/*
 * 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 java.lang.Double.MAX_EXPONENT;
import static java.lang.Double.MIN_EXPONENT;
import static java.lang.Double.POSITIVE_INFINITY;
import static java.lang.Double.doubleToRawLongBits;
import static java.lang.Double.isNaN;
import static java.lang.Double.longBitsToDouble;
import static java.lang.Math.getExponent;

import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.VisibleForTesting;
import java.math.BigInteger;

Utilities for double primitives.
Author:Louis Wasserman
/** * Utilities for {@code double} primitives. * * @author Louis Wasserman */
@GwtIncompatible final class DoubleUtils { private DoubleUtils() {} static double nextDown(double d) { return -Math.nextUp(-d); } // The mask for the significand, according to the {@link // Double#doubleToRawLongBits(double)} spec. static final long SIGNIFICAND_MASK = 0x000fffffffffffffL; // The mask for the exponent, according to the {@link // Double#doubleToRawLongBits(double)} spec. static final long EXPONENT_MASK = 0x7ff0000000000000L; // The mask for the sign, according to the {@link // Double#doubleToRawLongBits(double)} spec. static final long SIGN_MASK = 0x8000000000000000L; static final int SIGNIFICAND_BITS = 52; static final int EXPONENT_BIAS = 1023;
The implicit 1 bit that is omitted in significands of normal doubles.
/** The implicit 1 bit that is omitted in significands of normal doubles. */
static final long IMPLICIT_BIT = SIGNIFICAND_MASK + 1; static long getSignificand(double d) { checkArgument(isFinite(d), "not a normal value"); int exponent = getExponent(d); long bits = doubleToRawLongBits(d); bits &= SIGNIFICAND_MASK; return (exponent == MIN_EXPONENT - 1) ? bits << 1 : bits | IMPLICIT_BIT; } static boolean isFinite(double d) { return getExponent(d) <= MAX_EXPONENT; } static boolean isNormal(double d) { return getExponent(d) >= MIN_EXPONENT; } /* * Returns x scaled by a power of 2 such that it is in the range [1, 2). Assumes x is positive, * normal, and finite. */ static double scaleNormalize(double x) { long significand = doubleToRawLongBits(x) & SIGNIFICAND_MASK; return longBitsToDouble(significand | ONE_BITS); } static double bigToDouble(BigInteger x) { // This is an extremely fast implementation of BigInteger.doubleValue(). JDK patch pending. BigInteger absX = x.abs(); int exponent = absX.bitLength() - 1; // exponent == floor(log2(abs(x))) if (exponent < Long.SIZE - 1) { return x.longValue(); } else if (exponent > MAX_EXPONENT) { return x.signum() * POSITIVE_INFINITY; } /* * We need the top SIGNIFICAND_BITS + 1 bits, including the "implicit" one bit. To make rounding * easier, we pick out the top SIGNIFICAND_BITS + 2 bits, so we have one to help us round up or * down. twiceSignifFloor will contain the top SIGNIFICAND_BITS + 2 bits, and signifFloor the * top SIGNIFICAND_BITS + 1. * * It helps to consider the real number signif = absX * 2^(SIGNIFICAND_BITS - exponent). */ int shift = exponent - SIGNIFICAND_BITS - 1; long twiceSignifFloor = absX.shiftRight(shift).longValue(); long signifFloor = twiceSignifFloor >> 1; signifFloor &= SIGNIFICAND_MASK; // remove the implied bit /* * We round up if either the fractional part of signif is strictly greater than 0.5 (which is * true if the 0.5 bit is set and any lower bit is set), or if the fractional part of signif is * >= 0.5 and signifFloor is odd (which is true if both the 0.5 bit and the 1 bit are set). */ boolean increment = (twiceSignifFloor & 1) != 0 && ((signifFloor & 1) != 0 || absX.getLowestSetBit() < shift); long signifRounded = increment ? signifFloor + 1 : signifFloor; long bits = (long) ((exponent + EXPONENT_BIAS)) << SIGNIFICAND_BITS; bits += signifRounded; /* * If signifRounded == 2^53, we'd need to set all of the significand bits to zero and add 1 to * the exponent. This is exactly the behavior we get from just adding signifRounded to bits * directly. If the exponent is MAX_DOUBLE_EXPONENT, we round up (correctly) to * Double.POSITIVE_INFINITY. */ bits |= x.signum() & SIGN_MASK; return longBitsToDouble(bits); }
Returns its argument if it is non-negative, zero if it is negative.
/** Returns its argument if it is non-negative, zero if it is negative. */
static double ensureNonNegative(double value) { checkArgument(!isNaN(value)); if (value > 0.0) { return value; } else { return 0.0; } } @VisibleForTesting static final long ONE_BITS = 0x3ff0000000000000L; }