Diagonal Matrix Frobenius Norm second diagonal entry Solver

            from math import *

def diagonal_frobenius_norm_solve_b(c, a) -> float:
    return sqrt(((c * c) - (a * a)))

assert abs(diagonal_frobenius_norm_solve_b(13, 5) - 12) < 1e-6 * max(1.0, abs(12))
          

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

double diagonal_frobenius_norm_solve_b(double c, double a) {
    return sqrt(((c * c) - (a * a)));
}

int main(void) {
    const double expected = 12;
    const double actual = diagonal_frobenius_norm_solve_b(13, 5);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          

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

double diagonal_frobenius_norm_solve_b(double c, double a) {
    return std::sqrt(((c * c) - (a * a)));
}

int main() {
    constexpr double expected = 12;
    const double actual = diagonal_frobenius_norm_solve_b(13, 5);
    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 diagonal_frobenius_norm_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global diagonal_frobenius_norm_solve_b
section .text

diagonal_frobenius_norm_solve_b:
    push rbp
    mov rbp, rsp
    sub rsp, 48
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    mulsd xmm0, [rbp-8]
    movsd [rbp-40], xmm0
    movsd xmm0, [rbp-16]
    mulsd xmm0, [rbp-16]
    movsd [rbp-48], xmm0
    movsd xmm0, [rbp-40]
    subsd xmm0, [rbp-48]
    movsd [rbp-32], xmm0
    sqrtsd xmm0, [rbp-32]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          

            function result = diagonal_frobenius_norm_solve_b(c, a)
    result = sqrt(((c * c) - (a * a)));
end
          

            ClearAll[mwCalculate];
mwCalculate[c_, a_] := Sqrt[((c * c) - (a * a))];