big

package
v0.3.0 Latest Latest
Warning

This package is not in the latest version of its module.

 Go to latest Published: Jan 8, 2021 License: MIT Imports: 10 Imported by: 0

Documentation

Index

Constants

View Source 
const (
	MaxExp  = math.MaxInt32  // largest supported exponent
	MinExp  = math.MinInt32  // smallest supported exponent
	MaxPrec = math.MaxUint32 // largest (theoretically) supported precision; likely memory-limited
)

Exponent and precision limits.

Variables

This section is empty.

Functions

func Jacobi 

func Jacobi(x, y *Int) int

Jacobi returns the Jacobi symbol (x/y), either +1, -1, or 0. The y argument must be an odd integer.

Types

type Accuracy 

type Accuracy int8

Accuracy describes the rounding error produced by the most recent operation that generated a Float value, relative to the exact value. 

const (
	Below Accuracy = -1
	Exact Accuracy = 0
	Above Accuracy = +1
)

Constants describing the Accuracy of a Float.

type ErrNaN 

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

An ErrNaN panic is raised by a Float operation that would lead to a NaN under IEEE-754 rules. An ErrNaN implements the error interface.

func (ErrNaN) Error 

func (err ErrNaN) Error() string

type Float 

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

A nonzero finite Float represents a multi-precision floating point number 

sign × mantissa × 2**exponent

with 0.5 <= mantissa < 1.0, and MinExp <= exponent <= MaxExp. A Float may also be zero (+0, -0) or infinite (+Inf, -Inf). All Floats are ordered, and the ordering of two Floats x and y is defined by x.Cmp(y).

Each Float value also has a precision, rounding mode, and accuracy. The precision is the maximum number of mantissa bits available to represent the value. The rounding mode specifies how a result should be rounded to fit into the mantissa bits, and accuracy describes the rounding error with respect to the exact result.

Unless specified otherwise, all operations (including setters) that specify a *Float variable for the result (usually via the receiver with the exception of MantExp), round the numeric result according to the precision and rounding mode of the result variable.

If the provided result precision is 0 (see below), it is set to the precision of the argument with the largest precision value before any rounding takes place, and the rounding mode remains unchanged. Thus, uninitialized Floats provided as result arguments will have their precision set to a reasonable value determined by the operands, and their mode is the zero value for RoundingMode (ToNearestEven).

By setting the desired precision to 24 or 53 and using matching rounding mode (typically ToNearestEven), Float operations produce the same results as the corresponding float32 or float64 IEEE-754 arithmetic for operands that correspond to normal (i.e., not denormal) float32 or float64 numbers. Exponent underflow and overflow lead to a 0 or an Infinity for different values than IEEE-754 because Float exponents have a much larger range.

The zero (uninitialized) value for a Float is ready to use and represents the number +0.0 exactly, with precision 0 and rounding mode ToNearestEven.

Operations always take pointer arguments (*Float) rather than Float values, and each unique Float value requires its own unique *Float pointer. To "copy" a Float value, an existing (or newly allocated) Float must be set to a new value using the Float.Set method; shallow copies of Floats are not supported and may lead to errors.

func NewFloat 

func NewFloat(x float64) *Float

NewFloat allocates and returns a new Float set to x, with precision 53 and rounding mode ToNearestEven. NewFloat panics with ErrNaN if x is a NaN.

func ParseFloat 

func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b int, err error)

ParseFloat is like f.Parse(s, base) with f set to the given precision and rounding mode.

func (*Float) Abs 

func (z *Float) Abs(x *Float) *Float

Abs sets z to the (possibly rounded) value |x| (the absolute value of x) and returns z.

func (*Float) Acc 

func (x *Float) Acc() Accuracy

Acc returns the accuracy of x produced by the most recent operation, unless explicitly documented otherwise by that operation.

func (*Float) Add 

func (z *Float) Add(x, y *Float) *Float

Add sets z to the rounded sum x+y and returns z. If z's precision is 0, it is changed to the larger of x's or y's precision before the operation. Rounding is performed according to z's precision and rounding mode; and z's accuracy reports the result error relative to the exact (not rounded) result. Add panics with ErrNaN if x and y are infinities with opposite signs. The value of z is undefined in that case.

func (*Float) Append 

func (x *Float) Append(buf []byte, fmt byte, prec int) []byte

Append appends to buf the string form of the floating-point number x, as generated by x.Text, and returns the extended buffer.

func (*Float) Cmp 

func (x *Float) Cmp(y *Float) int

Cmp compares x and y and returns: 

-1 if x <  y
 0 if x == y (incl. -0 == 0, -Inf == -Inf, and +Inf == +Inf)
+1 if x >  y

func (*Float) Copy 

func (z *Float) Copy(x *Float) *Float

Copy sets z to x, with the same precision, rounding mode, and accuracy as x, and returns z. x is not changed even if z and x are the same.

func (*Float) Float32 

func (x *Float) Float32() (float32, Accuracy)

Float32 returns the float32 value nearest to x. If x is too small to be represented by a float32 (|x| < math.SmallestNonzeroFloat32), the result is (0, Below) or (-0, Above), respectively, depending on the sign of x. If x is too large to be represented by a float32 (|x| > math.MaxFloat32), the result is (+Inf, Above) or (-Inf, Below), depending on the sign of x.

func (*Float) Float64 

func (x *Float) Float64() (float64, Accuracy)

Float64 returns the float64 value nearest to x. If x is too small to be represented by a float64 (|x| < math.SmallestNonzeroFloat64), the result is (0, Below) or (-0, Above), respectively, depending on the sign of x. If x is too large to be represented by a float64 (|x| > math.MaxFloat64), the result is (+Inf, Above) or (-Inf, Below), depending on the sign of x.

func (*Float) Format 

func (x *Float) Format(s fmt.State, format rune)

Format implements fmt.Formatter. It accepts all the regular formats for floating-point numbers ('b', 'e', 'E', 'f', 'F', 'g', 'G', 'x') as well as 'p' and 'v'. See (*Float).Text for the interpretation of 'p'. The 'v' format is handled like 'g'. Format also supports specification of the minimum precision in digits, the output field width, as well as the format flags '+' and ' ' for sign control, '0' for space or zero padding, and '-' for left or right justification. See the fmt package for details.

func (*Float) Int 

func (x *Float) Int(z *Int) (*Int, Accuracy)

Int returns the result of truncating x towards zero; or nil if x is an infinity. The result is Exact if x.IsInt(); otherwise it is Below for x > 0, and Above for x < 0. If a non-nil *Int argument z is provided, Int stores the result in z instead of allocating a new Int.

func (*Float) Int64 

func (x *Float) Int64() (int64, Accuracy)

Int64 returns the integer resulting from truncating x towards zero. If math.MinInt64 <= x <= math.MaxInt64, the result is Exact if x is an integer, and Above (x < 0) or Below (x > 0) otherwise. The result is (math.MinInt64, Above) for x < math.MinInt64, and (math.MaxInt64, Below) for x > math.MaxInt64.

func (*Float) IsInf 

func (x *Float) IsInf() bool

IsInf reports whether x is +Inf or -Inf.

func (*Float) IsInt 

func (x *Float) IsInt() bool

IsInt reports whether x is an integer. ±Inf values are not integers.

func (*Float) MantExp 

func (x *Float) MantExp(mant *Float) (exp int)

MantExp breaks x into its mantissa and exponent components and returns the exponent. If a non-nil mant argument is provided its value is set to the mantissa of x, with the same precision and rounding mode as x. The components satisfy x == mant × 2**exp, with 0.5 <= |mant| < 1.0. Calling MantExp with a nil argument is an efficient way to get the exponent of the receiver.

Special cases are: 

(  ±0).MantExp(mant) = 0, with mant set to   ±0
(±Inf).MantExp(mant) = 0, with mant set to ±Inf

x and mant may be the same in which case x is set to its mantissa value.

func (*Float) MinPrec 

func (x *Float) MinPrec() uint

MinPrec returns the minimum precision required to represent x exactly (i.e., the smallest prec before x.SetPrec(prec) would start rounding x). The result is 0 for |x| == 0 and |x| == Inf.

func (*Float) Mode 

func (x *Float) Mode() RoundingMode

Mode returns the rounding mode of x.

func (*Float) Mul 

func (z *Float) Mul(x, y *Float) *Float

Mul sets z to the rounded product x*y and returns z. Precision, rounding, and accuracy reporting are as for Add. Mul panics with ErrNaN if one operand is zero and the other operand an infinity. The value of z is undefined in that case.

func (*Float) Neg 

func (z *Float) Neg(x *Float) *Float

Neg sets z to the (possibly rounded) value of x with its sign negated, and returns z.

func (*Float) Parse 

func (z *Float) Parse(s string, base int) (f *Float, b int, err error)

Parse parses s which must contain a text representation of a floating- point number with a mantissa in the given conversion base (the exponent is always a decimal number), or a string representing an infinite value.

For base 0, an underscore character “_” may appear between a base prefix and an adjacent digit, and between successive digits; such underscores do not change the value of the number, or the returned digit count. Incorrect placement of underscores is reported as an error if there are no other errors. If base != 0, underscores are not recognized and thus terminate scanning like any other character that is not a valid radix point or digit.

It sets z to the (possibly rounded) value of the corresponding floating- point value, and returns z, the actual base b, and an error err, if any. The entire string (not just a prefix) must be consumed for success. If z's precision is 0, it is changed to 64 before rounding takes effect. The number must be of the form: 

number    = [ sign ] ( float | "inf" | "Inf" ) .
sign      = "+" | "-" .
float     = ( mantissa | prefix pmantissa ) [ exponent ] .
prefix    = "0" [ "b" | "B" | "o" | "O" | "x" | "X" ] .
mantissa  = digits "." [ digits ] | digits | "." digits .
pmantissa = [ "_" ] digits "." [ digits ] | [ "_" ] digits | "." digits .
exponent  = ( "e" | "E" | "p" | "P" ) [ sign ] digits .
digits    = digit { [ "_" ] digit } .
digit     = "0" ... "9" | "a" ... "z" | "A" ... "Z" .

The base argument must be 0, 2, 8, 10, or 16. Providing an invalid base argument will lead to a run-time panic.

For base 0, the number prefix determines the actual base: A prefix of “0b” or “0B” selects base 2, “0o” or “0O” selects base 8, and “0x” or “0X” selects base 16. Otherwise, the actual base is 10 and no prefix is accepted. The octal prefix "0" is not supported (a leading "0" is simply considered a "0").

A "p" or "P" exponent indicates a base 2 (rather then base 10) exponent; for instance, "0x1.fffffffffffffp1023" (using base 0) represents the maximum float64 value. For hexadecimal mantissae, the exponent character must be one of 'p' or 'P', if present (an "e" or "E" exponent indicator cannot be distinguished from a mantissa digit).

The returned *Float f is nil and the value of z is valid but not defined if an error is reported.

func (*Float) Prec 

func (x *Float) Prec() uint

Prec returns the mantissa precision of x in bits. The result may be 0 for |x| == 0 and |x| == Inf.

func (*Float) Quo 

func (z *Float) Quo(x, y *Float) *Float

Quo sets z to the rounded quotient x/y and returns z. Precision, rounding, and accuracy reporting are as for Add. Quo panics with ErrNaN if both operands are zero or infinities. The value of z is undefined in that case.

func (*Float) Rat 

func (x *Float) Rat(z *Rat) (*Rat, Accuracy)

Rat returns the rational number corresponding to x; or nil if x is an infinity. The result is Exact if x is not an Inf. If a non-nil *Rat argument z is provided, Rat stores the result in z instead of allocating a new Rat.

func (*Float) Scan 

func (z *Float) Scan(s fmt.ScanState, ch rune) error

Scan is a support routine for fmt.Scanner; it sets z to the value of the scanned number. It accepts formats whose verbs are supported by fmt.Scan for floating point values, which are: 'b' (binary), 'e', 'E', 'f', 'F', 'g' and 'G'. Scan doesn't handle ±Inf.

func (*Float) Set 

func (z *Float) Set(x *Float) *Float

Set sets z to the (possibly rounded) value of x and returns z. If z's precision is 0, it is changed to the precision of x before setting z (and rounding will have no effect). Rounding is performed according to z's precision and rounding mode; and z's accuracy reports the result error relative to the exact (not rounded) result.

func (*Float) SetFloat64 

func (z *Float) SetFloat64(x float64) *Float

SetFloat64 sets z to the (possibly rounded) value of x and returns z. If z's precision is 0, it is changed to 53 (and rounding will have no effect). SetFloat64 panics with ErrNaN if x is a NaN.

func (*Float) SetInf 

func (z *Float) SetInf(signbit bool) *Float

SetInf sets z to the infinite Float -Inf if signbit is set, or +Inf if signbit is not set, and returns z. The precision of z is unchanged and the result is always Exact.

func (*Float) SetInt 

func (z *Float) SetInt(x *Int) *Float

SetInt sets z to the (possibly rounded) value of x and returns z. If z's precision is 0, it is changed to the larger of x.BitLen() or 64 (and rounding will have no effect).

func (*Float) SetInt64 

func (z *Float) SetInt64(x int64) *Float

SetInt64 sets z to the (possibly rounded) value of x and returns z. If z's precision is 0, it is changed to 64 (and rounding will have no effect).

func (*Float) SetMantExp 

func (z *Float) SetMantExp(mant *Float, exp int) *Float

SetMantExp sets z to mant × 2**exp and returns z. The result z has the same precision and rounding mode as mant. SetMantExp is an inverse of MantExp but does not require 0.5 <= |mant| < 1.0. Specifically: 

mant := new(Float)
new(Float).SetMantExp(mant, x.MantExp(mant)).Cmp(x) == 0

Special cases are: 

z.SetMantExp(  ±0, exp) =   ±0
z.SetMantExp(±Inf, exp) = ±Inf

z and mant may be the same in which case z's exponent is set to exp.

func (*Float) SetMode 

func (z *Float) SetMode(mode RoundingMode) *Float

SetMode sets z's rounding mode to mode and returns an exact z. z remains unchanged otherwise. z.SetMode(z.Mode()) is a cheap way to set z's accuracy to Exact.

func (*Float) SetPrec 

func (z *Float) SetPrec(prec uint) *Float

SetPrec sets z's precision to prec and returns the (possibly) rounded value of z. Rounding occurs according to z's rounding mode if the mantissa cannot be represented in prec bits without loss of precision. SetPrec(0) maps all finite values to ±0; infinite values remain unchanged. If prec > MaxPrec, it is set to MaxPrec.

func (*Float) SetRat 

func (z *Float) SetRat(x *Rat) *Float

SetRat sets z to the (possibly rounded) value of x and returns z. If z's precision is 0, it is changed to the largest of a.BitLen(), b.BitLen(), or 64; with x = a/b.

func (*Float) SetString 

func (z *Float) SetString(s string) (*Float, bool)

SetString sets z to the value of s and returns z and a boolean indicating success. s must be a floating-point number of the same format as accepted by Parse, with base argument 0. The entire string (not just a prefix) must be valid for success. If the operation failed, the value of z is undefined but the returned value is nil.

func (*Float) SetUint64 

func (z *Float) SetUint64(x uint64) *Float

SetUint64 sets z to the (possibly rounded) value of x and returns z. If z's precision is 0, it is changed to 64 (and rounding will have no effect).

func (*Float) Sign 

func (x *Float) Sign() int

Sign returns: 

-1 if x <   0
 0 if x is ±0
+1 if x >   0

func (*Float) Signbit 

func (x *Float) Signbit() bool

Signbit reports whether x is negative or negative zero.

func (*Float) String 

func (x *Float) String() string

String formats x like x.Text('g', 10). (String must be called explicitly, Float.Format does not support %s verb.)

func (*Float) Sub 

func (z *Float) Sub(x, y *Float) *Float

Sub sets z to the rounded difference x-y and returns z. Precision, rounding, and accuracy reporting are as for Add. Sub panics with ErrNaN if x and y are infinities with equal signs. The value of z is undefined in that case.

func (*Float) Text 

func (x *Float) Text(format byte, prec int) string

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! math/big/ftoa.go Text converts the floating-point number x to a string according to the given format and precision prec. The format is one of: 

'e'	-d.dddde±dd, decimal exponent, at least two (possibly 0) exponent digits
'E'	-d.ddddE±dd, decimal exponent, at least two (possibly 0) exponent digits
'f'	-ddddd.dddd, no exponent
'g'	like 'e' for large exponents, like 'f' otherwise
'G'	like 'E' for large exponents, like 'f' otherwise
'x'	-0xd.dddddp±dd, hexadecimal mantissa, decimal power of two exponent
'p'	-0x.dddp±dd, hexadecimal mantissa, decimal power of two exponent (non-standard)
'b'	-ddddddp±dd, decimal mantissa, decimal power of two exponent (non-standard)

For the power-of-two exponent formats, the mantissa is printed in normalized form: 

'x'	hexadecimal mantissa in [1, 2), or 0
'p'	hexadecimal mantissa in [½, 1), or 0
'b'	decimal integer mantissa using x.Prec() bits, or 0

Note that the 'x' form is the one used by most other languages and libraries.

If format is a different character, Text returns a "%" followed by the unrecognized format character.

The precision prec controls the number of digits (excluding the exponent) printed by the 'e', 'E', 'f', 'g', 'G', and 'x' formats. For 'e', 'E', 'f', and 'x', it is the number of digits after the decimal point. For 'g' and 'G' it is the total number of digits. A negative precision selects the smallest number of decimal digits necessary to identify the value x uniquely using x.Prec() mantissa bits. The prec value is ignored for the 'b' and 'p' formats.

func (*Float) Uint64 

func (x *Float) Uint64() (uint64, Accuracy)

Uint64 returns the unsigned integer resulting from truncating x towards zero. If 0 <= x <= math.MaxUint64, the result is Exact if x is an integer and Below otherwise. The result is (0, Above) for x < 0, and (math.MaxUint64, Below) for x > math.MaxUint64.

type Int 

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

An Int represents a signed multi-precision integer. The zero value for an Int represents the value 0.

Operations always take pointer arguments (*Int) rather than Int values, and each unique Int value requires its own unique *Int pointer. To "copy" an Int value, an existing (or newly allocated) Int must be set to a new value using the Int.Set method; shallow copies of Ints are not supported and may lead to errors.

func NewInt 

func NewInt(x int64) *Int

NewInt allocates and returns a new Int set to x.

func (*Int) Abs 

func (z *Int) Abs(x *Int) *Int

Abs sets z to |x| (the absolute value of x) and returns z.

func (*Int) Add 

func (z *Int) Add(x, y *Int) *Int

Add sets z to the sum x+y and returns z.

func (*Int) And 

func (z *Int) And(x, y *Int) *Int

And sets z = x & y and returns z.

func (*Int) AndNot 

func (z *Int) AndNot(x, y *Int) *Int

AndNot sets z = x &^ y and returns z.

func (*Int) Binomial 

func (z *Int) Binomial(n, k int64) *Int

Binomial sets z to the binomial coefficient of (n, k) and returns z.

func (*Int) Bit 

func (x *Int) Bit(i int) uint

Bit returns the value of the i'th bit of x. That is, it returns (x>>i)&1. The bit index i must be >= 0.

func (*Int) BitLen 

func (x *Int) BitLen() int

BitLen returns the length of the absolute value of x in bits. The bit length of 0 is 0.

func (*Int) Bits 

func (x *Int) Bits() []Word

Bits provides raw (unchecked but fast) access to x by returning its absolute value as a little-endian Word slice. The result and x share the same underlying array. Bits is intended to support implementation of missing low-level Int functionality outside this package; it should be avoided otherwise.

func (*Int) Bytes 

func (x *Int) Bytes() []byte

Bytes returns the absolute value of x as a big-endian byte slice.

To use a fixed length slice, or a preallocated one, use FillBytes.

func (*Int) Cmp 

func (x *Int) Cmp(y *Int) (r int)

Cmp compares x and y and returns: 

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

func (*Int) CmpAbs 

func (x *Int) CmpAbs(y *Int) int

CmpAbs compares the absolute values of x and y and returns: 

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

func (*Int) Div 

func (z *Int) Div(x, y *Int) *Int

Div sets z to the quotient x/y for y != 0 and returns z. If y == 0, a division-by-zero run-time panic occurs. Div implements Euclidean division (unlike Go); see DivMod for more details.

func (*Int) DivMod 

func (z *Int) DivMod(x, y, m *Int) (*Int, *Int)

DivMod sets z to the quotient x div y and m to the modulus x mod y and returns the pair (z, m) for y != 0. If y == 0, a division-by-zero run-time panic occurs.

DivMod implements Euclidean division and modulus (unlike Go): 

q = x div y  such that
m = x - y*q  with 0 <= m < |y|

(See Raymond T. Boute, “The Euclidean definition of the functions div and mod”. ACM Transactions on Programming Languages and Systems (TOPLAS), 14(2):127-144, New York, NY, USA, 4/1992. ACM press.) See QuoRem for T-division and modulus (like Go).

func (*Int) Exp 

func (z *Int) Exp(x, y, m *Int) *Int

Exp sets z = x**y mod |m| (i.e. the sign of m is ignored), and returns z. If m == nil or m == 0, z = x**y unless y <= 0 then z = 1. If m != 0, y < 0, and x and m are not relatively prime, z is unchanged and nil is returned.

Modular exponentiation of inputs of a particular size is not a cryptographically constant-time operation.

func (*Int) FillBytes 

func (x *Int) FillBytes(buf []byte) []byte

FillBytes sets buf to the absolute value of x, storing it as a zero-extended big-endian byte slice, and returns buf.

If the absolute value of x doesn't fit in buf, FillBytes will panic.

func (*Int) GCD 

func (z *Int) GCD(x, y, a, b *Int) *Int

GCD sets z to the greatest common divisor of a and b and returns z. If x or y are not nil, GCD sets their value such that z = a*x + b*y.

a and b may be positive, zero or negative. (Before Go 1.14 both had to be > 0.) Regardless of the signs of a and b, z is always >= 0.

If a == b == 0, GCD sets z = x = y = 0.

If a == 0 and b != 0, GCD sets z = |b|, x = 0, y = sign(b) * 1.

If a != 0 and b == 0, GCD sets z = |a|, x = sign(a) * 1, y = 0.

func (*Int) Int64 

func (x *Int) Int64() int64

Int64 returns the int64 representation of x. If x cannot be represented in an int64, the result is undefined.

func (*Int) IsInt64 

func (x *Int) IsInt64() bool

IsInt64 reports whether x can be represented as an int64.

func (*Int) IsUint64 

func (x *Int) IsUint64() bool

IsUint64 reports whether x can be represented as a uint64.

func (*Int) Lsh 

func (z *Int) Lsh(x *Int, n uint) *Int

Lsh sets z = x << n and returns z.

func (*Int) Mod 

func (z *Int) Mod(x, y *Int) *Int

Mod sets z to the modulus x%y for y != 0 and returns z. If y == 0, a division-by-zero run-time panic occurs. Mod implements Euclidean modulus (unlike Go); see DivMod for more details.

func (*Int) ModInverse 

func (z *Int) ModInverse(g, n *Int) *Int

ModInverse sets z to the multiplicative inverse of g in the ring ℤ/nℤ and returns z. If g and n are not relatively prime, g has no multiplicative inverse in the ring ℤ/nℤ. In this case, z is unchanged and the return value is nil.

func (*Int) ModSqrt 

func (z *Int) ModSqrt(x, p *Int) *Int

ModSqrt sets z to a square root of x mod p if such a square root exists, and returns z. The modulus p must be an odd prime. If x is not a square mod p, ModSqrt leaves z unchanged and returns nil. This function panics if p is not an odd integer.

func (*Int) Mul 

func (z *Int) Mul(x, y *Int) *Int

Mul sets z to the product x*y and returns z.

func (*Int) MulRange 

func (z *Int) MulRange(a, b int64) *Int

MulRange sets z to the product of all integers in the range [a, b] inclusively and returns z. If a > b (empty range), the result is 1.

func (*Int) Neg 

func (z *Int) Neg(x *Int) *Int

Neg sets z to -x and returns z.

func (*Int) Not 

func (z *Int) Not(x *Int) *Int

Not sets z = ^x and returns z.

func (*Int) Or 

func (z *Int) Or(x, y *Int) *Int

Or sets z = x | y and returns z.

func (*Int) Quo 

func (z *Int) Quo(x, y *Int) *Int

Quo sets z to the quotient x/y for y != 0 and returns z. If y == 0, a division-by-zero run-time panic occurs. Quo implements truncated division (like Go); see QuoRem for more details.

func (*Int) QuoRem 

func (z *Int) QuoRem(x, y, r *Int) (*Int, *Int)

QuoRem sets z to the quotient x/y and r to the remainder x%y and returns the pair (z, r) for y != 0. If y == 0, a division-by-zero run-time panic occurs.

QuoRem implements T-division and modulus (like Go): 

q = x/y      with the result truncated to zero
r = x - y*q

(See Daan Leijen, “Division and Modulus for Computer Scientists”.) See DivMod for Euclidean division and modulus (unlike Go).

func (*Int) Rand 

func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int

Rand sets z to a pseudo-random number in [0, n) and returns z.

As this uses the math/rand package, it must not be used for security-sensitive work. Use crypto/rand.Int instead.

func (*Int) Rem 

func (z *Int) Rem(x, y *Int) *Int

Rem sets z to the remainder x%y for y != 0 and returns z. If y == 0, a division-by-zero run-time panic occurs. Rem implements truncated modulus (like Go); see QuoRem for more details.

func (*Int) Rsh 

func (z *Int) Rsh(x *Int, n uint) *Int

Rsh sets z = x >> n and returns z.

func (*Int) Set 

func (z *Int) Set(x *Int) *Int

Set sets z to x and returns z.

func (*Int) SetBit 

func (z *Int) SetBit(x *Int, i int, b uint) *Int

SetBit sets z to x, with x's i'th bit set to b (0 or 1). That is, if b is 1 SetBit sets z = x | (1 << i); if b is 0 SetBit sets z = x &^ (1 << i). If b is not 0 or 1, SetBit will panic.

func (*Int) SetBits 

func (z *Int) SetBits(abs []Word) *Int

SetBits provides raw (unchecked but fast) access to z by setting its value to abs, interpreted as a little-endian Word slice, and returning z. The result and abs share the same underlying array. SetBits is intended to support implementation of missing low-level Int functionality outside this package; it should be avoided otherwise.

func (*Int) SetBytes 

func (z *Int) SetBytes(buf []byte) *Int

SetBytes interprets buf as the bytes of a big-endian unsigned integer, sets z to that value, and returns z.

func (*Int) SetInt64 

func (z *Int) SetInt64(x int64) *Int

SetInt64 sets z to x and returns z.

func (*Int) SetString 

func (z *Int) SetString(s string, base int) (*Int, bool)

SetString sets z to the value of s, interpreted in the given base, and returns z and a boolean indicating success. The entire string (not just a prefix) must be valid for success. If SetString fails, the value of z is undefined but the returned value is nil.

The base argument must be 0 or a value between 2 and MaxBase. For base 0, the number prefix determines the actual base: A prefix of “0b” or “0B” selects base 2, “0”, “0o” or “0O” selects base 8, and “0x” or “0X” selects base 16. Otherwise, the selected base is 10 and no prefix is accepted.

For bases <= 36, lower and upper case letters are considered the same: The letters 'a' to 'z' and 'A' to 'Z' represent digit values 10 to 35. For bases > 36, the upper case letters 'A' to 'Z' represent the digit values 36 to 61.

For base 0, an underscore character “_” may appear between a base prefix and an adjacent digit, and between successive digits; such underscores do not change the value of the number. Incorrect placement of underscores is reported as an error if there are no other errors. If base != 0, underscores are not recognized and act like any other character that is not a valid digit.

func (*Int) SetUint64 

func (z *Int) SetUint64(x uint64) *Int

SetUint64 sets z to x and returns z.

func (*Int) Sign 

func (x *Int) Sign() int

Sign returns: 

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

func (*Int) Sqrt 

func (z *Int) Sqrt(x *Int) *Int

Sqrt sets z to ⌊√x⌋, the largest integer such that z² ≤ x, and returns z. It panics if x is negative.

func (*Int) Sub 

func (z *Int) Sub(x, y *Int) *Int

Sub sets z to the difference x-y and returns z.

func (*Int) TrailingZeroBits 

func (x *Int) TrailingZeroBits() uint

TrailingZeroBits returns the number of consecutive least significant zero bits of |x|.

func (*Int) Uint64 

func (x *Int) Uint64() uint64

Uint64 returns the uint64 representation of x. If x cannot be represented in a uint64, the result is undefined.

func (*Int) Xor 

func (z *Int) Xor(x, y *Int) *Int

Xor sets z = x ^ y and returns z.

type RoundingMode 

type RoundingMode byte

RoundingMode determines how a Float value is rounded to the desired precision. Rounding may change the Float value; the rounding error is described by the Float's Accuracy. 

const (
	ToNearestEven RoundingMode = iota // == IEEE 754-2008 roundTiesToEven
	ToNearestAway                     // == IEEE 754-2008 roundTiesToAway
	ToZero                            // == IEEE 754-2008 roundTowardZero
	AwayFromZero                      // no IEEE 754-2008 equivalent
	ToNegativeInf                     // == IEEE 754-2008 roundTowardNegative
	ToPositiveInf                     // == IEEE 754-2008 roundTowardPositive
)

These constants define supported rounding modes.

type Word 

type Word uint

A Word represents a single digit of a multi-precision unsigned integer.

Source Files

View all Source files

Jump to

Keyboard shortcuts

? : This menu
/ : Search site
f or F : Jump to
y or Y : Canonical URL
go.dev uses cookies from Google to deliver and enhance the quality of its services and to analyze traffic. Learn more.