java.lang.Object

cloud.opencode.base.core.OpenMath

public final class OpenMath extends Object

Math Utility Class - High-precision arithmetic, statistics and number theory functions 数学工具类 - 高精度算术运算、统计函数和数论函数

Provides high-performance, high-precision mathematical calculations.

提供高性能、高精度的数学计算，包括算术运算、统计函数、数论函数。

Features | 主要功能:

High-precision arithmetic (add, subtract, multiply, divide) - 高精度运算
Rounding (round, ceil, floor) - 取整
Statistics (mean, median, variance, stdDev, sum) - 统计函数
Number theory (gcd, lcm, factorial, isPrime, fibonacci) - 数论函数
Power operations (pow, modPow) - 幂运算
Utility (abs, signum, isEven, isOdd) - 工具方法

Usage Examples | 使用示例:

// High-precision division - 高精度除法
BigDecimal result = OpenMath.divide(a, b, 2);

// Statistics - 统计
double avg = OpenMath.mean(1.0, 2.0, 3.0);
double mid = OpenMath.median(1.0, 2.0, 3.0);

// Number theory - 数论
int gcd = OpenMath.gcd(12, 18);         // 6
boolean prime = OpenMath.isPrime(17);    // true
long fib = OpenMath.fibonacci(10);       // 55

Security | 安全性:

Thread-safe: Yes (stateless) - 线程安全: 是 (无状态)
Null-safe: Yes - 空值安全: 是

Since:

JDK 25, opencode-base-core V1.0.0

Author:

Leon Soo www.LeonSoo.com

See Also:

Method Summary

Modifier and Type

Method

Description

static int

abs(int value)

Absolute value (safe: throws on Integer.MIN_VALUE instead of returning negative) 绝对值 (safe: throws on Integer.MIN_VALUE instead of returning negative) 绝对值 (安全：对 Integer.MIN_VALUE 抛出异常而非返回负数)

static long

abs(long value)

Absolute value (long, safe: throws on Long.MIN_VALUE instead of returning negative) 绝对值（long, safe: throws on Long.MIN_VALUE instead of returning negative）绝对值（long，安全：对 Long.MIN_VALUE 抛出异常而非返回负数）

static BigDecimal

add(BigDecimal a, BigDecimal b)

High-precision addition of two BigDecimal values.

static double

ceil(double value, int scale)

Rounds a double value up to the specified number of decimal places.

static BigDecimal

divide(BigDecimal a, BigDecimal b, int scale)

High-precision division with half-up rounding.

static BigDecimal

divide(BigDecimal a, BigDecimal b, int scale, RoundingMode mode)

High-precision division with specified rounding mode.

static long

factorial(int n)

Calculates the factorial of n (n must be in [0, 20]).

static BigInteger

factorialBig(int n)

Calculates the factorial of n as a BigInteger (arbitrary precision).

static long

fibonacci(int n)

Returns the n-th Fibonacci number (0-indexed: F(0)=0, F(1)=1, F(2)=1, ...).

static double

floor(double value, int scale)

Rounds a double value down to the specified number of decimal places.

static int

gcd(int a, int b)

Greatest Common Divisor (GCD) 最大公约数（GCD） Safe: throws ArithmeticException for Integer.MIN_VALUE inputs

static long

gcd(long a, long b)

Greatest Common Divisor (long) 最大公约数（long） Safe: throws ArithmeticException for Long.MIN_VALUE inputs

static boolean

isEven(int value)

Returns true if the value is even.

static boolean

isNegative(int value)

Returns true if the value is negative.

static boolean

isOdd(int value)

Returns true if the value is odd.

static boolean

isPositive(int value)

Returns true if the value is positive.

static boolean

isPrime(long n)

Returns true if n is a prime number.

static int

lcm(int a, int b)

Least Common Multiple (LCM) 最小公倍数（LCM） Safe: uses Math.absExact to detect overflow

static long

lcm(long a, long b)

Least Common Multiple (long) 最小公倍数（long） Safe: uses Math.absExact to detect overflow

static double

mean(double... values)

Calculates the arithmetic mean of the given values.

static double

median(double... values)

Calculates the median of the given values.

static long

modPow(long base, long exponent, long modulus)

Computes (base ^ exponent) mod modulus using BigInteger.

static BigDecimal

multiply(BigDecimal a, BigDecimal b)

High-precision multiplication of two BigDecimal values.

static long

pow(long base, int exponent)

Computes base raised to the power of exponent using overflow-safe multiplication.

static double

round(double value, int scale)

Rounds a double value to the specified number of decimal places using half-up rounding.

static double

sampleStdDev(double... values)

Calculates the sample standard deviation of the given values (uses sample variance with Bessel's correction).

static double

sampleVariance(double... values)

Calculates the sample variance of the given values using Bessel's correction (divides by n-1).

static int

signum(int value)

Returns the signum of the value: -1, 0, or 1.

static int

signum(long value)

Returns the signum of the long value: -1, 0, or 1.

static double

stdDev(double... values)

Calculates the population standard deviation of the given values (uses population variance).

static BigDecimal

subtract(BigDecimal a, BigDecimal b)

High-precision subtraction of two BigDecimal values.

static double

sum(double... values)

Calculates the sum of the given double values.

static int

sum(int... values)

Calculates the sum of the given int values using overflow-safe addition.

static long

sum(long... values)

Calculates the sum of the given long values using overflow-safe addition.

static double

variance(double... values)

Calculates the population variance of the given values (divides by n).

Methods inherited from class Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details
- add
  
  public static BigDecimal add(BigDecimal a, BigDecimal b)
  
  High-precision addition of two BigDecimal values. 高精度加法
- subtract
  
  public static BigDecimal subtract(BigDecimal a, BigDecimal b)
  
  High-precision subtraction of two BigDecimal values. 高精度减法
- multiply
  
  public static BigDecimal multiply(BigDecimal a, BigDecimal b)
  
  High-precision multiplication of two BigDecimal values. 高精度乘法
- divide
  
  public static BigDecimal divide(BigDecimal a, BigDecimal b, int scale)
  
  High-precision division with half-up rounding. 高精度除法
- divide
  
  public static BigDecimal divide(BigDecimal a, BigDecimal b, int scale, RoundingMode mode)
  
  High-precision division with specified rounding mode. 高精度除法（指定舍入模式）
- round
  
  public static double round(double value, int scale)
  
  Rounds a double value to the specified number of decimal places using half-up rounding. 四舍五入
- ceil
  
  public static double ceil(double value, int scale)
  
  Rounds a double value up to the specified number of decimal places. 向上取整
- floor
  
  public static double floor(double value, int scale)
  
  Rounds a double value down to the specified number of decimal places. 向下取整
- mean
  
  public static double mean(double... values)
  
  Calculates the arithmetic mean of the given values. 计算平均值
- median
  
  public static double median(double... values)
  
  Calculates the median of the given values. 计算中位数
- variance
  
  public static double variance(double... values)
  
  Calculates the population variance of the given values (divides by n). 计算总体方差（除以 n）
  This computes the population variance, which divides the sum of squared deviations by the number of values (n). Use sampleVariance(double...) for sample variance with Bessel's correction (divides by n-1).
  
  此方法计算总体方差，以数据个数 n 为分母。如需样本方差（贝塞尔校正，以 n-1 为分母），请使用 sampleVariance(double...)。
  
  Parameters:
  
  values - the values | 数值数组
  
  Returns:
  
  the population variance, or 0 if the array is null or empty 总体方差，若数组为 null 或空则返回 0
- sampleVariance
  
  public static double sampleVariance(double... values)
  
  Calculates the sample variance of the given values using Bessel's correction (divides by n-1). 计算样本方差（贝塞尔校正，除以 n-1）
  This computes the unbiased sample variance, which divides the sum of squared deviations by (n-1) instead of n. This is the appropriate estimator when computing variance from a sample rather than an entire population.
  
  此方法计算无偏样本方差，以 (n-1) 为分母而非 n。当数据为样本而非总体时，应使用此方法以获得无偏估计。
  
  Parameters:
  
  values - the values (must contain at least 2 elements) | 数值数组（至少需要 2 个元素）
  
  Returns:
  
  the sample variance, or 0 if the array is null or empty; returns 0 for a single-element array (no variance) 样本方差；若数组为 null 或空返回 0；单元素数组返回 0
- stdDev
  
  public static double stdDev(double... values)
  
  Calculates the population standard deviation of the given values (uses population variance). 计算总体标准差（基于总体方差）
  This is the square root of the population variance. Use sampleStdDev(double...) for the sample standard deviation.
  
  此方法为总体方差的平方根。如需样本标准差，请使用 sampleStdDev(double...)。
  
  Parameters:
  
  values - the values | 数值数组
  
  Returns:
  
  the population standard deviation | 总体标准差
- sampleStdDev
  
  public static double sampleStdDev(double... values)
  
  Calculates the sample standard deviation of the given values (uses sample variance with Bessel's correction). 计算样本标准差（基于样本方差，贝塞尔校正）
  This is the square root of the sample variance.
  
  此方法为样本方差的平方根。
  
  Parameters:
  
  values - the values (must contain at least 2 elements) | 数值数组（至少需要 2 个元素）
  
  Returns:
  
  the sample standard deviation | 样本标准差
- sum
  
  public static double sum(double... values)
  
  Calculates the sum of the given double values. 计算总和
- sum
  
  public static long sum(long... values)
  
  Calculates the sum of the given long values using overflow-safe addition. 计算总和（long）
- sum
  
  public static int sum(int... values)
  
  Calculates the sum of the given int values using overflow-safe addition. 计算总和（int）
- gcd
  
  public static int gcd(int a, int b)
  
  Greatest Common Divisor (GCD) 最大公约数（GCD） Safe: throws ArithmeticException for Integer.MIN_VALUE inputs
- gcd
  
  public static long gcd(long a, long b)
  
  Greatest Common Divisor (long) 最大公约数（long） Safe: throws ArithmeticException for Long.MIN_VALUE inputs
- lcm
  
  public static int lcm(int a, int b)
  
  Least Common Multiple (LCM) 最小公倍数（LCM） Safe: uses Math.absExact to detect overflow
- lcm
  
  public static long lcm(long a, long b)
  
  Least Common Multiple (long) 最小公倍数（long） Safe: uses Math.absExact to detect overflow
- factorial
  
  public static long factorial(int n)
  
  Calculates the factorial of n (n must be in [0, 20]). 阶乘
- factorialBig
  
  public static BigInteger factorialBig(int n)
  
  Calculates the factorial of n as a BigInteger (arbitrary precision). 阶乘（大数）
- isPrime
  
  public static boolean isPrime(long n)
  
  Returns true if n is a prime number. 素数判断
- fibonacci
  
  public static long fibonacci(int n)
  
  Returns the n-th Fibonacci number (0-indexed: F(0)=0, F(1)=1, F(2)=1, ...). 返回第 n 个斐波那契数（从 0 开始：F(0)=0, F(1)=1, F(2)=1, ...）。
  Valid range: 0 ≤ n ≤ 92. For n > 92, the result overflows long.
  
  有效范围：0 ≤ n ≤ 92。当 n > 92 时，结果溢出 long。
  
  Parameters:
  
  n - the index (must be in [0, 92]) | 索引（必须在 [0, 92] 范围内）
  
  Returns:
  
  the n-th Fibonacci number | 第 n 个斐波那契数
  
  Throws:
  
  IllegalArgumentException - if n is negative | 如果 n 为负数
  
  ArithmeticException - if n > 92 (result overflows long) | 如果 n > 92（结果溢出 long）
- pow
  
  public static long pow(long base, int exponent)
  
  Computes base raised to the power of exponent using overflow-safe multiplication. 幂运算
- modPow
  
  public static long modPow(long base, long exponent, long modulus)
  
  Computes (base ^ exponent) mod modulus using BigInteger. 模幂运算
- abs
  
  public static int abs(int value)
  
  Absolute value (safe: throws on Integer.MIN_VALUE instead of returning negative) 绝对值 (safe: throws on Integer.MIN_VALUE instead of returning negative) 绝对值 (安全：对 Integer.MIN_VALUE 抛出异常而非返回负数)
- abs
  
  public static long abs(long value)
  
  Absolute value (long, safe: throws on Long.MIN_VALUE instead of returning negative) 绝对值（long, safe: throws on Long.MIN_VALUE instead of returning negative）绝对值（long，安全：对 Long.MIN_VALUE 抛出异常而非返回负数）
- signum
  
  public static int signum(int value)
  
  Returns the signum of the value: -1, 0, or 1. 符号函数
- signum
  
  public static int signum(long value)
  
  Returns the signum of the long value: -1, 0, or 1. 符号函数（long）
- isEven
  
  public static boolean isEven(int value)
  
  Returns true if the value is even. 是否为偶数
- isOdd
  
  public static boolean isOdd(int value)
  
  Returns true if the value is odd. 是否为奇数
- isNegative
  
  public static boolean isNegative(int value)
  
  Returns true if the value is negative. 是否为负数
- isPositive
  
  public static boolean isPositive(int value)
  
  Returns true if the value is positive. 是否为正数

Class OpenMath

Method Summary

Methods inherited from class Object

Method Details

add

subtract

multiply

divide

divide

round

ceil

floor

mean

median

variance

sampleVariance

stdDev

sampleStdDev

sum

sum

sum

gcd

gcd

lcm

lcm

factorial

factorialBig

isPrime

fibonacci

pow

modPow

abs

abs

signum

signum

isEven

isOdd

isNegative

isPositive