| /* |
| * Copyright (c) 2015, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code is distributed in the hope that it will be useful, but WITHOUT |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| // This file is available under and governed by the GNU General Public |
| // License version 2 only, as published by the Free Software Foundation. |
| // However, the following notice accompanied the original version of this |
| // file: |
| // |
| // Copyright 2010 the V8 project authors. All rights reserved. |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above |
| // copyright notice, this list of conditions and the following |
| // disclaimer in the documentation and/or other materials provided |
| // with the distribution. |
| // * Neither the name of Google Inc. nor the names of its |
| // contributors may be used to endorse or promote products derived |
| // from this software without specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| |
| package jdk.nashorn.internal.runtime.doubleconv; |
| |
| class FixedDtoa { |
| |
| // Represents a 128bit type. This class should be replaced by a native type on |
| // platforms that support 128bit integers. |
| static class UInt128 { |
| |
| private static final long kMask32 = 0xFFFFFFFFL; |
| // Value == (high_bits_ << 64) + low_bits_ |
| private long high_bits_; |
| private long low_bits_; |
| |
| UInt128(final long high_bits, final long low_bits) { |
| this.high_bits_ = high_bits; |
| this.low_bits_ = low_bits; |
| } |
| |
| void multiply(final int multiplicand) { |
| long accumulator; |
| |
| accumulator = (low_bits_ & kMask32) * multiplicand; |
| long part = accumulator & kMask32; |
| accumulator >>>= 32; |
| accumulator = accumulator + (low_bits_ >>> 32) * multiplicand; |
| low_bits_ = (accumulator << 32) + part; |
| accumulator >>>= 32; |
| accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; |
| part = accumulator & kMask32; |
| accumulator >>>= 32; |
| accumulator = accumulator + (high_bits_ >>> 32) * multiplicand; |
| high_bits_ = (accumulator << 32) + part; |
| assert ((accumulator >>> 32) == 0); |
| } |
| |
| void shift(final int shift_amount) { |
| assert (-64 <= shift_amount && shift_amount <= 64); |
| if (shift_amount == 0) { |
| return; |
| } else if (shift_amount == -64) { |
| high_bits_ = low_bits_; |
| low_bits_ = 0; |
| } else if (shift_amount == 64) { |
| low_bits_ = high_bits_; |
| high_bits_ = 0; |
| } else if (shift_amount <= 0) { |
| high_bits_ <<= -shift_amount; |
| high_bits_ += low_bits_ >>> (64 + shift_amount); |
| low_bits_ <<= -shift_amount; |
| } else { |
| low_bits_ >>>= shift_amount; |
| low_bits_ += high_bits_ << (64 - shift_amount); |
| high_bits_ >>>= shift_amount; |
| } |
| } |
| |
| // Modifies *this to *this MOD (2^power). |
| // Returns *this DIV (2^power). |
| int divModPowerOf2(final int power) { |
| if (power >= 64) { |
| final int result = (int) (high_bits_ >>> (power - 64)); |
| high_bits_ -= (long) (result) << (power - 64); |
| return result; |
| } else { |
| final long part_low = low_bits_ >>> power; |
| final long part_high = high_bits_ << (64 - power); |
| final int result = (int) (part_low + part_high); |
| high_bits_ = 0; |
| low_bits_ -= part_low << power; |
| return result; |
| } |
| } |
| |
| boolean isZero() { |
| return high_bits_ == 0 && low_bits_ == 0; |
| } |
| |
| int bitAt(final int position) { |
| if (position >= 64) { |
| return (int) (high_bits_ >>> (position - 64)) & 1; |
| } else { |
| return (int) (low_bits_ >>> position) & 1; |
| } |
| } |
| |
| }; |
| |
| |
| static final int kDoubleSignificandSize = 53; // Includes the hidden bit. |
| |
| |
| static void fillDigits32FixedLength(int number, final int requested_length, |
| final DtoaBuffer buffer) { |
| for (int i = requested_length - 1; i >= 0; --i) { |
| buffer.chars[buffer.length + i] = (char) ('0' + Integer.remainderUnsigned(number, 10)); |
| number = Integer.divideUnsigned(number, 10); |
| } |
| buffer.length += requested_length; |
| } |
| |
| |
| static void fillDigits32(int number, final DtoaBuffer buffer) { |
| int number_length = 0; |
| // We fill the digits in reverse order and exchange them afterwards. |
| while (number != 0) { |
| final int digit = Integer.remainderUnsigned(number, 10); |
| number = Integer.divideUnsigned(number, 10); |
| buffer.chars[buffer.length + number_length] = (char) ('0' + digit); |
| number_length++; |
| } |
| // Exchange the digits. |
| int i = buffer.length; |
| int j = buffer.length + number_length - 1; |
| while (i < j) { |
| final char tmp = buffer.chars[i]; |
| buffer.chars[i] = buffer.chars[j]; |
| buffer.chars[j] = tmp; |
| i++; |
| j--; |
| } |
| buffer.length += number_length; |
| } |
| |
| |
| static void fillDigits64FixedLength(long number, final DtoaBuffer buffer) { |
| final int kTen7 = 10000000; |
| // For efficiency cut the number into 3 uint32_t parts, and print those. |
| final int part2 = (int) Long.remainderUnsigned(number, kTen7); |
| number = Long.divideUnsigned(number, kTen7); |
| final int part1 = (int) Long.remainderUnsigned(number, kTen7); |
| final int part0 = (int) Long.divideUnsigned(number, kTen7); |
| |
| fillDigits32FixedLength(part0, 3, buffer); |
| fillDigits32FixedLength(part1, 7, buffer); |
| fillDigits32FixedLength(part2, 7, buffer); |
| } |
| |
| |
| static void FillDigits64(long number, final DtoaBuffer buffer) { |
| final int kTen7 = 10000000; |
| // For efficiency cut the number into 3 uint32_t parts, and print those. |
| final int part2 = (int) Long.remainderUnsigned(number, kTen7); |
| number = Long.divideUnsigned(number, kTen7); |
| final int part1 = (int) Long.remainderUnsigned(number, kTen7); |
| final int part0 = (int) Long.divideUnsigned(number, kTen7); |
| |
| if (part0 != 0) { |
| fillDigits32(part0, buffer); |
| fillDigits32FixedLength(part1, 7, buffer); |
| fillDigits32FixedLength(part2, 7, buffer); |
| } else if (part1 != 0) { |
| fillDigits32(part1, buffer); |
| fillDigits32FixedLength(part2, 7, buffer); |
| } else { |
| fillDigits32(part2, buffer); |
| } |
| } |
| |
| |
| static void roundUp(final DtoaBuffer buffer) { |
| // An empty buffer represents 0. |
| if (buffer.length == 0) { |
| buffer.chars[0] = '1'; |
| buffer.decimalPoint = 1; |
| buffer.length = 1; |
| return; |
| } |
| // Round the last digit until we either have a digit that was not '9' or until |
| // we reached the first digit. |
| buffer.chars[buffer.length - 1]++; |
| for (int i = buffer.length - 1; i > 0; --i) { |
| if (buffer.chars[i] != '0' + 10) { |
| return; |
| } |
| buffer.chars[i] = '0'; |
| buffer.chars[i - 1]++; |
| } |
| // If the first digit is now '0' + 10, we would need to set it to '0' and add |
| // a '1' in front. However we reach the first digit only if all following |
| // digits had been '9' before rounding up. Now all trailing digits are '0' and |
| // we simply switch the first digit to '1' and update the decimal-point |
| // (indicating that the point is now one digit to the right). |
| if (buffer.chars[0] == '0' + 10) { |
| buffer.chars[0] = '1'; |
| buffer.decimalPoint++; |
| } |
| } |
| |
| |
| // The given fractionals number represents a fixed-point number with binary |
| // point at bit (-exponent). |
| // Preconditions: |
| // -128 <= exponent <= 0. |
| // 0 <= fractionals * 2^exponent < 1 |
| // The buffer holds the result. |
| // The function will round its result. During the rounding-process digits not |
| // generated by this function might be updated, and the decimal-point variable |
| // might be updated. If this function generates the digits 99 and the buffer |
| // already contained "199" (thus yielding a buffer of "19999") then a |
| // rounding-up will change the contents of the buffer to "20000". |
| static void fillFractionals(long fractionals, final int exponent, |
| final int fractional_count, final DtoaBuffer buffer) { |
| assert (-128 <= exponent && exponent <= 0); |
| // 'fractionals' is a fixed-decimalPoint number, with binary decimalPoint at bit |
| // (-exponent). Inside the function the non-converted remainder of fractionals |
| // is a fixed-decimalPoint number, with binary decimalPoint at bit 'decimalPoint'. |
| if (-exponent <= 64) { |
| // One 64 bit number is sufficient. |
| assert (fractionals >>> 56 == 0); |
| int point = -exponent; |
| for (int i = 0; i < fractional_count; ++i) { |
| if (fractionals == 0) break; |
| // Instead of multiplying by 10 we multiply by 5 and adjust the point |
| // location. This way the fractionals variable will not overflow. |
| // Invariant at the beginning of the loop: fractionals < 2^point. |
| // Initially we have: point <= 64 and fractionals < 2^56 |
| // After each iteration the point is decremented by one. |
| // Note that 5^3 = 125 < 128 = 2^7. |
| // Therefore three iterations of this loop will not overflow fractionals |
| // (even without the subtraction at the end of the loop body). At this |
| // time point will satisfy point <= 61 and therefore fractionals < 2^point |
| // and any further multiplication of fractionals by 5 will not overflow. |
| fractionals *= 5; |
| point--; |
| final int digit = (int) (fractionals >>> point); |
| assert (digit <= 9); |
| buffer.chars[buffer.length] = (char) ('0' + digit); |
| buffer.length++; |
| fractionals -= (long) (digit) << point; |
| } |
| // If the first bit after the point is set we have to round up. |
| assert (fractionals == 0 || point - 1 >= 0); |
| if ((fractionals != 0) && ((fractionals >>> (point - 1)) & 1) == 1) { |
| roundUp(buffer); |
| } |
| } else { // We need 128 bits. |
| assert (64 < -exponent && -exponent <= 128); |
| final UInt128 fractionals128 = new UInt128(fractionals, 0); |
| fractionals128.shift(-exponent - 64); |
| int point = 128; |
| for (int i = 0; i < fractional_count; ++i) { |
| if (fractionals128.isZero()) break; |
| // As before: instead of multiplying by 10 we multiply by 5 and adjust the |
| // point location. |
| // This multiplication will not overflow for the same reasons as before. |
| fractionals128.multiply(5); |
| point--; |
| final int digit = fractionals128.divModPowerOf2(point); |
| assert (digit <= 9); |
| buffer.chars[buffer.length] = (char) ('0' + digit); |
| buffer.length++; |
| } |
| if (fractionals128.bitAt(point - 1) == 1) { |
| roundUp(buffer); |
| } |
| } |
| } |
| |
| |
| // Removes leading and trailing zeros. |
| // If leading zeros are removed then the decimal point position is adjusted. |
| static void trimZeros(final DtoaBuffer buffer) { |
| while (buffer.length > 0 && buffer.chars[buffer.length - 1] == '0') { |
| buffer.length--; |
| } |
| int first_non_zero = 0; |
| while (first_non_zero < buffer.length && buffer.chars[first_non_zero] == '0') { |
| first_non_zero++; |
| } |
| if (first_non_zero != 0) { |
| for (int i = first_non_zero; i < buffer.length; ++i) { |
| buffer.chars[i - first_non_zero] = buffer.chars[i]; |
| } |
| buffer.length -= first_non_zero; |
| buffer.decimalPoint -= first_non_zero; |
| } |
| } |
| |
| |
| static boolean fastFixedDtoa(final double v, |
| final int fractional_count, |
| final DtoaBuffer buffer) { |
| final long kMaxUInt32 = 0xFFFFFFFFL; |
| final long l = IeeeDouble.doubleToLong(v); |
| long significand = IeeeDouble.significand(l); |
| final int exponent = IeeeDouble.exponent(l); |
| // v = significand * 2^exponent (with significand a 53bit integer). |
| // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we |
| // don't know how to compute the representation. 2^73 ~= 9.5*10^21. |
| // If necessary this limit could probably be increased, but we don't need |
| // more. |
| if (exponent > 20) return false; |
| if (fractional_count > 20) return false; |
| // At most kDoubleSignificandSize bits of the significand are non-zero. |
| // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero |
| // bits: 0..11*..0xxx..53*..xx |
| if (exponent + kDoubleSignificandSize > 64) { |
| // The exponent must be > 11. |
| // |
| // We know that v = significand * 2^exponent. |
| // And the exponent > 11. |
| // We simplify the task by dividing v by 10^17. |
| // The quotient delivers the first digits, and the remainder fits into a 64 |
| // bit number. |
| // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. |
| final long kFive17 = 0xB1A2BC2EC5L; // 5^17 |
| long divisor = kFive17; |
| final int divisor_power = 17; |
| long dividend = significand; |
| final int quotient; |
| final long remainder; |
| // Let v = f * 2^e with f == significand and e == exponent. |
| // Then need q (quotient) and r (remainder) as follows: |
| // v = q * 10^17 + r |
| // f * 2^e = q * 10^17 + r |
| // f * 2^e = q * 5^17 * 2^17 + r |
| // If e > 17 then |
| // f * 2^(e-17) = q * 5^17 + r/2^17 |
| // else |
| // f = q * 5^17 * 2^(17-e) + r/2^e |
| if (exponent > divisor_power) { |
| // We only allow exponents of up to 20 and therefore (17 - e) <= 3 |
| dividend <<= exponent - divisor_power; |
| quotient = (int) Long.divideUnsigned(dividend, divisor); |
| remainder = Long.remainderUnsigned(dividend, divisor) << divisor_power; |
| } else { |
| divisor <<= divisor_power - exponent; |
| quotient = (int) Long.divideUnsigned(dividend, divisor); |
| remainder = Long.remainderUnsigned(dividend, divisor) << exponent; |
| } |
| fillDigits32(quotient, buffer); |
| fillDigits64FixedLength(remainder, buffer); |
| buffer.decimalPoint = buffer.length; |
| } else if (exponent >= 0) { |
| // 0 <= exponent <= 11 |
| significand <<= exponent; |
| FillDigits64(significand, buffer); |
| buffer.decimalPoint = buffer.length; |
| } else if (exponent > -kDoubleSignificandSize) { |
| // We have to cut the number. |
| final long integrals = significand >>> -exponent; |
| final long fractionals = significand - (integrals << -exponent); |
| if (Long.compareUnsigned(integrals, kMaxUInt32) > 0) { |
| FillDigits64(integrals, buffer); |
| } else { |
| fillDigits32((int) (integrals), buffer); |
| } |
| buffer.decimalPoint = buffer.length; |
| fillFractionals(fractionals, exponent, fractional_count, buffer); |
| } else if (exponent < -128) { |
| // This configuration (with at most 20 digits) means that all digits must be |
| // 0. |
| assert (fractional_count <= 20); |
| buffer.reset(); |
| buffer.decimalPoint = -fractional_count; |
| } else { |
| buffer.decimalPoint = 0; |
| fillFractionals(significand, exponent, fractional_count, buffer); |
| } |
| trimZeros(buffer); |
| if (buffer.length == 0) { |
| // The string is empty and the decimal_point thus has no importance. Mimick |
| // Gay's dtoa and and set it to -fractional_count. |
| buffer.decimalPoint = -fractional_count; |
| } |
| return true; |
| } |
| |
| } |
