Category talk:Wren-math: Difference between revisions
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(Added source code for new 'Wren-math' module.) |
(→Source code: Added some type aliases, a new method & tweaked some code.) |
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} else { |
} else { |
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k = k + inc[i] |
k = k + inc[i] |
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i = ( |
i = (i + 1) % 8 |
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} |
} |
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} |
} |
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static geometricMean(a) { a.reduce { |prod, x| prod * x}.pow(1/a.count) } |
static geometricMean(a) { a.reduce { |prod, x| prod * x}.pow(1/a.count) } |
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static harmonicMean(a) { a.count / a.reduce { |acc, x| acc + 1/x } } |
static harmonicMean(a) { a.count / a.reduce { |acc, x| acc + 1/x } } |
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static quadraticMean(a) { (a.reduce(0) { |acc, x| acc + x*x }/a.count).sqrt } |
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static prod(a) { a.reduce(1) { |acc, x| acc * x } } |
static prod(a) { a.reduce(1) { |acc, x| acc * x } } |
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static max(a) { a.reduce { |acc, x| (x > acc) ? x : acc } } |
static max(a) { a.reduce { |acc, x| (x > acc) ? x : acc } } |
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return a.reduce { |acc, x| acc + (x - m).abs } / a.count |
return a.reduce { |acc, x| acc + (x - m).abs } / a.count |
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} |
} |
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} |
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}</lang> |
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// Type aliases for classes in case of any name clashes with other modules. |
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var Math_Math = Math |
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var Math_Int = Int |
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var Math_Stat = Stat</lang> |
Revision as of 10:30, 29 May 2020
Source code
<lang ecmascript>/* Module "math.wren" */
/* Math supplements the Num class with various other operations on numbers. */ class Math {
// Constants. static e { 2.71828182845904523536 } // base of natural logarithms static phi { 1.6180339887498948482 } // golden ratio static tau { 1.6180339887498948482 } // synonym for phi static ln2 { 0.69314718055994530942 } // natural logarithm of 2 static ln10 { 2.30258509299404568402 } // natural logarithm of 10
// Special values. static inf { 1/0 } // positive infinity static ninf { (-1)/0 } // negative infinity static nan { 0/0 } // nan
// Returns the base 'e' exponential of 'x' static exp(x) { e.pow(x) }
// Log functions. static log2(x) { x.log/ln2 } // Base 2 logarithm static log10(x) { x.log/ln10 } // Base 10 logarithm
// Hyperbolic trig functions. static sinh(x) { (exp(x) - exp(-x))/2 } // sine static cosh(x) { (exp(x) + exp(-x))/2 } // cosine static tanh(x) { sinh(x)/cosh(x) } // tangent
// Inverse hyperbolic trig functions. static asinh(x) { (x + (x*x + 1).sqrt).ln } // sine static acosh(x) { (x + (x*x - 1).sqrt).ln } // cosine static atanh(x) { ((1+x)/(1-x)).ln/2 } // tangent
// Angle conversions. static radians(d) { d * Num.pi / 180} static degrees(r) { r * 180 / Num.pi }
// Returns the cube root of 'x'. static cbrt(x) { x.pow(1/3) }
// Returns the square root of 'x' squared + 'y' squared. static hypot(x, y) { (x*x + y*y).sqrt }
// Returns the integer and fractional parts of 'x'. Both values have the same sign as 'x'. static modf(x) { [x.truncate, x.fraction] }
// Returns the IEEE 754 floating-point remainder of 'x/y'. static rem(x, y) { if (x.isNan || y.isNan || x.isInfinity || y == 0) return nan if (!x.isInfinity && y.isInfinity) return x var nf = modf(x/y) if (nf[1] != 0.5) { return x - (x/y).round * y } else { var n = nf[0] if (n%2 == 1) n = (n > 0) ? n + 1 : n - 1 return x - n * y } }
// Return the minimum and maximum of 'x' and 'y'. static min(x, y) { (x < y) ? x : y } static max(x, y) { (x > y) ? x : y }
// Round away from zero. static roundUp(x) { (x >= 0) ? x.ceil : x.floor }
// Round to 'p' decimal places, maximum 14. // Mode parameter specifies the rounding mode: // < 0 towards zero, == 0 nearest, > 0 away from zero. static toPlaces(x, p, mode) { if (p < 0) p = 0 if (p > 14) p = 14 var pw = 10.pow(p) var nf = modf(x) x = nf[1] * pw x = (mode < 0) ? x.truncate : (mode == 0) ? x.round : roundUp(x) return nf[0] + x/pw }
// Convenience version of above method which uses 0 for the 'mode' parameter. static toPlaces(x, p) { toPlaces(x, p, 0) }
// Gamma function using Lanczos approximation. static gamma(x) { var p = [ 0.99999999999980993, 676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7 ] var t = x + 6.5 var sum = p[0] for (i in 0..7) sum = sum + p[i+1]/(x + i) return 2.sqrt * Num.pi.sqrt * t.pow(x-0.5) * Math.exp(-t) * sum }
}
/* Int contains various routines which are only applicable to integers. */ class Int {
// Maximum safe integer = 2^53 - 1. static maxSafe { 9007199254740991 }
// Returns the greatest common divisor of 'x' and 'y'. static gcd(x, y) { while (y != 0) { var t = y y = x % y x = t } return x }
// Returns the least common multiple of 'x' and 'y'. static lcm(x, y) { (x*y).abs / gcd(x, y) }
// Returns the remainder when 'b' raised to the power 'e' is divided by 'm'. static modPow(b, e, m) { if (m == 1) return 0 var r = 1 b = b % m while (e > 0) { if (e%2 == 1) r = (r*b) % m e = e >> 1 b = (b*b) % m } return r }
// Returns the factorial of 'n'. Inaccurate for n > 18. static factorial(n) { if (!(n is Num && n >= 0)) Fiber.abort("Argument must be a non-negative integer") if (n < 2) return 1 var fact = 1 for (i in 2..n) fact = fact * i return fact }
// Determines whether 'n' is prime using a wheel with basis [2, 3]. static isPrime(n) { if (!n.isInteger || n < 2) return false if (n%2 == 0) return n == 2 if (n%3 == 0) return n == 3 var d = 5 while (d*d <= n) { if (n%d == 0) return false d = d + 2 if (n%d == 0) return false d = d + 4 } return true }
// Sieves for primes up to and including 'limit'. // If primesOnly is true returns a list of the primes found. // If primesOnly is false returns a bool list 'c' of size (limit + 1) where: // c[i] is false if 'i' is prime or true if 'i' is composite. static primeSieve(limit, primesOnly) { if (limit < 2) return [] var c = [false] * (limit + 1) // composite = true c[0] = true c[1] = true // if not primesOnly we need to process the even numbers > 2 if (!primesOnly) { var i = 4 while (i <= limit) { c[i] = true i = i + 2 } } var p = 3 var p2 = p * p while (p2 <= limit) { var i = p2 while (i <= limit) { c[i] = true i = i + 2*p } var ok = true while (ok) { p = p + 2 ok = c[p] } p2 = p * p } if (!primesOnly) return c var primes = [2] var i = 3 while (i <= limit) { if (!c[i]) primes.add(i) i = i + 2 } return primes }
// Convenience version of above method which uses true for the primesOnly parameter. static primeSieve(limit) { primeSieve(limit, true) }
// Returns the prime factors of 'n' in order using a wheel with basis [2, 3, 5]. static primeFactors(n) { if (!n.isInteger || n < 2) return [] var inc = [4, 2, 4, 2, 4, 6, 2, 6] var factors = [] while (n%2 == 0) { factors.add(2) n = (n/2).truncate } while (n%3 == 0) { factors.add(3) n = (n/3).truncate } while (n%5 == 0) { factors.add(5) n = (n/5).truncate } var k = 7 var i = 0 while (k * k <= n) { if (n%k == 0) { factors.add(k) n = (n/k).truncate } else { k = k + inc[i] i = (i + 1) % 8 } } if (n > 1) factors.add(n) return factors }
// Returns all the divisors of 'n' including 1 and 'n' itself. static divisors(n) { if (!n.isInteger || n < 1) return [] var divisors = [] var divisors2 = [] var i = 1 var k = (n%2 == 0) ? 1 : 2 while (i <= n.sqrt) { if (n%i == 0) { divisors.add(i) var j = (n/i).floor if (j != i) divisors2.add(j) } i = i + k } if (!divisors2.isEmpty) divisors = divisors + divisors2[-1..0] return divisors }
// Returns all the divisors of 'n' excluding 'n'. static properDivisors(n) { var d = divisors(n) var c = d.count return (c <= 1) ? [] : d[0..-2] }
}
/*
Stat contains various routines applicable to lists or ranges of numbers which are useful for statistical purposes.
- /
class Stat {
// Methods to calculate sum, various means, product and maximum/minimum element of 'a'. // The sum and product of an empty list are considered to be 0 and 1 respectively. static sum(a) { a.reduce(0) { |acc, x| acc + x } } static mean(a) { sum(a)/a.count } static geometricMean(a) { a.reduce { |prod, x| prod * x}.pow(1/a.count) } static harmonicMean(a) { a.count / a.reduce { |acc, x| acc + 1/x } } static quadraticMean(a) { (a.reduce(0) { |acc, x| acc + x*x }/a.count).sqrt } static prod(a) { a.reduce(1) { |acc, x| acc * x } } static max(a) { a.reduce { |acc, x| (x > acc) ? x : acc } } static min(a) { a.reduce { |acc, x| (x < acc) ? x : acc } }
// Returns the median of a sorted list. static median(a) { var c = a.count if (c == 0) { Fiber.abort("An empty list cannot have a median") } else if (c%2 == 1) { return a[(c/2).floor] } else { var d = (c/2).floor return (a[d] + a[d-1])/2 } }
// Return a list whose first element is the number of occurrences of the mode(s) // and the second element is a list of the mode(s) of a. static modes(a) { var m = {} for (e in a) m[e] = (!m[e]) ? 1 : m[e] + 1 var max = 0 for (e in a) if (m[e] > max) max = m[e] var res = [] for (k in m.keys) if (m[k] == max) res.add(k) return [max, res] }
// Returns the sample variance of 'a'. static variance(a) { var m = mean(a) var c = a.count return (a.reduce(0) { |acc, x| acc + x*x } - m*m*c) / (c-1) }
// Returns the population variance of 'a'. static popVariance(a) { var m = mean(a) return (a.reduce(0) { |acc, x| acc + x*x }) / a.count - m*m }
// Returns the sample standard deviation of 'a'. static stdDev(a) { variance(a).sqrt }
// Returns the population standard deviation of 'a'. static popStdDev { popVariance(a).sqrt }
// Returns the mean deviation of 'a'. static meanDev(a) { var m = mean(a) return a.reduce { |acc, x| acc + (x - m).abs } / a.count }
}
// Type aliases for classes in case of any name clashes with other modules. var Math_Math = Math var Math_Int = Int var Math_Stat = Stat</lang>