 + * The {@code double} value that is closer than any other to
1.83 + * <i>pi</i>, the ratio of the circumference of a circle to its
1.84 + * diameter.
1.85 + */
1.86 + public static final double PI = 3.14159265358979323846;
1.87 +
1.88 + /**
1.89 + * Returns the trigonometric sine of an angle. Special cases:
1.90 + * <ul><li>If the argument is NaN or an infinity, then the
1.91 + * result is NaN.
1.92 + * <li>If the argument is zero, then the result is a zero with the
1.93 + * same sign as the argument.</ul>
1.94 + *
1.95 + * @param a an angle, in radians.
1.96 + * @return the sine of the argument.
1.97 + */
1.98 + public static native double sin(double a);
1.99 +
1.100 + /**
1.101 + * Returns the trigonometric cosine of an angle. Special cases:
1.102 + * <ul><li>If the argument is NaN or an infinity, then the
1.103 + * result is NaN.</ul>
1.104 + *
1.105 + * @param a an angle, in radians.
1.106 + * @return the cosine of the argument.
1.107 + */
1.108 + public static native double cos(double a);
1.109 +
1.110 + /**
1.111 + * Returns the trigonometric tangent of an angle. Special cases:
1.112 + * <ul><li>If the argument is NaN or an infinity, then the result
1.113 + * is NaN.
1.114 + * <li>If the argument is zero, then the result is a zero with the
1.115 + * same sign as the argument.</ul>
1.116 + *
1.117 + * @param a an angle, in radians.
1.118 + * @return the tangent of the argument.
1.119 + */
1.120 + public static native double tan(double a);
1.121 +
1.122 + /**
1.123 + * Returns the arc sine of a value; the returned angle is in the
1.124 + * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
1.125 + * <ul><li>If the argument is NaN or its absolute value is greater
1.126 + * than 1, then the result is NaN.
1.127 + * <li>If the argument is zero, then the result is a zero with the
1.128 + * same sign as the argument.</ul>
1.129 + *
1.130 + * @param a the value whose arc sine is to be returned.
1.131 + * @return the arc sine of the argument.
1.132 + */
1.133 + public static native double asin(double a);
1.134 +
1.135 + /**
1.136 + * Returns the arc cosine of a value; the returned angle is in the
1.137 + * range 0.0 through <i>pi</i>. Special case:
1.138 + * <ul><li>If the argument is NaN or its absolute value is greater
1.139 + * than 1, then the result is NaN.</ul>
1.140 + *
1.141 + * @param a the value whose arc cosine is to be returned.
1.142 + * @return the arc cosine of the argument.
1.143 + */
1.144 + public static native double acos(double a);
1.145 +
1.146 + /**
1.147 + * Returns the arc tangent of a value; the returned angle is in the
1.148 + * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
1.149 + * <ul><li>If the argument is NaN, then the result is NaN.
1.150 + * <li>If the argument is zero, then the result is a zero with the
1.151 + * same sign as the argument.</ul>
1.152 + *
1.153 + * @param a the value whose arc tangent is to be returned.
1.154 + * @return the arc tangent of the argument.
1.155 + */
1.156 + public static native double atan(double a);
1.157 +
1.158 + /**
1.159 + * Converts an angle measured in degrees to an approximately
1.160 + * equivalent angle measured in radians. The conversion from
1.161 + * degrees to radians is generally inexact.
1.162 + *
1.163 + * @param angdeg an angle, in degrees
1.164 + * @return the measurement of the angle {@code angdeg}
1.165 + * in radians.
1.166 + */
1.167 + public static strictfp double toRadians(double angdeg) {
1.168 + return angdeg / 180.0 * PI;
1.169 + }
1.170 +
1.171 + /**
1.172 + * Converts an angle measured in radians to an approximately
1.173 + * equivalent angle measured in degrees. The conversion from
1.174 + * radians to degrees is generally inexact; users should
1.175 + * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
1.176 + * equal {@code 0.0}.
1.177 + *
1.178 + * @param angrad an angle, in radians
1.179 + * @return the measurement of the angle {@code angrad}
1.180 + * in degrees.
1.181 + */
1.182 + public static strictfp double toDegrees(double angrad) {
1.183 + return angrad * 180.0 / PI;
1.184 + }
1.185 +
1.186 + /**
1.187 + * Returns Euler's number <i>e</i> raised to the power of a
1.188 + * {@code double} value. Special cases:
1.189 + * <ul><li>If the argument is NaN, the result is NaN.
1.190 + * <li>If the argument is positive infinity, then the result is
1.191 + * positive infinity.
1.192 + * <li>If the argument is negative infinity, then the result is
1.193 + * positive zero.</ul>
1.194 + *
1.195 + * @param a the exponent to raise <i>e</i> to.
1.196 + * @return the value <i>e</i><sup>{@code a}</sup>,
1.197 + * where <i>e</i> is the base of the natural logarithms.
1.198 + */
1.199 + public static native double exp(double a);
1.200 +
1.201 + /**
1.202 + * Returns the natural logarithm (base <i>e</i>) of a {@code double}
1.203 + * value. Special cases:
1.204 + * <ul><li>If the argument is NaN or less than zero, then the result
1.205 + * is NaN.
1.206 + * <li>If the argument is positive infinity, then the result is
1.207 + * positive infinity.
1.208 + * <li>If the argument is positive zero or negative zero, then the
1.209 + * result is negative infinity.</ul>
1.210 + *
1.211 + * @param a a value
1.212 + * @return the value ln {@code a}, the natural logarithm of
1.213 + * {@code a}.
1.214 + */
1.215 + public static native double log(double a);
1.216 +
1.217 +
1.218 + /**
1.219 + * Returns the base 10 logarithm of a {@code double} value.
1.220 + * Special cases:
1.221 + *
1.222 + * <ul><li>If the argument is NaN or less than zero, then the result
1.223 + * is NaN.
1.224 + * <li>If the argument is positive infinity, then the result is
1.225 + * positive infinity.
1.226 + * <li>If the argument is positive zero or negative zero, then the
1.227 + * result is negative infinity.
1.228 + * <li> If the argument is equal to 10<sup><i>n</i></sup> for
1.229 + * integer <i>n</i>, then the result is <i>n</i>.
1.230 + * </ul>
1.231 + *
1.232 + * @param a a value
1.233 + * @return the base 10 logarithm of {@code a}.
1.234 + * @since 1.5
1.235 + */
1.236 + public static native double log10(double a);
1.237 +
1.238 + /**
1.239 + * Returns the correctly rounded positive square root of a
1.240 + * {@code double} value.
1.241 + * Special cases:
1.242 + * <ul><li>If the argument is NaN or less than zero, then the result
1.243 + * is NaN.
1.244 + * <li>If the argument is positive infinity, then the result is positive
1.245 + * infinity.
1.246 + * <li>If the argument is positive zero or negative zero, then the
1.247 + * result is the same as the argument.</ul>
1.248 + * Otherwise, the result is the {@code double} value closest to
1.249 + * the true mathematical square root of the argument value.
1.250 + *
1.251 + * @param a a value.
1.252 + * @return the positive square root of {@code a}.
1.253 + */
1.254 + public static native double sqrt(double a);
1.255 +
1.256 + /**
1.257 + * Returns the cube root of a {@code double} value. For
1.258 + * positive finite {@code x}, {@code cbrt(-x) ==
1.259 + * -cbrt(x)}; that is, the cube root of a negative value is
1.260 + * the negative of the cube root of that value's magnitude.
1.261 + * Special cases:
1.262 + *
1.263 + * <ul>
1.264 + *
1.265 + * <li>If the argument is NaN, then the result is NaN.
1.266 + *
1.267 + * <li>If the argument is infinite, then the result is an infinity
1.268 + * with the same sign as the argument.
1.269 + *
1.270 + * <li>If the argument is zero, then the result is a zero with the
1.271 + * same sign as the argument.
1.272 + *
1.273 + * </ul>
1.274 + *
1.275 + * @param a a value.
1.276 + * @return the cube root of {@code a}.
1.277 + * @since 1.5
1.278 + */
1.279 + public static native double cbrt(double a);
1.280 +
1.281 + /**
1.282 + * Computes the remainder operation on two arguments as prescribed
1.283 + * by the IEEE 754 standard.
1.284 + * The remainder value is mathematically equal to
1.285 + * <code>f1 - f2</code> × <i>n</i>,
1.286 + * where <i>n</i> is the mathematical integer closest to the exact
1.287 + * mathematical value of the quotient {@code f1/f2}, and if two
1.288 + * mathematical integers are equally close to {@code f1/f2},
1.289 + * then <i>n</i> is the integer that is even. If the remainder is
1.290 + * zero, its sign is the same as the sign of the first argument.
1.291 + * Special cases:
1.292 + * <ul><li>If either argument is NaN, or the first argument is infinite,
1.293 + * or the second argument is positive zero or negative zero, then the
1.294 + * result is NaN.
1.295 + * <li>If the first argument is finite and the second argument is
1.296 + * infinite, then the result is the same as the first argument.</ul>
1.297 + *
1.298 + * @param f1 the dividend.
1.299 + * @param f2 the divisor.
1.300 + * @return the remainder when {@code f1} is divided by
1.301 + * {@code f2}.
1.302 + */
1.303 + public static native double IEEEremainder(double f1, double f2);
1.304 +
1.305 + /**
1.306 + * Returns the smallest (closest to negative infinity)
1.307 + * {@code double} value that is greater than or equal to the
1.308 + * argument and is equal to a mathematical integer. Special cases:
1.309 + * <ul><li>If the argument value is already equal to a
1.310 + * mathematical integer, then the result is the same as the
1.311 + * argument. <li>If the argument is NaN or an infinity or
1.312 + * positive zero or negative zero, then the result is the same as
1.313 + * the argument. <li>If the argument value is less than zero but
1.314 + * greater than -1.0, then the result is negative zero.</ul> Note
1.315 + * that the value of {@code StrictMath.ceil(x)} is exactly the
1.316 + * value of {@code -StrictMath.floor(-x)}.
1.317 + *
1.318 + * @param a a value.
1.319 + * @return the smallest (closest to negative infinity)
1.320 + * floating-point value that is greater than or equal to
1.321 + * the argument and is equal to a mathematical integer.
1.322 + */
1.323 + public static double ceil(double a) {
1.324 + return floorOrCeil(a, -0.0, 1.0, 1.0);
1.325 + }
1.326 +
1.327 + /**
1.328 + * Returns the largest (closest to positive infinity)
1.329 + * {@code double} value that is less than or equal to the
1.330 + * argument and is equal to a mathematical integer. Special cases:
1.331 + * <ul><li>If the argument value is already equal to a
1.332 + * mathematical integer, then the result is the same as the
1.333 + * argument. <li>If the argument is NaN or an infinity or
1.334 + * positive zero or negative zero, then the result is the same as
1.335 + * the argument.</ul>
1.336 + *
1.337 + * @param a a value.
1.338 + * @return the largest (closest to positive infinity)
1.339 + * floating-point value that less than or equal to the argument
1.340 + * and is equal to a mathematical integer.
1.341 + */
1.342 + public static double floor(double a) {
1.343 + return floorOrCeil(a, -1.0, 0.0, -1.0);
1.344 + }
1.345 +
1.346 + /**
1.347 + * Internal method to share logic between floor and ceil.
1.348 + *
1.349 + * @param a the value to be floored or ceiled
1.350 + * @param negativeBoundary result for values in (-1, 0)
1.351 + * @param positiveBoundary result for values in (0, 1)
1.352 + * @param increment value to add when the argument is non-integral
1.353 + */
1.354 + private static double floorOrCeil(double a,
1.355 + double negativeBoundary,
1.356 + double positiveBoundary,
1.357 + double sign) {
1.358 + int exponent = Math.getExponent(a);
1.359 +
1.360 + if (exponent < 0) {
1.361 + /*
1.362 + * Absolute value of argument is less than 1.
1.363 + * floorOrceil(-0.0) => -0.0
1.364 + * floorOrceil(+0.0) => +0.0
1.365 + */
1.366 + return ((a == 0.0) ? a :
1.367 + ( (a < 0.0) ? negativeBoundary : positiveBoundary) );
1.368 + } else if (exponent >= 52) {
1.369 + /*
1.370 + * Infinity, NaN, or a value so large it must be integral.
1.371 + */
1.372 + return a;
1.373 + }
1.374 + // Else the argument is either an integral value already XOR it
1.375 + // has to be rounded to one.
1.376 + assert exponent >= 0 && exponent <= 51;
1.377 +
1.378 + long doppel = Double.doubleToRawLongBits(a);
1.379 + long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
1.380 +
1.381 + if ( (mask & doppel) == 0L )
1.382 + return a; // integral value
1.383 + else {
1.384 + double result = Double.longBitsToDouble(doppel & (~mask));
1.385 + if (sign*a > 0.0)
1.386 + result = result + sign;
1.387 + return result;
1.388 + }
1.389 + }
1.390 +
1.391 + /**
1.392 + * Returns the {@code double} value that is closest in value
1.393 + * to the argument and is equal to a mathematical integer. If two
1.394 + * {@code double} values that are mathematical integers are
1.395 + * equally close to the value of the argument, the result is the
1.396 + * integer value that is even. Special cases:
1.397 + * <ul><li>If the argument value is already equal to a mathematical
1.398 + * integer, then the result is the same as the argument.
1.399 + * <li>If the argument is NaN or an infinity or positive zero or negative
1.400 + * zero, then the result is the same as the argument.</ul>
1.401 + *
1.402 + * @param a a value.
1.403 + * @return the closest floating-point value to {@code a} that is
1.404 + * equal to a mathematical integer.
1.405 + * @author Joseph D. Darcy
1.406 + */
1.407 + public static double rint(double a) {
1.408 + /*
1.409 + * If the absolute value of a is not less than 2^52, it
1.410 + * is either a finite integer (the double format does not have
1.411 + * enough significand bits for a number that large to have any
1.412 + * fractional portion), an infinity, or a NaN. In any of
1.413 + * these cases, rint of the argument is the argument.
1.414 + *
1.415 + * Otherwise, the sum (twoToThe52 + a ) will properly round
1.416 + * away any fractional portion of a since ulp(twoToThe52) ==
1.417 + * 1.0; subtracting out twoToThe52 from this sum will then be
1.418 + * exact and leave the rounded integer portion of a.
1.419 + *
1.420 + * This method does *not* need to be declared strictfp to get
1.421 + * fully reproducible results. Whether or not a method is
1.422 + * declared strictfp can only make a difference in the
1.423 + * returned result if some operation would overflow or
1.424 + * underflow with strictfp semantics. The operation
1.425 + * (twoToThe52 + a ) cannot overflow since large values of a
1.426 + * are screened out; the add cannot underflow since twoToThe52
1.427 + * is too large. The subtraction ((twoToThe52 + a ) -
1.428 + * twoToThe52) will be exact as discussed above and thus
1.429 + * cannot overflow or meaningfully underflow. Finally, the
1.430 + * last multiply in the return statement is by plus or minus
1.431 + * 1.0, which is exact too.
1.432 + */
1.433 + double twoToThe52 = (double)(1L << 52); // 2^52
1.434 + double sign = FpUtils.rawCopySign(1.0, a); // preserve sign info
1.435 + a = Math.abs(a);
1.436 +
1.437 + if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
1.438 + a = ((twoToThe52 + a ) - twoToThe52);
1.439 + }
1.440 +
1.441 + return sign * a; // restore original sign
1.442 + }
1.443 +
1.444 + /**
1.445 + * Returns the angle <i>theta</i> from the conversion of rectangular
1.446 + * coordinates ({@code x}, {@code y}) to polar
1.447 + * coordinates (r, <i>theta</i>).
1.448 + * This method computes the phase <i>theta</i> by computing an arc tangent
1.449 + * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
1.450 + * cases:
1.451 + * <ul><li>If either argument is NaN, then the result is NaN.
1.452 + * <li>If the first argument is positive zero and the second argument
1.453 + * is positive, or the first argument is positive and finite and the
1.454 + * second argument is positive infinity, then the result is positive
1.455 + * zero.
1.456 + * <li>If the first argument is negative zero and the second argument
1.457 + * is positive, or the first argument is negative and finite and the
1.458 + * second argument is positive infinity, then the result is negative zero.
1.459 + * <li>If the first argument is positive zero and the second argument
1.460 + * is negative, or the first argument is positive and finite and the
1.461 + * second argument is negative infinity, then the result is the
1.462 + * {@code double} value closest to <i>pi</i>.
1.463 + * <li>If the first argument is negative zero and the second argument
1.464 + * is negative, or the first argument is negative and finite and the
1.465 + * second argument is negative infinity, then the result is the
1.466 + * {@code double} value closest to -<i>pi</i>.
1.467 + * <li>If the first argument is positive and the second argument is
1.468 + * positive zero or negative zero, or the first argument is positive
1.469 + * infinity and the second argument is finite, then the result is the
1.470 + * {@code double} value closest to <i>pi</i>/2.
1.471 + * <li>If the first argument is negative and the second argument is
1.472 + * positive zero or negative zero, or the first argument is negative
1.473 + * infinity and the second argument is finite, then the result is the
1.474 + * {@code double} value closest to -<i>pi</i>/2.
1.475 + * <li>If both arguments are positive infinity, then the result is the
1.476 + * {@code double} value closest to <i>pi</i>/4.
1.477 + * <li>If the first argument is positive infinity and the second argument
1.478 + * is negative infinity, then the result is the {@code double}
1.479 + * value closest to 3*<i>pi</i>/4.
1.480 + * <li>If the first argument is negative infinity and the second argument
1.481 + * is positive infinity, then the result is the {@code double} value
1.482 + * closest to -<i>pi</i>/4.
1.483 + * <li>If both arguments are negative infinity, then the result is the
1.484 + * {@code double} value closest to -3*<i>pi</i>/4.</ul>
1.485 + *
1.486 + * @param y the ordinate coordinate
1.487 + * @param x the abscissa coordinate
1.488 + * @return the <i>theta</i> component of the point
1.489 + * (<i>r</i>, <i>theta</i>)
1.490 + * in polar coordinates that corresponds to the point
1.491 + * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
1.492 + */
1.493 + public static native double atan2(double y, double x);
1.494 +
1.495 +
1.496 + /**
1.497 + * Returns the value of the first argument raised to the power of the
1.498 + * second argument. Special cases:
1.499 + *
1.500 + * <ul><li>If the second argument is positive or negative zero, then the
1.501 + * result is 1.0.
1.502 + * <li>If the second argument is 1.0, then the result is the same as the
1.503 + * first argument.
1.504 + * <li>If the second argument is NaN, then the result is NaN.
1.505 + * <li>If the first argument is NaN and the second argument is nonzero,
1.506 + * then the result is NaN.
1.507 + *
1.508 + * <li>If
1.509 + * <ul>
1.510 + * <li>the absolute value of the first argument is greater than 1
1.511 + * and the second argument is positive infinity, or
1.512 + * <li>the absolute value of the first argument is less than 1 and
1.513 + * the second argument is negative infinity,
1.514 + * </ul>
1.515 + * then the result is positive infinity.
1.516 + *
1.517 + * <li>If
1.518 + * <ul>
1.519 + * <li>the absolute value of the first argument is greater than 1 and
1.520 + * the second argument is negative infinity, or
1.521 + * <li>the absolute value of the
1.522 + * first argument is less than 1 and the second argument is positive
1.523 + * infinity,
1.524 + * </ul>
1.525 + * then the result is positive zero.
1.526 + *
1.527 + * <li>If the absolute value of the first argument equals 1 and the
1.528 + * second argument is infinite, then the result is NaN.
1.529 + *
1.530 + * <li>If
1.531 + * <ul>
1.532 + * <li>the first argument is positive zero and the second argument
1.533 + * is greater than zero, or
1.534 + * <li>the first argument is positive infinity and the second
1.535 + * argument is less than zero,
1.536 + * </ul>
1.537 + * then the result is positive zero.
1.538 + *
1.539 + * <li>If
1.540 + * <ul>
1.541 + * <li>the first argument is positive zero and the second argument
1.542 + * is less than zero, or
1.543 + * <li>the first argument is positive infinity and the second
1.544 + * argument is greater than zero,
1.545 + * </ul>
1.546 + * then the result is positive infinity.
1.547 + *
1.548 + * <li>If
1.549 + * <ul>
1.550 + * <li>the first argument is negative zero and the second argument
1.551 + * is greater than zero but not a finite odd integer, or
1.552 + * <li>the first argument is negative infinity and the second
1.553 + * argument is less than zero but not a finite odd integer,
1.554 + * </ul>
1.555 + * then the result is positive zero.
1.556 + *
1.557 + * <li>If
1.558 + * <ul>
1.559 + * <li>the first argument is negative zero and the second argument
1.560 + * is a positive finite odd integer, or
1.561 + * <li>the first argument is negative infinity and the second
1.562 + * argument is a negative finite odd integer,
1.563 + * </ul>
1.564 + * then the result is negative zero.
1.565 + *
1.566 + * <li>If
1.567 + * <ul>
1.568 + * <li>the first argument is negative zero and the second argument
1.569 + * is less than zero but not a finite odd integer, or
1.570 + * <li>the first argument is negative infinity and the second
1.571 + * argument is greater than zero but not a finite odd integer,
1.572 + * </ul>
1.573 + * then the result is positive infinity.
1.574 + *
1.575 + * <li>If
1.576 + * <ul>
1.577 + * <li>the first argument is negative zero and the second argument
1.578 + * is a negative finite odd integer, or
1.579 + * <li>the first argument is negative infinity and the second
1.580 + * argument is a positive finite odd integer,
1.581 + * </ul>
1.582 + * then the result is negative infinity.
1.583 + *
1.584 + * <li>If the first argument is finite and less than zero
1.585 + * <ul>
1.586 + * <li> if the second argument is a finite even integer, the
1.587 + * result is equal to the result of raising the absolute value of
1.588 + * the first argument to the power of the second argument
1.589 + *
1.590 + * <li>if the second argument is a finite odd integer, the result
1.591 + * is equal to the negative of the result of raising the absolute
1.592 + * value of the first argument to the power of the second
1.593 + * argument
1.594 + *
1.595 + * <li>if the second argument is finite and not an integer, then
1.596 + * the result is NaN.
1.597 + * </ul>
1.598 + *
1.599 + * <li>If both arguments are integers, then the result is exactly equal
1.600 + * to the mathematical result of raising the first argument to the power
1.601 + * of the second argument if that result can in fact be represented
1.602 + * exactly as a {@code double} value.</ul>
1.603 + *
1.604 + * <p>(In the foregoing descriptions, a floating-point value is
1.605 + * considered to be an integer if and only if it is finite and a
1.606 + * fixed point of the method {@link #ceil ceil} or,
1.607 + * equivalently, a fixed point of the method {@link #floor
1.608 + * floor}. A value is a fixed point of a one-argument
1.609 + * method if and only if the result of applying the method to the
1.610 + * value is equal to the value.)
1.611 + *
1.612 + * @param a base.
1.613 + * @param b the exponent.
1.614 + * @return the value {@code a}<sup>{@code b}</sup>.
1.615 + */
1.616 + public static native double pow(double a, double b);
1.617 +
1.618 + /**
1.619 + * Returns the closest {@code int} to the argument, with ties
1.620 + * rounding up.
1.621 + *
1.622 + * <p>Special cases:
1.623 + * <ul><li>If the argument is NaN, the result is 0.
1.624 + * <li>If the argument is negative infinity or any value less than or
1.625 + * equal to the value of {@code Integer.MIN_VALUE}, the result is
1.626 + * equal to the value of {@code Integer.MIN_VALUE}.
1.627 + * <li>If the argument is positive infinity or any value greater than or
1.628 + * equal to the value of {@code Integer.MAX_VALUE}, the result is
1.629 + * equal to the value of {@code Integer.MAX_VALUE}.</ul>
1.630 + *
1.631 + * @param a a floating-point value to be rounded to an integer.
1.632 + * @return the value of the argument rounded to the nearest
1.633 + * {@code int} value.
1.634 + * @see java.lang.Integer#MAX_VALUE
1.635 + * @see java.lang.Integer#MIN_VALUE
1.636 + */
1.637 + public static int round(float a) {
1.638 + return Math.round(a);
1.639 + }
1.640 +
1.641 + /**
1.642 + * Returns the closest {@code long} to the argument, with ties
1.643 + * rounding up.
1.644 + *
1.645 + * <p>Special cases:
1.646 + * <ul><li>If the argument is NaN, the result is 0.
1.647 + * <li>If the argument is negative infinity or any value less than or
1.648 + * equal to the value of {@code Long.MIN_VALUE}, the result is
1.649 + * equal to the value of {@code Long.MIN_VALUE}.
1.650 + * <li>If the argument is positive infinity or any value greater than or
1.651 + * equal to the value of {@code Long.MAX_VALUE}, the result is
1.652 + * equal to the value of {@code Long.MAX_VALUE}.</ul>
1.653 + *
1.654 + * @param a a floating-point value to be rounded to a
1.655 + * {@code long}.
1.656 + * @return the value of the argument rounded to the nearest
1.657 + * {@code long} value.
1.658 + * @see java.lang.Long#MAX_VALUE
1.659 + * @see java.lang.Long#MIN_VALUE
1.660 + */
1.661 + public static long round(double a) {
1.662 + return Math.round(a);
1.663 + }
1.664 +
1.665 + private static Random randomNumberGenerator;
1.666 +
1.667 + private static synchronized Random initRNG() {
1.668 + Random rnd = randomNumberGenerator;
1.669 + return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd;
1.670 + }
1.671 +
1.672 + /**
1.673 + * Returns a {@code double} value with a positive sign, greater
1.674 + * than or equal to {@code 0.0} and less than {@code 1.0}.
1.675 + * Returned values are chosen pseudorandomly with (approximately)
1.676 + * uniform distribution from that range.
1.677 + *
1.678 + * <p>When this method is first called, it creates a single new
1.679 + * pseudorandom-number generator, exactly as if by the expression
1.680 + *
1.681 + * <blockquote>{@code new java.util.Random()}</blockquote>
1.682 + *
1.683 + * This new pseudorandom-number generator is used thereafter for
1.684 + * all calls to this method and is used nowhere else.
1.685 + *
1.686 + * <p>This method is properly synchronized to allow correct use by
1.687 + * more than one thread. However, if many threads need to generate
1.688 + * pseudorandom numbers at a great rate, it may reduce contention
1.689 + * for each thread to have its own pseudorandom number generator.
1.690 + *
1.691 + * @return a pseudorandom {@code double} greater than or equal
1.692 + * to {@code 0.0} and less than {@code 1.0}.
1.693 + * @see Random#nextDouble()
1.694 + */
1.695 + public static double random() {
1.696 + Random rnd = randomNumberGenerator;
1.697 + if (rnd == null) rnd = initRNG();
1.698 + return rnd.nextDouble();
1.699 + }
1.700 +
1.701 + /**
1.702 + * Returns the absolute value of an {@code int} value..
1.703 + * If the argument is not negative, the argument is returned.
1.704 + * If the argument is negative, the negation of the argument is returned.
1.705 + *
1.706 + * <p>Note that if the argument is equal to the value of
1.707 + * {@link Integer#MIN_VALUE}, the most negative representable
1.708 + * {@code int} value, the result is that same value, which is
1.709 + * negative.
1.710 + *
1.711 + * @param a the argument whose absolute value is to be determined.
1.712 + * @return the absolute value of the argument.
1.713 + */
1.714 + public static int abs(int a) {
1.715 + return (a < 0) ? -a : a;
1.716 + }
1.717 +
1.718 + /**
1.719 + * Returns the absolute value of a {@code long} value.
1.720 + * If the argument is not negative, the argument is returned.
1.721 + * If the argument is negative, the negation of the argument is returned.
1.722 + *
1.723 + * <p>Note that if the argument is equal to the value of
1.724 + * {@link Long#MIN_VALUE}, the most negative representable
1.725 + * {@code long} value, the result is that same value, which
1.726 + * is negative.
1.727 + *
1.728 + * @param a the argument whose absolute value is to be determined.
1.729 + * @return the absolute value of the argument.
1.730 + */
1.731 + public static long abs(long a) {
1.732 + return (a < 0) ? -a : a;
1.733 + }
1.734 +
1.735 + /**
1.736 + * Returns the absolute value of a {@code float} value.
1.737 + * If the argument is not negative, the argument is returned.
1.738 + * If the argument is negative, the negation of the argument is returned.
1.739 + * Special cases:
1.740 + * <ul><li>If the argument is positive zero or negative zero, the
1.741 + * result is positive zero.
1.742 + * <li>If the argument is infinite, the result is positive infinity.
1.743 + * <li>If the argument is NaN, the result is NaN.</ul>
1.744 + * In other words, the result is the same as the value of the expression:
1.745 + * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
1.746 + *
1.747 + * @param a the argument whose absolute value is to be determined
1.748 + * @return the absolute value of the argument.
1.749 + */
1.750 + public static float abs(float a) {
1.751 + return (a <= 0.0F) ? 0.0F - a : a;
1.752 + }
1.753 +
1.754 + /**
1.755 + * Returns the absolute value of a {@code double} value.
1.756 + * If the argument is not negative, the argument is returned.
1.757 + * If the argument is negative, the negation of the argument is returned.
1.758 + * Special cases:
1.759 + * <ul><li>If the argument is positive zero or negative zero, the result
1.760 + * is positive zero.
1.761 + * <li>If the argument is infinite, the result is positive infinity.
1.762 + * <li>If the argument is NaN, the result is NaN.</ul>
1.763 + * In other words, the result is the same as the value of the expression:
1.764 + * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
1.765 + *
1.766 + * @param a the argument whose absolute value is to be determined
1.767 + * @return the absolute value of the argument.
1.768 + */
1.769 + public static double abs(double a) {
1.770 + return (a <= 0.0D) ? 0.0D - a : a;
1.771 + }
1.772 +
1.773 + /**
1.774 + * Returns the greater of two {@code int} values. That is, the
1.775 + * result is the argument closer to the value of
1.776 + * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1.777 + * the result is that same value.
1.778 + *
1.779 + * @param a an argument.
1.780 + * @param b another argument.
1.781 + * @return the larger of {@code a} and {@code b}.
1.782 + */
1.783 + public static int max(int a, int b) {
1.784 + return (a >= b) ? a : b;
1.785 + }
1.786 +
1.787 + /**
1.788 + * Returns the greater of two {@code long} values. That is, the
1.789 + * result is the argument closer to the value of
1.790 + * {@link Long#MAX_VALUE}. If the arguments have the same value,
1.791 + * the result is that same value.
1.792 + *
1.793 + * @param a an argument.
1.794 + * @param b another argument.
1.795 + * @return the larger of {@code a} and {@code b}.
1.796 + */
1.797 + public static long max(long a, long b) {
1.798 + return (a >= b) ? a : b;
1.799 + }
1.800 +
1.801 + // Use raw bit-wise conversions on guaranteed non-NaN arguments.
1.802 + private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f);
1.803 + private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
1.804 +
1.805 + /**
1.806 + * Returns the greater of two {@code float} values. That is,
1.807 + * the result is the argument closer to positive infinity. If the
1.808 + * arguments have the same value, the result is that same
1.809 + * value. If either value is NaN, then the result is NaN. Unlike
1.810 + * the numerical comparison operators, this method considers
1.811 + * negative zero to be strictly smaller than positive zero. If one
1.812 + * argument is positive zero and the other negative zero, the
1.813 + * result is positive zero.
1.814 + *
1.815 + * @param a an argument.
1.816 + * @param b another argument.
1.817 + * @return the larger of {@code a} and {@code b}.
1.818 + */
1.819 + public static float max(float a, float b) {
1.820 + if (a != a)
1.821 + return a; // a is NaN
1.822 + if ((a == 0.0f) &&
1.823 + (b == 0.0f) &&
1.824 + (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
1.825 + // Raw conversion ok since NaN can't map to -0.0.
1.826 + return b;
1.827 + }
1.828 + return (a >= b) ? a : b;
1.829 + }
1.830 +
1.831 + /**
1.832 + * Returns the greater of two {@code double} values. That
1.833 + * is, the result is the argument closer to positive infinity. If
1.834 + * the arguments have the same value, the result is that same
1.835 + * value. If either value is NaN, then the result is NaN. Unlike
1.836 + * the numerical comparison operators, this method considers
1.837 + * negative zero to be strictly smaller than positive zero. If one
1.838 + * argument is positive zero and the other negative zero, the
1.839 + * result is positive zero.
1.840 + *
1.841 + * @param a an argument.
1.842 + * @param b another argument.
1.843 + * @return the larger of {@code a} and {@code b}.
1.844 + */
1.845 + public static double max(double a, double b) {
1.846 + if (a != a)
1.847 + return a; // a is NaN
1.848 + if ((a == 0.0d) &&
1.849 + (b == 0.0d) &&
1.850 + (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
1.851 + // Raw conversion ok since NaN can't map to -0.0.
1.852 + return b;
1.853 + }
1.854 + return (a >= b) ? a : b;
1.855 + }
1.856 +
1.857 + /**
1.858 + * Returns the smaller of two {@code int} values. That is,
1.859 + * the result the argument closer to the value of
1.860 + * {@link Integer#MIN_VALUE}. If the arguments have the same
1.861 + * value, the result is that same value.
1.862 + *
1.863 + * @param a an argument.
1.864 + * @param b another argument.
1.865 + * @return the smaller of {@code a} and {@code b}.
1.866 + */
1.867 + public static int min(int a, int b) {
1.868 + return (a <= b) ? a : b;
1.869 + }
1.870 +
1.871 + /**
1.872 + * Returns the smaller of two {@code long} values. That is,
1.873 + * the result is the argument closer to the value of
1.874 + * {@link Long#MIN_VALUE}. If the arguments have the same
1.875 + * value, the result is that same value.
1.876 + *
1.877 + * @param a an argument.
1.878 + * @param b another argument.
1.879 + * @return the smaller of {@code a} and {@code b}.
1.880 + */
1.881 + public static long min(long a, long b) {
1.882 + return (a <= b) ? a : b;
1.883 + }
1.884 +
1.885 + /**
1.886 + * Returns the smaller of two {@code float} values. That is,
1.887 + * the result is the value closer to negative infinity. If the
1.888 + * arguments have the same value, the result is that same
1.889 + * value. If either value is NaN, then the result is NaN. Unlike
1.890 + * the numerical comparison operators, this method considers
1.891 + * negative zero to be strictly smaller than positive zero. If
1.892 + * one argument is positive zero and the other is negative zero,
1.893 + * the result is negative zero.
1.894 + *
1.895 + * @param a an argument.
1.896 + * @param b another argument.
1.897 + * @return the smaller of {@code a} and {@code b.}
1.898 + */
1.899 + public static float min(float a, float b) {
1.900 + if (a != a)
1.901 + return a; // a is NaN
1.902 + if ((a == 0.0f) &&
1.903 + (b == 0.0f) &&
1.904 + (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
1.905 + // Raw conversion ok since NaN can't map to -0.0.
1.906 + return b;
1.907 + }
1.908 + return (a <= b) ? a : b;
1.909 + }
1.910 +
1.911 + /**
1.912 + * Returns the smaller of two {@code double} values. That
1.913 + * is, the result is the value closer to negative infinity. If the
1.914 + * arguments have the same value, the result is that same
1.915 + * value. If either value is NaN, then the result is NaN. Unlike
1.916 + * the numerical comparison operators, this method considers
1.917 + * negative zero to be strictly smaller than positive zero. If one
1.918 + * argument is positive zero and the other is negative zero, the
1.919 + * result is negative zero.
1.920 + *
1.921 + * @param a an argument.
1.922 + * @param b another argument.
1.923 + * @return the smaller of {@code a} and {@code b}.
1.924 + */
1.925 + public static double min(double a, double b) {
1.926 + if (a != a)
1.927 + return a; // a is NaN
1.928 + if ((a == 0.0d) &&
1.929 + (b == 0.0d) &&
1.930 + (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
1.931 + // Raw conversion ok since NaN can't map to -0.0.
1.932 + return b;
1.933 + }
1.934 + return (a <= b) ? a : b;
1.935 + }
1.936 +
1.937 + /**
1.938 + * Returns the size of an ulp of the argument. An ulp of a
1.939 + * {@code double} value is the positive distance between this
1.940 + * floating-point value and the {@code double} value next
1.941 + * larger in magnitude. Note that for non-NaN <i>x</i>,
1.942 + * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1.943 + *
1.944 + * <p>Special Cases:
1.945 + * <ul>
1.946 + * <li> If the argument is NaN, then the result is NaN.
1.947 + * <li> If the argument is positive or negative infinity, then the
1.948 + * result is positive infinity.
1.949 + * <li> If the argument is positive or negative zero, then the result is
1.950 + * {@code Double.MIN_VALUE}.
1.951 + * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1.952 + * the result is equal to 2<sup>971</sup>.
1.953 + * </ul>
1.954 + *
1.955 + * @param d the floating-point value whose ulp is to be returned
1.956 + * @return the size of an ulp of the argument
1.957 + * @author Joseph D. Darcy
1.958 + * @since 1.5
1.959 + */
1.960 + public static double ulp(double d) {
1.961 + return sun.misc.FpUtils.ulp(d);
1.962 + }
1.963 +
1.964 + /**
1.965 + * Returns the size of an ulp of the argument. An ulp of a
1.966 + * {@code float} value is the positive distance between this
1.967 + * floating-point value and the {@code float} value next
1.968 + * larger in magnitude. Note that for non-NaN <i>x</i>,
1.969 + * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1.970 + *
1.971 + * <p>Special Cases:
1.972 + * <ul>
1.973 + * <li> If the argument is NaN, then the result is NaN.
1.974 + * <li> If the argument is positive or negative infinity, then the
1.975 + * result is positive infinity.
1.976 + * <li> If the argument is positive or negative zero, then the result is
1.977 + * {@code Float.MIN_VALUE}.
1.978 + * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1.979 + * the result is equal to 2<sup>104</sup>.
1.980 + * </ul>
1.981 + *
1.982 + * @param f the floating-point value whose ulp is to be returned
1.983 + * @return the size of an ulp of the argument
1.984 + * @author Joseph D. Darcy
1.985 + * @since 1.5
1.986 + */
1.987 + public static float ulp(float f) {
1.988 + return sun.misc.FpUtils.ulp(f);
1.989 + }
1.990 +
1.991 + /**
1.992 + * Returns the signum function of the argument; zero if the argument
1.993 + * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1.994 + * argument is less than zero.
1.995 + *
1.996 + * <p>Special Cases:
1.997 + * <ul>
1.998 + * <li> If the argument is NaN, then the result is NaN.
1.999 + * <li> If the argument is positive zero or negative zero, then the
1.1000 + * result is the same as the argument.
1.1001 + * </ul>
1.1002 + *
1.1003 + * @param d the floating-point value whose signum is to be returned
1.1004 + * @return the signum function of the argument
1.1005 + * @author Joseph D. Darcy
1.1006 + * @since 1.5
1.1007 + */
1.1008 + public static double signum(double d) {
1.1009 + return sun.misc.FpUtils.signum(d);
1.1010 + }
1.1011 +
1.1012 + /**
1.1013 + * Returns the signum function of the argument; zero if the argument
1.1014 + * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1.1015 + * argument is less than zero.
1.1016 + *
1.1017 + * <p>Special Cases:
1.1018 + * <ul>
1.1019 + * <li> If the argument is NaN, then the result is NaN.
1.1020 + * <li> If the argument is positive zero or negative zero, then the
1.1021 + * result is the same as the argument.
1.1022 + * </ul>
1.1023 + *
1.1024 + * @param f the floating-point value whose signum is to be returned
1.1025 + * @return the signum function of the argument
1.1026 + * @author Joseph D. Darcy
1.1027 + * @since 1.5
1.1028 + */
1.1029 + public static float signum(float f) {
1.1030 + return sun.misc.FpUtils.signum(f);
1.1031 + }
1.1032 +
1.1033 + /**
1.1034 + * Returns the hyperbolic sine of a {@code double} value.
1.1035 + * The hyperbolic sine of <i>x</i> is defined to be
1.1036 + * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1.1037 + * where <i>e</i> is {@linkplain Math#E Euler's number}.
1.1038 + *
1.1039 + * <p>Special cases:
1.1040 + * <ul>
1.1041 + *
1.1042 + * <li>If the argument is NaN, then the result is NaN.
1.1043 + *
1.1044 + * <li>If the argument is infinite, then the result is an infinity
1.1045 + * with the same sign as the argument.
1.1046 + *
1.1047 + * <li>If the argument is zero, then the result is a zero with the
1.1048 + * same sign as the argument.
1.1049 + *
1.1050 + * </ul>
1.1051 + *
1.1052 + * @param x The number whose hyperbolic sine is to be returned.
1.1053 + * @return The hyperbolic sine of {@code x}.
1.1054 + * @since 1.5
1.1055 + */
1.1056 + public static native double sinh(double x);
1.1057 +
1.1058 + /**
1.1059 + * Returns the hyperbolic cosine of a {@code double} value.
1.1060 + * The hyperbolic cosine of <i>x</i> is defined to be
1.1061 + * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1.1062 + * where <i>e</i> is {@linkplain Math#E Euler's number}.
1.1063 + *
1.1064 + * <p>Special cases:
1.1065 + * <ul>
1.1066 + *
1.1067 + * <li>If the argument is NaN, then the result is NaN.
1.1068 + *
1.1069 + * <li>If the argument is infinite, then the result is positive
1.1070 + * infinity.
1.1071 + *
1.1072 + * <li>If the argument is zero, then the result is {@code 1.0}.
1.1073 + *
1.1074 + * </ul>
1.1075 + *
1.1076 + * @param x The number whose hyperbolic cosine is to be returned.
1.1077 + * @return The hyperbolic cosine of {@code x}.
1.1078 + * @since 1.5
1.1079 + */
1.1080 + public static native double cosh(double x);
1.1081 +
1.1082 + /**
1.1083 + * Returns the hyperbolic tangent of a {@code double} value.
1.1084 + * The hyperbolic tangent of <i>x</i> is defined to be
1.1085 + * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1.1086 + * in other words, {@linkplain Math#sinh
1.1087 + * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1.1088 + * that the absolute value of the exact tanh is always less than
1.1089 + * 1.
1.1090 + *
1.1091 + * <p>Special cases:
1.1092 + * <ul>
1.1093 + *
1.1094 + * <li>If the argument is NaN, then the result is NaN.
1.1095 + *
1.1096 + * <li>If the argument is zero, then the result is a zero with the
1.1097 + * same sign as the argument.
1.1098 + *
1.1099 + * <li>If the argument is positive infinity, then the result is
1.1100 + * {@code +1.0}.
1.1101 + *
1.1102 + * <li>If the argument is negative infinity, then the result is
1.1103 + * {@code -1.0}.
1.1104 + *
1.1105 + * </ul>
1.1106 + *
1.1107 + * @param x The number whose hyperbolic tangent is to be returned.
1.1108 + * @return The hyperbolic tangent of {@code x}.
1.1109 + * @since 1.5
1.1110 + */
1.1111 + public static native double tanh(double x);
1.1112 +
1.1113 + /**
1.1114 + * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1.1115 + * without intermediate overflow or underflow.
1.1116 + *
1.1117 + * <p>Special cases:
1.1118 + * <ul>
1.1119 + *
1.1120 + * <li> If either argument is infinite, then the result
1.1121 + * is positive infinity.
1.1122 + *
1.1123 + * <li> If either argument is NaN and neither argument is infinite,
1.1124 + * then the result is NaN.
1.1125 + *
1.1126 + * </ul>
1.1127 + *
1.1128 + * @param x a value
1.1129 + * @param y a value
1.1130 + * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1.1131 + * without intermediate overflow or underflow
1.1132 + * @since 1.5
1.1133 + */
1.1134 + public static native double hypot(double x, double y);
1.1135 +
1.1136 + /**
1.1137 + * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1.1138 + * <i>x</i> near 0, the exact sum of
1.1139 + * {@code expm1(x)} + 1 is much closer to the true
1.1140 + * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1.1141 + *
1.1142 + * <p>Special cases:
1.1143 + * <ul>
1.1144 + * <li>If the argument is NaN, the result is NaN.
1.1145 + *
1.1146 + * <li>If the argument is positive infinity, then the result is
1.1147 + * positive infinity.
1.1148 + *
1.1149 + * <li>If the argument is negative infinity, then the result is
1.1150 + * -1.0.
1.1151 + *
1.1152 + * <li>If the argument is zero, then the result is a zero with the
1.1153 + * same sign as the argument.
1.1154 + *
1.1155 + * </ul>
1.1156 + *
1.1157 + * @param x the exponent to raise <i>e</i> to in the computation of
1.1158 + * <i>e</i><sup>{@code x}</sup> -1.
1.1159 + * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1.1160 + * @since 1.5
1.1161 + */
1.1162 + public static native double expm1(double x);
1.1163 +
1.1164 + /**
1.1165 + * Returns the natural logarithm of the sum of the argument and 1.
1.1166 + * Note that for small values {@code x}, the result of
1.1167 + * {@code log1p(x)} is much closer to the true result of ln(1
1.1168 + * + {@code x}) than the floating-point evaluation of
1.1169 + * {@code log(1.0+x)}.
1.1170 + *
1.1171 + * <p>Special cases:
1.1172 + * <ul>
1.1173 + *
1.1174 + * <li>If the argument is NaN or less than -1, then the result is
1.1175 + * NaN.
1.1176 + *
1.1177 + * <li>If the argument is positive infinity, then the result is
1.1178 + * positive infinity.
1.1179 + *
1.1180 + * <li>If the argument is negative one, then the result is
1.1181 + * negative infinity.
1.1182 + *
1.1183 + * <li>If the argument is zero, then the result is a zero with the
1.1184 + * same sign as the argument.
1.1185 + *
1.1186 + * </ul>
1.1187 + *
1.1188 + * @param x a value
1.1189 + * @return the value ln({@code x} + 1), the natural
1.1190 + * log of {@code x} + 1
1.1191 + * @since 1.5
1.1192 + */
1.1193 + public static native double log1p(double x);
1.1194 +
1.1195 + /**
1.1196 + * Returns the first floating-point argument with the sign of the
1.1197 + * second floating-point argument. For this method, a NaN
1.1198 + * {@code sign} argument is always treated as if it were
1.1199 + * positive.
1.1200 + *
1.1201 + * @param magnitude the parameter providing the magnitude of the result
1.1202 + * @param sign the parameter providing the sign of the result
1.1203 + * @return a value with the magnitude of {@code magnitude}
1.1204 + * and the sign of {@code sign}.
1.1205 + * @since 1.6
1.1206 + */
1.1207 + public static double copySign(double magnitude, double sign) {
1.1208 + return sun.misc.FpUtils.copySign(magnitude, sign);
1.1209 + }
1.1210 +
1.1211 + /**
1.1212 + * Returns the first floating-point argument with the sign of the
1.1213 + * second floating-point argument. For this method, a NaN
1.1214 + * {@code sign} argument is always treated as if it were
1.1215 + * positive.
1.1216 + *
1.1217 + * @param magnitude the parameter providing the magnitude of the result
1.1218 + * @param sign the parameter providing the sign of the result
1.1219 + * @return a value with the magnitude of {@code magnitude}
1.1220 + * and the sign of {@code sign}.
1.1221 + * @since 1.6
1.1222 + */
1.1223 + public static float copySign(float magnitude, float sign) {
1.1224 + return sun.misc.FpUtils.copySign(magnitude, sign);
1.1225 + }
1.1226 + /**
1.1227 + * Returns the unbiased exponent used in the representation of a
1.1228 + * {@code float}. Special cases:
1.1229 + *
1.1230 + * <ul>
1.1231 + * <li>If the argument is NaN or infinite, then the result is
1.1232 + * {@link Float#MAX_EXPONENT} + 1.
1.1233 + * <li>If the argument is zero or subnormal, then the result is
1.1234 + * {@link Float#MIN_EXPONENT} -1.
1.1235 + * </ul>
1.1236 + * @param f a {@code float} value
1.1237 + * @since 1.6
1.1238 + */
1.1239 + public static int getExponent(float f) {
1.1240 + return sun.misc.FpUtils.getExponent(f);
1.1241 + }
1.1242 +
1.1243 + /**
1.1244 + * Returns the unbiased exponent used in the representation of a
1.1245 + * {@code double}. Special cases:
1.1246 + *
1.1247 + * <ul>
1.1248 + * <li>If the argument is NaN or infinite, then the result is
1.1249 + * {@link Double#MAX_EXPONENT} + 1.
1.1250 + * <li>If the argument is zero or subnormal, then the result is
1.1251 + * {@link Double#MIN_EXPONENT} -1.
1.1252 + * </ul>
1.1253 + * @param d a {@code double} value
1.1254 + * @since 1.6
1.1255 + */
1.1256 + public static int getExponent(double d) {
1.1257 + return sun.misc.FpUtils.getExponent(d);
1.1258 + }
1.1259 +
1.1260 + /**
1.1261 + * Returns the floating-point number adjacent to the first
1.1262 + * argument in the direction of the second argument. If both
1.1263 + * arguments compare as equal the second argument is returned.
1.1264 + *
1.1265 + * <p>Special cases:
1.1266 + * <ul>
1.1267 + * <li> If either argument is a NaN, then NaN is returned.
1.1268 + *
1.1269 + * <li> If both arguments are signed zeros, {@code direction}
1.1270 + * is returned unchanged (as implied by the requirement of
1.1271 + * returning the second argument if the arguments compare as
1.1272 + * equal).
1.1273 + *
1.1274 + * <li> If {@code start} is
1.1275 + * ±{@link Double#MIN_VALUE} and {@code direction}
1.1276 + * has a value such that the result should have a smaller
1.1277 + * magnitude, then a zero with the same sign as {@code start}
1.1278 + * is returned.
1.1279 + *
1.1280 + * <li> If {@code start} is infinite and
1.1281 + * {@code direction} has a value such that the result should
1.1282 + * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1.1283 + * same sign as {@code start} is returned.
1.1284 + *
1.1285 + * <li> If {@code start} is equal to ±
1.1286 + * {@link Double#MAX_VALUE} and {@code direction} has a
1.1287 + * value such that the result should have a larger magnitude, an
1.1288 + * infinity with same sign as {@code start} is returned.
1.1289 + * </ul>
1.1290 + *
1.1291 + * @param start starting floating-point value
1.1292 + * @param direction value indicating which of
1.1293 + * {@code start}'s neighbors or {@code start} should
1.1294 + * be returned
1.1295 + * @return The floating-point number adjacent to {@code start} in the
1.1296 + * direction of {@code direction}.
1.1297 + * @since 1.6
1.1298 + */
1.1299 + public static double nextAfter(double start, double direction) {
1.1300 + return sun.misc.FpUtils.nextAfter(start, direction);
1.1301 + }
1.1302 +
1.1303 + /**
1.1304 + * Returns the floating-point number adjacent to the first
1.1305 + * argument in the direction of the second argument. If both
1.1306 + * arguments compare as equal a value equivalent to the second argument
1.1307 + * is returned.
1.1308 + *
1.1309 + * <p>Special cases:
1.1310 + * <ul>
1.1311 + * <li> If either argument is a NaN, then NaN is returned.
1.1312 + *
1.1313 + * <li> If both arguments are signed zeros, a value equivalent
1.1314 + * to {@code direction} is returned.
1.1315 + *
1.1316 + * <li> If {@code start} is
1.1317 + * ±{@link Float#MIN_VALUE} and {@code direction}
1.1318 + * has a value such that the result should have a smaller
1.1319 + * magnitude, then a zero with the same sign as {@code start}
1.1320 + * is returned.
1.1321 + *
1.1322 + * <li> If {@code start} is infinite and
1.1323 + * {@code direction} has a value such that the result should
1.1324 + * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1.1325 + * same sign as {@code start} is returned.
1.1326 + *
1.1327 + * <li> If {@code start} is equal to ±
1.1328 + * {@link Float#MAX_VALUE} and {@code direction} has a
1.1329 + * value such that the result should have a larger magnitude, an
1.1330 + * infinity with same sign as {@code start} is returned.
1.1331 + * </ul>
1.1332 + *
1.1333 + * @param start starting floating-point value
1.1334 + * @param direction value indicating which of
1.1335 + * {@code start}'s neighbors or {@code start} should
1.1336 + * be returned
1.1337 + * @return The floating-point number adjacent to {@code start} in the
1.1338 + * direction of {@code direction}.
1.1339 + * @since 1.6
1.1340 + */
1.1341 + public static float nextAfter(float start, double direction) {
1.1342 + return sun.misc.FpUtils.nextAfter(start, direction);
1.1343 + }
1.1344 +
1.1345 + /**
1.1346 + * Returns the floating-point value adjacent to {@code d} in
1.1347 + * the direction of positive infinity. This method is
1.1348 + * semantically equivalent to {@code nextAfter(d,
1.1349 + * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1.1350 + * implementation may run faster than its equivalent
1.1351 + * {@code nextAfter} call.
1.1352 + *
1.1353 + * <p>Special Cases:
1.1354 + * <ul>
1.1355 + * <li> If the argument is NaN, the result is NaN.
1.1356 + *
1.1357 + * <li> If the argument is positive infinity, the result is
1.1358 + * positive infinity.
1.1359 + *
1.1360 + * <li> If the argument is zero, the result is
1.1361 + * {@link Double#MIN_VALUE}
1.1362 + *
1.1363 + * </ul>
1.1364 + *
1.1365 + * @param d starting floating-point value
1.1366 + * @return The adjacent floating-point value closer to positive
1.1367 + * infinity.
1.1368 + * @since 1.6
1.1369 + */
1.1370 + public static double nextUp(double d) {
1.1371 + return sun.misc.FpUtils.nextUp(d);
1.1372 + }
1.1373 +
1.1374 + /**
1.1375 + * Returns the floating-point value adjacent to {@code f} in
1.1376 + * the direction of positive infinity. This method is
1.1377 + * semantically equivalent to {@code nextAfter(f,
1.1378 + * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1.1379 + * implementation may run faster than its equivalent
1.1380 + * {@code nextAfter} call.
1.1381 + *
1.1382 + * <p>Special Cases:
1.1383 + * <ul>
1.1384 + * <li> If the argument is NaN, the result is NaN.
1.1385 + *
1.1386 + * <li> If the argument is positive infinity, the result is
1.1387 + * positive infinity.
1.1388 + *
1.1389 + * <li> If the argument is zero, the result is
1.1390 + * {@link Float#MIN_VALUE}
1.1391 + *
1.1392 + * </ul>
1.1393 + *
1.1394 + * @param f starting floating-point value
1.1395 + * @return The adjacent floating-point value closer to positive
1.1396 + * infinity.
1.1397 + * @since 1.6
1.1398 + */
1.1399 + public static float nextUp(float f) {
1.1400 + return sun.misc.FpUtils.nextUp(f);
1.1401 + }
1.1402 +
1.1403 +
1.1404 + /**
1.1405 + * Return {@code d} ×
1.1406 + * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1.1407 + * by a single correctly rounded floating-point multiply to a
1.1408 + * member of the double value set. See the Java
1.1409 + * Language Specification for a discussion of floating-point
1.1410 + * value sets. If the exponent of the result is between {@link
1.1411 + * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1.1412 + * answer is calculated exactly. If the exponent of the result
1.1413 + * would be larger than {@code Double.MAX_EXPONENT}, an
1.1414 + * infinity is returned. Note that if the result is subnormal,
1.1415 + * precision may be lost; that is, when {@code scalb(x, n)}
1.1416 + * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1.1417 + * <i>x</i>. When the result is non-NaN, the result has the same
1.1418 + * sign as {@code d}.
1.1419 + *
1.1420 + * <p>Special cases:
1.1421 + * <ul>
1.1422 + * <li> If the first argument is NaN, NaN is returned.
1.1423 + * <li> If the first argument is infinite, then an infinity of the
1.1424 + * same sign is returned.
1.1425 + * <li> If the first argument is zero, then a zero of the same
1.1426 + * sign is returned.
1.1427 + * </ul>
1.1428 + *
1.1429 + * @param d number to be scaled by a power of two.
1.1430 + * @param scaleFactor power of 2 used to scale {@code d}
1.1431 + * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1.1432 + * @since 1.6
1.1433 + */
1.1434 + public static double scalb(double d, int scaleFactor) {
1.1435 + return sun.misc.FpUtils.scalb(d, scaleFactor);
1.1436 + }
1.1437 +
1.1438 + /**
1.1439 + * Return {@code f} ×
1.1440 + * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1.1441 + * by a single correctly rounded floating-point multiply to a
1.1442 + * member of the float value set. See the Java
1.1443 + * Language Specification for a discussion of floating-point
1.1444 + * value sets. If the exponent of the result is between {@link
1.1445 + * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1.1446 + * answer is calculated exactly. If the exponent of the result
1.1447 + * would be larger than {@code Float.MAX_EXPONENT}, an
1.1448 + * infinity is returned. Note that if the result is subnormal,
1.1449 + * precision may be lost; that is, when {@code scalb(x, n)}
1.1450 + * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1.1451 + * <i>x</i>. When the result is non-NaN, the result has the same
1.1452 + * sign as {@code f}.
1.1453 + *
1.1454 + * <p>Special cases:
1.1455 + * <ul>
1.1456 + * <li> If the first argument is NaN, NaN is returned.
1.1457 + * <li> If the first argument is infinite, then an infinity of the
1.1458 + * same sign is returned.
1.1459 + * <li> If the first argument is zero, then a zero of the same
1.1460 + * sign is returned.
1.1461 + * </ul>
1.1462 + *
1.1463 + * @param f number to be scaled by a power of two.
1.1464 + * @param scaleFactor power of 2 used to scale {@code f}
1.1465 + * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1.1466 + * @since 1.6
1.1467 + */
1.1468 + public static float scalb(float f, int scaleFactor) {
1.1469 + return sun.misc.FpUtils.scalb(f, scaleFactor);
1.1470 + }
1.1471 +}