1 /* 2 * Copyright (C) 2011 The Guava Authors 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 package com.google.common.math; 18 19 import static com.google.common.base.Preconditions.checkArgument; 20 import static java.lang.Double.MAX_EXPONENT; 21 import static java.lang.Double.MIN_EXPONENT; 22 import static java.lang.Double.POSITIVE_INFINITY; 23 import static java.lang.Double.doubleToRawLongBits; 24 import static java.lang.Double.isNaN; 25 import static java.lang.Double.longBitsToDouble; 26 import static java.lang.Math.getExponent; 27 28 import java.math.BigInteger; 29 30 /** 31 * Utilities for {@code double} primitives. 32 * 33 * @author Louis Wasserman 34 */ 35 final class DoubleUtils { DoubleUtils()36 private DoubleUtils() { 37 } 38 nextDown(double d)39 static double nextDown(double d) { 40 return -Math.nextUp(-d); 41 } 42 43 // The mask for the significand, according to the {@link 44 // Double#doubleToRawLongBits(double)} spec. 45 static final long SIGNIFICAND_MASK = 0x000fffffffffffffL; 46 47 // The mask for the exponent, according to the {@link 48 // Double#doubleToRawLongBits(double)} spec. 49 static final long EXPONENT_MASK = 0x7ff0000000000000L; 50 51 // The mask for the sign, according to the {@link 52 // Double#doubleToRawLongBits(double)} spec. 53 static final long SIGN_MASK = 0x8000000000000000L; 54 55 static final int SIGNIFICAND_BITS = 52; 56 57 static final int EXPONENT_BIAS = 1023; 58 59 /** 60 * The implicit 1 bit that is omitted in significands of normal doubles. 61 */ 62 static final long IMPLICIT_BIT = SIGNIFICAND_MASK + 1; 63 getSignificand(double d)64 static long getSignificand(double d) { 65 checkArgument(isFinite(d), "not a normal value"); 66 int exponent = getExponent(d); 67 long bits = doubleToRawLongBits(d); 68 bits &= SIGNIFICAND_MASK; 69 return (exponent == MIN_EXPONENT - 1) 70 ? bits << 1 71 : bits | IMPLICIT_BIT; 72 } 73 isFinite(double d)74 static boolean isFinite(double d) { 75 return getExponent(d) <= MAX_EXPONENT; 76 } 77 isNormal(double d)78 static boolean isNormal(double d) { 79 return getExponent(d) >= MIN_EXPONENT; 80 } 81 82 /* 83 * Returns x scaled by a power of 2 such that it is in the range [1, 2). Assumes x is positive, 84 * normal, and finite. 85 */ scaleNormalize(double x)86 static double scaleNormalize(double x) { 87 long significand = doubleToRawLongBits(x) & SIGNIFICAND_MASK; 88 return longBitsToDouble(significand | ONE_BITS); 89 } 90 bigToDouble(BigInteger x)91 static double bigToDouble(BigInteger x) { 92 // This is an extremely fast implementation of BigInteger.doubleValue(). JDK patch pending. 93 BigInteger absX = x.abs(); 94 int exponent = absX.bitLength() - 1; 95 // exponent == floor(log2(abs(x))) 96 if (exponent < Long.SIZE - 1) { 97 return x.longValue(); 98 } else if (exponent > MAX_EXPONENT) { 99 return x.signum() * POSITIVE_INFINITY; 100 } 101 102 /* 103 * We need the top SIGNIFICAND_BITS + 1 bits, including the "implicit" one bit. To make 104 * rounding easier, we pick out the top SIGNIFICAND_BITS + 2 bits, so we have one to help us 105 * round up or down. twiceSignifFloor will contain the top SIGNIFICAND_BITS + 2 bits, and 106 * signifFloor the top SIGNIFICAND_BITS + 1. 107 * 108 * It helps to consider the real number signif = absX * 2^(SIGNIFICAND_BITS - exponent). 109 */ 110 int shift = exponent - SIGNIFICAND_BITS - 1; 111 long twiceSignifFloor = absX.shiftRight(shift).longValue(); 112 long signifFloor = twiceSignifFloor >> 1; 113 signifFloor &= SIGNIFICAND_MASK; // remove the implied bit 114 115 /* 116 * We round up if either the fractional part of signif is strictly greater than 0.5 (which is 117 * true if the 0.5 bit is set and any lower bit is set), or if the fractional part of signif is 118 * >= 0.5 and signifFloor is odd (which is true if both the 0.5 bit and the 1 bit are set). 119 */ 120 boolean increment = (twiceSignifFloor & 1) != 0 121 && ((signifFloor & 1) != 0 || absX.getLowestSetBit() < shift); 122 long signifRounded = increment ? signifFloor + 1 : signifFloor; 123 long bits = (long) ((exponent + EXPONENT_BIAS)) << SIGNIFICAND_BITS; 124 bits += signifRounded; 125 /* 126 * If signifRounded == 2^53, we'd need to set all of the significand bits to zero and add 1 to 127 * the exponent. This is exactly the behavior we get from just adding signifRounded to bits 128 * directly. If the exponent is MAX_DOUBLE_EXPONENT, we round up (correctly) to 129 * Double.POSITIVE_INFINITY. 130 */ 131 bits |= x.signum() & SIGN_MASK; 132 return longBitsToDouble(bits); 133 } 134 135 /** 136 * Returns its argument if it is non-negative, zero if it is negative. 137 */ ensureNonNegative(double value)138 static double ensureNonNegative(double value) { 139 checkArgument(!isNaN(value)); 140 if (value > 0.0) { 141 return value; 142 } else { 143 return 0.0; 144 } 145 } 146 147 private static final long ONE_BITS = doubleToRawLongBits(1.0); 148 } 149