Roots of a quadratic function: Difference between revisions

=={{header|Nim}}==

<lang Nim>import math, complex, strformat

const Epsilon = 1e-15

type

SolKind = enum solDouble, solFloat, solComplex

Roots = object

case kind: SolKind

of solDouble:

fvalue: float

of solFloat:

fvalues: (float, float)

of solComplex:

cvalues: (Complex64, Complex64)

func quadRoots(a, b, c: float): Roots =

if a == 0:

raise newException(ValueError, "first coefficient cannot be null.")

let den = a * 2

let Δ = b * b - a * c * 4

if abs(Δ) < Epsilon:

result = Roots(kind: solDouble, fvalue: -b / den)

elif Δ < 0:

let r = -b / den

let i = sqrt(-Δ) / den

result = Roots(kind: solComplex, cvalues: (complex64(r, i), complex64(r, -i)))

else:

let r = (if b < 0: -b + sqrt(Δ) else: -b - sqrt(Δ)) / den

result = Roots(kind: solFloat, fvalues: (r, c / (a * r)))

func `$`(r: Roots): string =

case r.kind

of solDouble:

result = $r.fvalue

of solFloat:

result = &"{r.fvalues[0]}, {r.fvalues[1]}"

of solComplex:

result = &"{r.cvalues[0].re} + {r.cvalues[0].im}i, {r.cvalues[1].re} + {r.cvalues[1].im}i"

when isMainModule:

const Equations = [(1.0, -2.0, 1.0),

(10.0, 1.0, 1.0),

(1.0, -10.0, 1.0),

(1.0, -1000.0, 1.0),

(1.0, -1e9, 1.0)]

for (a, b, c) in Equations:

echo &"Equation: {a=}, {b=}, {c=}"

let roots = quadRoots(a, b, c)

let plural = if roots.kind == solDouble: "" else: "s"

echo &" root{plural}: {roots}"</lang>

{{out}}

<pre>Equation: a=1.0, b=-2.0, c=1.0

root: 1.0

Equation: a=10.0, b=1.0, c=1.0

roots: -0.05 + 0.3122498999199199i, -0.05 + -0.3122498999199199i

Equation: a=1.0, b=-10.0, c=1.0

roots: 9.898979485566356, 0.1010205144336438

Equation: a=1.0, b=-1000.0, c=1.0

roots: 999.998999999, 0.001000001000002

Equation: a=1.0, b=-1000000000.0, c=1.0

roots: 1000000000.0, 1e-09</pre>