Combinations and Permutations Calculator

            def combinations(n: int, r: int) -> int:
    if not 0 <= r <= n:
        raise ValueError("require 0 <= r <= n")
    r = min(r, n - r)
    out = 1
    for i in range(1, r + 1):
        out = out * (n - r + i) // i
    return out
assert combinations(5, 3) == 10
          

            #include <assert.h>
#include <stdint.h>
uint64_t combinations(uint64_t n,uint64_t r){if(r>n)return 0;if(r>n-r)r=n-r;uint64_t out=1;for(uint64_t i=1;i<=r;i++)out=out*(n-r+i)/i;return out;}
int main(void){assert(combinations(5,3)==10);}
          

            #include <cassert>
#include <cstdint>
std::uint64_t combinations(std::uint64_t n,std::uint64_t r){if(r>n)return 0;if(r>n-r)r=n-r;std::uint64_t out=1;for(std::uint64_t i=1;i<=r;++i)out=out*(n-r+i)/i;return out;}
int main(){assert(combinations(5,3)==10);}
          

x86-64 NASM · System V ABI · Linux · integer arguments in rdi, rsi and rdx

            ; uint64_t combinations(uint64_t n, uint64_t r)
global combinations
section .text
combinations:
    cmp rsi, rdi
    ja .invalid
    mov r8, rdi
    sub r8, rsi
    cmp rsi, r8
    cmova rsi, r8
    mov rax, 1
    mov rcx, 1
.loop:
    cmp rcx, rsi
    ja .done
    mov r9, rdi
    sub r9, rsi
    add r9, rcx
    mul r9
    div rcx
    inc rcx
    jmp .loop
.invalid:
    xor eax, eax
.done:
    ret
          

            function result = combinations(n, r)
    result = nchoosek(round(n), round(r));
end
          

            ClearAll[mwCalculate];
mwCalculate[n_Integer, r_Integer] := Binomial[n, r];