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April 3, 2016 03:00
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多倍長ライブラリ
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/* | |
* 多倍長ライブラリ | |
* | |
* 整数の、加減積乗だけ | |
* メソッドチェーンして使う | |
* | |
new Integer(n) :: Int -> Integer , () -> Integer(0) | |
n.add(m) :: Integer.Integer -> Integer | |
n.mul(m) :: Integer.Integer -> Integer, Integer.Int -> Integer | |
n.pow(m) :: Integer.Int -> Integer | |
n.show() :: Integer -> "String" | |
* | |
> print = console.log; | |
> n = new Integer(2) | |
> print(n.pow(58).show()) | |
288230376151711744 | |
* | |
* 普通にやると丸められる | |
> Math.pow(2,58) | |
288230376151711740 | |
* | |
* 掛け算とか筆算法なので特に速くもないことに注意 | |
*/ | |
function Integer(n) { | |
n = n || 0; | |
this.sign = n>0 ? 1 : n<0 ? -1 : 0; | |
this.number = [0]; | |
if (n<0) n = -n; | |
this.th = 1e10; | |
for (var i=0; n>0; ++i) { | |
this.number[i] = n % this.th; | |
n = (n/this.th) | 0; | |
} | |
} | |
var intp = Integer.prototype; | |
intp.normalize = function () { | |
var n = this; | |
var num = n.number; | |
if (num.every(function(x){return x==0})) return new Integer(0); | |
for (var i=0; i<num.length; ++i) { | |
if (num[i] < 0) { | |
if (!((i+1) in num)) break; | |
var k = Math.ceil(-num[i]/n.th); | |
num[i+1] -= k; | |
num[i] += n.th * k; | |
} | |
if (num[i] > n.th) { | |
if (!((i+1) in num)) num[i+1] = 0; | |
num[i+1] += (num[i]/n.th) | 0; | |
num[i] %= n.th; | |
} | |
} | |
for (var i=num.length-1; i>=0; --i) { | |
if (num[i] == 0) { | |
num.length--; | |
continue; | |
} | |
if (num[i] < 0) { | |
num[i] *= -1; | |
n.sign = -1; | |
break; | |
} else { | |
n.sign = 1; | |
break; | |
} | |
} | |
return n; | |
}; | |
intp.add = function(m) { | |
var n = this; | |
var r = new Integer(0); | |
var num1 = n.number, num2 = m.number; | |
for (var i=0, l=Math.max(num1.length, num2.length); i<l; ++i) { | |
r.number[i] = | |
(i in num1 ? num1[i] * n.sign : 0) | |
+ (i in num2 ? num2[i] * m.sign : 0) | |
} | |
return r.normalize(); | |
}; | |
intp.copy = function() { | |
var r = new Integer(); | |
r.sign = this.sign; | |
r.number = []; | |
for (var i=0; i<this.number.length; ++i) r.number[i] = this.number[i]; | |
return r; | |
}; | |
intp.neg = function() { | |
var r = this.copy(); | |
r.sign *= -1; | |
return r; | |
}; | |
intp.sub = function(m) { | |
return this.add(m.neg()); | |
}; | |
intp.mul = function(m) { | |
var n = this; | |
if (!(m instanceof Integer)) m = new Integer(m); | |
var r = new Integer(); | |
r.sign = n.sign * m.sign; | |
for (var i=0; i<n.number.length; ++i) { | |
for (var j=0; j<m.number.length; ++j) { | |
var k = i+j; | |
if (!(k in r.number)) r.number[k] = 0; | |
r.number[k] += n.number[i] * m.number[j]; | |
} | |
} | |
return r.normalize(); | |
}; | |
intp.pow = function(r) { | |
function pows(n, r) { | |
if (r == 0) return new Integer(1); | |
else if (r == 1) return n; | |
else if (r == 2) return n.mul(n); | |
var s = (r/2) | 0; | |
var x = pows(n,s); | |
var y = pows(n, r-s-s) | |
return x.mul(x.mul(y)) | |
} | |
return pows(this,r); | |
}; | |
intp.show = function() { | |
if (this.sign == 0) return "0"; | |
var s = this.sign<0 ? "-" : ""; | |
for (var i=this.number.length-1; i>=0; --i) s += this.number[i]; | |
return s; | |
} |
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