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envoid/vendor/modernc.org/mathutil/mathutil.go

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Initial commit Signed-off-by: Sagi Dayan <sagidayan@gmail.com>
2024-11-22 15:29:25 +00:00
// Copyright (c) 2014 The mathutil Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// Package mathutil provides utilities supplementing the standard 'math' and
// 'math/rand' packages.
//
// Release history and compatibility issues
//
// 2020-12-20 v1.2.1 fixes MulOverflowInt64.
//
// 2020-12-19 Added {Add,Sub,Mul}OverflowInt{8,16,32,64}
//
// 2018-10-21 Added BinaryLog
//
// 2018-04-25: New functions for determining Max/Min of nullable values. Ex:
// func MaxPtr(a, b *int) *int {
// func MinPtr(a, b *int) *int {
// func MaxBytePtr(a, b *byte) *byte {
// func MinBytePtr(a, b *byte) *byte {
// ...
//
// 2017-10-14: New variadic functions for Max/Min. Ex:
// func MaxVal(val int, vals ...int) int {
// func MinVal(val int, vals ...int) int {
// func MaxByteVal(val byte, vals ...byte) byte {
// func MinByteVal(val byte, vals ...byte) byte {
// ...
//
// 2016-10-10: New functions QuadPolyDiscriminant and QuadPolyFactors.
//
// 2013-12-13: The following functions have been REMOVED
//
// func Uint64ToBigInt(n uint64) *big.Int
// func Uint64FromBigInt(n *big.Int) (uint64, bool)
//
// 2013-05-13: The following functions are now DEPRECATED
//
// func Uint64ToBigInt(n uint64) *big.Int
// func Uint64FromBigInt(n *big.Int) (uint64, bool)
//
// These functions will be REMOVED with Go release 1.1+1.
//
// 2013-01-21: The following functions have been REMOVED
//
// func MaxInt() int
// func MinInt() int
// func MaxUint() uint
// func UintPtrBits() int
//
// They are now replaced by untyped constants
//
// MaxInt
// MinInt
// MaxUint
// UintPtrBits
//
// Additionally one more untyped constant was added
//
// IntBits
//
// This change breaks any existing code depending on the above removed
// functions. They should have not been published in the first place, that was
// unfortunate. Instead, defining such architecture and/or implementation
// specific integer limits and bit widths as untyped constants improves
// performance and allows for static dead code elimination if it depends on
// these values. Thanks to minux for pointing it out in the mail list
// (https://groups.google.com/d/msg/golang-nuts/tlPpLW6aJw8/NT3mpToH-a4J).
//
// 2012-12-12: The following functions will be DEPRECATED with Go release
// 1.0.3+1 and REMOVED with Go release 1.0.3+2, b/c of
// http://code.google.com/p/go/source/detail?r=954a79ee3ea8
//
// func Uint64ToBigInt(n uint64) *big.Int
// func Uint64FromBigInt(n *big.Int) (uint64, bool)
package mathutil // import "modernc.org/mathutil"
import (
"math"
"math/big"
)
// Architecture and/or implementation specific integer limits and bit widths.
const (
MaxInt = 1<<(IntBits-1) - 1
MinInt = -MaxInt - 1
MaxUint = 1<<IntBits - 1
IntBits = 1 << (^uint(0)>>32&1 + ^uint(0)>>16&1 + ^uint(0)>>8&1 + 3)
UintPtrBits = 1 << (^uintptr(0)>>32&1 + ^uintptr(0)>>16&1 + ^uintptr(0)>>8&1 + 3)
)
var (
_1 = big.NewInt(1)
_2 = big.NewInt(2)
)
// GCDByte returns the greatest common divisor of a and b. Based on:
// http://en.wikipedia.org/wiki/Euclidean_algorithm#Implementations
func GCDByte(a, b byte) byte {
for b != 0 {
a, b = b, a%b
}
return a
}
// GCDUint16 returns the greatest common divisor of a and b.
func GCDUint16(a, b uint16) uint16 {
for b != 0 {
a, b = b, a%b
}
return a
}
// GCDUint32 returns the greatest common divisor of a and b.
func GCDUint32(a, b uint32) uint32 {
for b != 0 {
a, b = b, a%b
}
return a
}
// GCDUint64 returns the greatest common divisor of a and b.
func GCDUint64(a, b uint64) uint64 {
for b != 0 {
a, b = b, a%b
}
return a
}
// ISqrt returns floor(sqrt(n)). Typical run time is few hundreds of ns.
func ISqrt(n uint32) (x uint32) {
if n == 0 {
return
}
if n >= math.MaxUint16*math.MaxUint16 {
return math.MaxUint16
}
var px, nx uint32
for x = n; ; px, x = x, nx {
nx = (x + n/x) / 2
if nx == x || nx == px {
break
}
}
return
}
// SqrtUint64 returns floor(sqrt(n)). Typical run time is about 0.5 µs.
func SqrtUint64(n uint64) (x uint64) {
if n == 0 {
return
}
if n >= math.MaxUint32*math.MaxUint32 {
return math.MaxUint32
}
var px, nx uint64
for x = n; ; px, x = x, nx {
nx = (x + n/x) / 2
if nx == x || nx == px {
break
}
}
return
}
// SqrtBig returns floor(sqrt(n)). It panics on n < 0.
func SqrtBig(n *big.Int) (x *big.Int) {
switch n.Sign() {
case -1:
panic(-1)
case 0:
return big.NewInt(0)
}
var px, nx big.Int
x = big.NewInt(0)
x.SetBit(x, n.BitLen()/2+1, 1)
for {
nx.Rsh(nx.Add(x, nx.Div(n, x)), 1)
if nx.Cmp(x) == 0 || nx.Cmp(&px) == 0 {
break
}
px.Set(x)
x.Set(&nx)
}
return
}
// Log2Byte returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Byte(n byte) int {
return log2[n]
}
// Log2Uint16 returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Uint16(n uint16) int {
if b := n >> 8; b != 0 {
return log2[b] + 8
}
return log2[n]
}
// Log2Uint32 returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Uint32(n uint32) int {
if b := n >> 24; b != 0 {
return log2[b] + 24
}
if b := n >> 16; b != 0 {
return log2[b] + 16
}
if b := n >> 8; b != 0 {
return log2[b] + 8
}
return log2[n]
}
// Log2Uint64 returns log base 2 of n. It's the same as index of the highest
// bit set in n. For n == 0 -1 is returned.
func Log2Uint64(n uint64) int {
if b := n >> 56; b != 0 {
return log2[b] + 56
}
if b := n >> 48; b != 0 {
return log2[b] + 48
}
if b := n >> 40; b != 0 {
return log2[b] + 40
}
if b := n >> 32; b != 0 {
return log2[b] + 32
}
if b := n >> 24; b != 0 {
return log2[b] + 24
}
if b := n >> 16; b != 0 {
return log2[b] + 16
}
if b := n >> 8; b != 0 {
return log2[b] + 8
}
return log2[n]
}
// ModPowByte computes (b^e)%m. It panics for m == 0 || b == e == 0.
//
// See also: http://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method
func ModPowByte(b, e, m byte) byte {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
r := uint16(1)
for b, m := uint16(b), uint16(m); e > 0; b, e = b*b%m, e>>1 {
if e&1 == 1 {
r = r * b % m
}
}
return byte(r)
}
// ModPowUint16 computes (b^e)%m. It panics for m == 0 || b == e == 0.
func ModPowUint16(b, e, m uint16) uint16 {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
r := uint32(1)
for b, m := uint32(b), uint32(m); e > 0; b, e = b*b%m, e>>1 {
if e&1 == 1 {
r = r * b % m
}
}
return uint16(r)
}
// ModPowUint32 computes (b^e)%m. It panics for m == 0 || b == e == 0.
func ModPowUint32(b, e, m uint32) uint32 {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
r := uint64(1)
for b, m := uint64(b), uint64(m); e > 0; b, e = b*b%m, e>>1 {
if e&1 == 1 {
r = r * b % m
}
}
return uint32(r)
}
// ModPowUint64 computes (b^e)%m. It panics for m == 0 || b == e == 0.
func ModPowUint64(b, e, m uint64) (r uint64) {
if b == 0 && e == 0 {
panic(0)
}
if m == 1 {
return 0
}
return modPowBigInt(big.NewInt(0).SetUint64(b), big.NewInt(0).SetUint64(e), big.NewInt(0).SetUint64(m)).Uint64()
}
func modPowBigInt(b, e, m *big.Int) (r *big.Int) {
r = big.NewInt(1)
for i, n := 0, e.BitLen(); i < n; i++ {
if e.Bit(i) != 0 {
r.Mod(r.Mul(r, b), m)
}
b.Mod(b.Mul(b, b), m)
}
return
}
// ModPowBigInt computes (b^e)%m. Returns nil for e < 0. It panics for m == 0 || b == e == 0.
func ModPowBigInt(b, e, m *big.Int) (r *big.Int) {
if b.Sign() == 0 && e.Sign() == 0 {
panic(0)
}
if m.Cmp(_1) == 0 {
return big.NewInt(0)
}
if e.Sign() < 0 {
return
}
return modPowBigInt(big.NewInt(0).Set(b), big.NewInt(0).Set(e), m)
}
var uint64ToBigIntDelta big.Int
func init() {
uint64ToBigIntDelta.SetBit(&uint64ToBigIntDelta, 63, 1)
}
var uintptrBits int
func init() {
x := uint64(math.MaxUint64)
uintptrBits = BitLenUintptr(uintptr(x))
}
// UintptrBits returns the bit width of an uintptr at the executing machine.
func UintptrBits() int {
return uintptrBits
}
// AddUint128_64 returns the uint128 sum of uint64 a and b.
func AddUint128_64(a, b uint64) (hi uint64, lo uint64) {
lo = a + b
if lo < a {
hi = 1
}
return hi, lo
}
// MulUint128_64 returns the uint128 bit product of uint64 a and b.
func MulUint128_64(a, b uint64) (hi, lo uint64) {
/*
2^(2 W) ahi bhi + 2^W alo bhi + 2^W ahi blo + alo blo
FEDCBA98 76543210 FEDCBA98 76543210
---- alo*blo ----
---- alo*bhi ----
---- ahi*blo ----
---- ahi*bhi ----
*/
const w = 32
const m = 1<<w - 1
ahi, bhi, alo, blo := a>>w, b>>w, a&m, b&m
lo = alo * blo
mid1 := alo * bhi
mid2 := ahi * blo
c1, lo := AddUint128_64(lo, mid1<<w)
c2, lo := AddUint128_64(lo, mid2<<w)
_, hi = AddUint128_64(ahi*bhi, mid1>>w+mid2>>w+c1+c2)
return
}
// PowerizeBigInt returns (e, p) such that e is the smallest number for which p
// == b^e is greater or equal n. For n < 0 or b < 2 (0, nil) is returned.
//
// NOTE: Run time for large values of n (above about 2^1e6 ~= 1e300000) can be
// significant and/or unacceptabe. For any smaller values of n the function
// typically performs in sub second time. For "small" values of n (cca bellow
// 2^1e3 ~= 1e300) the same can be easily below 10 µs.
//
// A special (and trivial) case of b == 2 is handled separately and performs
// much faster.
func PowerizeBigInt(b, n *big.Int) (e uint32, p *big.Int) {
switch {
case b.Cmp(_2) < 0 || n.Sign() < 0:
return
case n.Sign() == 0 || n.Cmp(_1) == 0:
return 0, big.NewInt(1)
case b.Cmp(_2) == 0:
p = big.NewInt(0)
e = uint32(n.BitLen() - 1)
p.SetBit(p, int(e), 1)
if p.Cmp(n) < 0 {
p.Mul(p, _2)
e++
}
return
}
bw := b.BitLen()
nw := n.BitLen()
p = big.NewInt(1)
var bb, r big.Int
for {
switch p.Cmp(n) {
case -1:
x := uint32((nw - p.BitLen()) / bw)
if x == 0 {
x = 1
}
e += x
switch x {
case 1:
p.Mul(p, b)
default:
r.Set(_1)
bb.Set(b)
e := x
for {
if e&1 != 0 {
r.Mul(&r, &bb)
}
if e >>= 1; e == 0 {
break
}
bb.Mul(&bb, &bb)
}
p.Mul(p, &r)
}
case 0, 1:
return
}
}
}
// PowerizeUint32BigInt returns (e, p) such that e is the smallest number for
// which p == b^e is greater or equal n. For n < 0 or b < 2 (0, nil) is
// returned.
//
// More info: see PowerizeBigInt.
func PowerizeUint32BigInt(b uint32, n *big.Int) (e uint32, p *big.Int) {
switch {
case b < 2 || n.Sign() < 0:
return
case n.Sign() == 0 || n.Cmp(_1) == 0:
return 0, big.NewInt(1)
case b == 2:
p = big.NewInt(0)
e = uint32(n.BitLen() - 1)
p.SetBit(p, int(e), 1)
if p.Cmp(n) < 0 {
p.Mul(p, _2)
e++
}
return
}
var bb big.Int
bb.SetInt64(int64(b))
return PowerizeBigInt(&bb, n)
}
/*
ProbablyPrimeUint32 returns true if n is prime or n is a pseudoprime to base a.
It implements the Miller-Rabin primality test for one specific value of 'a' and
k == 1.
Wrt pseudocode shown at
http://en.wikipedia.org/wiki/Miller-Rabin_primality_test#Algorithm_and_running_time
Input: n > 3, an odd integer to be tested for primality;
Input: k, a parameter that determines the accuracy of the test
Output: composite if n is composite, otherwise probably prime
write n − 1 as 2^s·d with d odd by factoring powers of 2 from n − 1
LOOP: repeat k times:
pick a random integer a in the range [2, n − 2]
x ← a^d mod n
if x = 1 or x = n − 1 then do next LOOP
for r = 1 .. s − 1
x ← x^2 mod n
if x = 1 then return composite
if x = n − 1 then do next LOOP
return composite
return probably prime
... this function behaves like passing 1 for 'k' and additionally a
fixed/non-random 'a'. Otherwise it's the same algorithm.
See also: http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html
*/
func ProbablyPrimeUint32(n, a uint32) bool {
d, s := n-1, 0
for ; d&1 == 0; d, s = d>>1, s+1 {
}
x := uint64(ModPowUint32(a, d, n))
if x == 1 || uint32(x) == n-1 {
return true
}
for ; s > 1; s-- {
if x = x * x % uint64(n); x == 1 {
return false
}
if uint32(x) == n-1 {
return true
}
}
return false
}
// ProbablyPrimeUint64_32 returns true if n is prime or n is a pseudoprime to
// base a. It implements the Miller-Rabin primality test for one specific value
// of 'a' and k == 1. See also ProbablyPrimeUint32.
func ProbablyPrimeUint64_32(n uint64, a uint32) bool {
d, s := n-1, 0
for ; d&1 == 0; d, s = d>>1, s+1 {
}
x := ModPowUint64(uint64(a), d, n)
if x == 1 || x == n-1 {
return true
}
bx, bn := big.NewInt(0).SetUint64(x), big.NewInt(0).SetUint64(n)
for ; s > 1; s-- {
if x = bx.Mod(bx.Mul(bx, bx), bn).Uint64(); x == 1 {
return false
}
if x == n-1 {
return true
}
}
return false
}
// ProbablyPrimeBigInt_32 returns true if n is prime or n is a pseudoprime to
// base a. It implements the Miller-Rabin primality test for one specific value
// of 'a' and k == 1. See also ProbablyPrimeUint32.
func ProbablyPrimeBigInt_32(n *big.Int, a uint32) bool {
var d big.Int
d.Set(n)
d.Sub(&d, _1) // d <- n-1
s := 0
for ; d.Bit(s) == 0; s++ {
}
nMinus1 := big.NewInt(0).Set(&d)
d.Rsh(&d, uint(s))
x := ModPowBigInt(big.NewInt(int64(a)), &d, n)
if x.Cmp(_1) == 0 || x.Cmp(nMinus1) == 0 {
return true
}
for ; s > 1; s-- {
if x = x.Mod(x.Mul(x, x), n); x.Cmp(_1) == 0 {
return false
}
if x.Cmp(nMinus1) == 0 {
return true
}
}
return false
}
// ProbablyPrimeBigInt returns true if n is prime or n is a pseudoprime to base
// a. It implements the Miller-Rabin primality test for one specific value of
// 'a' and k == 1. See also ProbablyPrimeUint32.
func ProbablyPrimeBigInt(n, a *big.Int) bool {
var d big.Int
d.Set(n)
d.Sub(&d, _1) // d <- n-1
s := 0
for ; d.Bit(s) == 0; s++ {
}
nMinus1 := big.NewInt(0).Set(&d)
d.Rsh(&d, uint(s))
x := ModPowBigInt(a, &d, n)
if x.Cmp(_1) == 0 || x.Cmp(nMinus1) == 0 {
return true
}
for ; s > 1; s-- {
if x = x.Mod(x.Mul(x, x), n); x.Cmp(_1) == 0 {
return false
}
if x.Cmp(nMinus1) == 0 {
return true
}
}
return false
}
// Max returns the larger of a and b.
func Max(a, b int) int {
if a > b {
return a
}
return b
}
// Min returns the smaller of a and b.
func Min(a, b int) int {
if a < b {
return a
}
return b
}
// MaxPtr returns a pointer to the larger of a and b, or nil.
func MaxPtr(a, b *int) *int {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinPtr returns a pointer to the smaller of a and b, or nil.
func MinPtr(a, b *int) *int {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxVal returns the largest argument passed.
func MaxVal(val int, vals ...int) int {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinVal returns the smallest argument passed.
func MinVal(val int, vals ...int) int {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// Clamp returns a value restricted between lo and hi.
func Clamp(v, lo, hi int) int {
return Min(Max(v, lo), hi)
}
// UMax returns the larger of a and b.
func UMax(a, b uint) uint {
if a > b {
return a
}
return b
}
// UMin returns the smaller of a and b.
func UMin(a, b uint) uint {
if a < b {
return a
}
return b
}
// UMaxPtr returns a pointer to the larger of a and b, or nil.
func UMaxPtr(a, b *uint) *uint {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// UMinPtr returns a pointer to the smaller of a and b, or nil.
func UMinPtr(a, b *uint) *uint {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// UMaxVal returns the largest argument passed.
func UMaxVal(val uint, vals ...uint) uint {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// UMinVal returns the smallest argument passed.
func UMinVal(val uint, vals ...uint) uint {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// UClamp returns a value restricted between lo and hi.
func UClamp(v, lo, hi uint) uint {
return UMin(UMax(v, lo), hi)
}
// MaxByte returns the larger of a and b.
func MaxByte(a, b byte) byte {
if a > b {
return a
}
return b
}
// MinByte returns the smaller of a and b.
func MinByte(a, b byte) byte {
if a < b {
return a
}
return b
}
// MaxBytePtr returns a pointer to the larger of a and b, or nil.
func MaxBytePtr(a, b *byte) *byte {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinBytePtr returns a pointer to the smaller of a and b, or nil.
func MinBytePtr(a, b *byte) *byte {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxByteVal returns the largest argument passed.
func MaxByteVal(val byte, vals ...byte) byte {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinByteVal returns the smallest argument passed.
func MinByteVal(val byte, vals ...byte) byte {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampByte returns a value restricted between lo and hi.
func ClampByte(v, lo, hi byte) byte {
return MinByte(MaxByte(v, lo), hi)
}
// MaxInt8 returns the larger of a and b.
func MaxInt8(a, b int8) int8 {
if a > b {
return a
}
return b
}
// MinInt8 returns the smaller of a and b.
func MinInt8(a, b int8) int8 {
if a < b {
return a
}
return b
}
// MaxInt8Ptr returns a pointer to the larger of a and b, or nil.
func MaxInt8Ptr(a, b *int8) *int8 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinInt8Ptr returns a pointer to the smaller of a and b, or nil.
func MinInt8Ptr(a, b *int8) *int8 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxInt8Val returns the largest argument passed.
func MaxInt8Val(val int8, vals ...int8) int8 {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinInt8Val returns the smallest argument passed.
func MinInt8Val(val int8, vals ...int8) int8 {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampInt8 returns a value restricted between lo and hi.
func ClampInt8(v, lo, hi int8) int8 {
return MinInt8(MaxInt8(v, lo), hi)
}
// MaxUint16 returns the larger of a and b.
func MaxUint16(a, b uint16) uint16 {
if a > b {
return a
}
return b
}
// MinUint16 returns the smaller of a and b.
func MinUint16(a, b uint16) uint16 {
if a < b {
return a
}
return b
}
// MaxUint16Ptr returns a pointer to the larger of a and b, or nil.
func MaxUint16Ptr(a, b *uint16) *uint16 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinUint16Ptr returns a pointer to the smaller of a and b, or nil.
func MinUint16Ptr(a, b *uint16) *uint16 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxUint16Val returns the largest argument passed.
func MaxUint16Val(val uint16, vals ...uint16) uint16 {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinUint16Val returns the smallest argument passed.
func MinUint16Val(val uint16, vals ...uint16) uint16 {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampUint16 returns a value restricted between lo and hi.
func ClampUint16(v, lo, hi uint16) uint16 {
return MinUint16(MaxUint16(v, lo), hi)
}
// MaxInt16 returns the larger of a and b.
func MaxInt16(a, b int16) int16 {
if a > b {
return a
}
return b
}
// MinInt16 returns the smaller of a and b.
func MinInt16(a, b int16) int16 {
if a < b {
return a
}
return b
}
// MaxInt16Ptr returns a pointer to the larger of a and b, or nil.
func MaxInt16Ptr(a, b *int16) *int16 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinInt16Ptr returns a pointer to the smaller of a and b, or nil.
func MinInt16Ptr(a, b *int16) *int16 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxInt16Val returns the largest argument passed.
func MaxInt16Val(val int16, vals ...int16) int16 {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinInt16Val returns the smallest argument passed.
func MinInt16Val(val int16, vals ...int16) int16 {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampInt16 returns a value restricted between lo and hi.
func ClampInt16(v, lo, hi int16) int16 {
return MinInt16(MaxInt16(v, lo), hi)
}
// MaxUint32 returns the larger of a and b.
func MaxUint32(a, b uint32) uint32 {
if a > b {
return a
}
return b
}
// MinUint32 returns the smaller of a and b.
func MinUint32(a, b uint32) uint32 {
if a < b {
return a
}
return b
}
// MaxUint32Ptr returns a pointer to the larger of a and b, or nil.
func MaxUint32Ptr(a, b *uint32) *uint32 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinUint32Ptr returns a pointer to the smaller of a and b, or nil.
func MinUint32Ptr(a, b *uint32) *uint32 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxUint32Val returns the largest argument passed.
func MaxUint32Val(val uint32, vals ...uint32) uint32 {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinUint32Val returns the smallest argument passed.
func MinUint32Val(val uint32, vals ...uint32) uint32 {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampUint32 returns a value restricted between lo and hi.
func ClampUint32(v, lo, hi uint32) uint32 {
return MinUint32(MaxUint32(v, lo), hi)
}
// MaxInt32 returns the larger of a and b.
func MaxInt32(a, b int32) int32 {
if a > b {
return a
}
return b
}
// MinInt32 returns the smaller of a and b.
func MinInt32(a, b int32) int32 {
if a < b {
return a
}
return b
}
// MaxInt32Ptr returns a pointer to the larger of a and b, or nil.
func MaxInt32Ptr(a, b *int32) *int32 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinInt32Ptr returns a pointer to the smaller of a and b, or nil.
func MinInt32Ptr(a, b *int32) *int32 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxInt32Val returns the largest argument passed.
func MaxInt32Val(val int32, vals ...int32) int32 {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinInt32Val returns the smallest argument passed.
func MinInt32Val(val int32, vals ...int32) int32 {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampInt32 returns a value restricted between lo and hi.
func ClampInt32(v, lo, hi int32) int32 {
return MinInt32(MaxInt32(v, lo), hi)
}
// MaxUint64 returns the larger of a and b.
func MaxUint64(a, b uint64) uint64 {
if a > b {
return a
}
return b
}
// MinUint64 returns the smaller of a and b.
func MinUint64(a, b uint64) uint64 {
if a < b {
return a
}
return b
}
// MaxUint64Ptr returns a pointer to the larger of a and b, or nil.
func MaxUint64Ptr(a, b *uint64) *uint64 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinUint64Ptr returns a pointer to the smaller of a and b, or nil.
func MinUint64Ptr(a, b *uint64) *uint64 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxUint64Val returns the largest argument passed.
func MaxUint64Val(val uint64, vals ...uint64) uint64 {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinUint64Val returns the smallest argument passed.
func MinUint64Val(val uint64, vals ...uint64) uint64 {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampUint64 returns a value restricted between lo and hi.
func ClampUint64(v, lo, hi uint64) uint64 {
return MinUint64(MaxUint64(v, lo), hi)
}
// MaxInt64 returns the larger of a and b.
func MaxInt64(a, b int64) int64 {
if a > b {
return a
}
return b
}
// MinInt64 returns the smaller of a and b.
func MinInt64(a, b int64) int64 {
if a < b {
return a
}
return b
}
// MaxInt64Ptr returns a pointer to the larger of a and b, or nil.
func MaxInt64Ptr(a, b *int64) *int64 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a > *b {
return a
}
return b
}
// MinInt64Ptr returns a pointer to the smaller of a and b, or nil.
func MinInt64Ptr(a, b *int64) *int64 {
if a == nil {
return b
}
if b == nil {
return a
}
if *a < *b {
return a
}
return b
}
// MaxInt64Val returns the largest argument passed.
func MaxInt64Val(val int64, vals ...int64) int64 {
res := val
for _, v := range vals {
if v > res {
res = v
}
}
return res
}
// MinInt64Val returns the smallest argument passed.
func MinInt64Val(val int64, vals ...int64) int64 {
res := val
for _, v := range vals {
if v < res {
res = v
}
}
return res
}
// ClampInt64 returns a value restricted between lo and hi.
func ClampInt64(v, lo, hi int64) int64 {
return MinInt64(MaxInt64(v, lo), hi)
}
// ToBase produces n in base b. For example
//
// ToBase(2047, 22) -> [1, 5, 4]
//
// 1 * 22^0 1
// 5 * 22^1 110
// 4 * 22^2 1936
// ----
// 2047
//
// ToBase panics for bases < 2.
func ToBase(n *big.Int, b int) []int {
var nn big.Int
nn.Set(n)
if b < 2 {
panic("invalid base")
}
k := 1
switch nn.Sign() {
case -1:
nn.Neg(&nn)
k = -1
case 0:
return []int{0}
}
bb := big.NewInt(int64(b))
var r []int
rem := big.NewInt(0)
for nn.Sign() != 0 {
nn.QuoRem(&nn, bb, rem)
r = append(r, k*int(rem.Int64()))
}
return r
}
// CheckAddInt64 returns the a+b and an indicator that the result is greater
// than math.MaxInt64.
func CheckAddInt64(a, b int64) (sum int64, gt bool) {
return a + b, a > 0 && b > math.MaxInt64-a || a < 0 && b < math.MinInt64-a
}
// CheckSubInt64 returns a-b and an indicator that the result is less than than
// math.MinInt64.
func CheckSubInt64(a, b int64) (sum int64, lt bool) {
return a - b, a > 0 && a-math.MaxInt64 > b || a < 0 && a-math.MinInt64 < b
}
// AddOverflowInt8 returns a + b and an indication whether the addition
// overflowed the int8 range.
func AddOverflowInt8(a, b int8) (r int8, ovf bool) {
r = a + b
if a > 0 && b > 0 {
return r, uint8(r) > math.MaxInt8
}
if a < 0 && b < 0 {
return r, uint8(r) <= math.MaxInt8
}
return r, false
}
// AddOverflowInt16 returns a + b and an indication whether the addition
// overflowed the int16 range.
func AddOverflowInt16(a, b int16) (r int16, ovf bool) {
r = a + b
if a > 0 && b > 0 {
return r, uint16(r) > math.MaxInt16
}
if a < 0 && b < 0 {
return r, uint16(r) <= math.MaxInt16
}
return r, false
}
// AddOverflowInt32 returns a + b and an indication whether the addition
// overflowed the int32 range.
func AddOverflowInt32(a, b int32) (r int32, ovf bool) {
r = a + b
if a > 0 && b > 0 {
return r, uint32(r) > math.MaxInt32
}
if a < 0 && b < 0 {
return r, uint32(r) <= math.MaxInt32
}
return r, false
}
// AddOverflowInt64 returns a + b and an indication whether the addition
// overflowed the int64 range.
func AddOverflowInt64(a, b int64) (r int64, ovf bool) {
r = a + b
if a > 0 && b > 0 {
return r, uint64(r) > math.MaxInt64
}
if a < 0 && b < 0 {
return r, uint64(r) <= math.MaxInt64
}
return r, false
}
// SubOverflowInt8 returns a - b and an indication whether the subtraction
// overflowed the int8 range.
func SubOverflowInt8(a, b int8) (r int8, ovf bool) {
r = a - b
if a >= 0 && b < 0 {
return r, uint8(r) >= math.MaxInt8+1
}
if a < 0 && b > 0 {
return r, uint8(r) <= math.MaxInt8
}
return r, false
}
// SubOverflowInt16 returns a - b and an indication whether the subtraction
// overflowed the int16 range.
func SubOverflowInt16(a, b int16) (r int16, ovf bool) {
r = a - b
if a >= 0 && b < 0 {
return r, uint16(r) >= math.MaxInt16+1
}
if a < 0 && b > 0 {
return r, uint16(r) <= math.MaxInt16
}
return r, false
}
// SubOverflowInt32 returns a - b and an indication whether the subtraction
// overflowed the int32 range.
func SubOverflowInt32(a, b int32) (r int32, ovf bool) {
r = a - b
if a >= 0 && b < 0 {
return r, uint32(r) >= math.MaxInt32+1
}
if a < 0 && b > 0 {
return r, uint32(r) <= math.MaxInt32
}
return r, false
}
// SubOverflowInt64 returns a - b and an indication whether the subtraction
// overflowed the int64 range.
func SubOverflowInt64(a, b int64) (r int64, ovf bool) {
r = a - b
if a >= 0 && b < 0 {
return r, uint64(r) >= math.MaxInt64+1
}
if a < 0 && b > 0 {
return r, uint64(r) <= math.MaxInt64
}
return r, false
}
// MulOverflowInt8 returns a * b and an indication whether the product
// overflowed the int8 range.
func MulOverflowInt8(a, b int8) (r int8, ovf bool) {
if a == 0 || b == 0 {
return 0, false
}
z := int16(a) * int16(b)
return int8(z), z < math.MinInt8 || z > math.MaxInt8
}
// MulOverflowInt16 returns a * b and an indication whether the product
// overflowed the int16 range.
func MulOverflowInt16(a, b int16) (r int16, ovf bool) {
if a == 0 || b == 0 {
return 0, false
}
z := int32(a) * int32(b)
return int16(z), z < math.MinInt16 || z > math.MaxInt16
}
// MulOverflowInt32 returns a * b and an indication whether the product
// overflowed the int32 range.
func MulOverflowInt32(a, b int32) (r int32, ovf bool) {
if a == 0 || b == 0 {
return 0, false
}
z := int64(a) * int64(b)
return int32(z), z < math.MinInt32 || z > math.MaxInt32
}
// MulOverflowInt64 returns a * b and an indication whether the product
// overflowed the int64 range.
func MulOverflowInt64(a, b int64) (r int64, ovf bool) {
// https://groups.google.com/g/golang-nuts/c/h5oSN5t3Au4/m/KaNQREhZh0QJ
const mostPositive = 1<<63 - 1
const mostNegative = -(mostPositive + 1)
r = a * b
if a == 0 || b == 0 || a == 1 || b == 1 {
return r, false
}
if a == mostNegative || b == mostNegative {
return r, true
}
return r, r/b != a
}
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