Task: Faulhaber's triangle

C: #include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int binomial(int n, int k) {
    int num, denom, i;

    if (n < 0 || k < 0 || n < k) return -1;
    if (n == 0 || k == 0) return 1;

    num = 1;
    for (i = k + 1; i <= n; ++i) {
        num = num * i;
    }

    denom = 1;
    for (i = 2; i <= n - k; ++i) {
        denom *= i;
    }

    return num / denom;
}

int gcd(int a, int b) {
    int temp;
    while (b != 0) {
        temp = a % b;
        a = b;
        b = temp;
    }
    return a;
}

typedef struct tFrac {
    int num, denom;
} Frac;

Frac makeFrac(int n, int d) {
    Frac result;
    int g;

    if (d == 0) {
        result.num = 0;
        result.denom = 0;
        return result;
    }

    if (n == 0) {
        d = 1;
    } else if (d < 0) {
        n = -n;
        d = -d;
    }

    g = abs(gcd(n, d));
    if (g > 1) {
        n = n / g;
        d = d / g;
    }

    result.num = n;
    result.denom = d;
    return result;
}

Frac negateFrac(Frac f) {
    return makeFrac(-f.num, f.denom);
}

Frac subFrac(Frac lhs, Frac rhs) {
    return makeFrac(lhs.num * rhs.denom - lhs.denom * rhs.num, rhs.denom * lhs.denom);
}

Frac multFrac(Frac lhs, Frac rhs) {
    return makeFrac(lhs.num * rhs.num, lhs.denom * rhs.denom);
}

bool equalFrac(Frac lhs, Frac rhs) {
    return (lhs.num == rhs.num) && (lhs.denom == rhs.denom);
}

bool lessFrac(Frac lhs, Frac rhs) {
    return (lhs.num * rhs.denom) < (rhs.num * lhs.denom);
}

void printFrac(Frac f) {
    char buffer[7];
    int len;

    if (f.denom != 1) {
        snprintf(buffer, 7, "%d/%d", f.num, f.denom);
    } else {
        snprintf(buffer, 7, "%d", f.num);
    }

    len = 7 - strlen(buffer);
    while (len-- > 0) {
        putc(' ', stdout);
    }

    printf(buffer);
}

Frac bernoulli(int n) {
    Frac a[16];
    int j, m;

    if (n < 0) {
        a[0].num = 0;
        a[0].denom = 0;
        return a[0];
    }

    for (m = 0; m <= n; ++m) {
        a[m] = makeFrac(1, m + 1);
        for (j = m; j >= 1; --j) {
            a[j - 1] = multFrac(subFrac(a[j - 1], a[j]), makeFrac(j, 1));
        }
    }

    if (n != 1) {
        return a[0];
    }

    return negateFrac(a[0]);
}

void faulhaber(int p) {
    Frac q, *coeffs;
    int j, sign;

    coeffs = malloc(sizeof(Frac)*(p + 1));

    q = makeFrac(1, p + 1);
    sign = -1;
    for (j = 0; j <= p; ++j) {
        sign = -1 * sign;
        coeffs[p - j] = multFrac(multFrac(multFrac(q, makeFrac(sign, 1)), makeFrac(binomial(p + 1, j), 1)), bernoulli(j));
    }

    for (j = 0; j <= p; ++j) {
        printFrac(coeffs[j]);
    }
    printf("\n");

    free(coeffs);
}

int main() {
    int i;

    for (i = 0; i < 10; ++i) {
        faulhaber(i);
    }

    return 0;
}




Go: package main

import (
    "fmt"
    "math/big"
)

func bernoulli(n uint) *big.Rat {
    a := make([]big.Rat, n+1)
    z := new(big.Rat)
    for m := range a {
        a[m].SetFrac64(1, int64(m+1))
        for j := m; j >= 1; j-- {
            d := &a[j-1]
            d.Mul(z.SetInt64(int64(j)), d.Sub(d, &a[j]))
        }
    }
    
    if n != 1 {
        return &a[0]
    }
    a[0].Neg(&a[0])
    return &a[0]
}

func binomial(n, k int) int64 {
    if n <= 0 || k <= 0 || n < k {
        return 1
    }
    var num, den int64 = 1, 1
    for i := k + 1; i <= n; i++ {
        num *= int64(i)
    }
    for i := 2; i <= n-k; i++ {
        den *= int64(i)
    }
    return num / den
}

func faulhaberTriangle(p int) []big.Rat {
    coeffs := make([]big.Rat, p+1)
    q := big.NewRat(1, int64(p)+1)
    t := new(big.Rat)
    u := new(big.Rat)
    sign := -1
    for j := range coeffs {
        sign *= -1
        d := &coeffs[p-j]
        t.SetInt64(int64(sign))
        u.SetInt64(binomial(p+1, j))
        d.Mul(q, t)
        d.Mul(d, u)
        d.Mul(d, bernoulli(uint(j)))
    }
    return coeffs
}

func main() {
    for i := 0; i < 10; i++ {
        coeffs := faulhaberTriangle(i)
        for _, coeff := range coeffs {
            fmt.Printf("%5s  ", coeff.RatString())
        }
        fmt.Println()
    }
    fmt.Println()
    
    k := 17
    cc := faulhaberTriangle(k)
    n := int64(1000)
    nn := big.NewRat(n, 1)
    np := big.NewRat(1, 1)
    sum := new(big.Rat)
    tmp := new(big.Rat)
    for _, c := range cc {
        np.Mul(np, nn)
        tmp.Set(np)
        tmp.Mul(tmp, &c)
        sum.Add(sum, tmp)
    }
    fmt.Println(sum.RatString())
}