深入学习java源码之Math.addExact()与 Math.multiplyExact()

^运算符

或的运算符，其运算规则是：

两个操作数的位中，相同则结果为0，不同则结果为1。

int i = 15, j = 2

运行结果是：i ^ j = 13.

分析上面程序，i=15转成二进制是1111，j=2转成二进制是0010，根据异或的运算规则得到的是1101，转成十进制就是13.

K+1个数，其中有2k个相同，需要找出不相同的那个数，比如：2、3、4、4、3、5、6、6、5。

int[] array = {2,3,4,4,3,5,6,6,5};

int v = 0;

for (int i = 0;i < array.length;i++) {

v ^= array[i];

System.out.println("只出现一次的数是:" + v);

}

只出现一次的数是2.

基本数据类型的加减乘除运算

加法

 int a = 10;
 long b = 35;
 float c = 36.95f;
 double d = 18.04;

减法

long a = 300;
int b = 18;
float c = 128.7f;
double d = 53.31;

float jian = (float)(a - b - c - (double)d);

乘法

int a = 1;
long b = 1000000;
float c = 0.000001f;
double d = 99.99;

除法

int a = 1000;
long b = 1000000;
float c = 0.001f;
double d = 99.99;

float chu = (float)((double)d/(a/b/c));

Modifier and Type	Method and Description
`static double`	`abs(double a)` 返回值为 `double`绝对值。
`static float`	`abs(float a)` 返回 `float`值的绝对值。
`static int`	`abs(int a)` 返回值为 `int`绝对值。
`static long`	`abs(long a)` 返回值为 `long`绝对值。
`static int`	`addExact(int x, int y)` 返回其参数的总和，如果结果溢出int，则抛出 `int` 。
`static long`	`addExact(long x, long y)` 返回其参数的总和，如果结果溢出long，则抛出 `long` 。
`static int`	`decrementExact(int a)` 返回一个递减1的参数，如果结果溢出int，则 `int` 。
`static long`	`decrementExact(long a)` 将返回的参数递减1，如果结果溢出long，则 `long` 。
`static double`	`floor(double a)` 返回小于或等于参数的最大（最接近正无穷大） `double`值，等于一个数学整数。
`static int`	`floorDiv(int x, int y)` 返回小于或等于代数商的最大（最接近正无穷大） `int`值。
`static long`	`floorDiv(long x, long y)` 返回小于或等于代数商的最大（最接近正无穷大） `long`值。
`static int`	`floorMod(int x, int y)` 返回 `int`参数的底部模数。
`static long`	`floorMod(long x, long y)` 返回 `long`参数的底模数。
`static int`	`incrementExact(int a)` 返回自变量1，如果结果溢出int，则 `int` 。
`static long`	`incrementExact(long a)` 返回一个增加1的参数，如果结果溢出long，则 `long` 。
`static int`	`multiplyExact(int x, int y)` 返回参数的乘积，如果结果溢出int，则抛出 `int` 。
`static long`	`multiplyExact(long x, long y)` 返回参数的乘积，如果结果溢出long，则抛出 `long` 。
`static int`	`negateExact(int a)` 返回参数的否定，如果结果溢出int，则 `int` 。
`static long`	`negateExact(long a)` 返回参数的否定，如果结果溢出long，则 `long` 。
`static long`	`round(double a)` 返回参数中最接近的 `long` ，其中 `long`四舍五入为正无穷大。
`static int`	`round(float a)` 返回参数中最接近的 `int` ，其中 `int`四舍五入为正无穷大。
`static int`	`subtractExact(int x, int y)` 返回参数的差异，如果结果溢出int，则抛出 `int` 。
`static long`	`subtractExact(long x, long y)` 返回参数的差异，如果结果溢出long，则抛出 `long` 。

static int

toIntExact(long value)

返回long参数的值; 如果值溢出int，则int 。

java源码

public final class Math {

    private Math() {}

    public static int round(float a) {
        int intBits = Float.floatToRawIntBits(a);
        int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)
                >> (FloatConsts.SIGNIFICAND_WIDTH - 1);
        int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2
                + FloatConsts.EXP_BIAS) - biasedExp;
        if ((shift & -32) == 0) { // shift >= 0 && shift < 32
            // a is a finite number such that pow(2,-32) <= ulp(a) < 1
            int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)
                    | (FloatConsts.SIGNIF_BIT_MASK + 1));
            if (intBits < 0) {
                r = -r;
            }
            // In the comments below each Java expression evaluates to the value
            // the corresponding mathematical expression:
            // (r) evaluates to a / ulp(a)
            // (r >> shift) evaluates to floor(a * 2)
            // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
            // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
            return ((r >> shift) + 1) >> 1;
        } else {
            // a is either
            // - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2
            // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
            // - an infinity or NaN
            return (int) a;
        }
    }	
	
    public static long round(double a) {
        long longBits = Double.doubleToRawLongBits(a);
        long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)
                >> (DoubleConsts.SIGNIFICAND_WIDTH - 1);
        long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2
                + DoubleConsts.EXP_BIAS) - biasedExp;
        if ((shift & -64) == 0) { // shift >= 0 && shift < 64
            // a is a finite number such that pow(2,-64) <= ulp(a) < 1
            long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)
                    | (DoubleConsts.SIGNIF_BIT_MASK + 1));
            if (longBits < 0) {
                r = -r;
            }
            // In the comments below each Java expression evaluates to the value
            // the corresponding mathematical expression:
            // (r) evaluates to a / ulp(a)
            // (r >> shift) evaluates to floor(a * 2)
            // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
            // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
            return ((r >> shift) + 1) >> 1;
        } else {
            // a is either
            // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2
            // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
            // - an infinity or NaN
            return (long) a;
        }
    }

    public static int addExact(int x, int y) {
        int r = x + y;
        // HD 2-12 Overflow iff both arguments have the opposite sign of the result
        if (((x ^ r) & (y ^ r)) < 0) {
            throw new ArithmeticException("integer overflow");
        }
        return r;
    }

    public static long addExact(long x, long y) {
        long r = x + y;
        // HD 2-12 Overflow iff both arguments have the opposite sign of the result
        if (((x ^ r) & (y ^ r)) < 0) {
            throw new ArithmeticException("long overflow");
        }
        return r;
    }

    public static int subtractExact(int x, int y) {
        int r = x - y;
        // HD 2-12 Overflow iff the arguments have different signs and
        // the sign of the result is different than the sign of x
        if (((x ^ y) & (x ^ r)) < 0) {
            throw new ArithmeticException("integer overflow");
        }
        return r;
    }
	
    public static long subtractExact(long x, long y) {
        long r = x - y;
        // HD 2-12 Overflow iff the arguments have different signs and
        // the sign of the result is different than the sign of x
        if (((x ^ y) & (x ^ r)) < 0) {
            throw new ArithmeticException("long overflow");
        }
        return r;
    }

    public static int multiplyExact(int x, int y) {
        long r = (long)x * (long)y;
        if ((int)r != r) {
            throw new ArithmeticException("integer overflow");
        }
        return (int)r;
    }

    public static long multiplyExact(long x, long y) {
        long r = x * y;
        long ax = Math.abs(x);
        long ay = Math.abs(y);
        if (((ax | ay) >>> 31 != 0)) {
            // Some bits greater than 2^31 that might cause overflow
            // Check the result using the divide operator
            // and check for the special case of Long.MIN_VALUE * -1
           if (((y != 0) && (r / y != x)) ||
               (x == Long.MIN_VALUE && y == -1)) {
                throw new ArithmeticException("long overflow");
            }
        }
        return r;
    }


    public static int incrementExact(int a) {
        if (a == Integer.MAX_VALUE) {
            throw new ArithmeticException("integer overflow");
        }

        return a + 1;
    }

    public static long incrementExact(long a) {
        if (a == Long.MAX_VALUE) {
            throw new ArithmeticException("long overflow");
        }

        return a + 1L;
    }

    public static int decrementExact(int a) {
        if (a == Integer.MIN_VALUE) {
            throw new ArithmeticException("integer overflow");
        }

        return a - 1;
    }

    public static long decrementExact(long a) {
        if (a == Long.MIN_VALUE) {
            throw new ArithmeticException("long overflow");
        }

        return a - 1L;
    }

    public static int negateExact(int a) {
        if (a == Integer.MIN_VALUE) {
            throw new ArithmeticException("integer overflow");
        }

        return -a;
    }

    public static long negateExact(long a) {
        if (a == Long.MIN_VALUE) {
            throw new ArithmeticException("long overflow");
        }

        return -a;
    }

    public static int toIntExact(long value) {
        if ((int)value != value) {
            throw new ArithmeticException("integer overflow");
        }
        return (int)value;
    }	

    public static int abs(int a) {
        return (a < 0) ? -a : a;
    }

    public static long abs(long a) {
        return (a < 0) ? -a : a;
    }

    public static float abs(float a) {
        return (a <= 0.0F) ? 0.0F - a : a;
    }

    public static double abs(double a) {
        return (a <= 0.0D) ? 0.0D - a : a;
    }	
	
    public static long floorDiv(long x, long y) {
        long r = x / y;
        // if the signs are different and modulo not zero, round down
        if ((x ^ y) < 0 && (r * y != x)) {
            r--;
        }
        return r;
    }

    public static int floorDiv(int x, int y) {
        int r = x / y;
        // if the signs are different and modulo not zero, round down
        if ((x ^ y) < 0 && (r * y != x)) {
            r--;
        }
        return r;
    }

    public static int floorMod(int x, int y) {
        int r = x - floorDiv(x, y) * y;
        return r;
    }

    public static long floorMod(long x, long y) {
        return x - floorDiv(x, y) * y;
    }

}

public final class StrictMath {

    private StrictMath() {}
	
    public static int round(float a) {
        return Math.round(a);
    }
	
    public static long round(double a) {
        return Math.round(a);
    }

    public static int addExact(int x, int y) {
        return Math.addExact(x, y);
    }

    public static long addExact(long x, long y) {
        return Math.addExact(x, y);
    }
	
    public static int subtractExact(int x, int y) {
        return Math.subtractExact(x, y);
    }

    public static long subtractExact(long x, long y) {
        return Math.subtractExact(x, y);
    }

    public static int multiplyExact(int x, int y) {
        return Math.multiplyExact(x, y);
    }

    public static long multiplyExact(long x, long y) {
        return Math.multiplyExact(x, y);
    }

    public static int toIntExact(long value) {
        return Math.toIntExact(value);
    }

    public static int floorDiv(int x, int y) {
        return Math.floorDiv(x, y);
    }

    public static long floorDiv(long x, long y) {
        return Math.floorDiv(x, y);
    }

    public static int floorMod(int x, int y) {
        return Math.floorMod(x , y);
    }

    public static long floorMod(long x, long y) {
        return Math.floorMod(x, y);
    }

    public static int abs(int a) {
        return Math.abs(a);
    }
    public static long abs(long a) {
        return Math.abs(a);
    }

    public static float abs(float a) {
        return Math.abs(a);
    }

    public static double abs(double a) {
        return Math.abs(a);
    }
	
}

深入学习java源码之Math.addExact()与 Math.multiplyExact()

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