* 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 } 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 e 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 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() { } }