Two-State Quantum Normalization Calculator

            from math import *

def two_state_normalization(a, b) -> float:
    return (a / sqrt(((a * a) + (b * b))))

assert abs(two_state_normalization(3, 4) - 0.6) < 1e-6 * max(1.0, abs(0.6))
          

            #include <assert.h>
#include <math.h>

double two_state_normalization(double a, double b) {
    return (a / sqrt(((a * a) + (b * b))));
}

int main(void) {
    const double expected = 0.6;
    const double actual = two_state_normalization(3, 4);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          

            #include <cassert>
#include <cmath>
#include <numbers>

double two_state_normalization(double a, double b) {
    return (a / std::sqrt(((a * a) + (b * b))));
}

int main() {
    constexpr double expected = 0.6;
    const double actual = two_state_normalization(3, 4);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double two_state_normalization(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global two_state_normalization
section .text

two_state_normalization:
    push rbp
    mov rbp, rsp
    sub rsp, 64
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-8]
    movsd [rbp-48], xmm0
    movsd xmm0, [rbp-16]
    mulsd xmm0, [rbp-16]
    movsd [rbp-56], xmm0
    movsd xmm0, [rbp-48]
    addsd xmm0, [rbp-56]
    movsd [rbp-40], xmm0
    sqrtsd xmm0, [rbp-40]
    movsd [rbp-32], xmm0
    movsd xmm0, [rbp-8]
    divsd xmm0, [rbp-32]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          

            function result = two_state_normalization(a, b)
    result = (a / sqrt(((a * a) + (b * b))));
end
          

            ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / Sqrt[((a * a) + (b * b))]);