corelang/big_int.cpp

/*
We use two's complement

- Adding the value, sub is similar
  Adding a positive number to a negative number is actually subtracting the value.
  Last bit is a biggest possible negative number for that bit range.
  0111 1111 => 127
  1111 1111 => -128 - 127 = 1

  1000 0000 => -128
  if we add 4 we get
  1000 0100 => -124

- Negating the value
  1000 0001 => -127
  flip bits
  0111 1110 => 126
  we need to add 1
  0111 1111 -> 127

- Division
  We don't need full 128 bit divide
  we just need to make sure we always divide
  smaller then U64MAX and -U64MAX
  10 / -1  = -10
  10 / 1   =  10
  -10 / -1 = 10
  -10 / 1  = 10
*/

struct S128{
  U64 hi, lo;
  constexpr S128 max(){return {S64MAX, U64MAX};}
  constexpr S128 min(){return {(U64)S64MIN, 0};}
  #define S128MAX S128::max()
  #define S128MIN S128::min()
};

function S64
is_negative(S128 v){
  S64 result = v.hi >> 63;
  return result;
}

function S64
sign(S128 val){
  S64 result = is_negative(val) ? -1 : 1;
  return result;
}

function S128
s128(S64 value){
  S128 result = {value < 0 ? ~0 : 0ull, (U64)value};
  return result;
}

function S128
s128_from_u64(U64 value){
  S128 result = {0, value};
  return result;
}

function S128
operator+(S128 a, S128 b){
  U64 lo = a.lo + b.lo;
  U64 hi = a.hi + b.hi + (a.lo > lo); // (a.lo > lo) is carry
  return {hi,lo};
}

function S128
operator-(S128 a, S128 b){
  U64 lo = a.lo - b.lo;
  U64 hi = a.hi - b.hi - (a.lo < lo); // (a.lo < lo) is carry
  return {hi,lo};
}

force_inline U64  lo32(U64 a){return a & 0xffffffff;}
force_inline U64  hi32(U64 a){return a >> 32;}
force_inline S128 operator~(S128 a){return {~a.hi, ~a.lo};}
force_inline S128 operator^(S128 a, S128 b){return {a.hi ^ b.hi, a.lo ^ b.lo};}
force_inline S128 operator&(S128 a, S128 b){return {a.hi & b.hi, a.lo & b.lo};}
force_inline S128 operator|(S128 a, S128 b){return {a.hi | b.hi, a.lo | b.lo};}

function S128
operator-(S128 a){
  a = (~a) + s128(1);
  return a;
}

void mult64to128(U64 u, U64 v, U64& h, U64 &l)
{
    U64 u1 = (u & 0xffffffff);
    U64 v1 = (v & 0xffffffff);
    U64 t = (u1 * v1);
    U64 w3 = (t & 0xffffffff); // w3 = t1_lo
    U64 k = (t >> 32); // k = t1_hi

    u >>= 32; // u_hi
    t = (u * v1) + k; // t2 = (u_hi * v_lo) + t1_hi
    k = (t & 0xffffffff); // t2_lo
    U64 w1 = (t >> 32); // t2_hi

    v >>= 32;
    t = (u1 * v) + k; // t3 = (u_lo * v_hi) + t2_lo
    k = (t >> 32); // t3_hi

    h = (u * v) + w1 + k;
    l = (t << 32) + w3;
}

function S128
operator/(S128 a, S128 b){
  S64 sign = 1;
  if(is_negative(a)){
    sign *= -1;
    a = -a;
  }
  if(is_negative(b)){
    sign *= -1;
    b = -b;
  }
  assert(a.hi == 0 && b.hi == 0);
  U64 division = a.lo / b.lo;
  S128 result = {0, division};
  if(sign == -1) result = -result;
  return result;
}

function S128
u64_mul(U64 u, U64 v){
  U64 u_lo = lo32(u);
  U64 v_lo = lo32(v);
  U64 u_hi = hi32(u);
  U64 v_hi = hi32(v);

  U64 t1 = u_lo * v_lo;
  U64 t2 = (u_hi * v_lo) + hi32(t1);
  U64 t3 = (u_lo * v_hi) + lo32(t2);

  U64 lo = (t3 << 32) + lo32(t1);
  U64 hi = (u_hi * v_hi) + hi32(t2) + hi32(t3);
  return {hi,lo};
}

function S128
operator*(S128 a, S128 b){
  S128 c = u64_mul(a.lo, b.lo);
  c.hi += (a.hi * b.lo) + (a.lo * b.hi);
  return c;
}

function B32
operator==(S128 a, S128 b){
  B32 result = (a.lo == b.lo) && (a.hi == b.hi);
  return result;
}

function void
test_big_int(){
  S128 v1 = s128(-1);
  assert(v1.hi == U64MAX && v1.lo == U64MAX);
  assert(is_negative(v1));
  assert(sign(v1) == -1);

  S128 v2 = s128_from_u64(U64MAX) + s128_from_u64(1);
  assert(v2.lo == 0 && v2.hi == 1);

  S128 v3 = s128_from_u64(U64MAX) + s128_from_u64(100);
  assert(v3.lo == 99 && v3.hi == 1);

  // S64 s64_max = S64MAX;
  S128 v4 = s128(S64MIN) + s128_from_u64(100);
  assert((v4.lo - S64MAX) == 101); // 101 cause S64MIN is larher by 1

  S128 v5 = {1, 0};
  S128 v6 = v5 - s128(1);
  assert(v6.lo == U64MAX && v6.hi == 0);

  {
    S128 v7 = u64_mul(S64MAX, S64MAX);
    U64 a,b;
    mult64to128(S64MAX,S64MAX,a,b);
    assert(v7.hi == a && v7.lo == b);
  }

  {
    S128 v7 = u64_mul(S64MIN, S64MIN);
    U64 a,b;
    mult64to128(S64MIN,S64MIN,a,b);
    assert(v7.hi == a && v7.lo == b);
  }

  {
    S128 v7 = u64_mul(15125125, -1424124);
    U64 a,b;
    mult64to128(15125125,-1424124,a,b);
    assert(v7.hi == a && v7.lo == b);
  }

  {
    S128 v7 = u64_mul(52242, 2);
    U64 a,b;
    mult64to128(52242, 2,a,b);
    assert(v7.hi == a && v7.lo == b);
    assert(v7.lo == 52242*2);
  }

  {
    S128 v7 = u64_mul(0, 0);
    assert(v7 == s128(0));
    // U64 a,b;
    // mult64to128(52242, 2,a,b);
    // assert(v7.hi == a && v7.lo == b);
    // assert(v7.lo == 52242*2);
  }
}