math: add an `unsigned` module, implementing Uint128, Uint256 and methods on them (#13186)

vlib/math/unsigned/uint128.v

@@ -0,0 +1,462 @@
+module uint
+
+import math.bits
+import encoding.binary
+
+pub struct Uint128 {
+pub mut:
+	lo u64
+	hi u64
+}
+
+pub const (
+	uint128_zero = Uint128{}
+	uint128_max  = Uint128{18446744073709551615, 18446744073709551615}
+)
+
+// is_zero returns true if u == 0
+pub fn (u Uint128) is_zero() bool {
+	return u == Uint128{}
+}
+
+// equals returns true if u == v.
+//
+// Uint128 values can be compared directly with ==, but use of the Equals method
+// is preferred for consistency.
+pub fn (u Uint128) equals(v Uint128) bool {
+	return u == v
+}
+
+// equals_64 returns true if u == v
+pub fn (u Uint128) equals_64(v u64) bool {
+	return u.lo == v && u.hi == 0
+}
+
+// cmp compares u and v and returns:
+//
+// -1 if u <  v
+//  0 if u == v
+// +1 if u >  v
+//
+pub fn (u Uint128) cmp(v Uint128) int {
+	if u == v {
+		return 0
+	} else if u.hi < v.hi || (u.hi == v.hi && u.lo < v.lo) {
+		return -1
+	} else {
+		return 1
+	}
+}
+
+// cmp_64 compares u and v and returns:
+//
+//   -1 if u <  v
+//    0 if u == v
+//   +1 if u >  v
+//
+pub fn (u Uint128) cmp_64(v u64) int {
+	if u.hi == 0 && u.lo == v {
+		return 0
+	} else if u.hi == 0 && u.lo < v {
+		return -1
+	} else {
+		return 1
+	}
+}
+
+// and returns u & v
+pub fn (u Uint128) and(v Uint128) Uint128 {
+	return Uint128{u.lo & v.lo, u.hi & v.hi}
+}
+
+// and_64 rreturns u & v
+pub fn (u Uint128) and_64(v u64) Uint128 {
+	return Uint128{u.lo & v, u.hi & 0}
+}
+
+// or returns u | v
+pub fn (u Uint128) or_(v Uint128) Uint128 {
+	return Uint128{u.lo | v.lo, u.hi | v.hi}
+}
+
+// or returns u | v
+pub fn (u Uint128) or_64(v u64) Uint128 {
+	return Uint128{u.lo | v, u.hi | 0}
+}
+
+// xor returns u ^ v
+pub fn (u Uint128) xor(v Uint128) Uint128 {
+	return Uint128{u.lo ^ v.lo, u.hi ^ v.hi}
+}
+
+// xor_64 returns u ^ v
+pub fn (u Uint128) xor_64(v u64) Uint128 {
+	return Uint128{u.lo ^ v, u.hi ^ 0}
+}
+
+// add returns u + v with wraparound semantics
+pub fn (u Uint128) add(v Uint128) Uint128 {
+	lo, carry := bits.add_64(u.lo, v.lo, 0)
+	hi, _ := bits.add_64(u.hi, v.hi, carry)
+	return Uint128{lo, hi}
+}
+
+pub fn add_128(x Uint128, y Uint128, carry u64) (Uint128, u64) {
+	mut sum := Uint128{}
+	mut carry_out := u64(0)
+	sum.lo, carry_out = bits.add_64(x.lo, y.lo, carry)
+	sum.hi, carry_out = bits.add_64(x.hi, y.hi, carry_out)
+	return sum, carry_out
+}
+
+pub fn sub_128(x Uint128, y Uint128, borrow u64) (Uint128, u64) {
+	mut diff := Uint128{}
+	mut borrow_out := u64(0)
+	diff.lo, borrow_out = bits.sub_64(x.lo, y.lo, borrow)
+	diff.hi, borrow_out = bits.sub_64(x.hi, y.hi, borrow_out)
+	return diff, borrow_out
+}
+
+pub fn mul_128(x Uint128, y Uint128) (Uint128, Uint128) {
+	mut lo := Uint128{}
+	mut hi := Uint128{}
+	lo.hi, lo.lo = bits.mul_64(x.lo, y.lo)
+	hi.hi, hi.lo = bits.mul_64(x.hi, y.hi)
+	t0, t1 := bits.mul_64(x.lo, y.hi)
+	t2, t3 := bits.mul_64(x.hi, y.lo)
+
+	mut c0 := u64(0)
+	mut c1 := u64(0)
+	lo.hi, c0 = bits.add_64(lo.hi, t1, 0)
+	lo.hi, c1 = bits.add_64(lo.hi, t3, 0)
+	hi.lo, c0 = bits.add_64(hi.lo, t0, c0)
+	hi.lo, c1 = bits.add_64(hi.lo, t2, c1)
+	hi.hi += c0 + c1
+	return hi, lo
+}
+
+pub fn div_128(hi Uint128, lo Uint128, y_ Uint128) (Uint128, Uint128) {
+	mut y := y_
+	if y.is_zero() {
+		panic('integer divide by zero')
+	}
+
+	if y.cmp(hi) <= 0 {
+		panic('integer overflow')
+	}
+
+	s := u32(y.leading_zeros())
+	y = y.lsh(s)
+
+	un32 := hi.lsh(s).or_(lo.rsh(128 - s))
+	un10 := lo.lsh(s)
+	mut q1, rhat := un32.quo_rem_64(y.hi)
+	mut r1 := uint128_from_64(rhat)
+	tmp := Uint128{r1.lo, un10.hi}
+	for q1.hi != 0 || q1.mul_64(y.lo).cmp(tmp) > 0 {
+		q1 = q1.sub_64(1)
+		r1 = r1.add_64(y.hi)
+		if r1.hi != 0 {
+			break
+		}
+	}
+
+	un21 := Uint128{un32.lo, un10.hi}.sub(q1.mul(y))
+	mut q0, rhat2 := un21.quo_rem_64(y.hi)
+	mut r0 := uint128_from_64(rhat2)
+	tmp2 := Uint128{r0.lo, un10.lo}
+	for q0.hi != 0 || q0.mul_64(y.lo).cmp(tmp2) > 0 {
+		q0 = q0.sub_64(1)
+		r0 = r0.add_64(y.hi)
+		if r0.hi != 0 {
+			break
+		}
+	}
+
+	return Uint128{q1.lo, q0.lo}, Uint128{un21.lo, un10.lo}.sub(q0.mul(y)).rsh(s)
+}
+
+// add_64 returns u + v with wraparound semantics
+pub fn (u Uint128) add_64(v u64) Uint128 {
+	lo, carry := bits.add_64(u.lo, v, 0)
+	hi := u.hi + carry
+	return Uint128{lo, hi}
+}
+
+// sub returns u - v with wraparound semantics
+pub fn (u Uint128) sub(v Uint128) Uint128 {
+	lo, borrow := bits.sub_64(u.lo, v.lo, 0)
+	hi, _ := bits.sub_64(u.hi, v.hi, borrow)
+	return Uint128{lo, hi}
+}
+
+// sub_64 returns u - v with wraparound semantics
+pub fn (u Uint128) sub_64(v u64) Uint128 {
+	lo, borrow := bits.sub_64(u.lo, v, 0)
+	hi := u.hi - borrow
+	return Uint128{lo, hi}
+}
+
+// mul returns u * v with wraparound semantics
+pub fn (u Uint128) mul(v Uint128) Uint128 {
+	mut hi, lo := bits.mul_64(u.lo, v.lo)
+	hi += u.hi * v.lo + u.lo * v.hi
+	return Uint128{lo, hi}
+}
+
+// mul_64 returns u * v with wraparound semantics
+pub fn (u Uint128) mul_64(v u64) Uint128 {
+	mut hi, lo := bits.mul_64(u.lo, v)
+	hi += u.hi * v
+	return Uint128{lo, hi}
+}
+
+pub fn (u Uint128) overflowing_mul_64(v u64) (Uint128, bool) {
+	hi, lo := bits.mul_64(u.lo, v)
+	p0, p1 := bits.mul_64(u.hi, v)
+	hi2, c0 := bits.add_64(hi, p1, 0)
+
+	return Uint128{lo, hi2}, p0 != 0 || c0 != 0
+}
+
+pub fn (u Uint128) overflowing_add_64(v u64) (Uint128, u64) {
+	lo, carry := bits.add_64(u.lo, v, 0)
+	hi, carry2 := bits.add_64(u.hi, 0, carry)
+
+	return Uint128{lo, hi}, carry2
+}
+
+// div returns u / v
+pub fn (u Uint128) div(v Uint128) Uint128 {
+	q, _ := u.quo_rem(v)
+	return q
+}
+
+// mod returns r = u % v
+pub fn (u Uint128) mod(v Uint128) Uint128 {
+	_, r := u.quo_rem(v)
+	return r
+}
+
+// mod_64 returns r = u % v
+pub fn (u Uint128) mod_64(v u64) u64 {
+	_, r := u.quo_rem_64(v)
+	return r
+}
+
+// quo_rem_64 returns q = u/v and r = u%v
+pub fn (u Uint128) quo_rem_64(v u64) (Uint128, u64) {
+	if u.hi < v {
+		mut r := u64(0)
+		mut q := Uint128{0, 0}
+		q.lo, r = bits.div_64(u.hi, u.lo, v)
+
+		return q, r
+	} else {
+		mut q := Uint128{0, 0}
+		mut r := u64(0)
+		mut r2 := u64(0)
+		q.hi, r = bits.div_64(0, u.hi, v)
+		q.lo, r2 = bits.div_64(r, u.lo, v)
+		return q, r2
+	}
+}
+
+// quo_rem returns q = u/v and r = u%v
+pub fn (u Uint128) quo_rem(v Uint128) (Uint128, Uint128) {
+	mut q := Uint128{}
+	mut r := Uint128{}
+	if v.hi == 0 {
+		mut r64 := u64(0)
+		q, r64 = u.quo_rem_64(v.lo)
+		r = Uint128{r64, 0}
+	} else {
+		n := bits.leading_zeros_64(v.hi)
+		v1 := v.lsh(u32(n))
+		u1 := v.rsh(1)
+
+		mut tq, _ := bits.div_64(u1.hi, u1.lo, v1.hi)
+		tq >>= u64(64 - n)
+		if tq != 0 {
+			tq -= 1
+		}
+
+		q = Uint128{tq, 0}
+		r = u - v.mul_64(tq)
+
+		if r.cmp(v) >= 0 {
+			q = q.add_64(1)
+			r = r - v
+		}
+	}
+
+	return q, r
+}
+
+// lsh returns u << n
+pub fn (u Uint128) lsh(n u32) Uint128 {
+	mut s := Uint128{}
+	if n > 64 {
+		s.lo = 0
+		s.hi = u.lo << (n - 64)
+	} else {
+		s.lo = u.lo << n
+		s.hi = u.hi << n | u.lo >> (64 - n)
+	}
+
+	return s
+}
+
+// lsh returns u >> n
+pub fn (u Uint128) rsh(n u32) Uint128 {
+	mut s := Uint128{}
+	if n > 64 {
+		s.hi = 0
+		s.lo = u.hi << (n - 64)
+	} else {
+		s.lo = u.lo >> n | u.hi << (64 - n)
+		s.hi = u.hi >> n
+	}
+
+	return s
+}
+
+// leading_zeros returns the number of leading zero bits in u; the result is 128
+// for u == 0.
+pub fn (u Uint128) leading_zeros() int {
+	if u.hi > 0 {
+		return bits.leading_zeros_64(u.hi)
+	}
+	return 64 + bits.leading_zeros_64(u.lo)
+}
+
+// trailing_zeros returns the number of trailing zero bits in u; the result is
+// 128 for u == 0.
+pub fn (u Uint128) trailing_zeros() int {
+	if u.lo > 0 {
+		return bits.trailing_zeros_64(u.lo)
+	}
+	return 64 + bits.trailing_zeros_64(u.hi)
+}
+
+// ones_count returns the number of one bits ("population count" in u)
+pub fn (u Uint128) ones_count() int {
+	return bits.ones_count_64(u.hi) + bits.ones_count_64(u.lo)
+}
+
+// rotate_left returns the value of u rotated left by (k mod 128) bits.
+pub fn (u Uint128) rotate_left(k int) Uint128 {
+	n := u32(128)
+	s := u32(k) & (n - 1)
+	return u.lsh(s).or_(u.rsh(n - s))
+}
+
+// rotate_right returns the value of u rotated right by (k mod 128) bits.
+pub fn (u Uint128) rotate_right(k int) Uint128 {
+	return u.rotate_left(-k)
+}
+
+// reverse returns the value of u with its bits in reversed order.
+pub fn (u Uint128) reverse() Uint128 {
+	return Uint128{bits.reverse_64(u.hi), bits.reverse_64(u.lo)}
+}
+
+// reverse_bytes returns the value of u with its bytes in reversed order.
+pub fn (u Uint128) reverse_bytes() Uint128 {
+	return Uint128{bits.reverse_bytes_64(u.hi), bits.reverse_bytes_64(u.lo)}
+}
+
+pub fn (u Uint128) not() Uint128 {
+	return Uint128{~u.lo, ~u.hi}
+}
+
+// len returns the minimum number of bits required to represent u; the result is
+// 0 for u == 0.
+pub fn (u Uint128) len() int {
+	return 128 - u.leading_zeros()
+}
+
+// string returns the base-10 representation of u as a string
+pub fn (u_ Uint128) str() string {
+	mut u := u_
+	if u.is_zero() {
+		return '0'
+	}
+
+	mut buf := '0000000000000000000000000000000000000000'.bytes() // log10(2^128) < 40
+
+	for i := buf.len; true; i -= 19 {
+		q, mut r := u.quo_rem_64(u64(1e19))
+
+		mut n := int(0)
+		for ; r != 0; r /= 10 {
+			n++
+			buf[i - n] += byte(r % 10)
+		}
+		if q.is_zero() {
+			return buf[i - n..].bytestr()
+		}
+		u = q
+	}
+
+	return ''
+}
+
+// put_bytes stores u in b in little-endian order
+pub fn (u Uint128) put_bytes(mut b []byte) {
+	binary.little_endian_put_u64(mut b, u.lo)
+	binary.little_endian_put_u64(mut b, u.hi)
+}
+
+// uint128_from_64 converts v to a Uint128 value
+pub fn uint128_from_64(v u64) Uint128 {
+	return uint128_new(v, 0)
+}
+
+pub fn uint128_new(lo u64, hi u64) Uint128 {
+	return Uint128{lo, hi}
+}
+
+pub fn uint128_from_dec_str(value string) ?Uint128 {
+	mut res := uint.uint128_zero
+	for b_ in value.bytes() {
+		b := b_ - '0'.bytes()[0]
+		if b > 9 {
+			return error('invalid character "$b"')
+		}
+
+		r, overflow := res.overflowing_mul_64(10)
+
+		if overflow {
+			return error('invalid length')
+		}
+		r2, overflow2 := r.overflowing_add_64(u64(b))
+
+		if overflow2 > 0 {
+			return error('invalid length')
+		}
+
+		res = r2
+	}
+	return res
+}
+
+pub fn (u Uint128) / (v Uint128) Uint128 {
+	return u.div(v)
+}
+
+pub fn (u Uint128) % (v Uint128) Uint128 {
+	return u.mod(v)
+}
+
+pub fn (u Uint128) + (v Uint128) Uint128 {
+	return u.add(v)
+}
+
+pub fn (u Uint128) - (v Uint128) Uint128 {
+	return u.sub(v)
+}
+
+pub fn (u Uint128) * (v Uint128) Uint128 {
+	return u.mul(v)
+}

vlib/math/unsigned/uint256.v

@@ -0,0 +1,376 @@
+module uint
+
+import math.bits
+
+pub const (
+	uint256_zero = Uint256{Uint128{}, Uint128{}}
+	uint256_max  = Uint256{uint128_max, uint128_max}
+)
+
+// Uint256 is an unsigned 256-bit number
+pub struct Uint256 {
+pub mut:
+	lo Uint128 = uint128_zero // lower 128 bit half
+	hi Uint128 = uint128_zero // upper 128 bit half
+}
+
+pub fn uint256_from_128(v Uint128) Uint256 {
+	return Uint256{v, uint128_zero}
+}
+
+pub fn uint256_from_64(v u64) Uint256 {
+	return uint256_from_128(uint128_from_64(v))
+}
+
+pub fn (u Uint256) is_zero() bool {
+	return u.lo.is_zero() && u.hi.is_zero()
+}
+
+pub fn (u Uint256) equals(v Uint256) bool {
+	return u.lo.equals(v.lo) && u.hi.equals(v.hi)
+}
+
+pub fn (u Uint256) euqals_128(v Uint128) bool {
+	return u.lo.equals(v) && u.hi.is_zero()
+}
+
+pub fn (u Uint256) cmp(v Uint256) int {
+	h := u.hi.cmp(v.hi)
+	if h != 0 {
+		return h
+	}
+	return u.lo.cmp(v.lo)
+}
+
+pub fn (u Uint256) cmp_128(v Uint128) int {
+	if !u.hi.is_zero() {
+		return 1
+	}
+	return u.lo.cmp(v)
+}
+
+pub fn (u Uint256) not() Uint256 {
+	return Uint256{u.lo.not(), u.hi.not()}
+}
+
+pub fn (u Uint256) and(v Uint256) Uint256 {
+	return Uint256{u.lo.and(v.lo), u.hi.and(v.hi)}
+}
+
+pub fn (u Uint256) and_128(v Uint128) Uint256 {
+	return Uint256{u.lo.and(v), uint128_zero}
+}
+
+pub fn (u Uint256) or_(v Uint256) Uint256 {
+	return Uint256{u.lo.or_(v.lo), u.hi.or_(v.hi)}
+}
+
+pub fn (u Uint256) or_128(v Uint128) Uint256 {
+	return Uint256{u.lo.or_(v), u.hi}
+}
+
+pub fn (u Uint256) xor(v Uint256) Uint256 {
+	return Uint256{u.lo.xor(v.lo), u.hi.xor(v.hi)}
+}
+
+pub fn (u Uint256) xor_128(v Uint128) Uint256 {
+	return Uint256{u.lo.xor(v), u.hi}
+}
+
+pub fn add_256(x Uint256, y Uint256, carry u64) (Uint256, u64) {
+	mut sum := Uint256{}
+	mut carry_out := u64(0)
+	sum.lo, carry_out = add_128(x.lo, y.lo, carry)
+	sum.hi, carry_out = add_128(x.hi, y.hi, carry_out)
+	return sum, carry_out
+}
+
+pub fn sub_256(x Uint256, y Uint256, borrow u64) (Uint256, u64) {
+	mut diff := Uint256{}
+	mut borrow_out := u64(0)
+	diff.lo, borrow_out = sub_128(x.lo, y.lo, borrow)
+	diff.hi, borrow_out = sub_128(x.hi, y.hi, borrow_out)
+	return diff, borrow_out
+}
+
+pub fn mul_256(x Uint256, y Uint256) (Uint256, Uint256) {
+	mut hi := Uint256{}
+	mut lo := Uint256{}
+
+	lo.hi, lo.lo = mul_128(x.lo, y.lo)
+	hi.hi, hi.lo = mul_128(x.hi, y.hi)
+	t0, t1 := mul_128(x.lo, y.hi)
+	t2, t3 := mul_128(x.hi, y.lo)
+
+	mut c0 := u64(0)
+	mut c1 := u64(0)
+
+	lo.hi, c0 = add_128(lo.hi, t1, 0)
+	lo.hi, c1 = add_128(lo.hi, t3, 0)
+	hi.lo, c0 = add_128(hi.lo, t0, c0)
+	hi.lo, c1 = add_128(hi.lo, t2, c1)
+	hi.hi = hi.hi.add_64(c0 + c1)
+
+	return hi, lo
+}
+
+pub fn (u Uint256) add(v Uint256) Uint256 {
+	sum, _ := add_256(u, v, 0)
+	return sum
+}
+
+pub fn (u Uint256) overflowing_add(v Uint256) (Uint256, u64) {
+	sum, overflow := add_256(u, v, 0)
+	return sum, overflow
+}
+
+pub fn (u Uint256) add_128(v Uint128) Uint256 {
+	lo, c0 := add_128(u.lo, v, 0)
+	return Uint256{lo, u.hi.add_64(c0)}
+}
+
+pub fn (u Uint256) sub(v Uint256) Uint256 {
+	diff, _ := sub_256(u, v, 0)
+	return diff
+}
+
+pub fn (u Uint256) sub_128(v Uint128) Uint256 {
+	lo, b0 := sub_128(u.lo, v, 0)
+	return Uint256{lo, u.hi.sub_64(b0)}
+}
+
+pub fn (u Uint256) mul(v Uint256) Uint256 {
+	mut hi, mut lo := mul_128(u.lo, v.lo)
+	hi = hi.add(u.hi.mul(v.lo))
+	hi = hi.add(u.lo.mul(v.hi))
+	return Uint256{lo, hi}
+}
+
+pub fn (u Uint256) mul_128(v Uint128) Uint256 {
+	hi, lo := mul_128(u.lo, v)
+	return Uint256{lo, hi.add(u.hi.mul(v))}
+}
+
+pub fn (u Uint256) quo_rem(v Uint256) (Uint256, Uint256) {
+	if v.hi.is_zero() {
+		q, r := u.quo_rem_128(v.lo)
+		return q, uint256_from_128(r)
+	}
+
+	n := u64(v.hi.leading_zeros())
+	u1, v1 := u.rsh(1), v.lsh(u32(n))
+	mut tq, _ := div_128(u1.hi, u1.lo, v1.hi)
+	tq = tq.rsh(u32(127 - n))
+	if !tq.is_zero() {
+		tq = tq.sub_64(1)
+	}
+
+	mut q, mut r := uint256_from_128(tq), u.sub(v.mul_128(tq))
+	if r.cmp(v) >= 0 {
+		q = q.add_128(Uint128{1, 0})
+		r = r.sub(v)
+	}
+	return q, r
+}
+
+pub fn (u Uint256) quo_rem_128(v Uint128) (Uint256, Uint128) {
+	if u.hi.cmp(v) < 0 {
+		lo, r := div_128(u.hi, u.lo, v)
+		return Uint256{lo, uint128_zero}, r
+	}
+
+	hi, r := div_128(uint128_zero, u.hi, v)
+	lo, r2 := div_128(r, u.lo, v)
+	return Uint256{lo, hi}, r2
+}
+
+pub fn (u Uint256) quo_rem_64(v u64) (Uint256, u64) {
+	mut q := Uint256{}
+	mut r := u64(0)
+	q.lo.hi, r = bits.div_64(r, u.lo.hi, v)
+	q.lo.lo, r = bits.div_64(r, u.lo.lo, v)
+	return q, r
+}
+
+pub fn (u Uint256) rsh(n_ u32) Uint256 {
+	mut n := n_
+	if n > 128 {
+		return Uint256{u.hi.rsh(n - 128), uint128_zero}
+	}
+
+	if n > 64 {
+		n -= 64
+		return Uint256{Uint128{u.lo.hi >> n | u.hi.lo << (64 - n), u.hi.lo >> n | u.hi.hi << (64 - n)}, Uint128{u.hi.hi >> n, 0}}
+	}
+	return Uint256{Uint128{u.lo.lo >> n | u.lo.hi << (64 - n), u.lo.hi >> n | u.hi.lo << (64 - n)}, Uint128{u.hi.lo >> n | u.hi.hi << (64 - n), u.hi.hi >> n}}
+}
+
+pub fn (u Uint256) lsh(n_ u32) Uint256 {
+	mut n := n_
+	if n > 128 {
+		return Uint256{u.lo.lsh(n - 128), uint128_zero}
+	}
+
+	if n > 64 {
+		n -= 64
+		return Uint256{Uint128{u.lo.lo << n, 0}, Uint128{u.lo.hi << n | u.lo.lo >> (64 - n), u.hi.lo << n | u.lo.hi >> (64 - n)}}
+	}
+
+	return Uint256{Uint128{u.lo.lo << n, u.lo.hi << n | u.lo.lo >> (64 - n)}, Uint128{u.hi.lo << n | u.lo.hi >> (64 - n), u.hi.hi << n | u.hi.lo >> (64 - n)}}
+}
+
+pub fn (u Uint256) div(v Uint256) Uint256 {
+	q, _ := u.quo_rem(v)
+	return q
+}
+
+pub fn (u Uint256) div_128(v Uint128) Uint256 {
+	q, _ := u.quo_rem_128(v)
+	return q
+}
+
+pub fn (u Uint256) div_64(v u64) Uint256 {
+	q, _ := u.quo_rem_64(v)
+	return q
+}
+
+pub fn (u Uint256) mod(v Uint256) Uint256 {
+	_, r := u.quo_rem(v)
+	return r
+}
+
+pub fn (u Uint256) mod_128(v Uint128) Uint128 {
+	_, r := u.quo_rem_128(v)
+	return r
+}
+
+pub fn (u Uint256) mod_64(v u64) u64 {
+	_, r := u.quo_rem_64(v)
+	return r
+}
+
+pub fn (u Uint256) rotate_left(k int) Uint256 {
+	mut n := u32(k) & 255
+	if n < 64 {
+		if n == 0 {
+			return u
+		}
+
+		return Uint256{Uint128{u.lo.lo << n | u.hi.hi >> (64 - n), u.lo.hi << n | u.lo.lo >> (64 - n)}, Uint128{u.hi.lo << n | u.lo.hi >> (64 - n), u.hi.hi << n | u.hi.lo >> (64 - n)}}
+	}
+	n -= 64
+	if n < 64 {
+		if n == 0 {
+			return Uint256{Uint128{u.hi.hi, u.lo.lo}, Uint128{u.lo.hi, u.hi.lo}}
+		}
+
+		return Uint256{Uint128{u.hi.hi << n | u.hi.lo >> (64 - n), u.lo.lo << n | u.hi.hi >> (64 - n)}, Uint128{u.lo.hi << n | u.lo.lo >> (64 - n), u.hi.lo << n | u.lo.hi >> (64 - n)}}
+	}
+
+	n -= 64
+	if n < 64 {
+		if n == 0 {
+			return Uint256{u.hi, u.lo}
+		}
+
+		return Uint256{Uint128{u.hi.lo << n | u.lo.hi >> (64 - n), u.hi.hi << n | u.hi.lo >> (64 - n)}, Uint128{}}
+	}
+	n -= 64
+	if n == 0 {
+		return Uint256{Uint128{u.lo.hi, u.hi.lo}, Uint128{u.hi.hi, u.lo.lo}}
+	}
+
+	return Uint256{Uint128{u.lo.hi << n | u.lo.lo >> (64 - n), u.hi.lo << n | u.lo.hi >> (64 - n)}, Uint128{u.hi.hi << n | u.hi.lo >> (64 - n), u.lo.lo << n | u.hi.hi >> (64 - n)}}
+}
+
+pub fn (u Uint256) rotate_right(k int) Uint256 {
+	return u.rotate_left(-k)
+}
+
+pub fn (u Uint256) len() int {
+	if !u.hi.is_zero() {
+		return 128 + u.hi.len()
+	}
+	return u.lo.len()
+}
+
+pub fn (u Uint256) leading_zeros() int {
+	if !u.hi.is_zero() {
+		return u.hi.leading_zeros()
+	}
+	return 128 + u.lo.leading_zeros()
+}
+
+pub fn (u Uint256) trailing_zeros() int {
+	if !u.lo.is_zero() {
+		return u.lo.trailing_zeros()
+	}
+
+	return 128 + u.hi.trailing_zeros()
+}
+
+pub fn (u Uint256) ones_count() int {
+	return u.lo.ones_count() + u.hi.ones_count()
+}
+
+pub fn (u_ Uint256) str() string {
+	mut u := u_
+	if u.hi.is_zero() {
+		if u.lo.is_zero() {
+			return '0'
+		}
+		return u.lo.str()
+	}
+
+	mut buf := '000000000000000000000000000000000000000000000000000000000000000000000000000000'.bytes()
+
+	for i := buf.len; true; i -= 19 {
+		q, mut r := u.quo_rem_64(u64(1e19))
+		mut n := 0
+		for ; r != 0; r /= 10 {
+			n++
+			buf[i - n] += byte(r % 10)
+		}
+		if q.is_zero() {
+			return buf[i - n..].bytestr()
+		}
+		u = q
+	}
+	return ''
+}
+
+pub fn uint256_from_dec_str(value string) ?Uint256 {
+	mut res := uint.uint256_zero
+	for b_ in value.bytes() {
+		b := b_ - '0'.bytes()[0]
+		if b > 9 {
+			return error('invalid character "$b"')
+		}
+
+		r := res.mul_128(uint128_from_64(10))
+
+		r2 := r.add_128(uint128_from_64(u64(b)))
+		res = r2
+	}
+	return res
+}
+
+pub fn (u Uint256) / (v Uint256) Uint256 {
+	return u.div(v)
+}
+
+pub fn (u Uint256) % (v Uint256) Uint256 {
+	return u.mod(v)
+}
+
+pub fn (u Uint256) + (v Uint256) Uint256 {
+	return u.add(v)
+}
+
+pub fn (u Uint256) - (v Uint256) Uint256 {
+	return u.sub(v)
+}
+
+pub fn (u Uint256) * (v Uint256) Uint256 {
+	return u.mul(v)
+}