LibBF

Computation with high-precision floats.

Constants

data BigFloat

Arbitrary precision floating point numbers.

Instances

Eq BigFloat

IEEE 754 equality

Defined in LibBF

Methods

(==) :: BigFloat -> BigFloat -> Bool

(/=) :: BigFloat -> BigFloat -> Bool

Ord BigFloat

IEEE 754 comparisons

Defined in LibBF

Methods

compare :: BigFloat -> BigFloat -> Ordering

(<) :: BigFloat -> BigFloat -> Bool

(<=) :: BigFloat -> BigFloat -> Bool

(>) :: BigFloat -> BigFloat -> Bool

(>=) :: BigFloat -> BigFloat -> Bool

max :: BigFloat -> BigFloat -> BigFloat

min :: BigFloat -> BigFloat -> BigFloat

Show BigFloat

Defined in LibBF

Methods

showsPrec :: Int -> BigFloat -> ShowS

show :: BigFloat -> String

showList :: [BigFloat] -> ShowS

NFData BigFloat

Defined in LibBF

Methods

rnf :: BigFloat -> ()

Hashable BigFloat

Defined in LibBF

Methods

hashWithSalt :: Int -> BigFloat -> Int

hash :: BigFloat -> Int

bfPosZero :: BigFloat

Positive zero.

bfNegZero :: BigFloat

Negative zero.

bfPosInf :: BigFloat

Positive infinity.

bfNegInf :: BigFloat

Negative infinity.

bfNaN :: BigFloat

Not-a-number.

Conversions

bfFromWord :: Word64 -> BigFloat

A floating point number corresponding to the given word.

bfFromInt :: Int64 -> BigFloat

A floating point number corresponding to the given int.

bfFromDouble :: Double -> BigFloat

A floating point number corresponding to the given double.

bfFromInteger :: Integer -> BigFloat

A floating point number corresponding to the given integer.

bfFromString

Arguments

:: Int

Base

-> BFOpts

-> String

-> (BigFloat, Status)

Parse a number from the given string. Returns @NaN` if the string does not correspond to a number we recognize.

bfToDouble :: RoundMode -> BigFloat -> (Double, Status)

Constant to a Double

bfToString

Arguments

:: Int

Base

-> ShowFmt

-> BigFloat

-> String

Render as a String, using the given settings.

bfToRep :: BigFloat -> BFRep

The float as an exponentiated Integer.

data BFRep

An explicit representation for big nums.

Constructors

BFRep !Sign !BFNum

A signed number

BFNaN

Not a number

Instances

Eq BFRep

Defined in LibBF.Mutable

Methods

(==) :: BFRep -> BFRep -> Bool

(/=) :: BFRep -> BFRep -> Bool

Ord BFRep

Defined in LibBF.Mutable

Methods

compare :: BFRep -> BFRep -> Ordering

(<) :: BFRep -> BFRep -> Bool

(<=) :: BFRep -> BFRep -> Bool

(>) :: BFRep -> BFRep -> Bool

(>=) :: BFRep -> BFRep -> Bool

max :: BFRep -> BFRep -> BFRep

min :: BFRep -> BFRep -> BFRep

Show BFRep

Defined in LibBF.Mutable

Methods

showsPrec :: Int -> BFRep -> ShowS

show :: BFRep -> String

showList :: [BFRep] -> ShowS

Hashable BFRep

Defined in LibBF.Mutable

Methods

hashWithSalt :: Int -> BFRep -> Int

hash :: BFRep -> Int

data BFNum

Representations for unsigned floating point numbers.

Constructors

Zero

zero

Num Integer !Int64

x * 2 ^ y

Inf

infinity

Instances

Eq BFNum

Defined in LibBF.Mutable

Methods

(==) :: BFNum -> BFNum -> Bool

(/=) :: BFNum -> BFNum -> Bool

Ord BFNum

Defined in LibBF.Mutable

Methods

compare :: BFNum -> BFNum -> Ordering

(<) :: BFNum -> BFNum -> Bool

(<=) :: BFNum -> BFNum -> Bool

(>) :: BFNum -> BFNum -> Bool

(>=) :: BFNum -> BFNum -> Bool

max :: BFNum -> BFNum -> BFNum

min :: BFNum -> BFNum -> BFNum

Show BFNum

Defined in LibBF.Mutable

Methods

showsPrec :: Int -> BFNum -> ShowS

show :: BFNum -> String

showList :: [BFNum] -> ShowS

Hashable BFNum

Defined in LibBF.Mutable

Methods

hashWithSalt :: Int -> BFNum -> Int

hash :: BFNum -> Int

bfFromBits

Arguments

:: BFOpts

-> Integer

Raw bits

-> BigFloat

Make a float using "raw" bits representing the bitvector representation of a floating-point value with the exponent and precision bits given by the options.

bfToBits :: BFOpts -> BigFloat -> Integer

Turn a float into raw bits. NaN is represented as a positive "quiet" NaN (most significant bit in the significand is set, the rest of it is 0).

Predicates

bfIsFinite :: BigFloat -> Bool

Is this a finite (i.e., non-infinite, non NaN) number.

bfIsInf :: BigFloat -> Bool

Is this value infinite

bfIsZero :: BigFloat -> Bool

Is this value a zero.

bfIsNaN :: BigFloat -> Bool

Is this value NaN.

bfIsNormal :: BFOpts -> BigFloat -> Bool

This is a "normal" number, which means it is not a NaN, not a zero, not infinite, and not subnormal.

bfIsSubnormal :: BFOpts -> BigFloat -> Bool

This number is "subnormal", which means it is among the smallest representable numbers for the given precision and exponent bits. These numbers differ from "normal" numbers in that they do not use an implicit leading 1 bit in the binary representation.

bfCompare :: BigFloat -> BigFloat -> Ordering

Compare the two numbers. The special values are ordered like this:

• -0 < 0
• NaN == NaN
• NaN is larger than all other numbers

Note that this differs from (<=)

bfSign :: BigFloat -> Maybe Sign

Get the sign of a number. Returns Nothing if the number is NaN.

bfExponent :: BigFloat -> Maybe Int64

Get the exponent for the given number. Infinity, zero and NaN do not have an exponent.

bfIsPos :: BigFloat -> Bool

Is this value positive

bfIsNeg :: BigFloat -> Bool

Is this value negative

data Sign

Indicates if a number is positive or negative.

Constructors

Neg

Negative

Pos

Positive

Instances

Eq Sign

Defined in LibBF.Mutable

Methods

(==) :: Sign -> Sign -> Bool

(/=) :: Sign -> Sign -> Bool

Ord Sign

Defined in LibBF.Mutable

Methods

compare :: Sign -> Sign -> Ordering

(<) :: Sign -> Sign -> Bool

(<=) :: Sign -> Sign -> Bool

(>) :: Sign -> Sign -> Bool

(>=) :: Sign -> Sign -> Bool

max :: Sign -> Sign -> Sign

min :: Sign -> Sign -> Sign

Show Sign

Defined in LibBF.Mutable

Methods

showsPrec :: Int -> Sign -> ShowS

show :: Sign -> String

showList :: [Sign] -> ShowS

Arithmetic

bfNeg :: BigFloat -> BigFloat

Negate a floating point number.

bfAbs :: BigFloat -> BigFloat

Compute the absolute value of a number.

bfAdd :: BFOpts -> BigFloat -> BigFloat -> (BigFloat, Status)

Add two numbers useing the given options.

bfSub :: BFOpts -> BigFloat -> BigFloat -> (BigFloat, Status)

Subtract two numbers useing the given options.

bfMul :: BFOpts -> BigFloat -> BigFloat -> (BigFloat, Status)

Multiply two numbers using the given options.

bfDiv :: BFOpts -> BigFloat -> BigFloat -> (BigFloat, Status)

Divide two numbers useing the given options.

bfRem :: BFOpts -> BigFloat -> BigFloat -> (BigFloat, Status)

Compute the remainder x - y * n where n is the integer nearest to x/y (with ties broken to even values of n).

bfFMA :: BFOpts -> BigFloat -> BigFloat -> BigFloat -> (BigFloat, Status)

Compute the fused-multiply-add (x*y)+z

bfMulWord :: BFOpts -> BigFloat -> Word64 -> (BigFloat, Status)

Multiply a number and a word, using the given options.

bfMulInt :: BFOpts -> BigFloat -> Int64 -> (BigFloat, Status)

Multiply a number and an int, using the given options.

bfMul2Exp :: BFOpts -> BigFloat -> Int -> (BigFloat, Status)

Multiply a number by 2^e.

bfSqrt :: BFOpts -> BigFloat -> (BigFloat, Status)

Square root of two numbers useing the given options.

bfPow :: BFOpts -> BigFloat -> BigFloat -> (BigFloat, Status)

Exponentiate a word to a positive integer power.

Rounding

bfRoundFloat :: BFOpts -> BigFloat -> (BigFloat, Status)

Round to a float matching the input parameters.

bfRoundInt :: RoundMode -> BigFloat -> (BigFloat, Status)

Round to an integer using the given rounding mode.

Mutability

bfUnsafeThaw :: BigFloat -> BF

Make a number mutable. WARNING: This does not copy the number, so it could break referential transperancy.

bfUnsafeFreeze :: BF -> BigFloat

Make a number immutable. WARNING: This does not copy the number, so it could break referential transperancy.

Limits

Configuration

module LibBF.Opts