v/vlib/math/unsigned/uint128.v

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2022-01-17 10:35:02 +01:00
module unsigned
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
}
// rsh 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++
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buf[i - n] += u8(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 {
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mut res := unsigned.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)
}
pub fn (u Uint128) < (v Uint128) bool {
return u.cmp(v) == -1
}