mirror of https://github.com/M66B/FairEmail.git
925 lines
37 KiB
Java
925 lines
37 KiB
Java
// Copyright 2010 the V8 project authors. All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following
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// disclaimer in the documentation and/or other materials provided
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// with the distribution.
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// * Neither the name of Google Inc. nor the names of its
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// contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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// Ported to Java from Mozilla's version of V8-dtoa by Hannes Wallnoefer.
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// The original revision was 67d1049b0bf9 from the mozilla-central tree.
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// Modified by Rikard Pavelic do avoid allocations
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// and unused code paths due to external checks
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package com.bugsnag.android.repackaged.dslplatform.json;
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@SuppressWarnings("fallthrough") // suppress pre-existing warnings
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abstract class Grisu3 {
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// FastDtoa will produce at most kFastDtoaMaximalLength digits.
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static final int kFastDtoaMaximalLength = 17;
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// The minimal and maximal target exponent define the range of w's binary
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// exponent, where 'w' is the result of multiplying the input by a cached power
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// of ten.
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//
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// A different range might be chosen on a different platform, to optimize digit
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// generation, but a smaller range requires more powers of ten to be cached.
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static final int minimal_target_exponent = -60;
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private static final class DiyFp {
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long f;
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int e;
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static final int kSignificandSize = 64;
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static final long kUint64MSB = 0x8000000000000000L;
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private static final long kM32 = 0xFFFFFFFFL;
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private static final long k10MSBits = 0xFFC00000L << 32;
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DiyFp() {
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this.f = 0;
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this.e = 0;
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}
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// this = this - other.
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// The exponents of both numbers must be the same and the significand of this
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// must be bigger than the significand of other.
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// The result will not be normalized.
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void subtract(DiyFp other) {
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f -= other.f;
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}
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// this = this * other.
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void multiply(DiyFp other) {
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// Simply "emulates" a 128 bit multiplication.
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// However: the resulting number only contains 64 bits. The least
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// significant 64 bits are only used for rounding the most significant 64
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// bits.
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long a = f >>> 32;
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long b = f & kM32;
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long c = other.f >>> 32;
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long d = other.f & kM32;
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long ac = a * c;
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long bc = b * c;
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long ad = a * d;
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long bd = b * d;
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long tmp = (bd >>> 32) + (ad & kM32) + (bc & kM32);
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// By adding 1U << 31 to tmp we round the final result.
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// Halfway cases will be round up.
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tmp += 1L << 31;
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long result_f = ac + (ad >>> 32) + (bc >>> 32) + (tmp >>> 32);
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e += other.e + 64;
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f = result_f;
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}
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void normalize() {
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long f = this.f;
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int e = this.e;
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// This method is mainly called for normalizing boundaries. In general
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// boundaries need to be shifted by 10 bits. We thus optimize for this case.
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while ((f & k10MSBits) == 0) {
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f <<= 10;
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e -= 10;
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}
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while ((f & kUint64MSB) == 0) {
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f <<= 1;
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e--;
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}
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this.f = f;
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this.e = e;
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}
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void reset() {
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e = 0;
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f = 0;
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}
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@Override
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public String toString() {
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return "[DiyFp f:" + f + ", e:" + e + "]";
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}
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}
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private static class CachedPowers {
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static final double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10)
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static class CachedPower {
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final long significand;
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final short binaryExponent;
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final short decimalExponent;
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CachedPower(long significand, short binaryExponent, short decimalExponent) {
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this.significand = significand;
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this.binaryExponent = binaryExponent;
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this.decimalExponent = decimalExponent;
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}
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}
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static int getCachedPower(int e, int alpha, DiyFp c_mk) {
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final int kQ = DiyFp.kSignificandSize;
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final double k = Math.ceil((alpha - e + kQ - 1) * kD_1_LOG2_10);
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final int index = (GRISU_CACHE_OFFSET + (int) k - 1) / CACHED_POWERS_SPACING + 1;
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final CachedPower cachedPower = CACHED_POWERS[index];
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c_mk.f = cachedPower.significand;
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c_mk.e = cachedPower.binaryExponent;
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return cachedPower.decimalExponent;
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}
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// Code below is converted from GRISU_CACHE_NAME(8) in file "powers-ten.h"
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// Regexp to convert this from original C++ source:
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// \{GRISU_UINT64_C\((\w+), (\w+)\), (\-?\d+), (\-?\d+)\}
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// interval between entries of the powers cache below
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static final int CACHED_POWERS_SPACING = 8;
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static final CachedPower[] CACHED_POWERS = {
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new CachedPower(0xe61acf033d1a45dfL, (short) -1087, (short) -308),
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new CachedPower(0xab70fe17c79ac6caL, (short) -1060, (short) -300),
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new CachedPower(0xff77b1fcbebcdc4fL, (short) -1034, (short) -292),
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new CachedPower(0xbe5691ef416bd60cL, (short) -1007, (short) -284),
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new CachedPower(0x8dd01fad907ffc3cL, (short) -980, (short) -276),
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new CachedPower(0xd3515c2831559a83L, (short) -954, (short) -268),
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new CachedPower(0x9d71ac8fada6c9b5L, (short) -927, (short) -260),
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new CachedPower(0xea9c227723ee8bcbL, (short) -901, (short) -252),
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new CachedPower(0xaecc49914078536dL, (short) -874, (short) -244),
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new CachedPower(0x823c12795db6ce57L, (short) -847, (short) -236),
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new CachedPower(0xc21094364dfb5637L, (short) -821, (short) -228),
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new CachedPower(0x9096ea6f3848984fL, (short) -794, (short) -220),
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new CachedPower(0xd77485cb25823ac7L, (short) -768, (short) -212),
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new CachedPower(0xa086cfcd97bf97f4L, (short) -741, (short) -204),
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new CachedPower(0xef340a98172aace5L, (short) -715, (short) -196),
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new CachedPower(0xb23867fb2a35b28eL, (short) -688, (short) -188),
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new CachedPower(0x84c8d4dfd2c63f3bL, (short) -661, (short) -180),
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new CachedPower(0xc5dd44271ad3cdbaL, (short) -635, (short) -172),
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new CachedPower(0x936b9fcebb25c996L, (short) -608, (short) -164),
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new CachedPower(0xdbac6c247d62a584L, (short) -582, (short) -156),
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new CachedPower(0xa3ab66580d5fdaf6L, (short) -555, (short) -148),
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new CachedPower(0xf3e2f893dec3f126L, (short) -529, (short) -140),
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new CachedPower(0xb5b5ada8aaff80b8L, (short) -502, (short) -132),
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new CachedPower(0x87625f056c7c4a8bL, (short) -475, (short) -124),
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new CachedPower(0xc9bcff6034c13053L, (short) -449, (short) -116),
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new CachedPower(0x964e858c91ba2655L, (short) -422, (short) -108),
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new CachedPower(0xdff9772470297ebdL, (short) -396, (short) -100),
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new CachedPower(0xa6dfbd9fb8e5b88fL, (short) -369, (short) -92),
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new CachedPower(0xf8a95fcf88747d94L, (short) -343, (short) -84),
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new CachedPower(0xb94470938fa89bcfL, (short) -316, (short) -76),
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new CachedPower(0x8a08f0f8bf0f156bL, (short) -289, (short) -68),
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new CachedPower(0xcdb02555653131b6L, (short) -263, (short) -60),
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new CachedPower(0x993fe2c6d07b7facL, (short) -236, (short) -52),
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new CachedPower(0xe45c10c42a2b3b06L, (short) -210, (short) -44),
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new CachedPower(0xaa242499697392d3L, (short) -183, (short) -36),
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new CachedPower(0xfd87b5f28300ca0eL, (short) -157, (short) -28),
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new CachedPower(0xbce5086492111aebL, (short) -130, (short) -20),
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new CachedPower(0x8cbccc096f5088ccL, (short) -103, (short) -12),
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new CachedPower(0xd1b71758e219652cL, (short) -77, (short) -4),
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new CachedPower(0x9c40000000000000L, (short) -50, (short) 4),
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new CachedPower(0xe8d4a51000000000L, (short) -24, (short) 12),
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new CachedPower(0xad78ebc5ac620000L, (short) 3, (short) 20),
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new CachedPower(0x813f3978f8940984L, (short) 30, (short) 28),
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new CachedPower(0xc097ce7bc90715b3L, (short) 56, (short) 36),
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new CachedPower(0x8f7e32ce7bea5c70L, (short) 83, (short) 44),
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new CachedPower(0xd5d238a4abe98068L, (short) 109, (short) 52),
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new CachedPower(0x9f4f2726179a2245L, (short) 136, (short) 60),
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new CachedPower(0xed63a231d4c4fb27L, (short) 162, (short) 68),
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new CachedPower(0xb0de65388cc8ada8L, (short) 189, (short) 76),
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new CachedPower(0x83c7088e1aab65dbL, (short) 216, (short) 84),
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new CachedPower(0xc45d1df942711d9aL, (short) 242, (short) 92),
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new CachedPower(0x924d692ca61be758L, (short) 269, (short) 100),
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new CachedPower(0xda01ee641a708deaL, (short) 295, (short) 108),
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new CachedPower(0xa26da3999aef774aL, (short) 322, (short) 116),
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new CachedPower(0xf209787bb47d6b85L, (short) 348, (short) 124),
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new CachedPower(0xb454e4a179dd1877L, (short) 375, (short) 132),
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new CachedPower(0x865b86925b9bc5c2L, (short) 402, (short) 140),
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new CachedPower(0xc83553c5c8965d3dL, (short) 428, (short) 148),
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new CachedPower(0x952ab45cfa97a0b3L, (short) 455, (short) 156),
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new CachedPower(0xde469fbd99a05fe3L, (short) 481, (short) 164),
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new CachedPower(0xa59bc234db398c25L, (short) 508, (short) 172),
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new CachedPower(0xf6c69a72a3989f5cL, (short) 534, (short) 180),
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new CachedPower(0xb7dcbf5354e9beceL, (short) 561, (short) 188),
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new CachedPower(0x88fcf317f22241e2L, (short) 588, (short) 196),
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new CachedPower(0xcc20ce9bd35c78a5L, (short) 614, (short) 204),
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new CachedPower(0x98165af37b2153dfL, (short) 641, (short) 212),
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new CachedPower(0xe2a0b5dc971f303aL, (short) 667, (short) 220),
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new CachedPower(0xa8d9d1535ce3b396L, (short) 694, (short) 228),
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new CachedPower(0xfb9b7cd9a4a7443cL, (short) 720, (short) 236),
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new CachedPower(0xbb764c4ca7a44410L, (short) 747, (short) 244),
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new CachedPower(0x8bab8eefb6409c1aL, (short) 774, (short) 252),
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new CachedPower(0xd01fef10a657842cL, (short) 800, (short) 260),
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new CachedPower(0x9b10a4e5e9913129L, (short) 827, (short) 268),
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new CachedPower(0xe7109bfba19c0c9dL, (short) 853, (short) 276),
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new CachedPower(0xac2820d9623bf429L, (short) 880, (short) 284),
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new CachedPower(0x80444b5e7aa7cf85L, (short) 907, (short) 292),
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new CachedPower(0xbf21e44003acdd2dL, (short) 933, (short) 300),
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new CachedPower(0x8e679c2f5e44ff8fL, (short) 960, (short) 308),
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new CachedPower(0xd433179d9c8cb841L, (short) 986, (short) 316),
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new CachedPower(0x9e19db92b4e31ba9L, (short) 1013, (short) 324),
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new CachedPower(0xeb96bf6ebadf77d9L, (short) 1039, (short) 332),
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new CachedPower(0xaf87023b9bf0ee6bL, (short) 1066, (short) 340)
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};
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// nb elements (8): 82
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static final int GRISU_CACHE_OFFSET = 308;
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}
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private static class DoubleHelper {
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static final long kExponentMask = 0x7FF0000000000000L;
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static final long kSignificandMask = 0x000FFFFFFFFFFFFFL;
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static final long kHiddenBit = 0x0010000000000000L;
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static void asDiyFp(long d64, DiyFp v) {
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v.f = significand(d64);
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v.e = exponent(d64);
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}
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// this->Significand() must not be 0.
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static void asNormalizedDiyFp(long d64, DiyFp w) {
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long f = significand(d64);
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int e = exponent(d64);
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// The current double could be a denormal.
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while ((f & kHiddenBit) == 0) {
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f <<= 1;
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e--;
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}
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// Do the final shifts in one go. Don't forget the hidden bit (the '-1').
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f <<= DiyFp.kSignificandSize - kSignificandSize - 1;
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e -= DiyFp.kSignificandSize - kSignificandSize - 1;
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w.f = f;
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w.e = e;
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}
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static int exponent(long d64) {
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if (isDenormal(d64)) return kDenormalExponent;
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int biased_e = (int) (((d64 & kExponentMask) >>> kSignificandSize) & 0xffffffffL);
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return biased_e - kExponentBias;
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}
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static long significand(long d64) {
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long significand = d64 & kSignificandMask;
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if (!isDenormal(d64)) {
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return significand + kHiddenBit;
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} else {
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return significand;
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}
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}
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// Returns true if the double is a denormal.
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private static boolean isDenormal(long d64) {
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return (d64 & kExponentMask) == 0L;
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}
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// Returns the two boundaries of first argument.
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// The bigger boundary (m_plus) is normalized. The lower boundary has the same
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// exponent as m_plus.
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static void normalizedBoundaries(DiyFp v, long d64, DiyFp m_minus, DiyFp m_plus) {
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asDiyFp(d64, v);
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final boolean significand_is_zero = (v.f == kHiddenBit);
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m_plus.f = (v.f << 1) + 1;
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m_plus.e = v.e - 1;
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m_plus.normalize();
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if (significand_is_zero && v.e != kDenormalExponent) {
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// The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
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// Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
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// at a distance of 1e8.
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// The only exception is for the smallest normal: the largest denormal is
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// at the same distance as its successor.
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// Note: denormals have the same exponent as the smallest normals.
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m_minus.f = (v.f << 2) - 1;
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m_minus.e = v.e - 2;
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} else {
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m_minus.f = (v.f << 1) - 1;
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m_minus.e = v.e - 1;
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}
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m_minus.f = m_minus.f << (m_minus.e - m_plus.e);
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m_minus.e = m_plus.e;
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}
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private static final int kSignificandSize = 52; // Excludes the hidden bit.
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private static final int kExponentBias = 0x3FF + kSignificandSize;
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private static final int kDenormalExponent = -kExponentBias + 1;
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}
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static class FastDtoa {
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// Adjusts the last digit of the generated number, and screens out generated
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// solutions that may be inaccurate. A solution may be inaccurate if it is
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// outside the safe interval, or if we ctannot prove that it is closer to the
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// input than a neighboring representation of the same length.
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//
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// Input: * buffer containing the digits of too_high / 10^kappa
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// * distance_too_high_w == (too_high - w).f() * unit
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// * unsafe_interval == (too_high - too_low).f() * unit
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// * rest = (too_high - buffer * 10^kappa).f() * unit
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// * ten_kappa = 10^kappa * unit
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// * unit = the common multiplier
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// Output: returns true if the buffer is guaranteed to contain the closest
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// representable number to the input.
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// Modifies the generated digits in the buffer to approach (round towards) w.
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static boolean roundWeed(
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final FastDtoaBuilder buffer,
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final long distance_too_high_w,
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final long unsafe_interval,
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long rest,
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final long ten_kappa,
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final long unit) {
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final long small_distance = distance_too_high_w - unit;
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final long big_distance = distance_too_high_w + unit;
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// Let w_low = too_high - big_distance, and
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// w_high = too_high - small_distance.
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// Note: w_low < w < w_high
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//
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// The real w (* unit) must lie somewhere inside the interval
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// ]w_low; w_low[ (often written as "(w_low; w_low)")
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// Basically the buffer currently contains a number in the unsafe interval
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// ]too_low; too_high[ with too_low < w < too_high
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//
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// too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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// ^v 1 unit ^ ^ ^ ^
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// boundary_high --------------------- . . . .
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// ^v 1 unit . . . .
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// - - - - - - - - - - - - - - - - - - - + - - + - - - - - - . .
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// . . ^ . .
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// . big_distance . . .
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// . . . . rest
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// small_distance . . . .
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// v . . . .
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// w_high - - - - - - - - - - - - - - - - - - . . . .
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// ^v 1 unit . . . .
|
|
// w ---------------------------------------- . . . .
|
|
// ^v 1 unit v . . .
|
|
// w_low - - - - - - - - - - - - - - - - - - - - - . . .
|
|
// . . v
|
|
// buffer --------------------------------------------------+-------+--------
|
|
// . .
|
|
// safe_interval .
|
|
// v .
|
|
// - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .
|
|
// ^v 1 unit .
|
|
// boundary_low ------------------------- unsafe_interval
|
|
// ^v 1 unit v
|
|
// too_low - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
|
|
//
|
|
//
|
|
// Note that the value of buffer could lie anywhere inside the range too_low
|
|
// to too_high.
|
|
//
|
|
// boundary_low, boundary_high and w are approximations of the real boundaries
|
|
// and v (the input number). They are guaranteed to be precise up to one unit.
|
|
// In fact the error is guaranteed to be strictly less than one unit.
|
|
//
|
|
// Anything that lies outside the unsafe interval is guaranteed not to round
|
|
// to v when read again.
|
|
// Anything that lies inside the safe interval is guaranteed to round to v
|
|
// when read again.
|
|
// If the number inside the buffer lies inside the unsafe interval but not
|
|
// inside the safe interval then we simply do not know and bail out (returning
|
|
// false).
|
|
//
|
|
// Similarly we have to take into account the imprecision of 'w' when rounding
|
|
// the buffer. If we have two potential representations we need to make sure
|
|
// that the chosen one is closer to w_low and w_high since v can be anywhere
|
|
// between them.
|
|
//
|
|
// By generating the digits of too_high we got the largest (closest to
|
|
// too_high) buffer that is still in the unsafe interval. In the case where
|
|
// w_high < buffer < too_high we try to decrement the buffer.
|
|
// This way the buffer approaches (rounds towards) w.
|
|
// There are 3 conditions that stop the decrementation process:
|
|
// 1) the buffer is already below w_high
|
|
// 2) decrementing the buffer would make it leave the unsafe interval
|
|
// 3) decrementing the buffer would yield a number below w_high and farther
|
|
// away than the current number. In other words:
|
|
// (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
|
|
// Instead of using the buffer directly we use its distance to too_high.
|
|
// Conceptually rest ~= too_high - buffer
|
|
while (rest < small_distance && // Negated condition 1
|
|
unsafe_interval - rest >= ten_kappa && // Negated condition 2
|
|
(rest + ten_kappa < small_distance || // buffer{-1} > w_high
|
|
small_distance - rest >= rest + ten_kappa - small_distance)) {
|
|
buffer.decreaseLast();
|
|
rest += ten_kappa;
|
|
}
|
|
|
|
// We have approached w+ as much as possible. We now test if approaching w-
|
|
// would require changing the buffer. If yes, then we have two possible
|
|
// representations close to w, but we cannot decide which one is closer.
|
|
if (rest < big_distance &&
|
|
unsafe_interval - rest >= ten_kappa &&
|
|
(rest + ten_kappa < big_distance ||
|
|
big_distance - rest > rest + ten_kappa - big_distance)) {
|
|
return false;
|
|
}
|
|
|
|
// Weeding test.
|
|
// The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
|
|
// Since too_low = too_high - unsafe_interval this is equivalent to
|
|
// [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
|
|
// Conceptually we have: rest ~= too_high - buffer
|
|
return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
|
|
}
|
|
|
|
static final int kTen4 = 10000;
|
|
static final int kTen5 = 100000;
|
|
static final int kTen6 = 1000000;
|
|
static final int kTen7 = 10000000;
|
|
static final int kTen8 = 100000000;
|
|
static final int kTen9 = 1000000000;
|
|
|
|
// Returns the biggest power of ten that is less than or equal than the given
|
|
// number. We furthermore receive the maximum number of bits 'number' has.
|
|
// If number_bits == 0 then 0^-1 is returned
|
|
// The number of bits must be <= 32.
|
|
// Precondition: (1 << number_bits) <= number < (1 << (number_bits + 1)).
|
|
static long biggestPowerTen(int number, int number_bits) {
|
|
int power, exponent;
|
|
switch (number_bits) {
|
|
case 32:
|
|
case 31:
|
|
case 30:
|
|
if (kTen9 <= number) {
|
|
power = kTen9;
|
|
exponent = 9;
|
|
break;
|
|
} // else fallthrough
|
|
case 29:
|
|
case 28:
|
|
case 27:
|
|
if (kTen8 <= number) {
|
|
power = kTen8;
|
|
exponent = 8;
|
|
break;
|
|
} // else fallthrough
|
|
case 26:
|
|
case 25:
|
|
case 24:
|
|
if (kTen7 <= number) {
|
|
power = kTen7;
|
|
exponent = 7;
|
|
break;
|
|
} // else fallthrough
|
|
case 23:
|
|
case 22:
|
|
case 21:
|
|
case 20:
|
|
if (kTen6 <= number) {
|
|
power = kTen6;
|
|
exponent = 6;
|
|
break;
|
|
} // else fallthrough
|
|
case 19:
|
|
case 18:
|
|
case 17:
|
|
if (kTen5 <= number) {
|
|
power = kTen5;
|
|
exponent = 5;
|
|
break;
|
|
} // else fallthrough
|
|
case 16:
|
|
case 15:
|
|
case 14:
|
|
if (kTen4 <= number) {
|
|
power = kTen4;
|
|
exponent = 4;
|
|
break;
|
|
} // else fallthrough
|
|
case 13:
|
|
case 12:
|
|
case 11:
|
|
case 10:
|
|
if (1000 <= number) {
|
|
power = 1000;
|
|
exponent = 3;
|
|
break;
|
|
} // else fallthrough
|
|
case 9:
|
|
case 8:
|
|
case 7:
|
|
if (100 <= number) {
|
|
power = 100;
|
|
exponent = 2;
|
|
break;
|
|
} // else fallthrough
|
|
case 6:
|
|
case 5:
|
|
case 4:
|
|
if (10 <= number) {
|
|
power = 10;
|
|
exponent = 1;
|
|
break;
|
|
} // else fallthrough
|
|
case 3:
|
|
case 2:
|
|
case 1:
|
|
if (1 <= number) {
|
|
power = 1;
|
|
exponent = 0;
|
|
break;
|
|
} // else fallthrough
|
|
case 0:
|
|
power = 0;
|
|
exponent = -1;
|
|
break;
|
|
default:
|
|
// Following assignments are here to silence compiler warnings.
|
|
power = 0;
|
|
exponent = 0;
|
|
// UNREACHABLE();
|
|
}
|
|
return ((long) power << 32) | (0xffffffffL & exponent);
|
|
}
|
|
|
|
// Generates the digits of input number w.
|
|
// w is a floating-point number (DiyFp), consisting of a significand and an
|
|
// exponent. Its exponent is bounded by minimal_target_exponent and
|
|
// maximal_target_exponent.
|
|
// Hence -60 <= w.e() <= -32.
|
|
//
|
|
// Returns false if it fails, in which case the generated digits in the buffer
|
|
// should not be used.
|
|
// Preconditions:
|
|
// * low, w and high are correct up to 1 ulp (unit in the last place). That
|
|
// is, their error must be less that a unit of their last digits.
|
|
// * low.e() == w.e() == high.e()
|
|
// * low < w < high, and taking into account their error: low~ <= high~
|
|
// * minimal_target_exponent <= w.e() <= maximal_target_exponent
|
|
// Postconditions: returns false if procedure fails.
|
|
// otherwise:
|
|
// * buffer is not null-terminated, but len contains the number of digits.
|
|
// * buffer contains the shortest possible decimal digit-sequence
|
|
// such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
|
|
// correct values of low and high (without their error).
|
|
// * if more than one decimal representation gives the minimal number of
|
|
// decimal digits then the one closest to W (where W is the correct value
|
|
// of w) is chosen.
|
|
// Remark: this procedure takes into account the imprecision of its input
|
|
// numbers. If the precision is not enough to guarantee all the postconditions
|
|
// then false is returned. This usually happens rarely (~0.5%).
|
|
//
|
|
// Say, for the sake of example, that
|
|
// w.e() == -48, and w.f() == 0x1234567890abcdef
|
|
// w's value can be computed by w.f() * 2^w.e()
|
|
// We can obtain w's integral digits by simply shifting w.f() by -w.e().
|
|
// -> w's integral part is 0x1234
|
|
// w's fractional part is therefore 0x567890abcdef.
|
|
// Printing w's integral part is easy (simply print 0x1234 in decimal).
|
|
// In order to print its fraction we repeatedly multiply the fraction by 10 and
|
|
// get each digit. Example the first digit after the point would be computed by
|
|
// (0x567890abcdef * 10) >> 48. -> 3
|
|
// The whole thing becomes slightly more complicated because we want to stop
|
|
// once we have enough digits. That is, once the digits inside the buffer
|
|
// represent 'w' we can stop. Everything inside the interval low - high
|
|
// represents w. However we have to pay attention to low, high and w's
|
|
// imprecision.
|
|
static boolean digitGen(FastDtoaBuilder buffer, int mk) {
|
|
final DiyFp low = buffer.scaled_boundary_minus;
|
|
final DiyFp w = buffer.scaled_w;
|
|
final DiyFp high = buffer.scaled_boundary_plus;
|
|
|
|
// low, w and high are imprecise, but by less than one ulp (unit in the last
|
|
// place).
|
|
// If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
|
|
// the new numbers are outside of the interval we want the final
|
|
// representation to lie in.
|
|
// Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
|
|
// numbers that are certain to lie in the interval. We will use this fact
|
|
// later on.
|
|
// We will now start by generating the digits within the uncertain
|
|
// interval. Later we will weed out representations that lie outside the safe
|
|
// interval and thus _might_ lie outside the correct interval.
|
|
long unit = 1;
|
|
final DiyFp too_low = buffer.too_low;
|
|
too_low.f = low.f - unit;
|
|
too_low.e = low.e;
|
|
final DiyFp too_high = buffer.too_high;
|
|
too_high.f = high.f + unit;
|
|
too_high.e = high.e;
|
|
// too_low and too_high are guaranteed to lie outside the interval we want the
|
|
// generated number in.
|
|
final DiyFp unsafe_interval = buffer.unsafe_interval;
|
|
unsafe_interval.f = too_high.f;
|
|
unsafe_interval.e = too_high.e;
|
|
unsafe_interval.subtract(too_low);
|
|
// We now cut the input number into two parts: the integral digits and the
|
|
// fractionals. We will not write any decimal separator though, but adapt
|
|
// kappa instead.
|
|
// Reminder: we are currently computing the digits (stored inside the buffer)
|
|
// such that: too_low < buffer * 10^kappa < too_high
|
|
// We use too_high for the digit_generation and stop as soon as possible.
|
|
// If we stop early we effectively round down.
|
|
final DiyFp one = buffer.one;
|
|
one.f = 1L << -w.e;
|
|
one.e = w.e;
|
|
// Division by one is a shift.
|
|
int integrals = (int) ((too_high.f >>> -one.e) & 0xffffffffL);
|
|
// Modulo by one is an and.
|
|
long fractionals = too_high.f & (one.f - 1);
|
|
long result = biggestPowerTen(integrals, DiyFp.kSignificandSize - (-one.e));
|
|
int divider = (int) ((result >>> 32) & 0xffffffffL);
|
|
int divider_exponent = (int) (result & 0xffffffffL);
|
|
int kappa = divider_exponent + 1;
|
|
// Loop invariant: buffer = too_high / 10^kappa (integer division)
|
|
// The invariant holds for the first iteration: kappa has been initialized
|
|
// with the divider exponent + 1. And the divider is the biggest power of ten
|
|
// that is smaller than integrals.
|
|
while (kappa > 0) {
|
|
int digit = integrals / divider;
|
|
buffer.append((byte) ('0' + digit));
|
|
integrals %= divider;
|
|
kappa--;
|
|
// Note that kappa now equals the exponent of the divider and that the
|
|
// invariant thus holds again.
|
|
final long rest = ((long) integrals << -one.e) + fractionals;
|
|
// Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
|
|
// Reminder: unsafe_interval.e() == one.e()
|
|
if (rest < unsafe_interval.f) {
|
|
// Rounding down (by not emitting the remaining digits) yields a number
|
|
// that lies within the unsafe interval.
|
|
buffer.point = buffer.end - mk + kappa;
|
|
final DiyFp minus_round = buffer.minus_round;
|
|
minus_round.f = too_high.f;
|
|
minus_round.e = too_high.e;
|
|
minus_round.subtract(w);
|
|
return roundWeed(buffer, minus_round.f,
|
|
unsafe_interval.f, rest,
|
|
(long) divider << -one.e, unit);
|
|
}
|
|
divider /= 10;
|
|
}
|
|
|
|
// The integrals have been generated. We are at the point of the decimal
|
|
// separator. In the following loop we simply multiply the remaining digits by
|
|
// 10 and divide by one. We just need to pay attention to multiply associated
|
|
// data (like the interval or 'unit'), too.
|
|
// Instead of multiplying by 10 we multiply by 5 (cheaper operation) and
|
|
// increase its (imaginary) exponent. At the same time we decrease the
|
|
// divider's (one's) exponent and shift its significand.
|
|
// Basically, if fractionals was a DiyFp (with fractionals.e == one.e):
|
|
// fractionals.f *= 10;
|
|
// fractionals.f >>= 1; fractionals.e++; // value remains unchanged.
|
|
// one.f >>= 1; one.e++; // value remains unchanged.
|
|
// and we have again fractionals.e == one.e which allows us to divide
|
|
// fractionals.f() by one.f()
|
|
// We simply combine the *= 10 and the >>= 1.
|
|
while (true) {
|
|
fractionals *= 5;
|
|
unit *= 5;
|
|
unsafe_interval.f = unsafe_interval.f * 5;
|
|
unsafe_interval.e = unsafe_interval.e + 1; // Will be optimized out.
|
|
one.f = one.f >>> 1;
|
|
one.e = one.e + 1;
|
|
// Integer division by one.
|
|
final int digit = (int) ((fractionals >>> -one.e) & 0xffffffffL);
|
|
buffer.append((byte) ('0' + digit));
|
|
fractionals &= one.f - 1; // Modulo by one.
|
|
kappa--;
|
|
if (fractionals < unsafe_interval.f) {
|
|
buffer.point = buffer.end - mk + kappa;
|
|
final DiyFp minus_round = buffer.minus_round;
|
|
minus_round.f = too_high.f;
|
|
minus_round.e = too_high.e;
|
|
minus_round.subtract(w);
|
|
return roundWeed(buffer, minus_round.f * unit,
|
|
unsafe_interval.f, fractionals, one.f, unit);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
public static boolean tryConvert(final double value, final FastDtoaBuilder buffer) {
|
|
final long bits;
|
|
final int firstDigit;
|
|
buffer.reset();
|
|
if (value < 0) {
|
|
buffer.append((byte) '-');
|
|
bits = Double.doubleToLongBits(-value);
|
|
firstDigit = 1;
|
|
} else {
|
|
bits = Double.doubleToLongBits(value);
|
|
firstDigit = 0;
|
|
}
|
|
|
|
// Provides a decimal representation of v.
|
|
// Returns true if it succeeds, otherwise the result cannot be trusted.
|
|
// There will be *length digits inside the buffer (not null-terminated).
|
|
// If the function returns true then
|
|
// v == (double) (buffer * 10^decimal_exponent).
|
|
// The digits in the buffer are the shortest representation possible: no
|
|
// 0.09999999999999999 instead of 0.1. The shorter representation will even be
|
|
// chosen even if the longer one would be closer to v.
|
|
// The last digit will be closest to the actual v. That is, even if several
|
|
// digits might correctly yield 'v' when read again, the closest will be
|
|
// computed.
|
|
final int mk = buffer.initialize(bits);
|
|
|
|
// DigitGen will generate the digits of scaled_w. Therefore we have
|
|
// v == (double) (scaled_w * 10^-mk).
|
|
// Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
|
|
// integer than it will be updated. For instance if scaled_w == 1.23 then
|
|
// the buffer will be filled with "123" und the decimal_exponent will be
|
|
// decreased by 2.
|
|
if (FastDtoa.digitGen(buffer, mk)) {
|
|
buffer.write(firstDigit);
|
|
return true;
|
|
} else {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
static class FastDtoaBuilder {
|
|
|
|
private final DiyFp v = new DiyFp();
|
|
private final DiyFp w = new DiyFp();
|
|
private final DiyFp boundary_minus = new DiyFp();
|
|
private final DiyFp boundary_plus = new DiyFp();
|
|
private final DiyFp ten_mk = new DiyFp();
|
|
private final DiyFp scaled_w = new DiyFp();
|
|
private final DiyFp scaled_boundary_minus = new DiyFp();
|
|
private final DiyFp scaled_boundary_plus = new DiyFp();
|
|
|
|
private final DiyFp too_low = new DiyFp();
|
|
private final DiyFp too_high = new DiyFp();
|
|
private final DiyFp unsafe_interval = new DiyFp();
|
|
private final DiyFp one = new DiyFp();
|
|
private final DiyFp minus_round = new DiyFp();
|
|
|
|
int initialize(final long bits) {
|
|
DoubleHelper.asNormalizedDiyFp(bits, w);
|
|
// boundary_minus and boundary_plus are the boundaries between v and its
|
|
// closest floating-point neighbors. Any number strictly between
|
|
// boundary_minus and boundary_plus will round to v when convert to a double.
|
|
// Grisu3 will never output representations that lie exactly on a boundary.
|
|
boundary_minus.reset();
|
|
boundary_plus.reset();
|
|
DoubleHelper.normalizedBoundaries(v, bits, boundary_minus, boundary_plus);
|
|
ten_mk.reset(); // Cached power of ten: 10^-k
|
|
final int mk = CachedPowers.getCachedPower(w.e + DiyFp.kSignificandSize, minimal_target_exponent, ten_mk);
|
|
// Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
|
|
// 64 bit significand and ten_mk is thus only precise up to 64 bits.
|
|
|
|
// The DiyFp::Times procedure rounds its result, and ten_mk is approximated
|
|
// too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
|
|
// off by a small amount.
|
|
// In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
|
|
// In other words: let f = scaled_w.f() and e = scaled_w.e(), then
|
|
// (f-1) * 2^e < w*10^k < (f+1) * 2^e
|
|
scaled_w.f = w.f;
|
|
scaled_w.e = w.e;
|
|
scaled_w.multiply(ten_mk);
|
|
// In theory it would be possible to avoid some recomputations by computing
|
|
// the difference between w and boundary_minus/plus (a power of 2) and to
|
|
// compute scaled_boundary_minus/plus by subtracting/adding from
|
|
// scaled_w. However the code becomes much less readable and the speed
|
|
// enhancements are not terriffic.
|
|
scaled_boundary_minus.f = boundary_minus.f;
|
|
scaled_boundary_minus.e = boundary_minus.e;
|
|
scaled_boundary_minus.multiply(ten_mk);
|
|
scaled_boundary_plus.f = boundary_plus.f;
|
|
scaled_boundary_plus.e = boundary_plus.e;
|
|
scaled_boundary_plus.multiply(ten_mk);
|
|
|
|
return mk;
|
|
}
|
|
|
|
// allocate buffer for generated digits + extra notation + padding zeroes
|
|
private final byte[] chars = new byte[kFastDtoaMaximalLength + 10];
|
|
private int end = 0;
|
|
private int point;
|
|
|
|
void reset() {
|
|
end = 0;
|
|
}
|
|
|
|
void append(byte c) {
|
|
chars[end++] = c;
|
|
}
|
|
|
|
void decreaseLast() {
|
|
chars[end - 1]--;
|
|
}
|
|
|
|
@Override
|
|
public String toString() {
|
|
return "[chars:" + new String(chars, 0, end) + ", point:" + point + "]";
|
|
}
|
|
|
|
int copyTo(final byte[] target, final int position) {
|
|
for (int i = 0; i < end; i++) {
|
|
target[i + position] = chars[i];
|
|
}
|
|
return end;
|
|
}
|
|
|
|
public void write(int firstDigit) {
|
|
// check for minus sign
|
|
int decPoint = point - firstDigit;
|
|
if (decPoint < -5 || decPoint > 21) {
|
|
toExponentialFormat(firstDigit, decPoint);
|
|
} else {
|
|
toFixedFormat(firstDigit, decPoint);
|
|
}
|
|
}
|
|
|
|
private void toFixedFormat(int firstDigit, int decPoint) {
|
|
if (point < end) {
|
|
// insert decimal point
|
|
if (decPoint > 0) {
|
|
// >= 1, split decimals and insert point
|
|
for (int i = end; i >= point; i--) {
|
|
chars[i + 1] = chars[i];
|
|
}
|
|
chars[point] = '.';
|
|
end++;
|
|
} else {
|
|
// < 1,
|
|
final int offset = 2 - decPoint;
|
|
for (int i = end + firstDigit; i >= firstDigit; i--) {
|
|
chars[i + offset] = chars[i];
|
|
}
|
|
chars[firstDigit] = '0';
|
|
chars[firstDigit + 1] = '.';
|
|
if (decPoint < 0) {
|
|
int target = firstDigit + 2 - decPoint;
|
|
for (int i = firstDigit + 2; i < target; i++) {
|
|
chars[i] = '0';
|
|
}
|
|
}
|
|
end += 2 - decPoint;
|
|
}
|
|
} else if (point > end) {
|
|
// large integer, add trailing zeroes
|
|
for (int i = end; i < point; i++) {
|
|
chars[i] = '0';
|
|
}
|
|
end += point - end;
|
|
chars[end] = '.';
|
|
chars[end + 1] = '0';
|
|
end += 2;
|
|
} else {
|
|
chars[end] = '.';
|
|
chars[end + 1] = '0';
|
|
end += 2;
|
|
}
|
|
}
|
|
|
|
private void toExponentialFormat(int firstDigit, int decPoint) {
|
|
if (end - firstDigit > 1) {
|
|
// insert decimal point if more than one digit was produced
|
|
int dot = firstDigit + 1;
|
|
System.arraycopy(chars, dot, chars, dot + 1, end - dot);
|
|
chars[dot] = '.';
|
|
end++;
|
|
}
|
|
chars[end++] = 'E';
|
|
byte sign = '+';
|
|
int exp = decPoint - 1;
|
|
if (exp < 0) {
|
|
sign = '-';
|
|
exp = -exp;
|
|
}
|
|
chars[end++] = sign;
|
|
|
|
int charPos = exp > 99 ? end + 2 : exp > 9 ? end + 1 : end;
|
|
end = charPos + 1;
|
|
|
|
do {
|
|
int r = exp % 10;
|
|
chars[charPos--] = digits[r];
|
|
exp = exp / 10;
|
|
} while (exp != 0);
|
|
}
|
|
|
|
final static byte[] digits = {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'};
|
|
}
|
|
}
|