guava学习笔记（十一）——数学运算

本部分为guava笔记第十一部分，主要整理guava中的数学运算工具——IntMath、LongMath、BigIntegerMath、DoubleMath。

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、LongMath和BigIntegerMath。

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(int, int))	[LongMath.checkedAdd](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedAdd(long, long))
[IntMath.checkedSubtract](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#checkedSubtract(int, int))	[LongMath.checkedSubtract](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedSubtract(long, long))
[IntMath.checkedMultiply](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#checkedMultiply(int, int))	[LongMath.checkedMultiply](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedMultiply(long, long))
[IntMath.checkedPow](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#checkedPow(int, int))	[LongMath.checkedPow](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#checkedPow(long, long))

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(int, int, java.math.RoundingMode))	[divide(long, long, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#divide(long, long, java.math.RoundingMode))	[divide(BigInteger, BigInteger, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#divide(java.math.BigInteger, java.math.BigInteger, java.math.RoundingMode))
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(int, java.math.RoundingMode))	[log2(long, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#log2(long, java.math.RoundingMode))	[log2(BigInteger, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#log2(java.math.BigInteger, java.math.RoundingMode))
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(int, java.math.RoundingMode))	[log10(long, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#log10(long, java.math.RoundingMode))	[log10(BigInteger, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#log10(java.math.BigInteger, java.math.RoundingMode))
平方根	[sqrt(int, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#sqrt(int, java.math.RoundingMode))	[sqrt(long, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#sqrt(long, java.math.RoundingMode))	[sqrt(BigInteger, RoundingMode)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#sqrt(java.math.BigInteger, java.math.RoundingMode))

// 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(int, int))	[gcd(long, long)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#gcd(long, long))	BigInteger.gcd(BigInteger)
取模	[mod(int, int)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#mod(int, int))	[mod(long, long)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#mod(long, long))	BigInteger.mod(BigInteger)
取幂	[pow(int, int)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/IntMath.html#pow(int, int))	[pow(long, int)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#pow(long, int))	BigInteger.pow(int)
是否2的幂	isPowerOfTwo(int)	isPowerOfTwo(long)	isPowerOfTwo(BigInteger)
阶乘*	factorial(int)	factorial(int)	factorial(int)
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(int, int))	[binomial(int, int)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/LongMath.html#binomial(int, int))	[binomial(int, int)](http://docs.guava-libraries.googlecode.com/git-history/release/javadoc/com/google/common/math/BigIntegerMath.html#binomial(int, int))

*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类中也提供了一些有用的方法。

isMathematicalInteger(double)	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(double, java.math.RoundingMode))	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(double, java.math.RoundingMode))	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(double, java.math.RoundingMode))	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(double, java.math.RoundingMode))	2的浮点对数，并且舍入为int，比JDK的Math.log(double) 更快

非原创内容，转载自并发编程网 – ifeve.com。