mathutil

package module
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 Go to latest Published: Nov 22, 2018 License: BSD-3-Clause Imports: 5 Imported by: 2,181

README

github.com/cznic/mathutil has moved to modernc.org/mathutil (vcs).

Please update your import paths to modernc.org/mathutil.

This repo is now archived.

Documentation

Overview

Package mathutil provides utilities supplementing the standard 'math' and 'math/rand' packages.

Release history and compatibility issues

2018-10-21 Added BinaryLog

2018-04-25: New functions for determinig 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)

Index

Examples

Constants

View Source 
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)
)

Architecture and/or implementation specific integer limits and bit widths.

Variables

View Source 
var (
	// The maximun Int128 value.
	MaxInt128 *big.Int
	// The minimun Int128 value.
	MinInt128 *big.Int
)

Functions

func AddUint128_64 

func AddUint128_64(a, b uint64) (hi uint64, lo uint64)

AddUint128_64 returns the uint128 sum of uint64 a and b.

func BinaryLog 

func BinaryLog(n *big.Int, mantissaBits int) (characteristic int, mantissa *big.Int)

BinaryLog computes the binary logarithm of n. The result consists of a characteristic and a mantissa having precision mantissaBits. The value of the binary logarithm is 

characteristic + mantissa*(2^-mantissaBits)

BinaryLog panics for n <= 0 or mantissaBits < 0.

Example 
const mantBits = 257
x, _ := big.NewInt(0).SetString("89940344608680314083397671686667731393131665861770496634981932531495305005604", 10)
c, m := BinaryLog(x, mantBits)
f := big.NewFloat(0).SetPrec(mantBits).SetInt(m)
f = f.SetMantExp(f, -mantBits)
f.Add(f, big.NewFloat(float64(c)))
f.Quo(f, big.NewFloat(4))
fmt.Printf("%.75f", f)

Output:

63.908875905794799149011030723455843229394283193466612998787786375106246936971

func BitLen 

func BitLen(n int) int

BitLen returns the bit width of the non zero part of n.

func BitLenByte 

func BitLenByte(n byte) int

BitLenByte returns the bit width of the non zero part of n.

func BitLenUint 

func BitLenUint(n uint) int

BitLenUint returns the bit width of the non zero part of n.

func BitLenUint16 

func BitLenUint16(n uint16) int

BitLenUint16 returns the bit width of the non zero part of n.

func BitLenUint32 

func BitLenUint32(n uint32) int

BitLenUint32 returns the bit width of the non zero part of n.

func BitLenUint64 

func BitLenUint64(n uint64) int

BitLenUint64 returns the bit width of the non zero part of n.

func BitLenUintptr 

func BitLenUintptr(n uintptr) int

BitLenUintptr returns the bit width of the non zero part of n.

func Clamp 

func Clamp(v, lo, hi int) int

Clamp returns a value restricted between lo and hi.

func ClampByte 

func ClampByte(v, lo, hi byte) byte

ClampByte returns a value restricted between lo and hi.

func ClampInt16 

func ClampInt16(v, lo, hi int16) int16

ClampInt16 returns a value restricted between lo and hi.

func ClampInt32 

func ClampInt32(v, lo, hi int32) int32

ClampInt32 returns a value restricted between lo and hi.

func ClampInt64 

func ClampInt64(v, lo, hi int64) int64

ClampInt64 returns a value restricted between lo and hi.

func ClampInt8 

func ClampInt8(v, lo, hi int8) int8

ClampInt8 returns a value restricted between lo and hi.

func ClampUint16 

func ClampUint16(v, lo, hi uint16) uint16

ClampUint16 returns a value restricted between lo and hi.

func ClampUint32 

func ClampUint32(v, lo, hi uint32) uint32

ClampUint32 returns a value restricted between lo and hi.

func ClampUint64 

func ClampUint64(v, lo, hi uint64) uint64

ClampUint64 returns a value restricted between lo and hi.

func Envelope 

func Envelope(x float64, points []float64, approximation Approximation) float64

Envelope is an utility for defining simple curves using a small (usually) set of data points. Envelope returns a value defined by x, points and approximation. The value of x must be in [0,1) otherwise the result is undefined or the function may panic. Points are interpreted as dividing the [0,1) interval in len(points)-1 sections, so len(points) must be > 1 or the function may panic. According to the left and right points closing/adjacent to the section the resulting value is interpolated using the chosen approximation method. Unsupported values of approximation are silently interpreted as 'Linear'.

func GCDByte 

func GCDByte(a, b byte) byte

GCDByte returns the greatest common divisor of a and b. Based on: http://en.wikipedia.org/wiki/Euclidean_algorithm#Implementations

func GCDUint16 

func GCDUint16(a, b uint16) uint16

GCDUint16 returns the greatest common divisor of a and b.

func GCDUint32 

func GCDUint32(a, b uint32) uint32

GCDUint32 returns the greatest common divisor of a and b.

func GCDUint64 

func GCDUint64(a, b uint64) uint64

GCDUint64 returns the greatest common divisor of a and b.

func ISqrt 

func ISqrt(n uint32) (x uint32)

ISqrt returns floor(sqrt(n)). Typical run time is few hundreds of ns.

func IsPrime 

func IsPrime(n uint32) bool

IsPrime returns true if n is prime. Typical run time is about 100 ns.

TODO rename to IsPrimeUint32

func IsPrimeUint16 

func IsPrimeUint16(n uint16) bool

IsPrimeUint16 returns true if n is prime. Typical run time is few ns.

func IsPrimeUint64 

func IsPrimeUint64(n uint64) bool

IsPrimeUint64 returns true if n is prime. Typical run time is few tens of µs.

SPRP bases: http://miller-rabin.appspot.com

func Log2Byte 

func Log2Byte(n byte) int

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 Log2Uint16 

func Log2Uint16(n uint16) int

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 Log2Uint32 

func Log2Uint32(n uint32) int

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 Log2Uint64 

func Log2Uint64(n uint64) int

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 Max 

func Max(a, b int) int

Max returns the larger of a and b.

func MaxByte 

func MaxByte(a, b byte) byte

MaxByte returns the larger of a and b.

func MaxBytePtr 

func MaxBytePtr(a, b *byte) *byte

MaxBytePtr returns a pointer to the larger of a and b, or nil.

func MaxByteVal 

func MaxByteVal(val byte, vals ...byte) byte

MaxByteVal returns the largest argument passed.

func MaxInt16 

func MaxInt16(a, b int16) int16

MaxInt16 returns the larger of a and b.

func MaxInt16Ptr 

func MaxInt16Ptr(a, b *int16) *int16

MaxInt16Ptr returns a pointer to the larger of a and b, or nil.

func MaxInt16Val 

func MaxInt16Val(val int16, vals ...int16) int16

MaxInt16Val returns the largest argument passed.

func MaxInt32 

func MaxInt32(a, b int32) int32

MaxInt32 returns the larger of a and b.

func MaxInt32Ptr 

func MaxInt32Ptr(a, b *int32) *int32

MaxInt32Ptr returns a pointer to the larger of a and b, or nil.

func MaxInt32Val 

func MaxInt32Val(val int32, vals ...int32) int32

MaxInt32Val returns the largest argument passed.

func MaxInt64 

func MaxInt64(a, b int64) int64

MaxInt64 returns the larger of a and b.

func MaxInt64Ptr 

func MaxInt64Ptr(a, b *int64) *int64

MaxInt64Ptr returns a pointer to the larger of a and b, or nil.

func MaxInt64Val 

func MaxInt64Val(val int64, vals ...int64) int64

MaxInt64Val returns the largest argument passed.

func MaxInt8 

func MaxInt8(a, b int8) int8

MaxInt8 returns the larger of a and b.

func MaxInt8Ptr 

func MaxInt8Ptr(a, b *int8) *int8

MaxInt8Ptr returns a pointer to the larger of a and b, or nil.

func MaxInt8Val 

func MaxInt8Val(val int8, vals ...int8) int8

MaxInt8Val returns the largest argument passed.

func MaxPtr 

func MaxPtr(a, b *int) *int

MaxPtr returns a pointer to the larger of a and b, or nil.

func MaxUint16 

func MaxUint16(a, b uint16) uint16

MaxUint16 returns the larger of a and b.

func MaxUint16Ptr 

func MaxUint16Ptr(a, b *uint16) *uint16

MaxUint16Ptr returns a pointer to the larger of a and b, or nil.

func MaxUint16Val 

func MaxUint16Val(val uint16, vals ...uint16) uint16

MaxUint16Val returns the largest argument passed.

func MaxUint32 

func MaxUint32(a, b uint32) uint32

MaxUint32 returns the larger of a and b.

func MaxUint32Ptr 

func MaxUint32Ptr(a, b *uint32) *uint32

MaxUint32Ptr returns a pointer to the larger of a and b, or nil.

func MaxUint32Val 

func MaxUint32Val(val uint32, vals ...uint32) uint32

MaxUint32Val returns the largest argument passed.

func MaxUint64 

func MaxUint64(a, b uint64) uint64

MaxUint64 returns the larger of a and b.

func MaxUint64Ptr 

func MaxUint64Ptr(a, b *uint64) *uint64

MaxUint64Ptr returns a pointer to the larger of a and b, or nil.

func MaxUint64Val 

func MaxUint64Val(val uint64, vals ...uint64) uint64

MaxUint64Val returns the largest argument passed.

func MaxVal 

func MaxVal(val int, vals ...int) int

MaxVal returns the largest argument passed.

func Min 

func Min(a, b int) int

Min returns the smaller of a and b.

func MinByte 

func MinByte(a, b byte) byte

MinByte returns the smaller of a and b.

func MinBytePtr 

func MinBytePtr(a, b *byte) *byte

MinBytePtr returns a pointer to the smaller of a and b, or nil.

func MinByteVal 

func MinByteVal(val byte, vals ...byte) byte

MinByteVal returns the smallest argument passed.

func MinInt16 

func MinInt16(a, b int16) int16

MinInt16 returns the smaller of a and b.

func MinInt16Ptr 

func MinInt16Ptr(a, b *int16) *int16

MinInt16Ptr returns a pointer to the smaller of a and b, or nil.

func MinInt16Val 

func MinInt16Val(val int16, vals ...int16) int16

MinInt16Val returns the smallest argument passed.

func MinInt32 

func MinInt32(a, b int32) int32

MinInt32 returns the smaller of a and b.

func MinInt32Ptr 

func MinInt32Ptr(a, b *int32) *int32

MinInt32Ptr returns a pointer to the smaller of a and b, or nil.

func MinInt32Val 

func MinInt32Val(val int32, vals ...int32) int32

MinInt32Val returns the smallest argument passed.

func MinInt64 

func MinInt64(a, b int64) int64

MinInt64 returns the smaller of a and b.

func MinInt64Ptr 

func MinInt64Ptr(a, b *int64) *int64

MinInt64Ptr returns a pointer to the smaller of a and b, or nil.

func MinInt64Val 

func MinInt64Val(val int64, vals ...int64) int64

MinInt64Val returns the smallest argument passed.

func MinInt8 

func MinInt8(a, b int8) int8

MinInt8 returns the smaller of a and b.

func MinInt8Ptr 

func MinInt8Ptr(a, b *int8) *int8

MinInt8Ptr returns a pointer to the smaller of a and b, or nil.

func MinInt8Val 

func MinInt8Val(val int8, vals ...int8) int8

MinInt8Val returns the smallest argument passed.

func MinPtr 

func MinPtr(a, b *int) *int

MinPtr returns a pointer to the smaller of a and b, or nil.

func MinUint16 

func MinUint16(a, b uint16) uint16

MinUint16 returns the smaller of a and b.

func MinUint16Ptr 

func MinUint16Ptr(a, b *uint16) *uint16

MinUint16Ptr returns a pointer to the smaller of a and b, or nil.

func MinUint16Val 

func MinUint16Val(val uint16, vals ...uint16) uint16

MinUint16Val returns the smallest argument passed.

func MinUint32 

func MinUint32(a, b uint32) uint32

MinUint32 returns the smaller of a and b.

func MinUint32Ptr 

func MinUint32Ptr(a, b *uint32) *uint32

MinUint32Ptr returns a pointer to the smaller of a and b, or nil.

func MinUint32Val 

func MinUint32Val(val uint32, vals ...uint32) uint32

MinUint32Val returns the smallest argument passed.

func MinUint64 

func MinUint64(a, b uint64) uint64

MinUint64 returns the smaller of a and b.

func MinUint64Ptr 

func MinUint64Ptr(a, b *uint64) *uint64

MinUint64Ptr returns a pointer to the smaller of a and b, or nil.

func MinUint64Val 

func MinUint64Val(val uint64, vals ...uint64) uint64

MinUint64Val returns the smallest argument passed.

func MinVal 

func MinVal(val int, vals ...int) int

MinVal returns the smallest argument passed.

func ModPowBigInt 

func ModPowBigInt(b, e, m *big.Int) (r *big.Int)

ModPowBigInt computes (b^e)%m. Returns nil for e < 0. It panics for m == 0 || b == e == 0.

func ModPowByte 

func ModPowByte(b, e, m byte) byte

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 ModPowUint16 

func ModPowUint16(b, e, m uint16) uint16

ModPowUint16 computes (b^e)%m. It panics for m == 0 || b == e == 0.

func ModPowUint32 

func ModPowUint32(b, e, m uint32) uint32

ModPowUint32 computes (b^e)%m. It panics for m == 0 || b == e == 0.

func ModPowUint64 

func ModPowUint64(b, e, m uint64) (r uint64)

ModPowUint64 computes (b^e)%m. It panics for m == 0 || b == e == 0.

func MulUint128_64 

func MulUint128_64(a, b uint64) (hi, lo uint64)

MulUint128_64 returns the uint128 bit product of uint64 a and b.

func NextPrime 

func NextPrime(n uint32) (p uint32, ok bool)

NextPrime returns first prime > n and true if successful or an undefined value and false if there is no next prime in the uint32 limits. Typical run time is about 2 µs.

TODO rename to NextPrimeUint32

func NextPrimeUint16 

func NextPrimeUint16(n uint16) (p uint16, ok bool)

NextPrimeUint16 returns first prime > n and true if successful or an undefined value and false if there is no next prime in the uint16 limits. Typical run time is few ns.

func NextPrimeUint64 

func NextPrimeUint64(n uint64) (p uint64, ok bool)

NextPrimeUint64 returns first prime > n and true if successful or an undefined value and false if there is no next prime in the uint64 limits. Typical run time is in hundreds of µs.

func PermutationFirst 

func PermutationFirst(data sort.Interface)

PermutationFirst generates the first permutation of data.

func PermutationNext 

func PermutationNext(data sort.Interface) bool

PermutationNext generates the next permutation of data if possible and return true. Return false if there is no more permutation left. Based on the algorithm described here: http://en.wikipedia.org/wiki/Permutation#Generation_in_lexicographic_order

func PopCount 

func PopCount(n int) int

PopCount returns population count of n (number of bits set in n).

func PopCountBigInt 

func PopCountBigInt(n *big.Int) (r int)

PopCountBigInt returns population count of |n| (number of bits set in |n|).

func PopCountByte 

func PopCountByte(n byte) int

PopCountByte returns population count of n (number of bits set in n).

func PopCountUint 

func PopCountUint(n uint) int

PopCountUint returns population count of n (number of bits set in n).

func PopCountUint16 

func PopCountUint16(n uint16) int

PopCountUint16 returns population count of n (number of bits set in n).

func PopCountUint32 

func PopCountUint32(n uint32) int

PopCountUint32 returns population count of n (number of bits set in n).

func PopCountUint64 

func PopCountUint64(n uint64) int

PopCountUint64 returns population count of n (number of bits set in n).

func PopCountUintptr 

func PopCountUintptr(n uintptr) int

PopCountUintptr returns population count of n (number of bits set in n).

func PowerizeBigInt 

func PowerizeBigInt(b, n *big.Int) (e uint32, p *big.Int)

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 PowerizeUint32BigInt 

func PowerizeUint32BigInt(b uint32, n *big.Int) (e uint32, p *big.Int)

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 PrimorialProductsUint32 

func PrimorialProductsUint32(lo, hi, max uint32) (r []uint32)

PrimorialProductsUint32 returns a slice of numbers in [lo, hi] which are a product of max 'max' primorials. The slice is not sorted.

See also: http://en.wikipedia.org/wiki/Primorial

func ProbablyPrimeBigInt 

func ProbablyPrimeBigInt(n, a *big.Int) bool

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_32 

func ProbablyPrimeBigInt_32(n *big.Int, a uint32) bool

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 ProbablyPrimeUint32 

func ProbablyPrimeUint32(n, a uint32) bool

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 ProbablyPrimeUint64_32 

func ProbablyPrimeUint64_32(n uint64, a uint32) bool

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 QCmpUint32 

func QCmpUint32(a, b, c, d uint32) int

QCmpUint32 compares a/b and c/d and returns: 

-1 if a/b <  c/d
 0 if a/b == c/d
+1 if a/b >  c/d

func QScaleUint32 

func QScaleUint32(b, c, d uint32) (a uint64)

QScaleUint32 returns a such that a/b >= c/d.

func QuadPolyDiscriminant 

func QuadPolyDiscriminant(a, b, c int) (ds, d int, _ error)

QuadPolyDiscriminant returns the discriminant of a quadratic polynomial in one variable of the form a*x^2+b*x+c with integer coefficients a, b, c, or an error on overflow.

ds is the square of the discriminant. If |ds| is a square number, d is set to sqrt(|ds|), otherwise d is < 0.

func QuadPolyDiscriminantBig 

func QuadPolyDiscriminantBig(a, b, c *big.Int) (ds, d *big.Int)

QuadPolyDiscriminantBig returns the discriminant of a quadratic polynomial in one variable of the form a*x^2+b*x+c with integer coefficients a, b, c.

ds is the square of the discriminant. If |ds| is a square number, d is set to sqrt(|ds|), otherwise d is nil.

func SqrtBig 

func SqrtBig(n *big.Int) (x *big.Int)

SqrtBig returns floor(sqrt(n)). It panics on n < 0.

func SqrtUint64 

func SqrtUint64(n uint64) (x uint64)

SqrtUint64 returns floor(sqrt(n)). Typical run time is about 0.5 µs.

func ToBase 

func ToBase(n *big.Int, b int) []int

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 UClamp 

func UClamp(v, lo, hi uint) uint

UClamp returns a value restricted between lo and hi.

func UMax 

func UMax(a, b uint) uint

UMax returns the larger of a and b.

func UMaxPtr 

func UMaxPtr(a, b *uint) *uint

UMaxPtr returns a pointer to the larger of a and b, or nil.

func UMaxVal 

func UMaxVal(val uint, vals ...uint) uint

UMaxVal returns the largest argument passed.

func UMin 

func UMin(a, b uint) uint

UMin returns the smaller of a and b.

func UMinPtr 

func UMinPtr(a, b *uint) *uint

UMinPtr returns a pointer to the smaller of a and b, or nil.

func UMinVal 

func UMinVal(val uint, vals ...uint) uint

UMinVal returns the smallest argument passed.

func UintptrBits 

func UintptrBits() int

UintptrBits returns the bit width of an uintptr at the executing machine.

Types

type Approximation 

type Approximation int

Approximation type determines approximation methods used by e.g. Envelope. 

const (
	Linear     Approximation // As named
	Sinusoidal               // Smooth for all derivations
)

Specific approximation method tags

type FC32 

type FC32 struct {
	// contains filtered or unexported fields
}

FC32 is a full cycle PRNG covering the 32 bit signed integer range. In contrast to full cycle generators shown at e.g. http://en.wikipedia.org/wiki/Full_cycle, this code doesn't produce values at constant delta (mod cycle length). The 32 bit limit is per this implementation, the algorithm used has no intrinsic limit on the cycle size. Properties include:

  • Adjustable limits on creation (hi, lo).
  • Positionable/randomly accessible (Pos, Seek).
  • Repeatable (deterministic).
  • Can run forward or backward (Next, Prev).
  • For a billion numbers cycle the Next/Prev PRN can be produced in cca 100-150ns. That's like 5-10 times slower compared to PRNs generated using the (non FC) rand package.

func NewFC32 

func NewFC32(lo, hi int, hq bool) (r *FC32, err error)

NewFC32 returns a newly created FC32 adjusted for the closed interval [lo, hi] or an Error if any. If hq == true then trade some generation time for improved (pseudo)randomness.

func (*FC32) Cycle 

func (r *FC32) Cycle() int64

Cycle reports the length of the inner FCPRNG cycle. Cycle is atmost the double (HQ: triple) of the generator period (hi - lo + 1).

func (*FC32) Next 

func (r *FC32) Next() int

Next returns the first PRN after Pos.

func (*FC32) Pos 

func (r *FC32) Pos() int64

Pos reports the current position within the inner cycle.

func (*FC32) Prev 

func (r *FC32) Prev() int

Prev return the first PRN before Pos.

func (*FC32) Seed 

func (r *FC32) Seed(seed int64)

Seed uses the provided seed value to initialize the generator to a deterministic state. A zero seed produces a "canonical" generator with worse randomness than for most non zero seeds. Still, the FC property holds for any seed value.

func (*FC32) Seek 

func (r *FC32) Seek(pos int64)

Seek sets Pos to |pos| % Cycle.

type FCBig 

type FCBig struct {
	// contains filtered or unexported fields
}

FCBig is a full cycle PRNG covering ranges outside of the int32 limits. For more info see the FC32 docs. Next/Prev PRN on a 1e15 cycle can be produced in about 2 µsec.

func NewFCBig 

func NewFCBig(lo, hi *big.Int, hq bool) (r *FCBig, err error)

NewFCBig returns a newly created FCBig adjusted for the closed interval [lo, hi] or an Error if any. If hq == true then trade some generation time for improved (pseudo)randomness.

func (*FCBig) Cycle 

func (r *FCBig) Cycle() *big.Int

Cycle reports the length of the inner FCPRNG cycle. Cycle is atmost the double (HQ: triple) of the generator period (hi - lo + 1).

func (*FCBig) Next 

func (r *FCBig) Next() *big.Int

Next returns the first PRN after Pos.

func (*FCBig) Pos 

func (r *FCBig) Pos() *big.Int

Pos reports the current position within the inner cycle.

func (*FCBig) Prev 

func (r *FCBig) Prev() *big.Int

Prev return the first PRN before Pos.

func (*FCBig) Seed 

func (r *FCBig) Seed(seed int64)

Seed uses the provided seed value to initialize the generator to a deterministic state. A zero seed produces a "canonical" generator with worse randomness than for most non zero seeds. Still, the FC property holds for any seed value.

func (*FCBig) Seek 

func (r *FCBig) Seek(pos *big.Int)

Seek sets Pos to |pos| % Cycle.

type FactorTerm 

type FactorTerm struct {
	Prime uint32 // The divisor
	Power uint32 // Term == Prime^Power
}

FactorTerm is one term of an integer factorization.

type FactorTerms 

type FactorTerms []FactorTerm

FactorTerms represent a factorization of an integer

func FactorInt 

func FactorInt(n uint32) (f FactorTerms)

FactorInt returns prime factorization of n > 1 or nil otherwise. Resulting factors are ordered by Prime. Typical run time is few µs.

type Int128 

type Int128 struct {
	Lo int64 // Bits 63..0.
	Hi int64 // Bits 127..64.
}

Int128 is an 128 bit integer.

func (Int128) Add 

func (x Int128) Add(y Int128) (r Int128, cy bool)

Add returns the sum of x and y and a carry indication.

func (Int128) BigInt 

func (x Int128) BigInt() *big.Int

BigInt returns x in the form of a big.Int.

func (Int128) Cmp 

func (x Int128) Cmp(y Int128) int

Cmp compares x and y and returns: 

-1 if x <  y
 0 if x == y
+1 if x >  y

func (Int128) Neg 

func (x Int128) Neg() (r Int128, ok bool)

Neg returns -x and an indication that x was not equal to MinInt128.

func (*Int128) SetBigInt 

func (x *Int128) SetBigInt(y *big.Int) (r Int128, err error)

SetBigInt sets x to y, returns x and an error, if any.

func (*Int128) SetInt64 

func (x *Int128) SetInt64(y int64) (r Int128)

SetInt64 sets x to y and returns x.

func (*Int128) SetUint64 

func (x *Int128) SetUint64(y uint64) (r Int128)

SetInt64 sets x to y and returns x.

func (Int128) Sign 

func (x Int128) Sign() int

Sign returns: 

-1 if x <  0
 0 if x == 0
+1 if x >  0

func (Int128) String 

func (x Int128) String() string

String implements fmt.Stringer()

type PolyFactor 

type PolyFactor struct {
	P, Q int
}

PolyFactor describes an irreducible factor of a polynomial in one variable with integer coefficients P, Q of the form P*x+Q.

func QuadPolyFactors 

func QuadPolyFactors(a, b, c int) (content int, primitivePart []PolyFactor, _ error)

QuadPolyFactors returns the content and the irreducible factors of the primitive part of a quadratic polynomial in one variable with integer coefficients a, b, c of the form a*x^2+b*x+c in integers, or an error on overflow.

If the factorization in integers does not exists, the return value is (0, nil, nil).

See also: https://en.wikipedia.org/wiki/Factorization_of_polynomials#Primitive_part.E2.80.93content_factorization

type PolyFactorBig 

type PolyFactorBig struct {
	P, Q *big.Int
}

PolyFactorBig describes an irreducible factor of a polynomial in one variable with integer coefficients P, Q of the form P*x+Q.

func QuadPolyFactorsBig 

func QuadPolyFactorsBig(a, b, c *big.Int) (content *big.Int, primitivePart []PolyFactorBig)

QuadPolyFactorsBig returns the content and the irreducible factors of the primitive part of a quadratic polynomial in one variable with integer coefficients a, b, c of the form a*x^2+b*x+c in integers.

If the factorization in integers does not exists, the return value is (nil, nil).

See also: https://en.wikipedia.org/wiki/Factorization_of_polynomials#Primitive_part.E2.80.93content_factorization

Source Files

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Directories

Path Synopsis
Package mersenne collects utilities related to Mersenne numbers[1] and/or some of their properties.
 Package mersenne collects utilities related to Mersenne numbers[1] and/or some of their properties.

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