Special cases: * *
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 } /** * 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 // Whenever both tests are cheap and functional, it's faster to use &, | instead of &&, || @SuppressWarnings({"fallthrough", "ShortCircuitBoolean"}) 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 {@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: * *
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 Boolean.compare(Double.isNaN(a), Double.isNaN(b)); } } /** * Returns the arithmetic mean of * {@code values}. * *
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 * {@code values}. * *
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 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 * {@code values}. * *
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 * {@code values}. * *
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 values) { return mean(values.iterator()); } /** * Returns the arithmetic mean of * {@code values}. * *
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 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() {} }