12-数学运算 · Java 开源项目中文文档

# 12-数学运算 [原文链接](http://code.google.com/p/guava-libraries/wiki/MathExplained) [译文链接](http://ifeve.com/google-guava-math) **译者：**沈义扬 ## 范例 ``` int logFloor = LongMath.log2(n, FLOOR); int mustNotOverflow = IntMath.checkedMultiply(x, y); long quotient = LongMath.divide(knownMultipleOfThree, 3, RoundingMode.UNNECESSARY); // fail fast on non-multiple of 3 BigInteger nearestInteger = DoubleMath.roundToBigInteger(d, RoundingMode.HALF_EVEN); BigInteger sideLength = BigIntegerMath.sqrt(area, CEILING); ``` ## 为什么使用Guava Math * Guava Math针对各种不常见的溢出情况都有充分的测试；对溢出语义，Guava文档也有相应的说明；如果运算的溢出检查不能通过，将导致快速失败； * Guava Math的性能经过了精心的设计和调优；虽然性能不可避免地依据具体硬件细节而有所差异，但Guava Math的速度通常可以与Apache Commons的MathUtils相比，在某些场景下甚至还有显著提升； * Guava Math在设计上考虑了可读性和正确的编程习惯；IntMath.log2(x, CEILING) 所表达的含义，即使在快速阅读时也是清晰明确的。而32-Integer.numberOfLeadingZeros(x – 1)对于阅读者来说则不够清晰。 _注意：Guava Math和GWT格外不兼容，这是因为Java和Java Script语言的运算溢出逻辑不一样。_ ## 整数运算 Guava Math主要处理三种整数类型：int、long和BigInteger。这三种类型的运算工具类分别叫做[IntMath](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html)、[LongMath](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html)和[BigIntegerMath](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html)。 ### 有溢出检查的运算 Guava Math提供了若干有溢出检查的运算方法：结果溢出时，这些方法将快速失败而不是忽略溢出 | [`IntMath.checkedAdd`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#checkedAdd%28int, int%29) | [`LongMath.checkedAdd`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedAdd%28long, long%29) | |:--- |:--- |:--- |:--- | | [`IntMath.checkedSubtract`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#checkedSubtract%28int, int%29) | [`LongMath.checkedSubtract`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedSubtract%28long, long%29) | | [`IntMath.checkedMultiply`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#checkedMultiply%28int, int%29) | [`LongMath.checkedMultiply`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedMultiply%28long, long%29) | | [`IntMath.checkedPow`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#checkedPow%28int, int%29) | [`LongMath.checkedPow`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedPow%28long, long%29) | ``` IntMath.checkedAdd(Integer.MAX_VALUE, Integer.MAX_VALUE); // throws ArithmeticException ``` ## 实数运算 IntMath、LongMath和BigIntegerMath提供了很多实数运算的方法，并把最终运算结果舍入成整数。这些方法接受一个[java.math.RoundingMode](http://docs.oracle.com/javase/7/docs/api/java/math/RoundingMode.html)枚举值作为舍入的模式： * DOWN：向零方向舍入（去尾法） * UP：远离零方向舍入 * FLOOR：向负无限大方向舍入 * CEILING：向正无限大方向舍入 * UNNECESSARY：不需要舍入，如果用此模式进行舍入，应直接抛出ArithmeticException * HALF_UP：向最近的整数舍入，其中x.5远离零方向舍入 * HALF_DOWN：向最近的整数舍入，其中x.5向零方向舍入 * HALF_EVEN：向最近的整数舍入，其中x.5向相邻的偶数舍入这些方法旨在提高代码的可读性，例如，divide(x, 3, CEILING) 即使在快速阅读时也是清晰。此外，这些方法内部采用构建整数近似值再计算的实现，除了在构建sqrt（平方根）运算的初始近似值时有浮点运算，其他方法的运算全过程都是整数或位运算，因此性能上更好。 | **运算** | **IntMath** | **LongMath** | **BigIntegerMath** | |:--- |:--- |:--- |:--- | | 除法 | [`divide(int, int, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#divide%28int, int, java.math.RoundingMode%29) | [`divide(long, long, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#divide%28long, long, java.math.RoundingMode%29) | [`divide(BigInteger, BigInteger, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#divide%28java.math.BigInteger, java.math.BigInteger, java.math.RoundingMode%29) | | 2为底的对数 | [`log2(int, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#log2%28int, java.math.RoundingMode%29) | [`log2(long, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#log2%28long, java.math.RoundingMode%29) | [`log2(BigInteger, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#log2%28java.math.BigInteger, java.math.RoundingMode%29) | | 10为底的对数 | [`log10(int, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#log10%28int, java.math.RoundingMode%29) | [`log10(long, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#log10%28long, java.math.RoundingMode%29) | [`log10(BigInteger, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#log10%28java.math.BigInteger, java.math.RoundingMode%29) | | 平方根 | [`sqrt(int, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#sqrt%28int, java.math.RoundingMode%29) | [`sqrt(long, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#sqrt%28long, java.math.RoundingMode%29) | [`sqrt(BigInteger, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#sqrt%28java.math.BigInteger, java.math.RoundingMode%29) | ``` // returns 31622776601683793319988935444327185337195551393252 BigIntegerMath.sqrt(BigInteger.TEN.pow(99), RoundingMode.HALF_EVEN); ``` ### 附加功能 Guava还另外提供了一些有用的运算函数 | **运算** | **IntMath** | **LongMath** | **BigIntegerMath******* | |:--- |:--- |:--- |:--- | | 最大公约数 | [`gcd(int, int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#gcd%28int, int%29) | [`gcd(long, long)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#gcd%28long, long%29) | [`BigInteger.gcd(BigInteger)`](http://docs.oracle.com/javase/6/docs/api/java/math/BigInteger.html#gcd%28java.math.BigInteger%29) | | 取模 | [`mod(int, int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#mod%28int, int%29) | [`mod(long, long)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#mod%28long, long%29) | [`BigInteger.mod(BigInteger)`](http://docs.oracle.com/javase/6/docs/api/java/math/BigInteger.html#mod%28java.math.BigInteger%29) | | 取幂 | [`pow(int, int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#pow%28int, int%29) | [`pow(long, int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#pow%28long, int%29) | [`BigInteger.pow(int)`](http://docs.oracle.com/javase/6/docs/api/java/math/BigInteger.html#pow%28int%29) | | 是否2的幂 | [`isPowerOfTwo(int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#isPowerOfTwo%28int%29) | [`isPowerOfTwo(long)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#isPowerOfTwo%28long%29) | [`isPowerOfTwo(BigInteger)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#isPowerOfTwo%28java.math.BigInteger%29) | | 阶乘* | [`factorial(int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#factorial%28int%29) | [`factorial(int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#factorial%28int%29) | [`factorial(int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#factorial%28int%29) | | 二项式系数* | [`binomial(int, int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#binomial%28int, int%29) | [`binomial(int, int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#binomial%28int, int%29) | [`binomial(int, int)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#binomial%28int, int%29) | *BigInteger的最大公约数和取模运算由JDK提供 *阶乘和二项式系数的运算结果如果溢出，则返回MAX_VALUE ## 浮点数运算 JDK比较彻底地涵盖了浮点数运算，但Guava在[DoubleMath](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/DoubleMath.html)类中也提供了一些有用的方法。 | [`isMathematicalInteger(double)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/DoubleMath.html#isMathematicalInteger%28double%29) | 判断该浮点数是不是一个整数 | |:--- |:--- | | [`roundToInt(double, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/DoubleMath.html#roundToInt%28double, java.math.RoundingMode%29) | 舍入为int；对无限小数、溢出抛出异常 | | [`roundToLong(double, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/DoubleMath.html#roundToLong%28double, java.math.RoundingMode%29) | 舍入为long；对无限小数、溢出抛出异常 | | [`roundToBigInteger(double, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/DoubleMath.html#roundToBigInteger%28double, java.math.RoundingMode%29) | 舍入为BigInteger；对无限小数抛出异常 | | [`log2(double, RoundingMode)`](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/DoubleMath.html#log2%28double, java.math.RoundingMode%29) | 2的浮点对数，并且舍入为int，比JDK的Math.log(double) 更快 |