constructive

package
v0.0.0-...-c99f163 Latest Latest
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 Go to latest Published: Dec 20, 2025 License: MIT Imports: 7 Imported by: 0

Documentation

Index

Constants

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const IntSize = 32 << (^uint(0) >> 63) // 32 or 64

Variables

View Source 
var E = sync.OnceValue(func() Real {
	return newNamed("e", newPrescaledExponential(FromInt(1)))
})

E calculates the mathematical constant e using its Taylor series expansion.

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var ErrNotConstructive = errors.New("not constructive")
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var Ln2 = sync.OnceValue(func() Real {
	t1 := Multiply(FromInt(7), SimpleLn(Divide(FromInt(10), FromInt(9))))
	t2 := Multiply(FromInt(2), SimpleLn(Divide(FromInt(25), FromInt(24))))
	t3 := Multiply(FromInt(3), SimpleLn(Divide(FromInt(81), FromInt(80))))
	return newNamed("ln2", Add(Subtract(t1, t2), t3))
})

Ln2 calculates ln(2) using the formula: ln(2) = 7*ln(10/9) - 2*ln(25/24) + 3*ln(81/80)

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var One = sync.OnceValue(func() Real {
	return newNamed("1", FromInt(1))
})

One represents the constant 1.

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var Phi = sync.OnceValue(func() Real {
	return newNamed("φ", Divide(Add(FromInt(1), Sqrt(FromInt(5))), FromInt(2)))
})

Phi calculates the golden ratio: φ = (1 + √5) / 2

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var Pi = sync.OnceValue(func() Real {
	m1 := Multiply(FromInt(6), newIntegralArctan(FromInt(8)))
	m2 := Multiply(FromInt(2), newIntegralArctan(FromInt(57)))
	m3 := newIntegralArctan(FromInt(239))
	return newNamed("π", Multiply(FromInt(4), Add(m1, Add(m2, m3))))
})

Pi calculates π using the Machin-like formula: π = 4 * (6 * arctan(1/8) + 2 * arctan(1/57) + arctan(1/239))

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var PrecisionOverflow error = precisionOverflowError{}
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var Sqrt2 = sync.OnceValue(func() Real {
	return newNamed("√2", Sqrt(FromInt(2)))
})

Sqrt2 calculates the square root of 2.

View Source 
var Ten = sync.OnceValue(func() Real {
	return newNamed("10", FromInt(10))
})

Ten represents the constant 10.

View Source 
var Two = sync.OnceValue(func() Real {
	return newNamed("2", FromInt(2))
})

Two represents the constant 2.

View Source 
var Zero = sync.OnceValue(func() Real {
	return newNamed("0", FromInt(0))
})

Zero represents the constant 0.

Functions

func Approximate 

func Approximate(c Real, p int) *big.Int

Approximate computes the approximation of a Real number, given a precision p. When possible, the approximation is cached to save time on future calls.

func AsConstruction 

func AsConstruction(c Real) string

AsConstruction returns a string representing the construction of the Real number c, which may provide insight into how the number is constructed. The construction is returned as a single line string.

func AsConstructionIndent 

func AsConstructionIndent(c Real, indent string) string

AsConstructionIndent returns a string representing the construction of the Real number c, which may provide insight into how the number is constructed.

When indent is empty, the construction is returned as a single line string.

Otherwise, every opening parenthesis increases the indentation level by one, and every closing parenthesis decreases it by one. Arguments are separated by commas, and each argument starts on a new line with the appropriate indentation.

func CheckPrecisionOverflow 

func CheckPrecisionOverflow(ctx context.Context, p int) error

func Cmp 

func Cmp(a, b Real) int

Cmp compares two Real numbers a and b with higher and higher precision until a non-zero result is found. It returns 1 if `a > b`, -1 if `a < b`.

This function never terminates if `a == b`; use PreciseCmp instead.

func ConstructiveName 

func ConstructiveName(c Real) (string, bool)

ConstructiveName returns the name of the constructive Real number c, if it has one. The second return value indicates whether a name was found.

func Identify 

func Identify(c Real) (*big.Int, bool, error)

func IsIntWithinBitTolerance 

func IsIntWithinBitTolerance(value, tolerance int) bool

IsIntWithinBitTolerance checks if the integer value is within the bit tolerance. A bit tolerance of 4 means that there must be at least 4 bits unused in the integer representation.

func IsPrecisionValid 

func IsPrecisionValid(p int) bool

IsPrecisionValid checks if the precision is within 4 bits of tolerance. That value depends on the size of the integer on our architecture, 32 or 64.

func PreciseCmp 

func PreciseCmp(a, b Real, p int) int

PreciseCmp compares two Real numbers a and b with a precision p.

func PreciseSign 

func PreciseSign(c Real, p int) int

PreciseSign computes the sign of a Real number c given precision p.

func PrecisionLimit 

func PrecisionLimit(ctx context.Context) (int, bool)

func Pretty 

func Pretty(c Real) string

func Sign 

func Sign(c Real) int

Sign computes the sign of a Real number c. It returns 1 if c > 0, or -1 if c < 0.

This function never terminates if c == 0; use PreciseSign instead.

func Text 

func Text(c Real, dec, radix int) (text string)

Text converts a Real number to a string representation. The function takes a Real number, a non-negative decimal precision, and a radix (base) for the conversion.

func WithPrecisionLimit 

func WithPrecisionLimit(parent context.Context, limit int) context.Context

func WithoutPrecisionLimit 

func WithoutPrecisionLimit(parent context.Context) context.Context

Types

type Real 

type Real interface {
	// contains filtered or unexported methods
}

Real represents a constructive real number.

func Abs 

func Abs(c Real) Real

Abs computes the absolute value of c.

func Add 

func Add(a, b Real) Real

Add computes the addition `a + b`.

func ContinuedFraction 

func ContinuedFraction(fracs []Real) Real

ContinuedFraction computes the continued fraction from the given slice of constructive Real values.

func ContinuedFraction64 

func ContinuedFraction64(fracs []int64) Real

ContinuedFraction64 computes the continued fraction from the given slice of int64 values.

func Cosine 

func Cosine(c Real) Real

Cosine computes the cosine of c.

func DegreesToRadians 

func DegreesToRadians(degrees Real) Real

func Divide 

func Divide(a, b Real) Real

Divide computes the division `a * (1/b)`, where `1/b` is the multiplicative inverse of b.

func Exp 

func Exp(c Real) Real

Exp computes the e^c.

func FromBigInt 

func FromBigInt(i *big.Int) Real

FromBigInt creates a Real number from a big.Int.

func FromBigIntSlice 

func FromBigIntSlice(ints []*big.Int) []Real

FromBigIntSlice creates a slice of Real numbers from a slice of big.Int.

func FromFloat32 

func FromFloat32(f float32) Real

FromFloat32 creates a Real number from a float32.

func FromFloat32Slice 

func FromFloat32Slice(floats []float32) []Real

FromFloat32Slice creates a slice of Real numbers from a slice of float32.

func FromFloat64 

func FromFloat64(f float64) Real

FromFloat64 creates a Real number from a float64.

func FromFloat64Slice 

func FromFloat64Slice(floats []float64) []Real

FromFloat64Slice creates a slice of Real numbers from a slice of float64.

func FromInt 

func FromInt(i int) Real

FromInt creates a Real number from an int.

func FromInt64 

func FromInt64(i int64) Real

FromInt64 creates a Real number from an int64.

func FromInt64Slice 

func FromInt64Slice(ints []int64) []Real

FromInt64Slice creates a slice of Real numbers from a slice of int64.

func FromIntSlice 

func FromIntSlice(ints []int) []Real

FromIntSlice creates a slice of Real numbers from a slice of int.

func FromRat 

func FromRat(a, b int) Real

FromRat creates a Real number from a rational number a/b, where b != 0.

func Inverse 

func Inverse(c Real) Real

Inverse computes the multiplicative inverse, which is 1/c.

func Ln 

func Ln(c Real) Real

func Max 

func Max(a, b Real) Real

Max computes the maximum of a and b.

func Min 

func Min(a, b Real) Real

Min computes the minimum of a and b.

func Multiply 

func Multiply(a, b Real) Real

Multiply computes the multiplication `a * b`.

func Negate 

func Negate(c Real) Real

Negate computes the negation `-c`. The approximation is actually `-Approximate(c, p)`.

func Pow 

func Pow(c, n Real) Real

Pow computes the power c^n.

func Pow10 

func Pow10(n Real) Real

Pow10 computes the power 10^n.

func RadiansToDegrees 

func RadiansToDegrees(radians Real) Real

func ShiftLeft 

func ShiftLeft(c Real, n int) Real

ShiftLeft computes the left shift `c * 2^n`.

func ShiftRight 

func ShiftRight(c Real, n int) Real

ShiftRight computes the right shift `c * 2^-n`.

func SimpleLn 

func SimpleLn(c Real) Real

SimpleLn computes the natural logarithm of `c`, for `1 < |c| < 2`.

func Sine 

func Sine(c Real) Real

Sine computes the sine of c, using the identity `sin(c) = cos(π/2 - c)`.

func Sqrt 

func Sqrt(c Real) Real

Sqrt computes the square root of c.

func Square 

func Square(c Real) Real

Square computes the square `c * c`.

func Subtract 

func Subtract(a, b Real) Real

Subtract computes the subtraction `a + (-b)`.

func Tangent 

func Tangent(c Real) Real

Tangent computes the tangent of c, using the identity `tan(c) = sin(c) / cos(c)`.

Source Files

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