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/* |
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* Copyright (c) 2017-2018 Rafael da Silva Rocha. |
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* Copyright (c) 2013 DeNA Co., Ltd. |
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* Copyright (c) 2010, Linden Research, Inc |
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* |
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* Permission is hereby granted, free of charge, to any person obtaining |
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* a copy of this software and associated documentation files (the |
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* "Software"), to deal in the Software without restriction, including |
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* without limitation the rights to use, copy, modify, merge, publish, |
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* distribute, sublicense, and/or sell copies of the Software, and to |
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* permit persons to whom the Software is furnished to do so, subject to |
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* the following conditions: |
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* |
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* The above copyright notice and this permission notice shall be |
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* included in all copies or substantial portions of the Software. |
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* |
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, |
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF |
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND |
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE |
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* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION |
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* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION |
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* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. |
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* |
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*/ |
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/** |
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* @fileoverview Functions to pack and unpack IEEE 754 floating point numbers. |
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* @see https://github.com/rochars/byte-data |
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*/ |
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/** |
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* Pack a IEEE754 floating point number. |
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* Derived from typedarray.js by Linden Research, MIT License. |
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* Adapted to round overflows and underflows to Infinity and -Infinity. |
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* @see https://bitbucket.org/lindenlab/llsd/raw/7d2646cd3f9b4c806e73aebc4b32bd81e4047fdc/js/typedarray.js |
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* @param {!Uint8Array|!Array<number>} buffer The buffer. |
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* @param {number} index The index to write on the buffer. |
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* @param {number} num The number. |
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* @param {number} ebits The number of bits of the exponent. |
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* @param {number} fbits The number of bits of the fraction. |
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* @return {number} The next index to write on the buffer. |
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*/ |
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export function pack(buffer, index, num, ebits, fbits) { |
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/** @type {number} */ |
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let bias = (1 << (ebits - 1)) - 1; |
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// Round overflows and underflows |
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if (Math.abs(num) > Math.pow(2, bias + 1) - ((ebits + fbits) * 2)) { |
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num = num < 0 ? -Infinity : Infinity; |
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} |
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/** |
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* sign, need this to handle negative zero |
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* @see http://cwestblog.com/2014/02/25/javascript-testing-for-negative-zero/ |
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* @type {number} |
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*/ |
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let sign = (((num = +num) || 1 / num) < 0) ? 1 : num < 0 ? 1 : 0; |
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num = Math.abs(num); |
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/** @type {number} */ |
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let exp = Math.min(Math.floor(Math.log(num) / Math.LN2), 1023); |
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/** @type {number} */ |
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let fraction = Math.round(num / Math.pow(2, exp) * Math.pow(2, fbits)); |
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// NaN |
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if (num !== num) { |
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fraction = Math.pow(2, fbits - 1); |
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exp = (1 << ebits) - 1; |
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// Number |
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} else if (num !== 0) { |
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if (num >= Math.pow(2, 1 - bias)) { |
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if (fraction / Math.pow(2, fbits) >= 2) { |
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exp = exp + 1; |
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fraction = 1; |
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} |
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// Overflow |
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if (exp > bias) { |
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exp = (1 << ebits) - 1; |
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fraction = 0; |
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} else { |
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exp = exp + bias; |
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fraction = fraction - Math.pow(2, fbits); |
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} |
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} else { |
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fraction = Math.round(num / Math.pow(2, 1 - bias - fbits)); |
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exp = 0; |
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} |
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} |
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return packFloatBits_(buffer, index, ebits, fbits, sign, exp, fraction); |
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} |
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/** |
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* Unpack a IEEE754 floating point number. |
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* Derived from IEEE754 by DeNA Co., Ltd., MIT License. |
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* Adapted to handle NaN. Should port the solution to the original repo. |
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* @see https://github.com/kazuho/ieee754.js/blob/master/ieee754.js |
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* @param {!Uint8Array|!Array<number>} buffer The byte buffer to unpack. |
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* @param {number} index the start index to read. |
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* @param {number} ebits The number of bits of the exponent. |
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* @param {number} fbits The number of bits of the fraction. |
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*/ |
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export function unpack(buffer, index, ebits, fbits) { |
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let exponentBias = (1 << (ebits - 1)) - 1; |
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let numBytes = Math.ceil((ebits + fbits) / 8); |
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/** @type {number} */ |
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let eMax = (1 << ebits) - 1; |
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/** @type {number} */ |
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let bias = Math.pow(2, -(8 * numBytes - 1 - ebits)); |
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/** @type {number} */ |
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let significand; |
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/** @type {string} */ |
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let leftBits = ""; |
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for (let i = numBytes - 1; i >= 0 ; i--) { |
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/** @type {string} */ |
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let t = buffer[i + index].toString(2); |
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leftBits += "00000000".substring(t.length) + t; |
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} |
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/** @type {number} */ |
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let sign = leftBits.charAt(0) == "1" ? -1 : 1; |
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leftBits = leftBits.substring(1); |
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/** @type {number} */ |
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let exponent = parseInt(leftBits.substring(0, ebits), 2); |
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leftBits = leftBits.substring(ebits); |
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if (exponent == eMax) { |
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if (parseInt(leftBits, 2) !== 0) { |
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return NaN; |
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} |
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return sign * Infinity; |
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} else if (exponent == 0) { |
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exponent += 1; |
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significand = parseInt(leftBits, 2); |
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} else { |
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significand = parseInt("1" + leftBits, 2); |
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} |
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return sign * significand * bias * Math.pow(2, exponent - exponentBias); |
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} |
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/** |
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* Pack a IEEE754 from its sign, exponent and fraction bits |
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* and place it in a byte buffer. |
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* @param {!Uint8Array|!Array<number>} buffer The byte buffer to write to. |
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* @param {number} index The buffer index to write. |
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* @param {number} ebits The number of bits of the exponent. |
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* @param {number} fbits The number of bits of the fraction. |
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* @param {number} sign The sign. |
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* @param {number} exp the exponent. |
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* @param {number} fraction The fraction. |
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* @return {number} |
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* @private |
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*/ |
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function packFloatBits_(buffer, index, ebits, fbits, sign, exp, fraction) { |
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/** @type {!Array<number>} */ |
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let bits = []; |
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// the signal |
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bits.push(sign); |
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// the exponent |
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for (let i = ebits; i > 0; i -= 1) { |
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bits[i] = (exp % 2 ? 1 : 0); |
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exp = Math.floor(exp / 2); |
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} |
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// the fraction |
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for (let i = fbits, len = bits.length; i > 0; i -= 1) { |
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bits[len + i] = (fraction % 2 ? 1 : 0); |
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fraction = Math.floor(fraction / 2); |
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} |
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// pack as bytes |
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/** @type {string} */ |
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let str = bits.join(''); |
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/** @type {number} */ |
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let numBytes = Math.ceil((ebits + fbits + 1) / 8) + index - 1; // FIXME |
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numBytes = numBytes == 2 ? 1 : numBytes; // FIXME |
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/** @type {number} */ |
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let k = index; |
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while (numBytes >= index) { |
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buffer[numBytes] = parseInt(str.substring(0, 8), 2); |
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str = str.substring(8); |
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numBytes--; |
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k++; |
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} |
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return k; |
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} |
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