gtsocial-umbx

uint128.go (10108B)

---

 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
 }