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Diffstat (limited to 'vendor/modernc.org/mathutil/mathutil.go')
| -rw-r--r-- | vendor/modernc.org/mathutil/mathutil.go | 1604 |
1 files changed, 1604 insertions, 0 deletions
diff --git a/vendor/modernc.org/mathutil/mathutil.go b/vendor/modernc.org/mathutil/mathutil.go new file mode 100644 index 0000000..6db6640 --- /dev/null +++ b/vendor/modernc.org/mathutil/mathutil.go @@ -0,0 +1,1604 @@ +// 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 +} |
