Category talk:Wren-math: Difference between revisions
Added Math.rootPoly method.
(→Source code: Added maxSafePrime and prevPrime methods and outlawed 'unsafe' arguments to several existing methods of the Int class.) |
(Added Math.rootPoly method.) |
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Line 113:
return deriv
}
// Attempts to find a real root of a polynomial using Newton's method from
// an initial guess, a given tolerance, a maximum number of iterations
// and a given multiplicity (usually 1).
// If a root is found, it is returned otherwise 'null' is returned.
// If the root is near an integer checks if the integer is in fact the root.
static rootPoly(coefs, guess, tol, maxIter, mult) {
var deg = coefs.count - 1
if (deg == 0) return null
if (deg == 1) return -coefs[1]/coefs[0]
if (deg == 2 && coefs[1]*coefs[1] - 4*coefs[0]*coefs[2] < 0) return null
if (Math.evalPoly(coefs, 0) == 0) return 0
var eps = 0.001
var deriv = Math.diffPoly(coefs)
var x0 = guess
var iter = 1
while (true) {
var den = Math.evalPoly(deriv, x0)
if (den == 0) {
x0 = (x0 >= 0) ? x0 + eps : x0 - eps
} else {
var num = Math.evalPoly(coefs, x0)
var x1 = x0 - num/den * mult
if ((x1 - x0).abs <= tol) {
var r = x1.round
if ((r - x1).abs <= eps && Math.evalPoly(coefs, r) == 0) return r
return x1
}
x0 = x1
}
if (iter == maxIter) break
iter = iter + 1
}
x0 = x0.round
if (Math.evalPoly(coefs, x0) == 0) return x0
return null
}
// Convenience versions of 'rootPoly' which use defaults for some parameters.
static rootpoly(coefs, guess) { rootPoly(coefs, guess, 1e-15, 100, 1) }
static rootPoly(coefs) { rootPoly(coefs, 0.001, 1e-15, 100, 1) }
// Gamma function using Lanczos approximation.
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