1 files changed, 417 insertions, 0 deletions
diff --git a/vendor/lukechampine.com/uint128/uint128.go b/vendor/lukechampine.com/uint128/uint128.go
new file mode 100644
index 00000000..0b74b9fc
--- /dev/null
+++ b/vendor/lukechampine.com/uint128/uint128.go
@@ -0,0 +1,417 @@
+package uint128 // import "lukechampine.com/uint128"
+
+import (
+	"encoding/binary"
+	"math"
+	"math/big"
+	"math/bits"
+)
+
+// Zero is a zero-valued uint128.
+var Zero Uint128
+
+// Max is the largest possible uint128 value.
+var Max = New(math.MaxUint64, math.MaxUint64)
+
+// A Uint128 is an unsigned 128-bit number.
+type Uint128 struct {
+	Lo, Hi uint64
+}
+
+// IsZero returns true if u == 0.
+func (u Uint128) IsZero() bool {
+	// NOTE: we do not compare against Zero, because that is a global variable
+	// that could be modified.
+	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.
+func (u Uint128) Equals(v Uint128) bool {
+	return u == v
+}
+
+// Equals64 returns true if u == v.
+func (u Uint128) Equals64(v uint64) 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
+//
+func (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
+	}
+}
+
+// Cmp64 compares u and v and returns:
+//
+//   -1 if u <  v
+//    0 if u == v
+//   +1 if u >  v
+//
+func (u Uint128) Cmp64(v uint64) 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.
+func (u Uint128) And(v Uint128) Uint128 {
+	return Uint128{u.Lo & v.Lo, u.Hi & v.Hi}
+}
+
+// And64 returns u&v.
+func (u Uint128) And64(v uint64) Uint128 {
+	return Uint128{u.Lo & v, u.Hi & 0}
+}
+
+// Or returns u|v.
+func (u Uint128) Or(v Uint128) Uint128 {
+	return Uint128{u.Lo | v.Lo, u.Hi | v.Hi}
+}
+
+// Or64 returns u|v.
+func (u Uint128) Or64(v uint64) Uint128 {
+	return Uint128{u.Lo | v, u.Hi | 0}
+}
+
+// Xor returns u^v.
+func (u Uint128) Xor(v Uint128) Uint128 {
+	return Uint128{u.Lo ^ v.Lo, u.Hi ^ v.Hi}
+}
+
+// Xor64 returns u^v.
+func (u Uint128) Xor64(v uint64) Uint128 {
+	return Uint128{u.Lo ^ v, u.Hi ^ 0}
+}
+
+// Add returns u+v.
+func (u Uint128) Add(v Uint128) Uint128 {
+	lo, carry := bits.Add64(u.Lo, v.Lo, 0)
+	hi, carry := bits.Add64(u.Hi, v.Hi, carry)
+	if carry != 0 {
+		panic("overflow")
+	}
+	return Uint128{lo, hi}
+}
+
+// AddWrap returns u+v with wraparound semantics; for example,
+// Max.AddWrap(From64(1)) == Zero.
+func (u Uint128) AddWrap(v Uint128) Uint128 {
+	lo, carry := bits.Add64(u.Lo, v.Lo, 0)
+	hi, _ := bits.Add64(u.Hi, v.Hi, carry)
+	return Uint128{lo, hi}
+}
+
+// Add64 returns u+v.
+func (u Uint128) Add64(v uint64) Uint128 {
+	lo, carry := bits.Add64(u.Lo, v, 0)
+	hi, carry := bits.Add64(u.Hi, 0, carry)
+	if carry != 0 {
+		panic("overflow")
+	}
+	return Uint128{lo, hi}
+}
+
+// AddWrap64 returns u+v with wraparound semantics; for example,
+// Max.AddWrap64(1) == Zero.
+func (u Uint128) AddWrap64(v uint64) Uint128 {
+	lo, carry := bits.Add64(u.Lo, v, 0)
+	hi := u.Hi + carry
+	return Uint128{lo, hi}
+}
+
+// Sub returns u-v.
+func (u Uint128) Sub(v Uint128) Uint128 {
+	lo, borrow := bits.Sub64(u.Lo, v.Lo, 0)
+	hi, borrow := bits.Sub64(u.Hi, v.Hi, borrow)
+	if borrow != 0 {
+		panic("underflow")
+	}
+	return Uint128{lo, hi}
+}
+
+// SubWrap returns u-v with wraparound semantics; for example,
+// Zero.SubWrap(From64(1)) == Max.
+func (u Uint128) SubWrap(v Uint128) Uint128 {
+	lo, borrow := bits.Sub64(u.Lo, v.Lo, 0)
+	hi, _ := bits.Sub64(u.Hi, v.Hi, borrow)
+	return Uint128{lo, hi}
+}
+
+// Sub64 returns u-v.
+func (u Uint128) Sub64(v uint64) Uint128 {
+	lo, borrow := bits.Sub64(u.Lo, v, 0)
+	hi, borrow := bits.Sub64(u.Hi, 0, borrow)
+	if borrow != 0 {
+		panic("underflow")
+	}
+	return Uint128{lo, hi}
+}
+
+// SubWrap64 returns u-v with wraparound semantics; for example,
+// Zero.SubWrap64(1) == Max.
+func (u Uint128) SubWrap64(v uint64) Uint128 {
+	lo, borrow := bits.Sub64(u.Lo, v, 0)
+	hi := u.Hi - borrow
+	return Uint128{lo, hi}
+}
+
+// Mul returns u*v, panicking on overflow.
+func (u Uint128) Mul(v Uint128) Uint128 {
+	hi, lo := bits.Mul64(u.Lo, v.Lo)
+	p0, p1 := bits.Mul64(u.Hi, v.Lo)
+	p2, p3 := bits.Mul64(u.Lo, v.Hi)
+	hi, c0 := bits.Add64(hi, p1, 0)
+	hi, c1 := bits.Add64(hi, p3, c0)
+	if (u.Hi != 0 && v.Hi != 0) || p0 != 0 || p2 != 0 || c1 != 0 {
+		panic("overflow")
+	}
+	return Uint128{lo, hi}
+}
+
+// MulWrap returns u*v with wraparound semantics; for example,
+// Max.MulWrap(Max) == 1.
+func (u Uint128) MulWrap(v Uint128) Uint128 {
+	hi, lo := bits.Mul64(u.Lo, v.Lo)
+	hi += u.Hi*v.Lo + u.Lo*v.Hi
+	return Uint128{lo, hi}
+}
+
+// Mul64 returns u*v, panicking on overflow.
+func (u Uint128) Mul64(v uint64) Uint128 {
+	hi, lo := bits.Mul64(u.Lo, v)
+	p0, p1 := bits.Mul64(u.Hi, v)
+	hi, c0 := bits.Add64(hi, p1, 0)
+	if p0 != 0 || c0 != 0 {
+		panic("overflow")
+	}
+	return Uint128{lo, hi}
+}
+
+// MulWrap64 returns u*v with wraparound semantics; for example,
+// Max.MulWrap64(2) == Max.Sub64(1).
+func (u Uint128) MulWrap64(v uint64) Uint128 {
+	hi, lo := bits.Mul64(u.Lo, v)
+	hi += u.Hi * v
+	return Uint128{lo, hi}
+}
+
+// Div returns u/v.
+func (u Uint128) Div(v Uint128) Uint128 {
+	q, _ := u.QuoRem(v)
+	return q
+}
+
+// Div64 returns u/v.
+func (u Uint128) Div64(v uint64) Uint128 {
+	q, _ := u.QuoRem64(v)
+	return q
+}
+
+// QuoRem returns q = u/v and r = u%v.
+func (u Uint128) QuoRem(v Uint128) (q, r Uint128) {
+	if v.Hi == 0 {
+		var r64 uint64
+		q, r64 = u.QuoRem64(v.Lo)
+		r = From64(r64)
+	} else {
+		// generate a "trial quotient," guaranteed to be within 1 of the actual
+		// quotient, then adjust.
+		n := uint(bits.LeadingZeros64(v.Hi))
+		v1 := v.Lsh(n)
+		u1 := u.Rsh(1)
+		tq, _ := bits.Div64(u1.Hi, u1.Lo, v1.Hi)
+		tq >>= 63 - n
+		if tq != 0 {
+			tq--
+		}
+		q = From64(tq)
+		// calculate remainder using trial quotient, then adjust if remainder is
+		// greater than divisor
+		r = u.Sub(v.Mul64(tq))
+		if r.Cmp(v) >= 0 {
+			q = q.Add64(1)
+			r = r.Sub(v)
+		}
+	}
+	return
+}
+
+// QuoRem64 returns q = u/v and r = u%v.
+func (u Uint128) QuoRem64(v uint64) (q Uint128, r uint64) {
+	if u.Hi < v {
+		q.Lo, r = bits.Div64(u.Hi, u.Lo, v)
+	} else {
+		q.Hi, r = bits.Div64(0, u.Hi, v)
+		q.Lo, r = bits.Div64(r, u.Lo, v)
+	}
+	return
+}
+
+// Mod returns r = u%v.
+func (u Uint128) Mod(v Uint128) (r Uint128) {
+	_, r = u.QuoRem(v)
+	return
+}
+
+// Mod64 returns r = u%v.
+func (u Uint128) Mod64(v uint64) (r uint64) {
+	_, r = u.QuoRem64(v)
+	return
+}
+
+// Lsh returns u<<n.
+func (u Uint128) Lsh(n uint) (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
+}
+
+// Rsh returns u>>n.
+func (u Uint128) Rsh(n uint) (s Uint128) {
+	if n > 64 {
+		s.Lo = u.Hi >> (n - 64)
+		s.Hi = 0
+	} else {
+		s.Lo = u.Lo>>n | u.Hi<<(64-n)
+		s.Hi = u.Hi >> n
+	}
+	return
+}
+
+// LeadingZeros returns the number of leading zero bits in u; the result is 128
+// for u == 0.
+func (u Uint128) LeadingZeros() int {
+	if u.Hi > 0 {
+		return bits.LeadingZeros64(u.Hi)
+	}
+	return 64 + bits.LeadingZeros64(u.Lo)
+}
+
+// TrailingZeros returns the number of trailing zero bits in u; the result is
+// 128 for u == 0.
+func (u Uint128) TrailingZeros() int {
+	if u.Lo > 0 {
+		return bits.TrailingZeros64(u.Lo)
+	}
+	return 64 + bits.TrailingZeros64(u.Hi)
+}
+
+// OnesCount returns the number of one bits ("population count") in u.
+func (u Uint128) OnesCount() int {
+	return bits.OnesCount64(u.Hi) + bits.OnesCount64(u.Lo)
+}
+
+// RotateLeft returns the value of u rotated left by (k mod 128) bits.
+func (u Uint128) RotateLeft(k int) Uint128 {
+	const n = 128
+	s := uint(k) & (n - 1)
+	return u.Lsh(s).Or(u.Rsh(n - s))
+}
+
+// RotateRight returns the value of u rotated left by (k mod 128) bits.
+func (u Uint128) RotateRight(k int) Uint128 {
+	return u.RotateLeft(-k)
+}
+
+// Reverse returns the value of u with its bits in reversed order.
+func (u Uint128) Reverse() Uint128 {
+	return Uint128{bits.Reverse64(u.Hi), bits.Reverse64(u.Lo)}
+}
+
+// ReverseBytes returns the value of u with its bytes in reversed order.
+func (u Uint128) ReverseBytes() Uint128 {
+	return Uint128{bits.ReverseBytes64(u.Hi), bits.ReverseBytes64(u.Lo)}
+}
+
+// Len returns the minimum number of bits required to represent u; the result is
+// 0 for u == 0.
+func (u Uint128) Len() int {
+	return 128 - u.LeadingZeros()
+}
+
+// String returns the base-10 representation of u as a string.
+func (u Uint128) String() string {
+	if u.IsZero() {
+		return "0"
+	}
+	buf := []byte("0000000000000000000000000000000000000000") // log10(2^128) < 40
+	for i := len(buf); ; i -= 19 {
+		q, r := u.QuoRem64(1e19) // largest power of 10 that fits in a uint64
+		var n int
+		for ; r != 0; r /= 10 {
+			n++
+			buf[i-n] += byte(r % 10)
+		}
+		if q.IsZero() {
+			return string(buf[i-n:])
+		}
+		u = q
+	}
+}
+
+// PutBytes stores u in b in little-endian order. It panics if len(b) < 16.
+func (u Uint128) PutBytes(b []byte) {
+	binary.LittleEndian.PutUint64(b[:8], u.Lo)
+	binary.LittleEndian.PutUint64(b[8:], u.Hi)
+}
+
+// Big returns u as a *big.Int.
+func (u Uint128) Big() *big.Int {
+	i := new(big.Int).SetUint64(u.Hi)
+	i = i.Lsh(i, 64)
+	i = i.Xor(i, new(big.Int).SetUint64(u.Lo))
+	return i
+}
+
+// New returns the Uint128 value (lo,hi).
+func New(lo, hi uint64) Uint128 {
+	return Uint128{lo, hi}
+}
+
+// From64 converts v to a Uint128 value.
+func From64(v uint64) Uint128 {
+	return New(v, 0)
+}
+
+// FromBytes converts b to a Uint128 value.
+func FromBytes(b []byte) Uint128 {
+	return New(
+		binary.LittleEndian.Uint64(b[:8]),
+		binary.LittleEndian.Uint64(b[8:]),
+	)
+}
+
+// FromBig converts i to a Uint128 value. It panics if i is negative or
+// overflows 128 bits.
+func FromBig(i *big.Int) (u Uint128) {
+	if i.Sign() < 0 {
+		panic("value cannot be negative")
+	} else if i.BitLen() > 128 {
+		panic("value overflows Uint128")
+	}
+	u.Lo = i.Uint64()
+	u.Hi = new(big.Int).Rsh(i, 64).Uint64()
+	return u
+}