Rat.isFinite - Code Metrics - Inspection of "More tests, etc" - acerix/cnum - Measure and Improve Code Quality continuously with Scrutinizer

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by Dylan

created 2021-07-24 17:40 UTC

Rat.isFinite A

↳ Parent: Rat

Complexity

Conditions

Size

Total Lines	6
Code Lines	3

Duplication

Lines	0
Ratio	0 %

Code Coverage

Tests	1
CRAP Score	1

Importance

Changes

Metric	Value
eloc	3
dl	0
loc	6
rs	10
c	0
b	0
f	0
ccs	1
cts	1
cp	1
cc	1
crap	1

import {EPSILON} from './config'
import {ZERO, ONE, gcd} from './bigint'
import {rationalApproximation, continuedFraction} from './SternBrocotTree'

/**
 * @class Rational Number
 * @name Rat
 */
export class Rat {
  n: bigint
  d: bigint

  /**
   * Initialize a rational number.
   */
  constructor(numerator: bigint|number=ZERO, denominator: bigint|number=ONE) {
    this.n = BigInt(numerator)
    this.d = BigInt(denominator)
    this.normalize()
  }

  /**
   * The decimal approximation.
   */
  valueOf(): number {
    return Number(this.n) / Number(this.d)
  }

  /**
   * The text representation.
   */
  toString(): string {
    return this.n.toString() + ( this.d === ONE ? '' : '/' + this.d.toString() )
  }

  /**
   * Returns a text profile of the number in various formats and it's value after common transformations.
   */
  public get profile(): string {
    const p = [`${this.constructor.name}: ${this.toString()} (≈${+this})`]
    // p.push(`Continued: ${this.continuedFraction()}`)
    // p.push(`Babylonian: ${this.babylonian()}`)
    // p.push(`Egyptian: ${this.egyptian()}`)
    p.push(`psin(t): ${this.psin().toString()}`)
    p.push(`pcos(t): ${this.pcos().toString()}`)
    p.push(`ptan(t): ${this.ptan().toString()}`)
    return p.join('\n')
  }

  /**
   * Clone this.
   */
  clone(): Rat {
    return new Rat(this.n, this.d)
  }

  /**
   * Normalize the numerator and denominator by factoring out the common denominators.
   */
  normalize(): void {

    // normalize 0/1, 1/0, 0/0
    if (this.n === ZERO) {
      if (this.d !== ZERO) {
        this.d = ONE
      }
      return
    }
    if (this.d === ZERO) {
      this.n = this.n > ZERO ? ONE : -ONE
      return
    }
    
    // normalize 1/1
    if (this.n === this.d) {
      this.n = this.d = ONE
      return
    }

    // remove negative denominator
    if (this.d < ZERO) {
      this.n = -this.n
      this.d = -this.d
    }
    
    // reduce numerator and denomitator by the greatest common divisor
    const divisor = gcd(this.n, this.d)
    this.n /= divisor
    this.d /= divisor

  }

  /**
   * Add this to that.
   */
  add(that: Rat): Rat {
    const r = new Rat(this.n * that.d + that.n * this.d, this.d * that.d)
    r.normalize()
    return r
  }

  /**
   * Subtract this from that.
   */
  sub(that: Rat): Rat {
    return this.add(that.neg())
  }

  /**
   * Multiply that by this.
   */
  mul(that: Rat): Rat {
    const r = new Rat(this.n * that.n, this.d * that.d)
    r.normalize()
    return r
  }

  /**
   * Divide this by that.
   */
  div(that: Rat): Rat {
    const r = new Rat(this.n * that.d, this.d * that.n)
    r.normalize()
    return r
  }

  /**
   * Mediant of this and that.
   */
  mediant(that: Rat): Rat {
    const r = new Rat(this.n + that.n, this.d + that.d)
    r.normalize()
    return r
  }

  /**
   * Minimum of this and that.
   */
  min(that: Rat): Rat {
    return this.isLessThan(that) ? this : that
  }

  /**
   * Maximum of this and that.
   */
  max(that: Rat): Rat {
    return this.isGreaterThan(that) ? this : that
  }

  /**
   * Raise this to the power of that.
   */
  pow(that: Rat): Rat {
    // zero
    if (that.n === ZERO) {
      return new Rat(ONE)
    }
    // integer
    if (that.d === ONE) {
      return new Rat(this.n**that.n, this.d**that.n)
    }
    // fraction
    else {
      const estimate = Math.pow(+this, +that)
      return FloatToRat(estimate)
    }
  }

  /**
   * Returns the dot product of this and that.
   */
  dot(that: Rat): bigint {
    return this.n * that.n + this.d * that.d
  }

  /**
   * Returns true if this equals that.
   */
  equals(that: Rat): boolean {
    return this.n === that.n && this.d === that.d
  }

  /**
   * Returns true if this approximates the number.
   */
  approximates(n: number): boolean {
    return Math.abs(+this - n) < EPSILON
  }

  /**
   * Returns true if this is greater than that.
   */
  isGreaterThan(that: Rat): boolean {
    return this.n * that.d > that.n * this.d
  }

  /**
   * Returns true if this is less than that.
   */
  isLessThan(that: Rat): boolean {
    return this.n * that.d < that.n * this.d
  }

  /**
   * Absolute value of this.
   */
  abs(): Rat {
    const r = this.clone()
    if (r.n < 0) r.n = -r.n
    return r
  }

  /**
   * Opposite (negative) of this.
   */
  neg(): Rat {
    const r = this.clone()
    r.n = -r.n
    return r
  }

  /**
   * Returns true if this is less than zero.
   */
  isNegative(): boolean {
    return this.n < 0
  }

  /**
   * Returns true if this is a finite number.
   */
  isFinite(): boolean {
    return this.d !== ZERO
  }

  /**
   * The reciprocal, or multiplicative inverse, of this.
   */
  inv(): Rat {
    return new Rat(this.d, this.n)
  }

  /**
   * Square root of this.
   */
  sqrt(): Rat {
    return this.root(2)
  }
 
  /**
   * Returns the nth root, a number which approximates this when multiplied by itself n times.
   */
  root(n: number): Rat {

    // Handle 0/1, 1/0, -1/0, 0/0, 1/1
    if (this.n === ZERO || this.d === ZERO || this.n === this.d) {
      return this.clone()
    }
    
    if (this.isNegative()) {
      throw `Roots of negative numbers like ${this.toString()} are too complex for this basic library`
    }

    return FloatToRat(Math.pow(+this, 1/n))
    // return FunctionToRat(r => r.pow(n), +this)
  }

  /**
   * Return the closest integer approximation.
   */
  round(): bigint {
    return BigInt(Math.round(+this))
  }

  /**
   * Parametric sine: 2t / (1 + t²)
   * @see https://youtu.be/Ui8OvmzDn7o?t=245
   */
  psin(): Rat {
    if (this.d === ZERO) return new Rat(ZERO)
    const one = new Rat(1)
    const two = new Rat(2)
    const n = two.mul(this)
    const d = one.add(this.pow(two))
    return n.div(d)
  }

  /**
   * Parametric cosine: (1 - t²) / (1 + t²)
   */
  pcos(): Rat {
    if (this.d === ZERO) return new Rat(-ONE)
    const one = new Rat(1)
    const two = new Rat(2)
    const t2 = this.pow(two)
    const n = one.sub(t2)
    const d = one.add(t2)
    return n.div(d)
  }

  /**
   * Parametric tangent: psin() / pcos()
   */
  ptan(): Rat {
    // const one = new Rat(1)
    // const two = new Rat(2)
    // const four = new Rat(4)
    // const n = this.pow(four).sub(one)
    // const d = this.pow(two).mul(two)
    // return n.div(d)
    return this.psin().div(this.pcos())
  }

  /**
   * Returns the integers representing the continued fraction.
   */
  *continuedFraction(): Generator<number> {
    for (const n of continuedFraction(+this)) {
      yield n
    }
  }

}

/**
 * Find a Rat approximation of the floating point number.
 */
export const FloatToRat = (n: number): Rat => {

  // Handle special values: 0/0, 1/0, -1/0
  if (isNaN(n)) return new Rat(0, 0)
  if (n===Infinity) return new Rat(1, 0)
  if (n===-Infinity) return new Rat(-1, 0)

  // Shortcut for numbers close to an integer or 1/integer
  if (Math.abs(n%1) < EPSILON) return new Rat(Math.round(n))
  if (Math.abs(1/n%1) < EPSILON) return new Rat(1, Math.round(1/n))

  // Traverse the Stern–Brocot tree until a good approximation is found
  // If negative, search for the positive value and negate the result
  const negative = n < 1
  const r = rationalApproximation(Math.abs(n))
  return negative ? r.neg() : r
}

export default Rat


1	3	import {EPSILON} from './config'
2	3	import {ZERO, ONE, gcd} from './bigint'
3	3	import {rationalApproximation, continuedFraction} from './SternBrocotTree'
4
5		/**
6		* @class Rational Number
7		* @name Rat
8		*/
9	3	export class Rat {
10		n: bigint
11		d: bigint
12
13		/**
14		* Initialize a rational number.
15		*/
16		constructor(numerator: bigint\|number=ZERO, denominator: bigint\|number=ONE) {
17	281	this.n = BigInt(numerator)
18	281	this.d = BigInt(denominator)
19	281	this.normalize()
20		}
21
22		/**
23		* The decimal approximation.
24		*/
25		valueOf(): number {
26	33555607	return Number(this.n) / Number(this.d)
27		}
28
29		/**
30		* The text representation.
31		*/
32		toString(): string {
33	23	return this.n.toString() + ( this.d === ONE ? '' : '/' + this.d.toString() )
34		}
35
36		/**
37		* Returns a text profile of the number in various formats and it's value after common transformations.
38		*/
39		public get profile(): string {
40	1	const p = [`${this.constructor.name}: ${this.toString()} (≈${+this})`]
41		// p.push(`Continued: ${this.continuedFraction()}`)
42		// p.push(`Babylonian: ${this.babylonian()}`)
43		// p.push(`Egyptian: ${this.egyptian()}`)
44	1	p.push(`psin(t): ${this.psin().toString()}`)
45	1	p.push(`pcos(t): ${this.pcos().toString()}`)
46	1	p.push(`ptan(t): ${this.ptan().toString()}`)
47	1	return p.join('\n')
48		}
49
50		/**
51		* Clone this.
52		*/
53		clone(): Rat {
54	20	return new Rat(this.n, this.d)
55		}
56
57		/**
58		* Normalize the numerator and denominator by factoring out the common denominators.
59		*/
60		normalize(): void {
61
62		// normalize 0/1, 1/0, 0/0
63	359	if (this.n === ZERO) {
64	52	if (this.d !== ZERO) {
65	50	this.d = ONE
66		}
67	52	return
68		}
69	307	if (this.d === ZERO) {
70	14	this.n = this.n > ZERO ? ONE : -ONE
71	14	return
72		}
73
74		// normalize 1/1
75	293	if (this.n === this.d) {
76	80	this.n = this.d = ONE
77	80	return
78		}
79
80		// remove negative denominator
81	213	if (this.d < ZERO) {
82	5	this.n = -this.n
83	5	this.d = -this.d
84		}
85
86		// reduce numerator and denomitator by the greatest common divisor
87	213	const divisor = gcd(this.n, this.d)
88	213	this.n /= divisor
89	213	this.d /= divisor
90
91		}
92
93		/**
94		* Add this to that.
95		*/
96		add(that: Rat): Rat {
97	36	const r = new Rat(this.n * that.d + that.n * this.d, this.d * that.d)
98	36	r.normalize()
99	36	return r
100		}
101
102		/**
103		* Subtract this from that.
104		*/
105		sub(that: Rat): Rat {
106	12	return this.add(that.neg())
107		}
108
109		/**
110		* Multiply that by this.
111		*/
112		mul(that: Rat): Rat {
113	12	const r = new Rat(this.n * that.n, this.d * that.d)
114	12	r.normalize()
115	12	return r
116		}
117
118		/**
119		* Divide this by that.
120		*/
121		div(that: Rat): Rat {
122	28	const r = new Rat(this.n * that.d, this.d * that.n)
123	28	r.normalize()
124	28	return r
125		}
126
127		/**
128		* Mediant of this and that.
129		*/
130		mediant(that: Rat): Rat {
131	2	const r = new Rat(this.n + that.n, this.d + that.d)
132	2	r.normalize()
133	2	return r
134		}
135
136		/**
137		* Minimum of this and that.
138		*/
139		min(that: Rat): Rat {
140	2	return this.isLessThan(that) ? this : that
141		}
142
143		/**
144		* Maximum of this and that.
145		*/
146		max(that: Rat): Rat {
147	2	return this.isGreaterThan(that) ? this : that
148		}
149
150		/**
151		* Raise this to the power of that.
152		*/
153		pow(that: Rat): Rat {
154		// zero
155	25	if (that.n === ZERO) {
156	1	return new Rat(ONE)
157		}
158		// integer
159	24	if (that.d === ONE) {
160	23	return new Rat(this.nthat.n, this.dthat.n)
161		}
162		// fraction
163		else {
164	1	const estimate = Math.pow(+this, +that)
165	1	return FloatToRat(estimate)
166		}
167		}
168
169		/**
170		* Returns the dot product of this and that.
171		*/
172		dot(that: Rat): bigint {
173	1	return this.n * that.n + this.d * that.d
174		}
175
176		/**
177		* Returns true if this equals that.
178		*/
179		equals(that: Rat): boolean {
180	2	return this.n === that.n && this.d === that.d
181		}
182
183		/**
184		* Returns true if this approximates the number.
185		*/
186		approximates(n: number): boolean {
187	16777784	return Math.abs(+this - n) < EPSILON
188		}
189
190		/**
191		* Returns true if this is greater than that.
192		*/
193		isGreaterThan(that: Rat): boolean {
194	3	return this.n * that.d > that.n * this.d
195		}
196
197		/**
198		* Returns true if this is less than that.
199		*/
200		isLessThan(that: Rat): boolean {
201	3	return this.n * that.d < that.n * this.d
202		}
203
204		/**
205		* Absolute value of this.
206		*/
207		abs(): Rat {
208	2	const r = this.clone()
209	2	if (r.n < 0) r.n = -r.n
210	2	return r
211		}
212
213		/**
214		* Opposite (negative) of this.
215		*/
216		neg(): Rat {
217	14	const r = this.clone()
218	14	r.n = -r.n
219	14	return r
220		}
221
222		/**
223		* Returns true if this is less than zero.
224		*/
225		isNegative(): boolean {
226	5	return this.n < 0
227		}
228
229		/**
230		* Returns true if this is a finite number.
231		*/
232		isFinite(): boolean {
233	2	return this.d !== ZERO
234		}
235
236		/**
237		* The reciprocal, or multiplicative inverse, of this.
238		*/
239		inv(): Rat {
240	1	return new Rat(this.d, this.n)
241		}
242
243		/**
244		* Square root of this.
245		*/
246		sqrt(): Rat {
247	2	return this.root(2)
248		}
249
250		/**
251		* Returns the nth root, a number which approximates this when multiplied by itself n times.
252		*/
253		root(n: number): Rat {
254
255		// Handle 0/1, 1/0, -1/0, 0/0, 1/1
256	5	if (this.n === ZERO \|\| this.d === ZERO \|\| this.n === this.d) {
257	2	return this.clone()
258		}
259
260	3	if (this.isNegative()) {
261	1	throw `Roots of negative numbers like ${this.toString()} are too complex for this basic library`
262		}
263
264	2	return FloatToRat(Math.pow(+this, 1/n))
265		// return FunctionToRat(r => r.pow(n), +this)
266		}
267
268		/**
269		* Return the closest integer approximation.
270		*/
271		round(): bigint {
272	1	return BigInt(Math.round(+this))
273		}
274
275		/**
276		* Parametric sine: 2t / (1 + t²)
277		* @see https://youtu.be/Ui8OvmzDn7o?t=245
278		*/
279		psin(): Rat {
280	13	if (this.d === ZERO) return new Rat(ZERO)
281	11	const one = new Rat(1)
282	11	const two = new Rat(2)
283	11	const n = two.mul(this)
284	11	const d = one.add(this.pow(two))
285	11	return n.div(d)
286		}
287
288		/**
289		* Parametric cosine: (1 - t²) / (1 + t²)
290		*/
291		pcos(): Rat {
292	13	if (this.d === ZERO) return new Rat(-ONE)
293	11	const one = new Rat(1)
294	11	const two = new Rat(2)
295	11	const t2 = this.pow(two)
296	11	const n = one.sub(t2)
297	11	const d = one.add(t2)
298	11	return n.div(d)
299		}
300
301		/**
302		* Parametric tangent: psin() / pcos()
303		*/
304		ptan(): Rat {
305		// const one = new Rat(1)
306		// const two = new Rat(2)
307		// const four = new Rat(4)
308		// const n = this.pow(four).sub(one)
309		// const d = this.pow(two).mul(two)
310		// return n.div(d)
311	5	return this.psin().div(this.pcos())
312		}
313
314		/**
315		* Returns the integers representing the continued fraction.
316		*/
317		*continuedFraction(): Generator<number> {
318	1	for (const n of continuedFraction(+this)) {
319	2	yield n
320		}
321		}
322
323		}
324
325		/**
326		* Find a Rat approximation of the floating point number.
327		*/
328	3	export const FloatToRat = (n: number): Rat => {
329
330		// Handle special values: 0/0, 1/0, -1/0
331	14	if (isNaN(n)) return new Rat(0, 0)
332	13	if (n===Infinity) return new Rat(1, 0)
333	8	if (n===-Infinity) return new Rat(-1, 0)
334
335		// Shortcut for numbers close to an integer or 1/integer
336	7	if (Math.abs(n%1) < EPSILON) return new Rat(Math.round(n))
337	5	if (Math.abs(1/n%1) < EPSILON) return new Rat(1, Math.round(1/n))
338
339		// Traverse the Stern–Brocot tree until a good approximation is found
340		// If negative, search for the positive value and negate the result
341	3	const negative = n < 1
342	3	const r = rationalApproximation(Math.abs(n))
343	3	return negative ? r.neg() : r
344		}
345
346		export default Rat
347

acerix / cnum

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Rat.isFinite A

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