first commit
This commit is contained in:
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build/node_modules/bn.js/.npmignore
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build/node_modules/bn.js/.npmignore
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benchmarks/
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coverage/
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test/
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node_modules/
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npm-debug.log
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1.js
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logo.png
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.travis.yml
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||||
221
build/node_modules/bn.js/README.md
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221
build/node_modules/bn.js/README.md
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||||
# <img src="./logo.png" alt="bn.js" width="160" height="160" />
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||||
|
||||
> BigNum in pure javascript
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||||
|
||||
[](http://travis-ci.org/indutny/bn.js)
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||||
|
||||
## Install
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||||
`npm install --save bn.js`
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|
||||
## Usage
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||||
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||||
```js
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const BN = require('bn.js');
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var a = new BN('dead', 16);
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var b = new BN('101010', 2);
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var res = a.add(b);
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console.log(res.toString(10)); // 57047
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```
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**Note**: decimals are not supported in this library.
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## Notation
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|
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### Prefixes
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There are several prefixes to instructions that affect the way the work. Here
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||||
is the list of them in the order of appearance in the function name:
|
||||
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||||
* `i` - perform operation in-place, storing the result in the host object (on
|
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which the method was invoked). Might be used to avoid number allocation costs
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||||
* `u` - unsigned, ignore the sign of operands when performing operation, or
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||||
always return positive value. Second case applies to reduction operations
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||||
like `mod()`. In such cases if the result will be negative - modulo will be
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||||
added to the result to make it positive
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||||
|
||||
### Postfixes
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||||
The only available postfix at the moment is:
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* `n` - which means that the argument of the function must be a plain JavaScript
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Number. Decimals are not supported.
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||||
|
||||
### Examples
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|
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* `a.iadd(b)` - perform addition on `a` and `b`, storing the result in `a`
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* `a.umod(b)` - reduce `a` modulo `b`, returning positive value
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* `a.iushln(13)` - shift bits of `a` left by 13
|
||||
|
||||
## Instructions
|
||||
|
||||
Prefixes/postfixes are put in parens at the of the line. `endian` - could be
|
||||
either `le` (little-endian) or `be` (big-endian).
|
||||
|
||||
### Utilities
|
||||
|
||||
* `a.clone()` - clone number
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||||
* `a.toString(base, length)` - convert to base-string and pad with zeroes
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||||
* `a.toNumber()` - convert to Javascript Number (limited to 53 bits)
|
||||
* `a.toJSON()` - convert to JSON compatible hex string (alias of `toString(16)`)
|
||||
* `a.toArray(endian, length)` - convert to byte `Array`, and optionally zero
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||||
pad to length, throwing if already exceeding
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* `a.toArrayLike(type, endian, length)` - convert to an instance of `type`,
|
||||
which must behave like an `Array`
|
||||
* `a.toBuffer(endian, length)` - convert to Node.js Buffer (if available). For
|
||||
compatibility with browserify and similar tools, use this instead:
|
||||
`a.toArrayLike(Buffer, endian, length)`
|
||||
* `a.bitLength()` - get number of bits occupied
|
||||
* `a.zeroBits()` - return number of less-significant consequent zero bits
|
||||
(example: `1010000` has 4 zero bits)
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||||
* `a.byteLength()` - return number of bytes occupied
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||||
* `a.isNeg()` - true if the number is negative
|
||||
* `a.isEven()` - no comments
|
||||
* `a.isOdd()` - no comments
|
||||
* `a.isZero()` - no comments
|
||||
* `a.cmp(b)` - compare numbers and return `-1` (a `<` b), `0` (a `==` b), or `1` (a `>` b)
|
||||
depending on the comparison result (`ucmp`, `cmpn`)
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||||
* `a.lt(b)` - `a` less than `b` (`n`)
|
||||
* `a.lte(b)` - `a` less than or equals `b` (`n`)
|
||||
* `a.gt(b)` - `a` greater than `b` (`n`)
|
||||
* `a.gte(b)` - `a` greater than or equals `b` (`n`)
|
||||
* `a.eq(b)` - `a` equals `b` (`n`)
|
||||
* `a.toTwos(width)` - convert to two's complement representation, where `width` is bit width
|
||||
* `a.fromTwos(width)` - convert from two's complement representation, where `width` is the bit width
|
||||
* `BN.isBN(object)` - returns true if the supplied `object` is a BN.js instance
|
||||
|
||||
### Arithmetics
|
||||
|
||||
* `a.neg()` - negate sign (`i`)
|
||||
* `a.abs()` - absolute value (`i`)
|
||||
* `a.add(b)` - addition (`i`, `n`, `in`)
|
||||
* `a.sub(b)` - subtraction (`i`, `n`, `in`)
|
||||
* `a.mul(b)` - multiply (`i`, `n`, `in`)
|
||||
* `a.sqr()` - square (`i`)
|
||||
* `a.pow(b)` - raise `a` to the power of `b`
|
||||
* `a.div(b)` - divide (`divn`, `idivn`)
|
||||
* `a.mod(b)` - reduct (`u`, `n`) (but no `umodn`)
|
||||
* `a.divRound(b)` - rounded division
|
||||
|
||||
### Bit operations
|
||||
|
||||
* `a.or(b)` - or (`i`, `u`, `iu`)
|
||||
* `a.and(b)` - and (`i`, `u`, `iu`, `andln`) (NOTE: `andln` is going to be replaced
|
||||
with `andn` in future)
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||||
* `a.xor(b)` - xor (`i`, `u`, `iu`)
|
||||
* `a.setn(b)` - set specified bit to `1`
|
||||
* `a.shln(b)` - shift left (`i`, `u`, `iu`)
|
||||
* `a.shrn(b)` - shift right (`i`, `u`, `iu`)
|
||||
* `a.testn(b)` - test if specified bit is set
|
||||
* `a.maskn(b)` - clear bits with indexes higher or equal to `b` (`i`)
|
||||
* `a.bincn(b)` - add `1 << b` to the number
|
||||
* `a.notn(w)` - not (for the width specified by `w`) (`i`)
|
||||
|
||||
### Reduction
|
||||
|
||||
* `a.gcd(b)` - GCD
|
||||
* `a.egcd(b)` - Extended GCD results (`{ a: ..., b: ..., gcd: ... }`)
|
||||
* `a.invm(b)` - inverse `a` modulo `b`
|
||||
|
||||
## Fast reduction
|
||||
|
||||
When doing lots of reductions using the same modulo, it might be beneficial to
|
||||
use some tricks: like [Montgomery multiplication][0], or using special algorithm
|
||||
for [Mersenne Prime][1].
|
||||
|
||||
### Reduction context
|
||||
|
||||
To enable this tricks one should create a reduction context:
|
||||
|
||||
```js
|
||||
var red = BN.red(num);
|
||||
```
|
||||
where `num` is just a BN instance.
|
||||
|
||||
Or:
|
||||
|
||||
```js
|
||||
var red = BN.red(primeName);
|
||||
```
|
||||
|
||||
Where `primeName` is either of these [Mersenne Primes][1]:
|
||||
|
||||
* `'k256'`
|
||||
* `'p224'`
|
||||
* `'p192'`
|
||||
* `'p25519'`
|
||||
|
||||
Or:
|
||||
|
||||
```js
|
||||
var red = BN.mont(num);
|
||||
```
|
||||
|
||||
To reduce numbers with [Montgomery trick][0]. `.mont()` is generally faster than
|
||||
`.red(num)`, but slower than `BN.red(primeName)`.
|
||||
|
||||
### Converting numbers
|
||||
|
||||
Before performing anything in reduction context - numbers should be converted
|
||||
to it. Usually, this means that one should:
|
||||
|
||||
* Convert inputs to reducted ones
|
||||
* Operate on them in reduction context
|
||||
* Convert outputs back from the reduction context
|
||||
|
||||
Here is how one may convert numbers to `red`:
|
||||
|
||||
```js
|
||||
var redA = a.toRed(red);
|
||||
```
|
||||
Where `red` is a reduction context created using instructions above
|
||||
|
||||
Here is how to convert them back:
|
||||
|
||||
```js
|
||||
var a = redA.fromRed();
|
||||
```
|
||||
|
||||
### Red instructions
|
||||
|
||||
Most of the instructions from the very start of this readme have their
|
||||
counterparts in red context:
|
||||
|
||||
* `a.redAdd(b)`, `a.redIAdd(b)`
|
||||
* `a.redSub(b)`, `a.redISub(b)`
|
||||
* `a.redShl(num)`
|
||||
* `a.redMul(b)`, `a.redIMul(b)`
|
||||
* `a.redSqr()`, `a.redISqr()`
|
||||
* `a.redSqrt()` - square root modulo reduction context's prime
|
||||
* `a.redInvm()` - modular inverse of the number
|
||||
* `a.redNeg()`
|
||||
* `a.redPow(b)` - modular exponentiation
|
||||
|
||||
## LICENSE
|
||||
|
||||
This software is licensed under the MIT License.
|
||||
|
||||
Copyright Fedor Indutny, 2015.
|
||||
|
||||
Permission is hereby granted, free of charge, to any person obtaining a
|
||||
copy of this software and associated documentation files (the
|
||||
"Software"), to deal in the Software without restriction, including
|
||||
without limitation the rights to use, copy, modify, merge, publish,
|
||||
distribute, sublicense, and/or sell copies of the Software, and to permit
|
||||
persons to whom the Software is furnished to do so, subject to the
|
||||
following conditions:
|
||||
|
||||
The above copyright notice and this permission notice shall be included
|
||||
in all copies or substantial portions of the Software.
|
||||
|
||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
||||
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
|
||||
NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
|
||||
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
|
||||
OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
|
||||
USE OR OTHER DEALINGS IN THE SOFTWARE.
|
||||
|
||||
[0]: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication
|
||||
[1]: https://en.wikipedia.org/wiki/Mersenne_prime
|
||||
3427
build/node_modules/bn.js/lib/bn.js
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3427
build/node_modules/bn.js/lib/bn.js
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File diff suppressed because it is too large
Load Diff
71
build/node_modules/bn.js/package.json
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build/node_modules/bn.js/package.json
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vendored
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|
||||
{
|
||||
"_from": "bn.js@^4.1.1",
|
||||
"_id": "bn.js@4.11.8",
|
||||
"_inBundle": false,
|
||||
"_integrity": "sha512-ItfYfPLkWHUjckQCk8xC+LwxgK8NYcXywGigJgSwOP8Y2iyWT4f2vsZnoOXTTbo+o5yXmIUJ4gn5538SO5S3gA==",
|
||||
"_location": "/bn.js",
|
||||
"_phantomChildren": {},
|
||||
"_requested": {
|
||||
"type": "range",
|
||||
"registry": true,
|
||||
"raw": "bn.js@^4.1.1",
|
||||
"name": "bn.js",
|
||||
"escapedName": "bn.js",
|
||||
"rawSpec": "^4.1.1",
|
||||
"saveSpec": null,
|
||||
"fetchSpec": "^4.1.1"
|
||||
},
|
||||
"_requiredBy": [
|
||||
"/asn1.js",
|
||||
"/browserify-rsa",
|
||||
"/browserify-sign",
|
||||
"/create-ecdh",
|
||||
"/diffie-hellman",
|
||||
"/elliptic",
|
||||
"/miller-rabin",
|
||||
"/public-encrypt"
|
||||
],
|
||||
"_resolved": "https://registry.npmjs.org/bn.js/-/bn.js-4.11.8.tgz",
|
||||
"_shasum": "2cde09eb5ee341f484746bb0309b3253b1b1442f",
|
||||
"_spec": "bn.js@^4.1.1",
|
||||
"_where": "/Users/asciidisco/Desktop/asciidisco.com/build/node_modules/browserify-sign",
|
||||
"author": {
|
||||
"name": "Fedor Indutny",
|
||||
"email": "fedor@indutny.com"
|
||||
},
|
||||
"browser": {
|
||||
"buffer": false
|
||||
},
|
||||
"bugs": {
|
||||
"url": "https://github.com/indutny/bn.js/issues"
|
||||
},
|
||||
"bundleDependencies": false,
|
||||
"deprecated": false,
|
||||
"description": "Big number implementation in pure javascript",
|
||||
"devDependencies": {
|
||||
"istanbul": "^0.3.5",
|
||||
"mocha": "^2.1.0",
|
||||
"semistandard": "^7.0.4"
|
||||
},
|
||||
"homepage": "https://github.com/indutny/bn.js",
|
||||
"keywords": [
|
||||
"BN",
|
||||
"BigNum",
|
||||
"Big number",
|
||||
"Modulo",
|
||||
"Montgomery"
|
||||
],
|
||||
"license": "MIT",
|
||||
"main": "lib/bn.js",
|
||||
"name": "bn.js",
|
||||
"repository": {
|
||||
"type": "git",
|
||||
"url": "git+ssh://git@github.com/indutny/bn.js.git"
|
||||
},
|
||||
"scripts": {
|
||||
"lint": "semistandard",
|
||||
"test": "npm run lint && npm run unit",
|
||||
"unit": "mocha --reporter=spec test/*-test.js"
|
||||
},
|
||||
"version": "4.11.8"
|
||||
}
|
||||
65
build/node_modules/bn.js/util/genCombMulTo.js
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65
build/node_modules/bn.js/util/genCombMulTo.js
generated
vendored
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@@ -0,0 +1,65 @@
|
||||
'use strict';
|
||||
|
||||
// NOTE: This could be potentionally used to generate loop-less multiplications
|
||||
function genCombMulTo (alen, blen) {
|
||||
var len = alen + blen - 1;
|
||||
var src = [
|
||||
'var a = self.words;',
|
||||
'var b = num.words;',
|
||||
'var o = out.words;',
|
||||
'var c = 0;',
|
||||
'var lo;',
|
||||
'var mid;',
|
||||
'var hi;'
|
||||
];
|
||||
for (var i = 0; i < alen; i++) {
|
||||
src.push('var a' + i + ' = a[' + i + '] | 0;');
|
||||
src.push('var al' + i + ' = a' + i + ' & 0x1fff;');
|
||||
src.push('var ah' + i + ' = a' + i + ' >>> 13;');
|
||||
}
|
||||
for (i = 0; i < blen; i++) {
|
||||
src.push('var b' + i + ' = b[' + i + '] | 0;');
|
||||
src.push('var bl' + i + ' = b' + i + ' & 0x1fff;');
|
||||
src.push('var bh' + i + ' = b' + i + ' >>> 13;');
|
||||
}
|
||||
src.push('');
|
||||
src.push('out.negative = self.negative ^ num.negative;');
|
||||
src.push('out.length = ' + len + ';');
|
||||
|
||||
for (var k = 0; k < len; k++) {
|
||||
var minJ = Math.max(0, k - alen + 1);
|
||||
var maxJ = Math.min(k, blen - 1);
|
||||
|
||||
src.push('\/* k = ' + k + ' *\/');
|
||||
src.push('var w' + k + ' = c;');
|
||||
src.push('c = 0;');
|
||||
for (var j = minJ; j <= maxJ; j++) {
|
||||
i = k - j;
|
||||
|
||||
src.push('lo = Math.imul(al' + i + ', bl' + j + ');');
|
||||
src.push('mid = Math.imul(al' + i + ', bh' + j + ');');
|
||||
src.push('mid = (mid + Math.imul(ah' + i + ', bl' + j + ')) | 0;');
|
||||
src.push('hi = Math.imul(ah' + i + ', bh' + j + ');');
|
||||
|
||||
src.push('w' + k + ' = (w' + k + ' + lo) | 0;');
|
||||
src.push('w' + k + ' = (w' + k + ' + ((mid & 0x1fff) << 13)) | 0;');
|
||||
src.push('c = (c + hi) | 0;');
|
||||
src.push('c = (c + (mid >>> 13)) | 0;');
|
||||
src.push('c = (c + (w' + k + ' >>> 26)) | 0;');
|
||||
src.push('w' + k + ' &= 0x3ffffff;');
|
||||
}
|
||||
}
|
||||
// Store in separate step for better memory access
|
||||
for (k = 0; k < len; k++) {
|
||||
src.push('o[' + k + '] = w' + k + ';');
|
||||
}
|
||||
src.push('if (c !== 0) {',
|
||||
' o[' + k + '] = c;',
|
||||
' out.length++;',
|
||||
'}',
|
||||
'return out;');
|
||||
|
||||
return src.join('\n');
|
||||
}
|
||||
|
||||
console.log(genCombMulTo(10, 10));
|
||||
65
build/node_modules/bn.js/util/genCombMulTo10.js
generated
vendored
Normal file
65
build/node_modules/bn.js/util/genCombMulTo10.js
generated
vendored
Normal file
@@ -0,0 +1,65 @@
|
||||
'use strict';
|
||||
|
||||
function genCombMulTo (alen, blen) {
|
||||
var len = alen + blen - 1;
|
||||
var src = [
|
||||
'var a = self.words;',
|
||||
'var b = num.words;',
|
||||
'var o = out.words;',
|
||||
'var c = 0;',
|
||||
'var lo;',
|
||||
'var mid;',
|
||||
'var hi;'
|
||||
];
|
||||
for (var i = 0; i < alen; i++) {
|
||||
src.push('var a' + i + ' = a[' + i + '] | 0;');
|
||||
src.push('var al' + i + ' = a' + i + ' & 0x1fff;');
|
||||
src.push('var ah' + i + ' = a' + i + ' >>> 13;');
|
||||
}
|
||||
for (i = 0; i < blen; i++) {
|
||||
src.push('var b' + i + ' = b[' + i + '] | 0;');
|
||||
src.push('var bl' + i + ' = b' + i + ' & 0x1fff;');
|
||||
src.push('var bh' + i + ' = b' + i + ' >>> 13;');
|
||||
}
|
||||
src.push('');
|
||||
src.push('out.negative = self.negative ^ num.negative;');
|
||||
src.push('out.length = ' + len + ';');
|
||||
|
||||
for (var k = 0; k < len; k++) {
|
||||
var minJ = Math.max(0, k - alen + 1);
|
||||
var maxJ = Math.min(k, blen - 1);
|
||||
|
||||
src.push('\/* k = ' + k + ' *\/');
|
||||
src.push('lo = Math.imul(al' + (k - minJ) + ', bl' + minJ + ');');
|
||||
src.push('mid = Math.imul(al' + (k - minJ) + ', bh' + minJ + ');');
|
||||
src.push(
|
||||
'mid = (mid + Math.imul(ah' + (k - minJ) + ', bl' + minJ + ')) | 0;');
|
||||
src.push('hi = Math.imul(ah' + (k - minJ) + ', bh' + minJ + ');');
|
||||
|
||||
for (var j = minJ + 1; j <= maxJ; j++) {
|
||||
i = k - j;
|
||||
|
||||
src.push('lo = (lo + Math.imul(al' + i + ', bl' + j + ')) | 0;');
|
||||
src.push('mid = (mid + Math.imul(al' + i + ', bh' + j + ')) | 0;');
|
||||
src.push('mid = (mid + Math.imul(ah' + i + ', bl' + j + ')) | 0;');
|
||||
src.push('hi = (hi + Math.imul(ah' + i + ', bh' + j + ')) | 0;');
|
||||
}
|
||||
|
||||
src.push('var w' + k + ' = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;');
|
||||
src.push('c = (((hi + (mid >>> 13)) | 0) + (w' + k + ' >>> 26)) | 0;');
|
||||
src.push('w' + k + ' &= 0x3ffffff;');
|
||||
}
|
||||
// Store in separate step for better memory access
|
||||
for (k = 0; k < len; k++) {
|
||||
src.push('o[' + k + '] = w' + k + ';');
|
||||
}
|
||||
src.push('if (c !== 0) {',
|
||||
' o[' + k + '] = c;',
|
||||
' out.length++;',
|
||||
'}',
|
||||
'return out;');
|
||||
|
||||
return src.join('\n');
|
||||
}
|
||||
|
||||
console.log(genCombMulTo(10, 10));
|
||||
Reference in New Issue
Block a user