46 lines
919 B
Plaintext
46 lines
919 B
Plaintext
func P(n, k) { n! / ((n-k)!) }
|
||
func C(n, k) { binomial(n, k) }
|
||
|
||
class Logarithm(value) {
|
||
method to_s {
|
||
var e = int(value/10.log)
|
||
"%.8fE%+d" % (exp(value - e*10.log), e)
|
||
}
|
||
}
|
||
|
||
func lstirling(n) {
|
||
n < 10 ? (lstirling(n+1) - log(n+1))
|
||
: (0.5*log(2*Num.pi*n) + n*log(n/Num.e + 1/(12*Num.e*n)))
|
||
}
|
||
|
||
func P_approx(n, k) {
|
||
Logarithm((lstirling(n) - lstirling(n -k)))
|
||
}
|
||
|
||
func C_approx(n, k) {
|
||
Logarithm((lstirling(n) - lstirling(n -k) - lstirling(k)))
|
||
}
|
||
|
||
say "=> Exact results:"
|
||
for n (1..12) {
|
||
var p = n//3
|
||
say "P(#{n}, #{p}) = #{P(n, p)}"
|
||
}
|
||
|
||
for n (10..60 `by` 10) {
|
||
var p = n//3
|
||
say "C(#{n}, #{p}) = #{C(n, p)}"
|
||
}
|
||
|
||
say '';
|
||
say "=> Floating point approximations:"
|
||
for n ([5, 50, 500, 1000, 5000, 15000]) {
|
||
var p = n//3
|
||
say "P(#{n}, #{p}) = #{P_approx(n, p)}"
|
||
}
|
||
|
||
for n (100..1000 `by` 100) {
|
||
var p = n//3
|
||
say "C(#{n}, #{p}) = #{C_approx(n, p)}"
|
||
}
|