https://github.com/google/guava/guava: Guava is a suite of core and expanded libraries that include utility classes, google's collections, io classes, and much much more. 
/*
 * Copyright (C) 2011 The Guava Authors
 *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
 * in compliance with the License. You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software distributed under the License
 * is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
 * or implied. See the License for the specific language governing permissions and limitations under
 * the License.
 */

package com.google.common.math;

import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.math.DoubleUtils.IMPLICIT_BIT;
import static com.google.common.math.DoubleUtils.SIGNIFICAND_BITS;
import static com.google.common.math.DoubleUtils.getSignificand;
import static com.google.common.math.DoubleUtils.isFinite;
import static com.google.common.math.DoubleUtils.isNormal;
import static com.google.common.math.DoubleUtils.scaleNormalize;
import static com.google.common.math.MathPreconditions.checkInRangeForRoundingInputs;
import static com.google.common.math.MathPreconditions.checkNonNegative;
import static com.google.common.math.MathPreconditions.checkRoundingUnnecessary;
import static java.lang.Math.abs;
import static java.lang.Math.copySign;
import static java.lang.Math.getExponent;
import static java.lang.Math.log;
import static java.lang.Math.rint;

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.VisibleForTesting;
import com.google.common.primitives.Booleans;
import com.google.errorprone.annotations.CanIgnoreReturnValue;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.Iterator;


A class for arithmetic on doubles that is not covered by Math. 
Author:Louis Wasserman
Since:11.0
/**
 * A class for arithmetic on doubles that is not covered by {@link java.lang.Math}.
 *
 * @author Louis Wasserman
 * @since 11.0
 */
@GwtCompatible(emulated = true)
public final class DoubleMath {
  /*
   * This method returns a value y such that rounding y DOWN (towards zero) gives the same result as
   * rounding x according to the specified mode.
   */
  @GwtIncompatible // #isMathematicalInteger, com.google.common.math.DoubleUtils
  static double roundIntermediate(double x, RoundingMode mode) {
    if (!isFinite(x)) {
      throw new ArithmeticException("input is infinite or NaN");
    }
    switch (mode) {
      case UNNECESSARY:
        checkRoundingUnnecessary(isMathematicalInteger(x));
        return x;

      case FLOOR:
        if (x >= 0.0 || isMathematicalInteger(x)) {
          return x;
        } else {
          return (long) x - 1;
        }

      case CEILING:
        if (x <= 0.0 || isMathematicalInteger(x)) {
          return x;
        } else {
          return (long) x + 1;
        }

      case DOWN:
        return x;

      case UP:
        if (isMathematicalInteger(x)) {
          return x;
        } else {
          return (long) x + (x > 0 ? 1 : -1);
        }

      case HALF_EVEN:
        return rint(x);

      case HALF_UP:
        {
          double z = rint(x);
          if (abs(x - z) == 0.5) {
            return x + copySign(0.5, x);
          } else {
            return z;
          }
        }

      case HALF_DOWN:
        {
          double z = rint(x);
          if (abs(x - z) == 0.5) {
            return x;
          } else {
            return z;
          }
        }

      default:
        throw new AssertionError();
    }
  }

  
Returns the int value that is equal to x rounded with the specified rounding mode, if possible. 
Throws:
  • ArithmeticException – if
    
      
      
    • x is infinite or NaN 
    • x, after being rounded to a mathematical integer using the specified rounding mode, is either less than Integer.MIN_VALUE or greater than 
          Integer.MAX_VALUE 
    • x is not a mathematical integer and mode is RoundingMode.UNNECESSARY 
/**
   * Returns the {@code int} value that is equal to {@code x} rounded with the specified rounding
   * mode, if possible.
   *
   * @throws ArithmeticException if
   *     <ul>
   *       <li>{@code x} is infinite or NaN
   *       <li>{@code x}, after being rounded to a mathematical integer using the specified rounding
   *           mode, is either less than {@code Integer.MIN_VALUE} or greater than {@code
   *           Integer.MAX_VALUE}
   *       <li>{@code x} is not a mathematical integer and {@code mode} is {@link
   *           RoundingMode#UNNECESSARY}
   *     </ul>
   */
  @GwtIncompatible // #roundIntermediate
  public static int roundToInt(double x, RoundingMode mode) {
    double z = roundIntermediate(x, mode);
    checkInRangeForRoundingInputs(
        z > MIN_INT_AS_DOUBLE - 1.0 & z < MAX_INT_AS_DOUBLE + 1.0, x, mode);
    return (int) z;
  }

  private static final double MIN_INT_AS_DOUBLE = -0x1p31;
  private static final double MAX_INT_AS_DOUBLE = 0x1p31 - 1.0;

  
Returns the long value that is equal to x rounded with the specified rounding mode, if possible. 
Throws:
  • ArithmeticException – if
    
      
      
    • x is infinite or NaN 
    • x, after being rounded to a mathematical integer using the specified rounding mode, is either less than Long.MIN_VALUE or greater than 
          Long.MAX_VALUE 
    • x is not a mathematical integer and mode is RoundingMode.UNNECESSARY 
/**
   * Returns the {@code long} value that is equal to {@code x} rounded with the specified rounding
   * mode, if possible.
   *
   * @throws ArithmeticException if
   *     <ul>
   *       <li>{@code x} is infinite or NaN
   *       <li>{@code x}, after being rounded to a mathematical integer using the specified rounding
   *           mode, is either less than {@code Long.MIN_VALUE} or greater than {@code
   *           Long.MAX_VALUE}
   *       <li>{@code x} is not a mathematical integer and {@code mode} is {@link
   *           RoundingMode#UNNECESSARY}
   *     </ul>
   */
  @GwtIncompatible // #roundIntermediate
  public static long roundToLong(double x, RoundingMode mode) {
    double z = roundIntermediate(x, mode);
    checkInRangeForRoundingInputs(
        MIN_LONG_AS_DOUBLE - z < 1.0 & z < MAX_LONG_AS_DOUBLE_PLUS_ONE, x, mode);
    return (long) z;
  }

  private static final double MIN_LONG_AS_DOUBLE = -0x1p63;
  /*
   * We cannot store Long.MAX_VALUE as a double without losing precision. Instead, we store
   * Long.MAX_VALUE + 1 == -Long.MIN_VALUE, and then offset all comparisons by 1.
   */
  private static final double MAX_LONG_AS_DOUBLE_PLUS_ONE = 0x1p63;

  
Returns the BigInteger value that is equal to x rounded with the specified rounding mode, if possible. 
Throws:
/**
   * Returns the {@code BigInteger} value that is equal to {@code x} rounded with the specified
   * rounding mode, if possible.
   *
   * @throws ArithmeticException if
   *     <ul>
   *       <li>{@code x} is infinite or NaN
   *       <li>{@code x} is not a mathematical integer and {@code mode} is {@link
   *           RoundingMode#UNNECESSARY}
   *     </ul>
   */
  // #roundIntermediate, java.lang.Math.getExponent, com.google.common.math.DoubleUtils
  @GwtIncompatible
  public static BigInteger roundToBigInteger(double x, RoundingMode mode) {
    x = roundIntermediate(x, mode);
    if (MIN_LONG_AS_DOUBLE - x < 1.0 & x < MAX_LONG_AS_DOUBLE_PLUS_ONE) {
      return BigInteger.valueOf((long) x);
    }
    int exponent = getExponent(x);
    long significand = getSignificand(x);
    BigInteger result = BigInteger.valueOf(significand).shiftLeft(exponent - SIGNIFICAND_BITS);
    return (x < 0) ? result.negate() : result;
  }

  
Returns true if x is exactly equal to 2^k for some finite integer k. 
/**
   * Returns {@code true} if {@code x} is exactly equal to {@code 2^k} for some finite integer
   * {@code k}.
   */
  @GwtIncompatible // com.google.common.math.DoubleUtils
  public static boolean isPowerOfTwo(double x) {
    if (x > 0.0 && isFinite(x)) {
      long significand = getSignificand(x);
      return (significand & (significand - 1)) == 0;
    }
    return false;
  }

  
Returns the base 2 logarithm of a double value.

Special cases:

    
  
  • If x is NaN or less than zero, the result is NaN. 
  • If x is positive infinity, the result is positive infinity. 
  • If x is positive or negative zero, the result is negative infinity. 


The computed result is within 1 ulp of the exact result.

If the result of this method will be immediately rounded to an int, log2(double, RoundingMode) is faster. 
/**
   * Returns the base 2 logarithm of a double value.
   *
   * <p>Special cases:
   *
   * <ul>
   *   <li>If {@code x} is NaN or less than zero, the result is NaN.
   *   <li>If {@code x} is positive infinity, the result is positive infinity.
   *   <li>If {@code x} is positive or negative zero, the result is negative infinity.
   * </ul>
   *
   * <p>The computed result is within 1 ulp of the exact result.
   *
   * <p>If the result of this method will be immediately rounded to an {@code int}, {@link
   * #log2(double, RoundingMode)} is faster.
   */
  public static double log2(double x) {
    return log(x) / LN_2; // surprisingly within 1 ulp according to tests
  }

  
Returns the base 2 logarithm of a double value, rounded with the specified rounding mode to an int. 
Regardless of the rounding mode, this is faster than (int) log2(x). 
Throws:
/**
   * Returns the base 2 logarithm of a double value, rounded with the specified rounding mode to an
   * {@code int}.
   *
   * <p>Regardless of the rounding mode, this is faster than {@code (int) log2(x)}.
   *
   * @throws IllegalArgumentException if {@code x <= 0.0}, {@code x} is NaN, or {@code x} is
   *     infinite
   */
  @GwtIncompatible // java.lang.Math.getExponent, com.google.common.math.DoubleUtils
  @SuppressWarnings("fallthrough")
  public static int log2(double x, RoundingMode mode) {
    checkArgument(x > 0.0 && isFinite(x), "x must be positive and finite");
    int exponent = getExponent(x);
    if (!isNormal(x)) {
      return log2(x * IMPLICIT_BIT, mode) - SIGNIFICAND_BITS;
      // Do the calculation on a normal value.
    }
    // x is positive, finite, and normal
    boolean increment;
    switch (mode) {
      case UNNECESSARY:
        checkRoundingUnnecessary(isPowerOfTwo(x));
        // fall through
      case FLOOR:
        increment = false;
        break;
      case CEILING:
        increment = !isPowerOfTwo(x);
        break;
      case DOWN:
        increment = exponent < 0 & !isPowerOfTwo(x);
        break;
      case UP:
        increment = exponent >= 0 & !isPowerOfTwo(x);
        break;
      case HALF_DOWN:
      case HALF_EVEN:
      case HALF_UP:
        double xScaled = scaleNormalize(x);
        // sqrt(2) is irrational, and the spec is relative to the "exact numerical result,"
        // so log2(x) is never exactly exponent + 0.5.
        increment = (xScaled * xScaled) > 2.0;
        break;
      default:
        throw new AssertionError();
    }
    return increment ? exponent + 1 : exponent;
  }

  private static final double LN_2 = log(2);

  
Returns true if x represents a mathematical integer. 
This is equivalent to, but not necessarily implemented as, the expression 
!Double.isNaN(x) && !Double.isInfinite(x) && x == Math.rint(x). 
/**
   * Returns {@code true} if {@code x} represents a mathematical integer.
   *
   * <p>This is equivalent to, but not necessarily implemented as, the expression {@code
   * !Double.isNaN(x) && !Double.isInfinite(x) && x == Math.rint(x)}.
   */
  @GwtIncompatible // java.lang.Math.getExponent, com.google.common.math.DoubleUtils
  public static boolean isMathematicalInteger(double x) {
    return isFinite(x)
        && (x == 0.0
            || SIGNIFICAND_BITS - Long.numberOfTrailingZeros(getSignificand(x)) <= getExponent(x));
  }

  
Returns n!, that is, the product of the first n positive integers, 1 if n == 0, or n!, or Double.POSITIVE_INFINITY if n! >
Double.MAX_VALUE. 
The result is within 1 ulp of the true value.

Throws:
/**
   * Returns {@code n!}, that is, the product of the first {@code n} positive integers, {@code 1} if
   * {@code n == 0}, or {@code n!}, or {@link Double#POSITIVE_INFINITY} if {@code n! >
   * Double.MAX_VALUE}.
   *
   * <p>The result is within 1 ulp of the true value.
   *
   * @throws IllegalArgumentException if {@code n < 0}
   */
  public static double factorial(int n) {
    checkNonNegative("n", n);
    if (n > MAX_FACTORIAL) {
      return Double.POSITIVE_INFINITY;
    } else {
      // Multiplying the last (n & 0xf) values into their own accumulator gives a more accurate
      // result than multiplying by everySixteenthFactorial[n >> 4] directly.
      double accum = 1.0;
      for (int i = 1 + (n & ~0xf); i <= n; i++) {
        accum *= i;
      }
      return accum * everySixteenthFactorial[n >> 4];
    }
  }

  @VisibleForTesting static final int MAX_FACTORIAL = 170;

  @VisibleForTesting
  static final double[] everySixteenthFactorial = {
    0x1.0p0,
    0x1.30777758p44,
    0x1.956ad0aae33a4p117,
    0x1.ee69a78d72cb6p202,
    0x1.fe478ee34844ap295,
    0x1.c619094edabffp394,
    0x1.3638dd7bd6347p498,
    0x1.7cac197cfe503p605,
    0x1.1e5dfc140e1e5p716,
    0x1.8ce85fadb707ep829,
    0x1.95d5f3d928edep945
  };

  
Returns true if a and b are within tolerance of each other. 
Technically speaking, this is equivalent to Math.abs(a - b) <= tolerance ||
Double.valueOf(a).equals(Double.valueOf(b)). 
Notable special cases include:

    
  
  • All NaNs are fuzzily equal.
  
  • If a == b, then a and b are always fuzzily equal. 
  • Positive and negative zero are always fuzzily equal.
  
  • If tolerance is zero, and neither a nor b is NaN, then a and b are fuzzily equal if and only if a == b. 
  • With Double.POSITIVE_INFINITY tolerance, all non-NaN values are fuzzily equal. 
  • With finite tolerance, Double.POSITIVE_INFINITY and 
      Double.NEGATIVE_INFINITY are fuzzily equal only to themselves. 


This is reflexive and symmetric, but not transitive, so it is not an
equivalence relation and not suitable for use in Object.equals implementations. 
Throws:
Since:13.0
/**
   * Returns {@code true} if {@code a} and {@code b} are within {@code tolerance} of each other.
   *
   * <p>Technically speaking, this is equivalent to {@code Math.abs(a - b) <= tolerance ||
   * Double.valueOf(a).equals(Double.valueOf(b))}.
   *
   * <p>Notable special cases include:
   *
   * <ul>
   *   <li>All NaNs are fuzzily equal.
   *   <li>If {@code a == b}, then {@code a} and {@code b} are always fuzzily equal.
   *   <li>Positive and negative zero are always fuzzily equal.
   *   <li>If {@code tolerance} is zero, and neither {@code a} nor {@code b} is NaN, then {@code a}
   *       and {@code b} are fuzzily equal if and only if {@code a == b}.
   *   <li>With {@link Double#POSITIVE_INFINITY} tolerance, all non-NaN values are fuzzily equal.
   *   <li>With finite tolerance, {@code Double.POSITIVE_INFINITY} and {@code
   *       Double.NEGATIVE_INFINITY} are fuzzily equal only to themselves.
   * </ul>
   *
   * <p>This is reflexive and symmetric, but <em>not</em> transitive, so it is <em>not</em> an
   * equivalence relation and <em>not</em> suitable for use in {@link Object#equals}
   * implementations.
   *
   * @throws IllegalArgumentException if {@code tolerance} is {@code < 0} or NaN
   * @since 13.0
   */
  public static boolean fuzzyEquals(double a, double b, double tolerance) {
    MathPreconditions.checkNonNegative("tolerance", tolerance);
    return Math.copySign(a - b, 1.0) <= tolerance
        // copySign(x, 1.0) is a branch-free version of abs(x), but with different NaN semantics
        || (a == b) // needed to ensure that infinities equal themselves
        || (Double.isNaN(a) && Double.isNaN(b));
  }

  
Compares a and b "fuzzily," with a tolerance for nearly-equal values. 
This method is equivalent to fuzzyEquals(a, b, tolerance) ? 0 : Double.compare(a,
b). In particular, like Double.compare(double, double), it treats all NaN values as equal and greater than all other values (including Double.POSITIVE_INFINITY). 
This is not a total ordering and is not suitable for use in Comparable.compareTo implementations. In particular, it is not transitive. 
Throws:
Since:13.0
/**
   * Compares {@code a} and {@code b} "fuzzily," with a tolerance for nearly-equal values.
   *
   * <p>This method is equivalent to {@code fuzzyEquals(a, b, tolerance) ? 0 : Double.compare(a,
   * b)}. In particular, like {@link Double#compare(double, double)}, it treats all NaN values as
   * equal and greater than all other values (including {@link Double#POSITIVE_INFINITY}).
   *
   * <p>This is <em>not</em> a total ordering and is <em>not</em> suitable for use in {@link
   * Comparable#compareTo} implementations. In particular, it is not transitive.
   *
   * @throws IllegalArgumentException if {@code tolerance} is {@code < 0} or NaN
   * @since 13.0
   */
  public static int fuzzyCompare(double a, double b, double tolerance) {
    if (fuzzyEquals(a, b, tolerance)) {
      return 0;
    } else if (a < b) {
      return -1;
    } else if (a > b) {
      return 1;
    } else {
      return Booleans.compare(Double.isNaN(a), Double.isNaN(b));
    }
  }

  
Returns the arithmetic mean of values. 
If these values are a sample drawn from a population, this is also an unbiased estimator of
the arithmetic mean of the population.

Params:
  • values – a nonempty series of values
Throws:
Deprecated:Use Stats.meanOf instead, noting the less strict handling of non-finite values.
/**
   * Returns the <a href="http://en.wikipedia.org/wiki/Arithmetic_mean">arithmetic mean</a> of
   * {@code values}.
   *
   * <p>If these values are a sample drawn from a population, this is also an unbiased estimator of
   * the arithmetic mean of the population.
   *
   * @param values a nonempty series of values
   * @throws IllegalArgumentException if {@code values} is empty or contains any non-finite value
   * @deprecated Use {@link Stats#meanOf} instead, noting the less strict handling of non-finite
   *     values.
   */
  @Deprecated
  // com.google.common.math.DoubleUtils
  @GwtIncompatible
  public static double mean(double... values) {
    checkArgument(values.length > 0, "Cannot take mean of 0 values");
    long count = 1;
    double mean = checkFinite(values[0]);
    for (int index = 1; index < values.length; ++index) {
      checkFinite(values[index]);
      count++;
      // Art of Computer Programming vol. 2, Knuth, 4.2.2, (15)
      mean += (values[index] - mean) / count;
    }
    return mean;
  }

  
Returns the arithmetic mean of values. 
If these values are a sample drawn from a population, this is also an unbiased estimator of
the arithmetic mean of the population.

Params:
  • values – a nonempty series of values
Throws:
Deprecated:Use Stats.meanOf instead, noting the less strict handling of non-finite values.
/**
   * Returns the <a href="http://en.wikipedia.org/wiki/Arithmetic_mean">arithmetic mean</a> of
   * {@code values}.
   *
   * <p>If these values are a sample drawn from a population, this is also an unbiased estimator of
   * the arithmetic mean of the population.
   *
   * @param values a nonempty series of values
   * @throws IllegalArgumentException if {@code values} is empty
   * @deprecated Use {@link Stats#meanOf} instead, noting the less strict handling of non-finite
   *     values.
   */
  @Deprecated
  public static double mean(int... values) {
    checkArgument(values.length > 0, "Cannot take mean of 0 values");
    // The upper bound on the the length of an array and the bounds on the int values mean that, in
    // this case only, we can compute the sum as a long without risking overflow or loss of
    // precision. So we do that, as it's slightly quicker than the Knuth algorithm.
    long sum = 0;
    for (int index = 0; index < values.length; ++index) {
      sum += values[index];
    }
    return (double) sum / values.length;
  }

  
Returns the arithmetic mean of values. 
If these values are a sample drawn from a population, this is also an unbiased estimator of
the arithmetic mean of the population.

Params:
  • values – a nonempty series of values, which will be converted to double values (this may cause loss of precision for longs of magnitude over 2^53 (slightly over 9e15))
Throws:
Deprecated:Use Stats.meanOf instead, noting the less strict handling of non-finite values.
/**
   * Returns the <a href="http://en.wikipedia.org/wiki/Arithmetic_mean">arithmetic mean</a> of
   * {@code values}.
   *
   * <p>If these values are a sample drawn from a population, this is also an unbiased estimator of
   * the arithmetic mean of the population.
   *
   * @param values a nonempty series of values, which will be converted to {@code double} values
   *     (this may cause loss of precision for longs of magnitude over 2^53 (slightly over 9e15))
   * @throws IllegalArgumentException if {@code values} is empty
   * @deprecated Use {@link Stats#meanOf} instead, noting the less strict handling of non-finite
   *     values.
   */
  @Deprecated
  public static double mean(long... values) {
    checkArgument(values.length > 0, "Cannot take mean of 0 values");
    long count = 1;
    double mean = values[0];
    for (int index = 1; index < values.length; ++index) {
      count++;
      // Art of Computer Programming vol. 2, Knuth, 4.2.2, (15)
      mean += (values[index] - mean) / count;
    }
    return mean;
  }

  
Returns the arithmetic mean of values. 
If these values are a sample drawn from a population, this is also an unbiased estimator of
the arithmetic mean of the population.

Params:
  • values – a nonempty series of values, which will be converted to double values (this may cause loss of precision)
Throws:
Deprecated:Use Stats.meanOf instead, noting the less strict handling of non-finite values.
/**
   * Returns the <a href="http://en.wikipedia.org/wiki/Arithmetic_mean">arithmetic mean</a> of
   * {@code values}.
   *
   * <p>If these values are a sample drawn from a population, this is also an unbiased estimator of
   * the arithmetic mean of the population.
   *
   * @param values a nonempty series of values, which will be converted to {@code double} values
   *     (this may cause loss of precision)
   * @throws IllegalArgumentException if {@code values} is empty or contains any non-finite value
   * @deprecated Use {@link Stats#meanOf} instead, noting the less strict handling of non-finite
   *     values.
   */
  @Deprecated
  // com.google.common.math.DoubleUtils
  @GwtIncompatible
  public static double mean(Iterable<? extends Number> values) {
    return mean(values.iterator());
  }

  
Returns the arithmetic mean of values. 
If these values are a sample drawn from a population, this is also an unbiased estimator of
the arithmetic mean of the population.

Params:
  • values – a nonempty series of values, which will be converted to double values (this may cause loss of precision)
Throws:
Deprecated:Use Stats.meanOf instead, noting the less strict handling of non-finite values.
/**
   * Returns the <a href="http://en.wikipedia.org/wiki/Arithmetic_mean">arithmetic mean</a> of
   * {@code values}.
   *
   * <p>If these values are a sample drawn from a population, this is also an unbiased estimator of
   * the arithmetic mean of the population.
   *
   * @param values a nonempty series of values, which will be converted to {@code double} values
   *     (this may cause loss of precision)
   * @throws IllegalArgumentException if {@code values} is empty or contains any non-finite value
   * @deprecated Use {@link Stats#meanOf} instead, noting the less strict handling of non-finite
   *     values.
   */
  @Deprecated
  // com.google.common.math.DoubleUtils
  @GwtIncompatible
  public static double mean(Iterator<? extends Number> values) {
    checkArgument(values.hasNext(), "Cannot take mean of 0 values");
    long count = 1;
    double mean = checkFinite(values.next().doubleValue());
    while (values.hasNext()) {
      double value = checkFinite(values.next().doubleValue());
      count++;
      // Art of Computer Programming vol. 2, Knuth, 4.2.2, (15)
      mean += (value - mean) / count;
    }
    return mean;
  }

  @GwtIncompatible // com.google.common.math.DoubleUtils
  @CanIgnoreReturnValue
  private static double checkFinite(double argument) {
    checkArgument(isFinite(argument));
    return argument;
  }

  private DoubleMath() {}
}