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/*
 * 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.checkInRange;
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 java.math.BigInteger;
import java.math.RoundingMode;
import java.util.Iterator;

/**
 * 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 x - 1.0;
        }

      case CEILING:
        if (x <= 0.0 || isMathematicalInteger(x)) {
          return x;
        } else {
          return x + 1.0;
        }

      case DOWN:
        return x;

      case UP:
        if (isMathematicalInteger(x)) {
          return x;
        } else {
          return x + Math.copySign(1.0, x);
        }

      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 {@code int} value that is equal to {@code x} rounded with the specified rounding
   * mode, if possible.
   *
   * @throws ArithmeticException if
   *         
    *
  • {@code x} is infinite or NaN *
  • {@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} *
  • {@code x} is not a mathematical integer and {@code mode} is * {@link RoundingMode#UNNECESSARY} *
*/ @GwtIncompatible("#roundIntermediate") public static int roundToInt(double x, RoundingMode mode) { double z = roundIntermediate(x, mode); checkInRange(z > MIN_INT_AS_DOUBLE - 1.0 & z < MAX_INT_AS_DOUBLE + 1.0); 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 {@code long} value that is equal to {@code x} rounded with the specified rounding * mode, if possible. * * @throws ArithmeticException if *
    *
  • {@code x} is infinite or NaN *
  • {@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} *
  • {@code x} is not a mathematical integer and {@code mode} is * {@link RoundingMode#UNNECESSARY} *
*/ @GwtIncompatible("#roundIntermediate") public static long roundToLong(double x, RoundingMode mode) { double z = roundIntermediate(x, mode); checkInRange(MIN_LONG_AS_DOUBLE - z < 1.0 & z < MAX_LONG_AS_DOUBLE_PLUS_ONE); 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 {@code BigInteger} value that is equal to {@code x} rounded with the specified * rounding mode, if possible. * * @throws ArithmeticException if *
    *
  • {@code x} is infinite or NaN *
  • {@code x} is not a mathematical integer and {@code mode} is * {@link RoundingMode#UNNECESSARY} *
*/ @GwtIncompatible("#roundIntermediate, java.lang.Math.getExponent, " + "com.google.common.math.DoubleUtils") 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 {@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) { return x > 0.0 && isFinite(x) && LongMath.isPowerOfTwo(getSignificand(x)); } /** * Returns the base 2 logarithm of a double value. * *

Special cases: *

    *
  • If {@code x} is NaN or less than zero, the result is NaN. *
  • If {@code x} is positive infinity, the result is positive infinity. *
  • If {@code 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 {@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 } private static final double LN_2 = log(2); /** * Returns the base 2 logarithm of a double value, rounded with the specified rounding mode to an * {@code int}. * *

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; } /** * Returns {@code true} if {@code x} represents a mathematical integer. * *

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 {@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}. * *

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 {@code true} if {@code a} and {@code b} are within {@code tolerance} of each other. * *

Technically speaking, this is equivalent to * {@code Math.abs(a - b) <= tolerance || Double.valueOf(a).equals(Double.valueOf(b))}. * *

Notable special cases include: *

    *
  • All NaNs are fuzzily equal. *
  • If {@code a == b}, then {@code a} and {@code b} are always fuzzily equal. *
  • Positive and negative zero are always fuzzily equal. *
  • 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}. *
  • With {@link Double#POSITIVE_INFINITY} tolerance, all non-NaN values are fuzzily equal. *
  • With finite tolerance, {@code Double.POSITIVE_INFINITY} and {@code * 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 {@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 {@code a} and {@code b} "fuzzily," with a tolerance for nearly-equal values. * *

    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}). * *

    This is not a total ordering and is not 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)); } } @GwtIncompatible("com.google.common.math.DoubleUtils") private static final class MeanAccumulator { private long count = 0; private double mean = 0.0; void add(double value) { checkArgument(isFinite(value)); ++count; // Art of Computer Programming vol. 2, Knuth, 4.2.2, (15) mean += (value - mean) / count; } double mean() { checkArgument(count > 0, "Cannot take mean of 0 values"); return mean; } } /** * Returns the arithmetic mean of the values. There must be at least one value, and they must all * be finite. */ @GwtIncompatible("MeanAccumulator") public static double mean(double... values) { MeanAccumulator accumulator = new MeanAccumulator(); for (double value : values) { accumulator.add(value); } return accumulator.mean(); } /** * Returns the arithmetic mean of the values. There must be at least one value. The values will * be converted to doubles, which does not cause any loss of precision for ints. */ @GwtIncompatible("MeanAccumulator") public static double mean(int... values) { MeanAccumulator accumulator = new MeanAccumulator(); for (int value : values) { accumulator.add(value); } return accumulator.mean(); } /** * Returns the arithmetic mean of the values. There must be at least one value. The values will * be converted to doubles, which causes loss of precision for longs of magnitude over 2^53 * (slightly over 9e15). */ @GwtIncompatible("MeanAccumulator") public static double mean(long... values) { MeanAccumulator accumulator = new MeanAccumulator(); for (long value : values) { accumulator.add(value); } return accumulator.mean(); } /** * Returns the arithmetic mean of the values. There must be at least one value, and they must all * be finite. The values will be converted to doubles, which may cause loss of precision for some * numeric types. */ @GwtIncompatible("MeanAccumulator") public static double mean(Iterable values) { MeanAccumulator accumulator = new MeanAccumulator(); for (Number value : values) { accumulator.add(value.doubleValue()); } return accumulator.mean(); } /** * Returns the arithmetic mean of the values. There must be at least one value, and they must all * be finite. The values will be converted to doubles, which may cause loss of precision for some * numeric types. */ @GwtIncompatible("MeanAccumulator") public static double mean(Iterator values) { MeanAccumulator accumulator = new MeanAccumulator(); while (values.hasNext()) { accumulator.add(values.next().doubleValue()); } return accumulator.mean(); } private DoubleMath() {} }





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