source: code/trunk/vendor/lukechampine.com/uint128/uint128.go@ 822

package uint128 // import "lukechampine.com/uint128"

import (
        "encoding/binary"
        "errors"
        "fmt"
        "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
}

// Scan implements fmt.Scanner.
func (u *Uint128) Scan(s fmt.ScanState, ch rune) error {
        i := new(big.Int)
        if err := i.Scan(s, ch); err != nil {
                return err
        } else if i.Sign() < 0 {
                return errors.New("value cannot be negative")
        } else if i.BitLen() > 128 {
                return errors.New("value overflows Uint128")
        }
        u.Lo = i.Uint64()
        u.Hi = i.Rsh(i, 64).Uint64()
        return nil
}

// 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 = i.Rsh(i, 64).Uint64()
        return u
}

// FromString parses s as a Uint128 value.
func FromString(s string) (u Uint128, err error) {
        _, err = fmt.Sscan(s, &u)
        return
}