開発環境
- OS X El Capitan - Apple (OS)
- Emacs (Text Editor)
- JavaScript (プログラミング言語)
- kjs-math-number (JavaScript Library)
- Safari(Web browser)
- JavaScript 第6版 (David Flanagan(著)、村上 列(翻訳)、オライリージャパン)(参考書籍)
'use strict' を書き加えて厳しめに検証するように変更。
コード(Emacs)
(function (global) {
'use strict';
var Complex,
Rational,
Integer,
RADIX = Math.pow(10, 5),
NUM_SIZE = Math.log10(RADIX),
sign;
sign = function (n) {
if (n > 0) {
return 1;
}
if (n === 0) {
return 0;
}
if (n < 0) {
return -1;
}
};
Number.prototype.neg = function () {
var n = this.valueOf();
if (n === 0) {
return 0;
}
return -this.valueOf();
};
Number.prototype.getSign = function () {
var n = this.valueOf();
return sign(n);
};
Number.prototype.isZero = function () {
return this.getSign() === 0;
};
Number.prototype.isPositive = function () {
return this.getSign() === 1;
};
Number.prototype.isNegative = function () {
return this.getSign() === -1;
};
Number.prototype.isEqual =function (z) {
if (typeof z === 'number') {
return this.valueOf() === z;
}
return z.isEqual(this.valueOf());
};
Complex = function (real, imag) {
if (!(this instanceof Complex)) {
return new Complex(real, imag);
}
var real = real,
imag = imag;
this.getReal = function () {
return real;
};
this.getImag = function () {
return imag;
};
};
Number.prototype.toComplex = function () {
return new Complex(this.valueOf(), 0);
};
Complex.prototype.toString = function () {
var real = this.getReal(),
imag = this.getImag(),
str = real.toString();
if (imag === 0) {
return str;
}
if (imag > 0) {
str += '+';
}
if (imag === 1) {
str += 'i';
} else if (imag === -1) {
str += '-i';
} else {
str += imag + 'i';
}
return str;
};
Complex.prototype.toString = function () {
var real = this.getReal(),
imag = this.getImag(),
str = real.toString();
if (imag === 0) {
return str;
}
if (imag > 0) {
str += '+';
}
if (imag === 1) {
str += 'i';
} else if (imag === -1) {
str += '-i';
} else {
str += imag + 'i';
}
return str;
};
Complex.prototype.isEqual = function (z) {
if (!(z instanceof Complex)) {
return this.isEqual(z.toComplex);
}
return this.getReal() === z.getReal() && this.getImag() === z.getImag();
};
Complex.prototype.neg = function () {
return new Complex(this.getReal().neg(), this.getImag().neg());
};
Complex.prototype.conjugate = function () {
return new Complex(this.getReal(), this.getImag().neg());
};
Complex.prototype.isReal = function() {
return this.getImag() === 0;
};
Complex.prototype.getSign = function () {
var real;
if (this.isReal()) {
real = this.getReal();
return sign(real);
}
throw {
name: 'getSign',
message: 'wrong type argument: ' + this
};
};
Complex.prototype.isZero = function () {
if (this.isReal()) {
return this.getSign() === 0;
}
return this.getReal().isZero() && this.getImag().isZero();
};
Complex.prototype.isPositive = function () {
return this.getSign() === 1;
};
Complex.prototype.isNegative = function () {
return this.getSign() === -1;
};
Complex.prototype.add = function (z) {
if (!(z instanceof Complex)) {
return this.add(z.toComplex());
}
return new Complex(this.getReal() + z.getReal(),
this.getImag() + z.getImag());
};
Complex.prototype.sub = function (z) {
if (!(z instanceof Complex)) {
return this.sub(z.toComplex());
}
return new Complex(this.getReal() - z.getReal(),
this.getImag() - z.getImag());
};
Complex.prototype.mul = function (z) {
if (!(z instanceof Complex)) {
return this.mul(z.toComplex());
}
var real = this.getReal() * z.getReal() - this.getImag() * z.getImag(),
imag = this.getReal() * z.getImag() + this.getImag() * z.getReal();
return new Complex(real, imag);
};
Complex.prototype.div = function (z) {
if (!(z instanceof Complex)) {
return this.div(z.toComplex());
}
var z1 = z.conjugate(),
z2 = this.mul(z1),
n = z.mul(z1).getReal(),
real = z2.getReal() / n,
imag = z2.getImag() / n;
return new Complex(real, imag);
};
Complex.prototype.lt = function (z) {
return this.sub(z).isNegative();
};
Complex.prototype.le = function (z) {
return this.isEqual(z) || this.lt(z);
};
Complex.prototype.gt = function (z) {
return this.sub(z).isPositive();
};
Complex.prototype.ge = function (z) {
return this.isEqual(z) || this.gt(z);
};
Number.prototype.lt = function (z) {
return this.sub(z).isNegative();
};
Number.prototype.le = function (z) {
return this.isEqual(z) || this.lt(z);
};
Number.prototype.gt = function (z) {
return this.sub(z).isPositive();
};
Number.prototype.ge = function (z) {
return this.isEqual(z) || this.lt(z);
};
Number.prototype.add = function (z) {
if (z instanceof Complex) {
return this.toComplex().add(z);
}
if (typeof z === 'number') {
return this.valueOf() + z;
}
return this.add(z.toNumber());
};
Number.prototype.sub = function (z) {
if (z instanceof Complex) {
return this.toComplex().sub(z);
}
if (typeof z === 'number') {
return this.valueOf() - z;
}
return this.sub(z.toNumber());
};
Number.prototype.mul = function (z) {
if (z instanceof Complex) {
return this.toComplex().mul(z);
}
if (typeof z === 'number') {
return this.valueOf() * z;
}
return this.mul(z.toNumber());
};
Number.prototype.div = function (z) {
if (z instanceof Complex) {
return this.toComplex().div(z);
}
if (typeof z === 'number') {
return this.valueOf() / z;
}
return this.div(z.toNumber());
};
Number.prototype.getReal = function () {
return this.valueOf();
};
Number.prototype.getImag = function () {
return 0;
};
Rational = function (num, den) {
if (!(this instanceof Rational)) {
return new Rational(num, den);
}
var num = num,
den = den,
sign;
if (num.isZero()) {
sign = 0;
} else {
sign = num.getSign() * den.getSign();
}
num = num.abs();
den = den.abs();
this.getSign = function () {
return sign;
}
this.getNumerator = function () {
return num;
};
this.setNumerator = function (n) {
sign *= n.getSign();
num = n.abs();
};
this.getDenominator = function () {
return den;
};
this.setDenominator = function (n) {
sign *= n.getSign();
den = n.abs();
};
};
Rational.prototype.toNumber = function () {
var sign = this.getSign(),
num,
den,
q,
r;
if (sign === 0) {
return 0;
}
this.canonicalize();
num = this.getNumerator().abs();
den = this.getDenominator().abs();
q = num.floorQuotient(den);
r = num.floorRemainder(den);
return q.add(r.toNumber().div(den));
};
Rational.prototype.toComplex = function () {
return new Complex(this.toNumber(), 0);
};
Rational.prototype.toString = function () {
var num,
den,
result = '';
this.canonicalize();
if (this.getSign() === -1) {
result += '-';
}
num = this.getNumerator();
den = this.getDenominator();
result += num + '/' + den;
return result;
};
Rational.prototype.isEqual = function (z) {
if (z instanceof Integer) {
return this.isEqual(z.toRational());
}
if (z instanceof Rational) {
this.canonicalize();
z.canonicalize();
return this.toString() === z.toString();
}
return this.toNumber().isEqual(z);
};
Rational.prototype.lt = function (z) {
return this.sub(z).isNegative();
};
Rational.prototype.le = function (z) {
return this.isEqual(z) || this.lt(z);
};
Rational.prototype.gt = function (z) {
return this.sub(z).isPositive();
};
Rational.prototype.ge = function (z) {
return this.isEqual(z) || this.gt(z);
};
Rational.prototype.canonicalize = function () {
var num = this.getNumerator(),
den = this.getDenominator(),
g = num.gcd(den);
this.setNumerator(num.floorQuotient(g));
this.setDenominator(den.floorQuotient(g));
};
Rational.prototype.neg = function () {
return this.mul(new Integer('-1'));
};
Rational.prototype.isZero = function () {
return this.getSign() === 0;
};
Rational.prototype.isPositive = function () {
return this.getSign() === 1;
};
Rational.prototype.isNegative = function () {
return this.getSign() === -1;
};
Rational.prototype.add = function (z) {
if (z instanceof Integer) {
return this.add(z.toRational());
}
if (z instanceof Rational) {
var num1 = this.getNumerator(),
den1 = this.getDenominator(),
sign1 = this.getSign(),
num2 = z.getNumerator(),
den2 = z.getDenominator(),
sign2 = z.getSign();
if (sign1 === -1) {
num1 = num1.neg();
}
if (sign2 === -1) {
num2 = num2.neg();
}
return new Rational(num1.mul(den2).add(num2.mul(den1)),
den1.mul(den2));
}
return this.toNumber().add(z);
};
Rational.prototype.sub = function (z) {
return this.add(z.neg());
};
Rational.prototype.mul = function (z) {
if (z instanceof Integer) {
return this.mul(z.toRational());
}
if (z instanceof Rational) {
var sign = this.getSign() * z.getSign();
sign = new Integer(sign.toString());
return new Rational(
this.getNumerator().mul(z.getNumerator()).mul(sign),
this.getDenominator().mul(z.getDenominator()));
}
return this.toNumber().mul(z);
};
Rational.prototype.div = function (z) {
if (z instanceof Integer) {
return this.div(z.toRational());
}
if (z instanceof Rational) {
var sign = this.getSign() * z.getSign();
sign = new Integer(sign.toString());
return new Rational(
this.getNumerator().mul(z.getDenominator()).mul(sign),
this.getDenominator().mul(z.getNumerator()));
}
return this.toNumber().div(z);
};
Rational.prototype.getReal = function () {
var sign = new Integer(this.getSign().toString());
return new Rational(this.getNumerator().mul(sign),
this.getDenominator())
};
Rational.prototype.getImag = function () {
return new Integer('0');
};
Integer = function (s) {
if (!(this instanceof Integer)) {
return new Integer(s);
}
var sign = 1,
nums = [],
len = 0,
s0 = s;
if (s0 === '0') {
sign = 0;
}
if (s0[0] === '-') {
sign = -1;
s0 = s0.slice(1);
}
nums.push(parseInt(s0.slice(-NUM_SIZE), 10));
s0 = s0.slice(0, -NUM_SIZE);
for (len = s0.length; len !== 0; len = s0.length) {
nums.push(parseInt(s0.slice(-NUM_SIZE), 10));
s0 = s0.slice(0, -NUM_SIZE);
}
this.getSign = function () {
return sign;
};
this.getNums = function () {
return nums.slice();
};
this.copy = function () {
return new Integer(s);
};
};
Integer.prototype.toRational = function () {
return new Rational(this, new Integer('1'));
};
Integer.prototype.toNumber = function () {
return parseFloat(this.toString());
};
Integer.prototype.toComplex = function () {
return this.toRational().toComplex();
};
Integer.prototype.toString = function () {
var result = '',
nums = this.getNums(),
len = nums.length,
i,
s,
flag = false;
if (this.getSign() === -1) {
result += '-';
}
for (i = len; i > 0; i -= 1) {
s = nums[i - 1].toString();
if (flag) {
if (s.length < NUM_SIZE) {
result += new Array(NUM_SIZE - s.length + 1).join('0');
}
} else {
flag = true;
}
result += s;
}
return result;
};
Integer.prototype.isEqual = function (z) {
if (z instanceof Rational) {
return this.toRational().isEqual(z);
}
if (typeof z === 'number') {
return this.toNumber().isEqual(z);
}
if (z instanceof Complex) {
return this.toComplex().isEqual(z);
}
return this.toString() === z.toString();
};
Integer.prototype.lt = function (z) {
return this.sub(z).isNegative();
};
Integer.prototype.le = function (z) {
return this.isEqual(z) || this.lt(z);
};
Integer.prototype.gt = function (z) {
return this.sub(z).isPositive();
};
Integer.prototype.ge = function (z) {
return this.isEqual(z) || this.gt(z);
};
Integer.prototype.gcd = function (n) {
var x = this.abs(),
y = n.abs(),
q = x.floorQuotient(y),
r = x.floorRemainder(y);
if (r.isZero()) {
return y;
}
return y.gcd(r);
};
Integer.prototype.neg = function () {
var s = this.toString();
if (s[0] === '-') {
return new Integer(s.slice(1));
}
return new Integer('-' + s);
};
Integer.prototype.isZero = function () {
return this.getSign() === 0;
};
Integer.prototype.isPositive = function () {
return this.getSign() === 1;
};
Integer.prototype.isNegative = function () {
return this.getSign() === -1;
};
Integer.prototype.factorial = function () {
var result = new Integer('1'),
t = new Integer(this.toString()),
one = new Integer('1');
for (;t.isPositive(); t = t.sub(one)) {
result = result.mul(t);
}
return result;
};
Integer.prototype.add = function (z) {
if (z instanceof Rational) {
return this.toRational().add(z);
}
if (typeof z === 'number') {
return this.toNumber().add(z);
}
if (z instanceof Complex) {
return this.toComplex().add(z);
}
var nums1 = this.getNums(),
sign1 = this.getSign(),
len1 = nums1.length,
nums2 = z.getNums(),
sign2 = z.getSign(),
len2 = nums2.length,
nums3,
nums4,
len3,
len4,
sign3,
n,
a = 0,
b,
i,
result = '',
s,
flag;
if (len1 > len2) {
nums3 = nums1;
len3 = len1;
sign3 = sign1;
nums4 = nums2;
len4 = len2;
} else if (len1 < len2) {
nums3 = nums2;
len3 = len2;
sign3 = sign2;
nums4 = nums1;
len4 = len1;
} else if (nums1[len1 - 1] > nums2[len1 - 1]) {
nums3 = nums1;
len3 = len1;
sign3 = sign1;
nums4 = nums2;
len4 = len2;
} else {
nums3 = nums2;
len3 = len2;
sign3 = sign2;
nums4 = nums1;
len4 = len1;
}
if (sign1 === sign2) {
for (i = 0; i < len4; i += 1) {
n = nums3[i] + nums4[i] + a;
if (n >= RADIX) {
a = 1;
b = n - RADIX;
} else {
a = 0;
b = n;
}
nums3[i] = b;
}
for (i = len4; i < len3; i += 1) {
n = nums3[i] + a;
if (n >= RADIX) {
a = 1;
nums3[i] = n - RADIX;
} else {
a = 0;
break;
}
}
if (a !== 0) {
nums3[i] = a;
}
if (sign1 === -1) {
result += '-';
}
} else {
for (i = 0; i < len4; i += 1) {
nums3[i] -= a;
if (nums3[i] < nums4[i]) {
a = 1;
nums3[i] += RADIX;
} else {
a = 0;
}
nums3[i] -= nums4[i];
}
for (i = len4; i < len3; i += 1) {
nums3[i] -= a;
if (nums3[i] < 0) {
a = 1;
nums3[i] += RADIX;
} else {
break;
}
}
for (i = len3; i > 0; i -= 1) {
if (nums3[i - 1] === 0) {
nums3.pop();
} else {
break;
}
}
if (i === 0) {
return new Integer("0");
}
if (sign3 === -1) {
result += '-';
}
}
flag = false;
for (i = nums3.length; i > 0; i -= 1) {
s = nums3[i - 1].toString();
if (flag) {
if (s.length < NUM_SIZE) {
result += new Array(NUM_SIZE - s.length + 1).join('0');
}
} else {
flag = true;
}
result += s;
}
return new Integer(result);
};
Integer.prototype.mul = function (z) {
if (!(z instanceof Integer)) {
return this.toRational().mul(z);
}
var nums1 = this.getNums(),
sign1 = this.getSign(),
len1 = nums1.length,
nums2 = z.getNums(),
sign2 = z.getSign(),
len2 = nums2.length,
nums3 = [],
sign3 = sign1 * sign2,
len3,
n,
a,
b,
i,
j,
result = '',
s,
flag = false;
for (j = 0; j < len2; j += 1) {
for (i = 0; i < len1; i += 1) {
if (nums3[j + i] === undefined) {
nums3[j + i] = nums1[i] * nums2[j];
} else {
nums3[j + i] += nums1[i] * nums2[j];
}
}
}
a = 0;
for (i = 0, len3 = nums3.length; i < len3; i += 1) {
n = nums3[i] + a;
a = Math.floor(n / RADIX);
b = n % RADIX;
nums3[i] = b;
}
if (a !== 0) {
nums3[i] = a;
}
if (sign3 === -1) {
result += '-';
}
flag = false;
for (i = nums3.length; i > 0; i -= 1) {
s = nums3[i - 1].toString();
if (flag) {
if (s.length < NUM_SIZE) {
result += new Array(NUM_SIZE - s.length + 1).join('0');
}
} else {
flag = true;
}
result += s;
}
return new Integer(result);
};
Integer.prototype.sub = function (z) {
return this.add(z.neg());
};
Integer.prototype.div = function (z) {
if (z instanceof Rational) {
return this.toRational().div(z);
}
if (typeof z === 'number') {
return this.toNumber().div(z);
}
if (z instanceof Complex) {
return this.toComplex().div(z);
}
return new Rational(this, z);
};
Integer.prototype.abs = function () {
if (this.isPositive() || this.isZero()) {
return this.copy();
}
return this.neg();
};
Integer.prototype.floorQuotient = function (n) {
var n1 = this.copy(),
n2 = n.copy(),
one = new Integer('1'),
q = new Integer('0');
if (n.isZero()) {
return NaN;
}
if (this.isZero()) {
return this.copy();
}
if (this.isPositive() && n.isPositive()) {
for (; n1.ge(n2);) {
q = q.add(one);
n1 = n1.sub(n2);
}
return q;
}
if (this.isPositive() && n.isNegative()) {
for (; n1.isPositive();) {
q = q.sub(one);
n1 = n1.add(n2);
}
return q;
}
if (this.isNegative() && n.isPositive()) {
for (; n1.isNegative(); ) {
q = q.sub(one);
n1 = n1.add(n2);
}
return q;
}
if (this.isNegative() && n.isNegative()) {
for (; n1.le(n2); ) {
q = q.add(one);
n1 = n1.sub(n2);
}
return q;
}
throw {
name: 'unknown',
message: 'Integer floorQuotient',
}
};
Integer.prototype.floorRemainder = function (n) {
return this.sub(n.mul(this.floorQuotient(n)));
};
Integer.prototype.getReal = function () {
return new Integer(this.toString());
};
Integer.prototype.getImag = function () {
return new Integer('0');
};
global.Complex = Complex;
global.Rational = Rational;
global.Integer = Integer;
}(this['window'] || global));
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