[Metal] Goldilocks add and mul

goldilocks.metal

#include <metal_stdlib>
/*
  Goldilocks add and mul with ❤️ from Carter (Public Domain)
*/
inline ulong reduce128(ulong x_hi, ulong x_lo){
    ulong x_hi_hi = x_hi>>32;
    ulong x_hi_lo = x_hi & 0xffffffff;
    ulong t0 = x_lo - x_hi_hi;
    if(t0 > x_lo){
        t0 -= 0xffffffff;
    }
    ulong t1 = x_hi_lo*0xffffffff;
    ulong t2 = t0 + t1;
    if(t2 < t1){
        t2 += 0xffffffff;
    }
    return t2;
}

inline ulong goldilocks_mul(ulong x, ulong y) {
    ulong a = x >> 32;
    ulong b = x & 0xFFFFFFFF;
    ulong c = y >> 32;
    ulong d = y & 0xFFFFFFFF;

    ulong ad = a * d;
    ulong bd = b * d;

    ulong adbc = ad + (b * c);
    ulong adbc_carry = adbc < ad ? 1 : 0;

    ulong product_lo = bd + (adbc << 32);
    ulong product_lo_carry = product_lo < bd ? 1 : 0;
    ulong product_hi = (a * c) + (adbc >> 32) + (adbc_carry << 32) + product_lo_carry;
    return reduce128(product_hi, product_lo)%0xffffffff00000001;
}

inline ulong goldilocks_add(ulong x, ulong y){
    ulong x_plus_y = x+y;
    if(x_plus_y < x){
        ulong c = x_plus_y + 0xffffffff;
        if(c<x_plus_y){
            return c+0xffffffff;
        }
        return c;
    }
    return x_plus_y;
}