HMath.Numeric

Module index · Numerical conventions

Description

Numeric representations and deterministic IEEE utilities. Standard integer, rational, binary32/64 and complex types are re-exported. Conversions never silently promote precision: BigFloat operations explicitly select the larger operand precision, decimal/fixed operations the larger scale. The host IEEE rounding environment is not modified. Explicit rounding returns software flags.

On this page

API	Purpose
Int8	8-bit signed integer type
Int16	16-bit signed integer type
Int32	32-bit signed integer type
Int64	64-bit signed integer type
Word8	8-bit unsigned integer type
Word16	16-bit unsigned integer type
Word32	32-bit unsigned integer type
Word64	64-bit unsigned integer type
Float32	Alias for Haskell Float (IEEE binary32 on supported targets).
Float64	Alias for Haskell Double (IEEE binary64 on supported targets).
Complex	A data type representing complex numbers.
:+	forms a complex number from its real and imaginary rectangular components.
Rational	Arbitrary-precision rational numbers, represented as a ratio of two Integer values.
RoundingMode	Software rounding direction: nearest-even,toward zero,toward positive infinity,or toward negative infinity.
NearestEven	Declaration and type contract below.
TowardZero	Declaration and type contract below.
TowardPositive	Declaration and type contract below.
TowardNegative	Declaration and type contract below.
NumericException	Software operation flags: invalid operation,division by zero,overflow,underflow,or inexact conversion.
InvalidOperation	Declaration and type contract below.
DivisionByZero	Declaration and type contract below.
NumericOverflow	Declaration and type contract below.
NumericUnderflow	Declaration and type contract below.
Inexact	Declaration and type contract below.
Rounded	Rounded numeric result paired with software exception flags.
Rounded	Declaration and type contract below.
roundedValue	Value produced by the explicitly selected software rounding operation.
numericalExceptions	Software rounding flags; these do not modify the host IEEE exception environment.
roundRational	Given software rounding mode then exact Rational, return Integer rounded by nearest-even, toward zero, toward positive infinity, or toward negative infinity.
IEEEClass	IEEE classification distinguishing NaN,signed infinity,signed zero,subnormal,and normal finite values.
NotANumber	Declaration and type contract below.
PositiveInfinity	Declaration and type contract below.
NegativeInfinity	Declaration and type contract below.
PositiveZero	Declaration and type contract below.
NegativeZero	Declaration and type contract below.
Subnormal	Declaration and type contract below.
Normal	Declaration and type contract below.
classify	Classify a RealFloat value as NaN, signed infinity, signed zero, subnormal, or normal.
NumericLimits	Format limits and precision metadata derived from RealFloat or the explicit 16-bit format definition.
NumericLimits	Declaration and type contract below.
minimumNormal	Smallest positive normal value of the represented floating format.
minimumSubnormal	Smallest positive subnormal value of the represented floating format.
maximumFinite	Largest finite positive value of the represented floating format.
machineEpsilon	Gap between one and its next larger representable value.
significandDigits	Number of radix digits in the floating significand.
minimumExponent	Lower exponent bound returned by RealFloat.floatRange.
maximumExponent	Upper exponent bound returned by RealFloat.floatRange.
numericLimits	Derived from RealFloat radixdigitsrange, not hardcoded for Double.
integerLimits	Given a bounded integral type witness, return its exact (minimum,maximum) as Integers.
float16Limits	Limits returned as exact binary64 values for the two 16-bit storage formats.
bfloat16Limits	Limits returned as exact binary64 values for the two 16-bit storage formats.
nextAfter	Adjacent representable value toward target, including gradual underflow.
frexp	x=m*2^e, with abs m in [1/2,1) for nonzero finite binary inputs.
ldexp	Given real value then Int exponent, scale by the numeric radix to that power using scaleFloat (binary types use powers of two).
ulpDistance	IEEE binary64 distance.
withinULPs	Given nonnegative allowed ULP distance then two Doubles, test their binary64 representable-value distance.
safeIntegralCast	Convert an integral value to a bounded integral destination only if in range.
saturatingCast	Convert an integral value to a bounded integral destination, clamping to minBound/maxBound when out of range.
realToIntegral	Given software rounding mode then finite real value, round exactly through Rational then range-check the bounded integral destination.
narrowFloat	A narrowing conversion must be finite and exact; choose explicit quantized Float16/BigFloat rounding APIs when loss of precision is intentional.
Float16	IEEE binary16 and bfloat16 storage.
float16	Given rounding mode then Double, round directly to IEEE binary16 and return Rounded storage plus software flags.
fromFloat16	Decode binary16 storage to Double, preserving finite values, signed zero, infinity and NaN classification.
float16Bits	Return raw IEEE binary16 storage bits, including sign, exponent and fraction, as Word16.
float16FromBits	Construct binary16 storage from raw Word16 without validation or rounding; all bit patterns, including NaNs, are representable.
BFloat16	Opaque bfloat16 storage with 8 exponent and 7 explicit fraction bits.
bfloat16	Given rounding mode then Double, round directly to bfloat16 without an intermediate binary32 rounding.
fromBFloat16	Decode bfloat16 storage to Double, preserving finite values, signed zero and non-finite classification.
bfloat16Bits	Return raw bfloat16 storage bits as Word16.
bfloat16FromBits	Construct bfloat16 storage from raw Word16 without conversion; all bit patterns are retained.
BigFloat	An unbounded-exponent binary floating value backed by an exact Rational, rounded to a runtime number of significant bits (2..1,000,000).
bigFloat	Given precision in [2,1000000] bits, rounding mode, then Rational, construct configurable-precision BigFloat plus Inexact flag if rounded.
bigPrecision	Return the runtime number of significant binary bits retained by a BigFloat.
bigRational	Return the exact Rational value of the already-rounded BigFloat, without another conversion or rounding.
bigToDouble	Round BigFloat to host Double through fromRational.
bigAdd	Add two BigFloats exactly then round once to the larger operand precision, nearest-even.
bigSubtract	Subtract the second BigFloat from the first, rounding once nearest-even at the larger operand precision.
bigMultiply	Multiply two BigFloats exactly then round once nearest-even to the larger operand precision.
bigDivide	Divide two BigFloats and round once nearest-even to the larger precision.
bigSqrt	Compute nonnegative BigFloat square root using integer/rational guard precision then round to the input precision.
bigExp	Absolute tail controlled rational series; final rounding is accurate to the requested precision up to one final ulp, not a correctly-rounded promise.
bigLog	Compute natural logarithm at the BigFloat precision using rational series and guard bits.
extended	Software extended precision: 64 significant bits, unbounded exponent.
mixedAdd	Given BigFloat then finite Double, add via exact Rational intermediates at max(BigFloat precision,53) bits, nearest-even.
mixedMultiply	Given BigFloat then finite Double, multiply at max(BigFloat precision,53) bits using exact intermediates and nearest-even.
Fixed	Runtime-scale base-ten fixed point: coefficient * 10^(-scale).
fixed	Given decimal scale in [0,10000], rounding mode, then Rational, return Rounded Fixed and Inexact when required.
fixedScale	Return nonnegative decimal scale s of a Fixed value; its exact value is coefficient / 10^s.
fixedCoefficient	Return exact stored Integer coefficient of a Fixed value, before division by 10^fixedScale.
fixedRational	Return exact coefficient/10^scale represented by a Fixed value, without rounding.
fixedAdd	Add two Fixed values using the larger decimal scale, nearest-even, returning Rounded result and software flags.
fixedMultiply	Given rounding mode then two Fixed values, multiply and round to their larger scale, returning Rounded result and flags.
fixedDivide	Given rounding mode then Fixed numerator and denominator, divide and round to their larger scale.
Decimal	Opaque decimal fixed-point value with fractional-place scale, built through decimal with explicit rounding.
decimal	Given decimal fractional-place scale, rounding mode, then Rational, construct Rounded Decimal through fixed.
decimalRational	Return exact Rational value stored in a Decimal without further rounding.
decimalAdd	Add two Decimals at their larger decimal scale, nearest-even, returning Rounded result and software flags.
decimalMultiply	Given rounding mode then two Decimals, multiply at the larger fractional-place scale and return Rounded result with flags.
decimalDivide	Given rounding mode then two Decimals, divide at their larger scale and return Rounded result.
Interval	Finite closed binary64 intervals.
interval	Given finite lower and upper bounds in increasing order, construct a closed binary64 Interval.
intervalBounds	Return (lower,upper) binary64 endpoints of a validated closed interval.
intervalAdd	Add finite intervals with exact Rational endpoint arithmetic rounded outward, enclosing the exact sum.
intervalSubtract	Subtract intervals with endpoints [a-d,b-c], rounding outward.
intervalMultiply	Multiply intervals using the minimum/maximum of all four endpoint products and outward rounding.
intervalDivide	Divide intervals using endpoint quotients with outward rounding.
intervalContains	Given interval then Double, test closed-bound membership lower<=x<=upper.
Dual	Forward-mode automatic differentiation, f(a+b epsilon), epsilon^2=0.
Dual	Declaration and type contract below.
primal	Primal component of a forward-mode Dual number.
tangent	Directional derivative component of a forward-mode Dual number.
derivative	Given a function on Dual numbers then primal input x, seed Dual x 1 and extract the output tangent.
Quaternion	Hamilton quaternion (real, i, j, k); multiplication is noncommutative.
Quaternion	Declaration and type contract below.
quaternionConjugate	For Quaternion real i j k, negate the three imaginary components and preserve the real part.
quaternionNorm	Return scaled Euclidean norm of four quaternion components, reducing avoidable intermediate overflow.
quaternionInverse	Invert a finite nonzero quaternion using scaled norm arithmetic.
rotateVector	Given nonzero finite quaternion q then (x,y,z), return imaginary part of q(0,x,y,z)inverse(q).
DualQuaternion	Real and dual quaternion pair, commonly representing a rigid rotation/translation.
DualQuaternion	Declaration and type contract below.
dualQuaternionMultiply	Multiply real/dual quaternion pairs as (a,b)(c,d)=(ac,ad+bc).
dualQuaternionInverse	Invert the real quaternion a, returning (inverse(a), -inverse(a)binverse(a)).
rigidTransform	Construct a rigid transform from a nonzero rotation quaternion and translation.
transformPoint	Given dual-quaternion transform then point tuple, rotate by its real part and add translation from twice the dual part times the real inverse.
kahanSum	Sum a finite list using Kahan compensation; empty input yields zero.
neumaierSum	Sum a finite list with Neumaier compensation, correcting for differing term magnitudes.
pairwiseSum	Recursively split and sum a finite list to reduce sequential rounding accumulation.
logsumexp	Empty input is -infinity; +infinity dominates finite/-infinite inputs.
sumErrorBound	Conservative sequential sum bound gamma_(n-1) * sum abs x.

Documentation

Int8

data Int8 #

8-bit signed integer type

Instances

Instances details

PrintfArg Int8	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Int8 -> FieldFormatter # parseFormat :: Int8 -> ModifierParser #
Bits Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (.&.) :: Int8 -> Int8 -> Int8 # (.|.) :: Int8 -> Int8 -> Int8 # xor :: Int8 -> Int8 -> Int8 # complement :: Int8 -> Int8 # shift :: Int8 -> Int -> Int8 # rotate :: Int8 -> Int -> Int8 # zeroBits :: Int8 # bit :: Int -> Int8 # setBit :: Int8 -> Int -> Int8 # clearBit :: Int8 -> Int -> Int8 # complementBit :: Int8 -> Int -> Int8 # testBit :: Int8 -> Int -> Bool # bitSizeMaybe :: Int8 -> Maybe Int # bitSize :: Int8 -> Int # isSigned :: Int8 -> Bool # shiftL :: Int8 -> Int -> Int8 # unsafeShiftL :: Int8 -> Int -> Int8 # shiftR :: Int8 -> Int -> Int8 # unsafeShiftR :: Int8 -> Int -> Int8 # rotateL :: Int8 -> Int -> Int8 # rotateR :: Int8 -> Int -> Int8 # popCount :: Int8 -> Int #
FiniteBits Int8	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Int Methods finiteBitSize :: Int8 -> Int # countLeadingZeros :: Int8 -> Int # countTrailingZeros :: Int8 -> Int #
Bounded Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods minBound :: Int8 # maxBound :: Int8 #
Enum Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int8 -> Int8 # pred :: Int8 -> Int8 # toEnum :: Int -> Int8 # fromEnum :: Int8 -> Int # enumFrom :: Int8 -> [Int8] # enumFromThen :: Int8 -> Int8 -> [Int8] # enumFromTo :: Int8 -> Int8 -> [Int8] # enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] #
Storable Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Int8 -> Int # alignment :: Int8 -> Int # peekElemOff :: Ptr Int8 -> Int -> IO Int8 # pokeElemOff :: Ptr Int8 -> Int -> Int8 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int8 # pokeByteOff :: Ptr b -> Int -> Int8 -> IO () # peek :: Ptr Int8 -> IO Int8 # poke :: Ptr Int8 -> Int8 -> IO () #
Ix Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods range :: (Int8, Int8) -> [Int8] # index :: (Int8, Int8) -> Int8 -> Int # unsafeIndex :: (Int8, Int8) -> Int8 -> Int # inRange :: (Int8, Int8) -> Int8 -> Bool # rangeSize :: (Int8, Int8) -> Int # unsafeRangeSize :: (Int8, Int8) -> Int #
Num Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int8 -> Int8 -> Int8 # (-) :: Int8 -> Int8 -> Int8 # (*) :: Int8 -> Int8 -> Int8 # negate :: Int8 -> Int8 # abs :: Int8 -> Int8 # signum :: Int8 -> Int8 # fromInteger :: Integer -> Int8 #
Read Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods readsPrec :: Int -> ReadS Int8 # readList :: ReadS [Int8] # readPrec :: ReadPrec Int8 # readListPrec :: ReadPrec [Int8] #
Integral Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods quot :: Int8 -> Int8 -> Int8 # rem :: Int8 -> Int8 -> Int8 # div :: Int8 -> Int8 -> Int8 # mod :: Int8 -> Int8 -> Int8 # quotRem :: Int8 -> Int8 -> (Int8, Int8) # divMod :: Int8 -> Int8 -> (Int8, Int8) # toInteger :: Int8 -> Integer #
Real Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods toRational :: Int8 -> Rational #
Show Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods showsPrec :: Int -> Int8 -> ShowS # show :: Int8 -> String # showList :: [Int8] -> ShowS #
Eq Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int8 -> Int8 -> Bool # (/=) :: Int8 -> Int8 -> Bool #
Ord Int8	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods compare :: Int8 -> Int8 -> Ordering # (<) :: Int8 -> Int8 -> Bool # (<=) :: Int8 -> Int8 -> Bool # (>) :: Int8 -> Int8 -> Bool # (>=) :: Int8 -> Int8 -> Bool # max :: Int8 -> Int8 -> Int8 # min :: Int8 -> Int8 -> Int8 #
Element Int8 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Int8 -> DType Source # putElement :: Endian -> Int8 -> Put Source # getElement :: Endian -> Get Int8 Source #
IArray UArray Int8
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int8 -> (i, i) # numElements :: Ix i => UArray i Int8 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Int8)] -> UArray i Int8 # unsafeAt :: Ix i => UArray i Int8 -> Int -> Int8 # unsafeReplace :: Ix i => UArray i Int8 -> [(Int, Int8)] -> UArray i Int8 # unsafeAccum :: Ix i => (Int8 -> e' -> Int8) -> UArray i Int8 -> [(Int, e')] -> UArray i Int8 # unsafeAccumArray :: Ix i => (Int8 -> e' -> Int8) -> Int8 -> (i, i) -> [(Int, e')] -> UArray i Int8 #
MArray IOUArray Int8 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Int8 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Int8 -> IO Int # newArray :: Ix i => (i, i) -> Int8 -> IO (IOUArray i Int8) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Int8) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Int8) # unsafeRead :: Ix i => IOUArray i Int8 -> Int -> IO Int8 # unsafeWrite :: Ix i => IOUArray i Int8 -> Int -> Int8 -> IO () #
MArray (STUArray s) Int8 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int8 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Int8 -> ST s Int # newArray :: Ix i => (i, i) -> Int8 -> ST s (STUArray s i Int8) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int8) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int8) # unsafeRead :: Ix i => STUArray s i Int8 -> Int -> ST s Int8 # unsafeWrite :: Ix i => STUArray s i Int8 -> Int -> Int8 -> ST s () #

Int16

data Int16 #

16-bit signed integer type

Instances

Instances details

PrintfArg Int16	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Int16 -> FieldFormatter # parseFormat :: Int16 -> ModifierParser #
Bits Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (.&.) :: Int16 -> Int16 -> Int16 # (.|.) :: Int16 -> Int16 -> Int16 # xor :: Int16 -> Int16 -> Int16 # complement :: Int16 -> Int16 # shift :: Int16 -> Int -> Int16 # rotate :: Int16 -> Int -> Int16 # zeroBits :: Int16 # bit :: Int -> Int16 # setBit :: Int16 -> Int -> Int16 # clearBit :: Int16 -> Int -> Int16 # complementBit :: Int16 -> Int -> Int16 # testBit :: Int16 -> Int -> Bool # bitSizeMaybe :: Int16 -> Maybe Int # bitSize :: Int16 -> Int # isSigned :: Int16 -> Bool # shiftL :: Int16 -> Int -> Int16 # unsafeShiftL :: Int16 -> Int -> Int16 # shiftR :: Int16 -> Int -> Int16 # unsafeShiftR :: Int16 -> Int -> Int16 # rotateL :: Int16 -> Int -> Int16 # rotateR :: Int16 -> Int -> Int16 # popCount :: Int16 -> Int #
FiniteBits Int16	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Int Methods finiteBitSize :: Int16 -> Int # countLeadingZeros :: Int16 -> Int # countTrailingZeros :: Int16 -> Int #
Bounded Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods minBound :: Int16 # maxBound :: Int16 #
Enum Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int16 -> Int16 # pred :: Int16 -> Int16 # toEnum :: Int -> Int16 # fromEnum :: Int16 -> Int # enumFrom :: Int16 -> [Int16] # enumFromThen :: Int16 -> Int16 -> [Int16] # enumFromTo :: Int16 -> Int16 -> [Int16] # enumFromThenTo :: Int16 -> Int16 -> Int16 -> [Int16] #
Storable Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Int16 -> Int # alignment :: Int16 -> Int # peekElemOff :: Ptr Int16 -> Int -> IO Int16 # pokeElemOff :: Ptr Int16 -> Int -> Int16 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int16 # pokeByteOff :: Ptr b -> Int -> Int16 -> IO () # peek :: Ptr Int16 -> IO Int16 # poke :: Ptr Int16 -> Int16 -> IO () #
Ix Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods range :: (Int16, Int16) -> [Int16] # index :: (Int16, Int16) -> Int16 -> Int # unsafeIndex :: (Int16, Int16) -> Int16 -> Int # inRange :: (Int16, Int16) -> Int16 -> Bool # rangeSize :: (Int16, Int16) -> Int # unsafeRangeSize :: (Int16, Int16) -> Int #
Num Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int16 -> Int16 -> Int16 # (-) :: Int16 -> Int16 -> Int16 # (*) :: Int16 -> Int16 -> Int16 # negate :: Int16 -> Int16 # abs :: Int16 -> Int16 # signum :: Int16 -> Int16 # fromInteger :: Integer -> Int16 #
Read Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods readsPrec :: Int -> ReadS Int16 # readList :: ReadS [Int16] # readPrec :: ReadPrec Int16 # readListPrec :: ReadPrec [Int16] #
Integral Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods quot :: Int16 -> Int16 -> Int16 # rem :: Int16 -> Int16 -> Int16 # div :: Int16 -> Int16 -> Int16 # mod :: Int16 -> Int16 -> Int16 # quotRem :: Int16 -> Int16 -> (Int16, Int16) # divMod :: Int16 -> Int16 -> (Int16, Int16) # toInteger :: Int16 -> Integer #
Real Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods toRational :: Int16 -> Rational #
Show Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods showsPrec :: Int -> Int16 -> ShowS # show :: Int16 -> String # showList :: [Int16] -> ShowS #
Eq Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int16 -> Int16 -> Bool # (/=) :: Int16 -> Int16 -> Bool #
Ord Int16	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods compare :: Int16 -> Int16 -> Ordering # (<) :: Int16 -> Int16 -> Bool # (<=) :: Int16 -> Int16 -> Bool # (>) :: Int16 -> Int16 -> Bool # (>=) :: Int16 -> Int16 -> Bool # max :: Int16 -> Int16 -> Int16 # min :: Int16 -> Int16 -> Int16 #
Element Int16 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Int16 -> DType Source # putElement :: Endian -> Int16 -> Put Source # getElement :: Endian -> Get Int16 Source #
IArray UArray Int16
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int16 -> (i, i) # numElements :: Ix i => UArray i Int16 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Int16)] -> UArray i Int16 # unsafeAt :: Ix i => UArray i Int16 -> Int -> Int16 # unsafeReplace :: Ix i => UArray i Int16 -> [(Int, Int16)] -> UArray i Int16 # unsafeAccum :: Ix i => (Int16 -> e' -> Int16) -> UArray i Int16 -> [(Int, e')] -> UArray i Int16 # unsafeAccumArray :: Ix i => (Int16 -> e' -> Int16) -> Int16 -> (i, i) -> [(Int, e')] -> UArray i Int16 #
MArray IOUArray Int16 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Int16 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Int16 -> IO Int # newArray :: Ix i => (i, i) -> Int16 -> IO (IOUArray i Int16) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Int16) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Int16) # unsafeRead :: Ix i => IOUArray i Int16 -> Int -> IO Int16 # unsafeWrite :: Ix i => IOUArray i Int16 -> Int -> Int16 -> IO () #
MArray (STUArray s) Int16 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int16 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Int16 -> ST s Int # newArray :: Ix i => (i, i) -> Int16 -> ST s (STUArray s i Int16) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int16) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int16) # unsafeRead :: Ix i => STUArray s i Int16 -> Int -> ST s Int16 # unsafeWrite :: Ix i => STUArray s i Int16 -> Int -> Int16 -> ST s () #

Int32

data Int32 #

32-bit signed integer type

Instances

Instances details

PrintfArg Int32	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Int32 -> FieldFormatter # parseFormat :: Int32 -> ModifierParser #
Bits Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (.&.) :: Int32 -> Int32 -> Int32 # (.|.) :: Int32 -> Int32 -> Int32 # xor :: Int32 -> Int32 -> Int32 # complement :: Int32 -> Int32 # shift :: Int32 -> Int -> Int32 # rotate :: Int32 -> Int -> Int32 # zeroBits :: Int32 # bit :: Int -> Int32 # setBit :: Int32 -> Int -> Int32 # clearBit :: Int32 -> Int -> Int32 # complementBit :: Int32 -> Int -> Int32 # testBit :: Int32 -> Int -> Bool # bitSizeMaybe :: Int32 -> Maybe Int # bitSize :: Int32 -> Int # isSigned :: Int32 -> Bool # shiftL :: Int32 -> Int -> Int32 # unsafeShiftL :: Int32 -> Int -> Int32 # shiftR :: Int32 -> Int -> Int32 # unsafeShiftR :: Int32 -> Int -> Int32 # rotateL :: Int32 -> Int -> Int32 # rotateR :: Int32 -> Int -> Int32 # popCount :: Int32 -> Int #
FiniteBits Int32	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Int Methods finiteBitSize :: Int32 -> Int # countLeadingZeros :: Int32 -> Int # countTrailingZeros :: Int32 -> Int #
Bounded Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods minBound :: Int32 # maxBound :: Int32 #
Enum Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int32 -> Int32 # pred :: Int32 -> Int32 # toEnum :: Int -> Int32 # fromEnum :: Int32 -> Int # enumFrom :: Int32 -> [Int32] # enumFromThen :: Int32 -> Int32 -> [Int32] # enumFromTo :: Int32 -> Int32 -> [Int32] # enumFromThenTo :: Int32 -> Int32 -> Int32 -> [Int32] #
Storable Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Int32 -> Int # alignment :: Int32 -> Int # peekElemOff :: Ptr Int32 -> Int -> IO Int32 # pokeElemOff :: Ptr Int32 -> Int -> Int32 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int32 # pokeByteOff :: Ptr b -> Int -> Int32 -> IO () # peek :: Ptr Int32 -> IO Int32 # poke :: Ptr Int32 -> Int32 -> IO () #
Ix Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods range :: (Int32, Int32) -> [Int32] # index :: (Int32, Int32) -> Int32 -> Int # unsafeIndex :: (Int32, Int32) -> Int32 -> Int # inRange :: (Int32, Int32) -> Int32 -> Bool # rangeSize :: (Int32, Int32) -> Int # unsafeRangeSize :: (Int32, Int32) -> Int #
Num Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int32 -> Int32 -> Int32 # (-) :: Int32 -> Int32 -> Int32 # (*) :: Int32 -> Int32 -> Int32 # negate :: Int32 -> Int32 # abs :: Int32 -> Int32 # signum :: Int32 -> Int32 # fromInteger :: Integer -> Int32 #
Read Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods readsPrec :: Int -> ReadS Int32 # readList :: ReadS [Int32] # readPrec :: ReadPrec Int32 # readListPrec :: ReadPrec [Int32] #
Integral Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods quot :: Int32 -> Int32 -> Int32 # rem :: Int32 -> Int32 -> Int32 # div :: Int32 -> Int32 -> Int32 # mod :: Int32 -> Int32 -> Int32 # quotRem :: Int32 -> Int32 -> (Int32, Int32) # divMod :: Int32 -> Int32 -> (Int32, Int32) # toInteger :: Int32 -> Integer #
Real Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods toRational :: Int32 -> Rational #
Show Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods showsPrec :: Int -> Int32 -> ShowS # show :: Int32 -> String # showList :: [Int32] -> ShowS #
Eq Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int32 -> Int32 -> Bool # (/=) :: Int32 -> Int32 -> Bool #
Ord Int32	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods compare :: Int32 -> Int32 -> Ordering # (<) :: Int32 -> Int32 -> Bool # (<=) :: Int32 -> Int32 -> Bool # (>) :: Int32 -> Int32 -> Bool # (>=) :: Int32 -> Int32 -> Bool # max :: Int32 -> Int32 -> Int32 # min :: Int32 -> Int32 -> Int32 #
Element Int32 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Int32 -> DType Source # putElement :: Endian -> Int32 -> Put Source # getElement :: Endian -> Get Int32 Source #
IArray UArray Int32
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int32 -> (i, i) # numElements :: Ix i => UArray i Int32 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Int32)] -> UArray i Int32 # unsafeAt :: Ix i => UArray i Int32 -> Int -> Int32 # unsafeReplace :: Ix i => UArray i Int32 -> [(Int, Int32)] -> UArray i Int32 # unsafeAccum :: Ix i => (Int32 -> e' -> Int32) -> UArray i Int32 -> [(Int, e')] -> UArray i Int32 # unsafeAccumArray :: Ix i => (Int32 -> e' -> Int32) -> Int32 -> (i, i) -> [(Int, e')] -> UArray i Int32 #
MArray IOUArray Int32 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Int32 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Int32 -> IO Int # newArray :: Ix i => (i, i) -> Int32 -> IO (IOUArray i Int32) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Int32) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Int32) # unsafeRead :: Ix i => IOUArray i Int32 -> Int -> IO Int32 # unsafeWrite :: Ix i => IOUArray i Int32 -> Int -> Int32 -> IO () #
MArray (STUArray s) Int32 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int32 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Int32 -> ST s Int # newArray :: Ix i => (i, i) -> Int32 -> ST s (STUArray s i Int32) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int32) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int32) # unsafeRead :: Ix i => STUArray s i Int32 -> Int -> ST s Int32 # unsafeWrite :: Ix i => STUArray s i Int32 -> Int -> Int32 -> ST s () #

Int64

data Int64 #

64-bit signed integer type

Instances

Instances details

PrintfArg Int64	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Int64 -> FieldFormatter # parseFormat :: Int64 -> ModifierParser #
Bits Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (.&.) :: Int64 -> Int64 -> Int64 # (.|.) :: Int64 -> Int64 -> Int64 # xor :: Int64 -> Int64 -> Int64 # complement :: Int64 -> Int64 # shift :: Int64 -> Int -> Int64 # rotate :: Int64 -> Int -> Int64 # zeroBits :: Int64 # bit :: Int -> Int64 # setBit :: Int64 -> Int -> Int64 # clearBit :: Int64 -> Int -> Int64 # complementBit :: Int64 -> Int -> Int64 # testBit :: Int64 -> Int -> Bool # bitSizeMaybe :: Int64 -> Maybe Int # bitSize :: Int64 -> Int # isSigned :: Int64 -> Bool # shiftL :: Int64 -> Int -> Int64 # unsafeShiftL :: Int64 -> Int -> Int64 # shiftR :: Int64 -> Int -> Int64 # unsafeShiftR :: Int64 -> Int -> Int64 # rotateL :: Int64 -> Int -> Int64 # rotateR :: Int64 -> Int -> Int64 # popCount :: Int64 -> Int #
FiniteBits Int64	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Int Methods finiteBitSize :: Int64 -> Int # countLeadingZeros :: Int64 -> Int # countTrailingZeros :: Int64 -> Int #
Bounded Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods minBound :: Int64 # maxBound :: Int64 #
Enum Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods succ :: Int64 -> Int64 # pred :: Int64 -> Int64 # toEnum :: Int -> Int64 # fromEnum :: Int64 -> Int # enumFrom :: Int64 -> [Int64] # enumFromThen :: Int64 -> Int64 -> [Int64] # enumFromTo :: Int64 -> Int64 -> [Int64] # enumFromThenTo :: Int64 -> Int64 -> Int64 -> [Int64] #
Storable Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Int64 -> Int # alignment :: Int64 -> Int # peekElemOff :: Ptr Int64 -> Int -> IO Int64 # pokeElemOff :: Ptr Int64 -> Int -> Int64 -> IO () # peekByteOff :: Ptr b -> Int -> IO Int64 # pokeByteOff :: Ptr b -> Int -> Int64 -> IO () # peek :: Ptr Int64 -> IO Int64 # poke :: Ptr Int64 -> Int64 -> IO () #
Ix Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods range :: (Int64, Int64) -> [Int64] # index :: (Int64, Int64) -> Int64 -> Int # unsafeIndex :: (Int64, Int64) -> Int64 -> Int # inRange :: (Int64, Int64) -> Int64 -> Bool # rangeSize :: (Int64, Int64) -> Int # unsafeRangeSize :: (Int64, Int64) -> Int #
Num Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (+) :: Int64 -> Int64 -> Int64 # (-) :: Int64 -> Int64 -> Int64 # (*) :: Int64 -> Int64 -> Int64 # negate :: Int64 -> Int64 # abs :: Int64 -> Int64 # signum :: Int64 -> Int64 # fromInteger :: Integer -> Int64 #
Read Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods readsPrec :: Int -> ReadS Int64 # readList :: ReadS [Int64] # readPrec :: ReadPrec Int64 # readListPrec :: ReadPrec [Int64] #
Integral Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods quot :: Int64 -> Int64 -> Int64 # rem :: Int64 -> Int64 -> Int64 # div :: Int64 -> Int64 -> Int64 # mod :: Int64 -> Int64 -> Int64 # quotRem :: Int64 -> Int64 -> (Int64, Int64) # divMod :: Int64 -> Int64 -> (Int64, Int64) # toInteger :: Int64 -> Integer #
Real Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods toRational :: Int64 -> Rational #
Show Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods showsPrec :: Int -> Int64 -> ShowS # show :: Int64 -> String # showList :: [Int64] -> ShowS #
Eq Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods (==) :: Int64 -> Int64 -> Bool # (/=) :: Int64 -> Int64 -> Bool #
Ord Int64	Since: base-2.1
Instance details Defined in GHC.Internal.Int Methods compare :: Int64 -> Int64 -> Ordering # (<) :: Int64 -> Int64 -> Bool # (<=) :: Int64 -> Int64 -> Bool # (>) :: Int64 -> Int64 -> Bool # (>=) :: Int64 -> Int64 -> Bool # max :: Int64 -> Int64 -> Int64 # min :: Int64 -> Int64 -> Int64 #
Element Int64 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Int64 -> DType Source # putElement :: Endian -> Int64 -> Put Source # getElement :: Endian -> Get Int64 Source #
IArray UArray Int64
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int64 -> (i, i) # numElements :: Ix i => UArray i Int64 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Int64)] -> UArray i Int64 # unsafeAt :: Ix i => UArray i Int64 -> Int -> Int64 # unsafeReplace :: Ix i => UArray i Int64 -> [(Int, Int64)] -> UArray i Int64 # unsafeAccum :: Ix i => (Int64 -> e' -> Int64) -> UArray i Int64 -> [(Int, e')] -> UArray i Int64 # unsafeAccumArray :: Ix i => (Int64 -> e' -> Int64) -> Int64 -> (i, i) -> [(Int, e')] -> UArray i Int64 #
MArray IOUArray Int64 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Int64 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Int64 -> IO Int # newArray :: Ix i => (i, i) -> Int64 -> IO (IOUArray i Int64) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Int64) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Int64) # unsafeRead :: Ix i => IOUArray i Int64 -> Int -> IO Int64 # unsafeWrite :: Ix i => IOUArray i Int64 -> Int -> Int64 -> IO () #
MArray (STUArray s) Int64 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int64 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Int64 -> ST s Int # newArray :: Ix i => (i, i) -> Int64 -> ST s (STUArray s i Int64) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int64) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int64) # unsafeRead :: Ix i => STUArray s i Int64 -> Int -> ST s Int64 # unsafeWrite :: Ix i => STUArray s i Int64 -> Int -> Int64 -> ST s () #

Word8

data Word8 #

8-bit unsigned integer type

Instances

Instances details

PrintfArg Word8	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Word8 -> FieldFormatter # parseFormat :: Word8 -> ModifierParser #
Bits Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (.&.) :: Word8 -> Word8 -> Word8 # (.|.) :: Word8 -> Word8 -> Word8 # xor :: Word8 -> Word8 -> Word8 # complement :: Word8 -> Word8 # shift :: Word8 -> Int -> Word8 # rotate :: Word8 -> Int -> Word8 # zeroBits :: Word8 # bit :: Int -> Word8 # setBit :: Word8 -> Int -> Word8 # clearBit :: Word8 -> Int -> Word8 # complementBit :: Word8 -> Int -> Word8 # testBit :: Word8 -> Int -> Bool # bitSizeMaybe :: Word8 -> Maybe Int # bitSize :: Word8 -> Int # isSigned :: Word8 -> Bool # shiftL :: Word8 -> Int -> Word8 # unsafeShiftL :: Word8 -> Int -> Word8 # shiftR :: Word8 -> Int -> Word8 # unsafeShiftR :: Word8 -> Int -> Word8 # rotateL :: Word8 -> Int -> Word8 # rotateR :: Word8 -> Int -> Word8 # popCount :: Word8 -> Int #
FiniteBits Word8	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Word Methods finiteBitSize :: Word8 -> Int # countLeadingZeros :: Word8 -> Int # countTrailingZeros :: Word8 -> Int #
Bounded Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods minBound :: Word8 # maxBound :: Word8 #
Enum Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word8 -> Word8 # pred :: Word8 -> Word8 # toEnum :: Int -> Word8 # fromEnum :: Word8 -> Int # enumFrom :: Word8 -> [Word8] # enumFromThen :: Word8 -> Word8 -> [Word8] # enumFromTo :: Word8 -> Word8 -> [Word8] # enumFromThenTo :: Word8 -> Word8 -> Word8 -> [Word8] #
Storable Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Word8 -> Int # alignment :: Word8 -> Int # peekElemOff :: Ptr Word8 -> Int -> IO Word8 # pokeElemOff :: Ptr Word8 -> Int -> Word8 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word8 # pokeByteOff :: Ptr b -> Int -> Word8 -> IO () # peek :: Ptr Word8 -> IO Word8 # poke :: Ptr Word8 -> Word8 -> IO () #
Ix Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods range :: (Word8, Word8) -> [Word8] # index :: (Word8, Word8) -> Word8 -> Int # unsafeIndex :: (Word8, Word8) -> Word8 -> Int # inRange :: (Word8, Word8) -> Word8 -> Bool # rangeSize :: (Word8, Word8) -> Int # unsafeRangeSize :: (Word8, Word8) -> Int #
Num Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word8 -> Word8 -> Word8 # (-) :: Word8 -> Word8 -> Word8 # (*) :: Word8 -> Word8 -> Word8 # negate :: Word8 -> Word8 # abs :: Word8 -> Word8 # signum :: Word8 -> Word8 # fromInteger :: Integer -> Word8 #
Read Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Word8 # readList :: ReadS [Word8] # readPrec :: ReadPrec Word8 # readListPrec :: ReadPrec [Word8] #
Integral Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods quot :: Word8 -> Word8 -> Word8 # rem :: Word8 -> Word8 -> Word8 # div :: Word8 -> Word8 -> Word8 # mod :: Word8 -> Word8 -> Word8 # quotRem :: Word8 -> Word8 -> (Word8, Word8) # divMod :: Word8 -> Word8 -> (Word8, Word8) # toInteger :: Word8 -> Integer #
Real Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods toRational :: Word8 -> Rational #
Show Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods showsPrec :: Int -> Word8 -> ShowS # show :: Word8 -> String # showList :: [Word8] -> ShowS #
Eq Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word8 -> Word8 -> Bool # (/=) :: Word8 -> Word8 -> Bool #
Ord Word8	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods compare :: Word8 -> Word8 -> Ordering # (<) :: Word8 -> Word8 -> Bool # (<=) :: Word8 -> Word8 -> Bool # (>) :: Word8 -> Word8 -> Bool # (>=) :: Word8 -> Word8 -> Bool # max :: Word8 -> Word8 -> Word8 # min :: Word8 -> Word8 -> Word8 #
Element Word8 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Word8 -> DType Source # putElement :: Endian -> Word8 -> Put Source # getElement :: Endian -> Get Word8 Source #
IArray UArray Word8
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word8 -> (i, i) # numElements :: Ix i => UArray i Word8 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Word8)] -> UArray i Word8 # unsafeAt :: Ix i => UArray i Word8 -> Int -> Word8 # unsafeReplace :: Ix i => UArray i Word8 -> [(Int, Word8)] -> UArray i Word8 # unsafeAccum :: Ix i => (Word8 -> e' -> Word8) -> UArray i Word8 -> [(Int, e')] -> UArray i Word8 # unsafeAccumArray :: Ix i => (Word8 -> e' -> Word8) -> Word8 -> (i, i) -> [(Int, e')] -> UArray i Word8 #
MArray IOUArray Word8 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Word8 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Word8 -> IO Int # newArray :: Ix i => (i, i) -> Word8 -> IO (IOUArray i Word8) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Word8) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Word8) # unsafeRead :: Ix i => IOUArray i Word8 -> Int -> IO Word8 # unsafeWrite :: Ix i => IOUArray i Word8 -> Int -> Word8 -> IO () #
MArray (STUArray s) Word8 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word8 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word8 -> ST s Int # newArray :: Ix i => (i, i) -> Word8 -> ST s (STUArray s i Word8) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word8) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word8) # unsafeRead :: Ix i => STUArray s i Word8 -> Int -> ST s Word8 # unsafeWrite :: Ix i => STUArray s i Word8 -> Int -> Word8 -> ST s () #

Word16

data Word16 #

16-bit unsigned integer type

Instances

Instances details

PrintfArg Word16	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Word16 -> FieldFormatter # parseFormat :: Word16 -> ModifierParser #
Bits Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (.&.) :: Word16 -> Word16 -> Word16 # (.|.) :: Word16 -> Word16 -> Word16 # xor :: Word16 -> Word16 -> Word16 # complement :: Word16 -> Word16 # shift :: Word16 -> Int -> Word16 # rotate :: Word16 -> Int -> Word16 # zeroBits :: Word16 # bit :: Int -> Word16 # setBit :: Word16 -> Int -> Word16 # clearBit :: Word16 -> Int -> Word16 # complementBit :: Word16 -> Int -> Word16 # testBit :: Word16 -> Int -> Bool # bitSizeMaybe :: Word16 -> Maybe Int # bitSize :: Word16 -> Int # isSigned :: Word16 -> Bool # shiftL :: Word16 -> Int -> Word16 # unsafeShiftL :: Word16 -> Int -> Word16 # shiftR :: Word16 -> Int -> Word16 # unsafeShiftR :: Word16 -> Int -> Word16 # rotateL :: Word16 -> Int -> Word16 # rotateR :: Word16 -> Int -> Word16 # popCount :: Word16 -> Int #
FiniteBits Word16	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Word Methods finiteBitSize :: Word16 -> Int # countLeadingZeros :: Word16 -> Int # countTrailingZeros :: Word16 -> Int #
Bounded Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods minBound :: Word16 # maxBound :: Word16 #
Enum Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word16 -> Word16 # pred :: Word16 -> Word16 # toEnum :: Int -> Word16 # fromEnum :: Word16 -> Int # enumFrom :: Word16 -> [Word16] # enumFromThen :: Word16 -> Word16 -> [Word16] # enumFromTo :: Word16 -> Word16 -> [Word16] # enumFromThenTo :: Word16 -> Word16 -> Word16 -> [Word16] #
Storable Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Word16 -> Int # alignment :: Word16 -> Int # peekElemOff :: Ptr Word16 -> Int -> IO Word16 # pokeElemOff :: Ptr Word16 -> Int -> Word16 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word16 # pokeByteOff :: Ptr b -> Int -> Word16 -> IO () # peek :: Ptr Word16 -> IO Word16 # poke :: Ptr Word16 -> Word16 -> IO () #
Ix Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods range :: (Word16, Word16) -> [Word16] # index :: (Word16, Word16) -> Word16 -> Int # unsafeIndex :: (Word16, Word16) -> Word16 -> Int # inRange :: (Word16, Word16) -> Word16 -> Bool # rangeSize :: (Word16, Word16) -> Int # unsafeRangeSize :: (Word16, Word16) -> Int #
Num Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word16 -> Word16 -> Word16 # (-) :: Word16 -> Word16 -> Word16 # (*) :: Word16 -> Word16 -> Word16 # negate :: Word16 -> Word16 # abs :: Word16 -> Word16 # signum :: Word16 -> Word16 # fromInteger :: Integer -> Word16 #
Read Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Word16 # readList :: ReadS [Word16] # readPrec :: ReadPrec Word16 # readListPrec :: ReadPrec [Word16] #
Integral Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods quot :: Word16 -> Word16 -> Word16 # rem :: Word16 -> Word16 -> Word16 # div :: Word16 -> Word16 -> Word16 # mod :: Word16 -> Word16 -> Word16 # quotRem :: Word16 -> Word16 -> (Word16, Word16) # divMod :: Word16 -> Word16 -> (Word16, Word16) # toInteger :: Word16 -> Integer #
Real Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods toRational :: Word16 -> Rational #
Show Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods showsPrec :: Int -> Word16 -> ShowS # show :: Word16 -> String # showList :: [Word16] -> ShowS #
Eq Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word16 -> Word16 -> Bool # (/=) :: Word16 -> Word16 -> Bool #
Ord Word16	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods compare :: Word16 -> Word16 -> Ordering # (<) :: Word16 -> Word16 -> Bool # (<=) :: Word16 -> Word16 -> Bool # (>) :: Word16 -> Word16 -> Bool # (>=) :: Word16 -> Word16 -> Bool # max :: Word16 -> Word16 -> Word16 # min :: Word16 -> Word16 -> Word16 #
Element Word16 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Word16 -> DType Source # putElement :: Endian -> Word16 -> Put Source # getElement :: Endian -> Get Word16 Source #
IArray UArray Word16
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word16 -> (i, i) # numElements :: Ix i => UArray i Word16 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Word16)] -> UArray i Word16 # unsafeAt :: Ix i => UArray i Word16 -> Int -> Word16 # unsafeReplace :: Ix i => UArray i Word16 -> [(Int, Word16)] -> UArray i Word16 # unsafeAccum :: Ix i => (Word16 -> e' -> Word16) -> UArray i Word16 -> [(Int, e')] -> UArray i Word16 # unsafeAccumArray :: Ix i => (Word16 -> e' -> Word16) -> Word16 -> (i, i) -> [(Int, e')] -> UArray i Word16 #
MArray IOUArray Word16 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Word16 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Word16 -> IO Int # newArray :: Ix i => (i, i) -> Word16 -> IO (IOUArray i Word16) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Word16) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Word16) # unsafeRead :: Ix i => IOUArray i Word16 -> Int -> IO Word16 # unsafeWrite :: Ix i => IOUArray i Word16 -> Int -> Word16 -> IO () #
MArray (STUArray s) Word16 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word16 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word16 -> ST s Int # newArray :: Ix i => (i, i) -> Word16 -> ST s (STUArray s i Word16) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word16) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word16) # unsafeRead :: Ix i => STUArray s i Word16 -> Int -> ST s Word16 # unsafeWrite :: Ix i => STUArray s i Word16 -> Int -> Word16 -> ST s () #

Word32

data Word32 #

32-bit unsigned integer type

Instances

Instances details

PrintfArg Word32	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Word32 -> FieldFormatter # parseFormat :: Word32 -> ModifierParser #
Bits Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (.&.) :: Word32 -> Word32 -> Word32 # (.|.) :: Word32 -> Word32 -> Word32 # xor :: Word32 -> Word32 -> Word32 # complement :: Word32 -> Word32 # shift :: Word32 -> Int -> Word32 # rotate :: Word32 -> Int -> Word32 # zeroBits :: Word32 # bit :: Int -> Word32 # setBit :: Word32 -> Int -> Word32 # clearBit :: Word32 -> Int -> Word32 # complementBit :: Word32 -> Int -> Word32 # testBit :: Word32 -> Int -> Bool # bitSizeMaybe :: Word32 -> Maybe Int # bitSize :: Word32 -> Int # isSigned :: Word32 -> Bool # shiftL :: Word32 -> Int -> Word32 # unsafeShiftL :: Word32 -> Int -> Word32 # shiftR :: Word32 -> Int -> Word32 # unsafeShiftR :: Word32 -> Int -> Word32 # rotateL :: Word32 -> Int -> Word32 # rotateR :: Word32 -> Int -> Word32 # popCount :: Word32 -> Int #
FiniteBits Word32	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Word Methods finiteBitSize :: Word32 -> Int # countLeadingZeros :: Word32 -> Int # countTrailingZeros :: Word32 -> Int #
Bounded Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods minBound :: Word32 # maxBound :: Word32 #
Enum Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word32 -> Word32 # pred :: Word32 -> Word32 # toEnum :: Int -> Word32 # fromEnum :: Word32 -> Int # enumFrom :: Word32 -> [Word32] # enumFromThen :: Word32 -> Word32 -> [Word32] # enumFromTo :: Word32 -> Word32 -> [Word32] # enumFromThenTo :: Word32 -> Word32 -> Word32 -> [Word32] #
Storable Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Word32 -> Int # alignment :: Word32 -> Int # peekElemOff :: Ptr Word32 -> Int -> IO Word32 # pokeElemOff :: Ptr Word32 -> Int -> Word32 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word32 # pokeByteOff :: Ptr b -> Int -> Word32 -> IO () # peek :: Ptr Word32 -> IO Word32 # poke :: Ptr Word32 -> Word32 -> IO () #
Ix Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods range :: (Word32, Word32) -> [Word32] # index :: (Word32, Word32) -> Word32 -> Int # unsafeIndex :: (Word32, Word32) -> Word32 -> Int # inRange :: (Word32, Word32) -> Word32 -> Bool # rangeSize :: (Word32, Word32) -> Int # unsafeRangeSize :: (Word32, Word32) -> Int #
Num Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word32 -> Word32 -> Word32 # (-) :: Word32 -> Word32 -> Word32 # (*) :: Word32 -> Word32 -> Word32 # negate :: Word32 -> Word32 # abs :: Word32 -> Word32 # signum :: Word32 -> Word32 # fromInteger :: Integer -> Word32 #
Read Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Word32 # readList :: ReadS [Word32] # readPrec :: ReadPrec Word32 # readListPrec :: ReadPrec [Word32] #
Integral Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods quot :: Word32 -> Word32 -> Word32 # rem :: Word32 -> Word32 -> Word32 # div :: Word32 -> Word32 -> Word32 # mod :: Word32 -> Word32 -> Word32 # quotRem :: Word32 -> Word32 -> (Word32, Word32) # divMod :: Word32 -> Word32 -> (Word32, Word32) # toInteger :: Word32 -> Integer #
Real Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods toRational :: Word32 -> Rational #
Show Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods showsPrec :: Int -> Word32 -> ShowS # show :: Word32 -> String # showList :: [Word32] -> ShowS #
Eq Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word32 -> Word32 -> Bool # (/=) :: Word32 -> Word32 -> Bool #
Ord Word32	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods compare :: Word32 -> Word32 -> Ordering # (<) :: Word32 -> Word32 -> Bool # (<=) :: Word32 -> Word32 -> Bool # (>) :: Word32 -> Word32 -> Bool # (>=) :: Word32 -> Word32 -> Bool # max :: Word32 -> Word32 -> Word32 # min :: Word32 -> Word32 -> Word32 #
Element Word32 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Word32 -> DType Source # putElement :: Endian -> Word32 -> Put Source # getElement :: Endian -> Get Word32 Source #
IArray UArray Word32
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word32 -> (i, i) # numElements :: Ix i => UArray i Word32 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Word32)] -> UArray i Word32 # unsafeAt :: Ix i => UArray i Word32 -> Int -> Word32 # unsafeReplace :: Ix i => UArray i Word32 -> [(Int, Word32)] -> UArray i Word32 # unsafeAccum :: Ix i => (Word32 -> e' -> Word32) -> UArray i Word32 -> [(Int, e')] -> UArray i Word32 # unsafeAccumArray :: Ix i => (Word32 -> e' -> Word32) -> Word32 -> (i, i) -> [(Int, e')] -> UArray i Word32 #
MArray IOUArray Word32 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Word32 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Word32 -> IO Int # newArray :: Ix i => (i, i) -> Word32 -> IO (IOUArray i Word32) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Word32) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Word32) # unsafeRead :: Ix i => IOUArray i Word32 -> Int -> IO Word32 # unsafeWrite :: Ix i => IOUArray i Word32 -> Int -> Word32 -> IO () #
MArray (STUArray s) Word32 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word32 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word32 -> ST s Int # newArray :: Ix i => (i, i) -> Word32 -> ST s (STUArray s i Word32) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word32) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word32) # unsafeRead :: Ix i => STUArray s i Word32 -> Int -> ST s Word32 # unsafeWrite :: Ix i => STUArray s i Word32 -> Int -> Word32 -> ST s () #

Word64

data Word64 #

64-bit unsigned integer type

Instances

Instances details

PrintfArg Word64	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Word64 -> FieldFormatter # parseFormat :: Word64 -> ModifierParser #
Bits Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (.&.) :: Word64 -> Word64 -> Word64 # (.|.) :: Word64 -> Word64 -> Word64 # xor :: Word64 -> Word64 -> Word64 # complement :: Word64 -> Word64 # shift :: Word64 -> Int -> Word64 # rotate :: Word64 -> Int -> Word64 # zeroBits :: Word64 # bit :: Int -> Word64 # setBit :: Word64 -> Int -> Word64 # clearBit :: Word64 -> Int -> Word64 # complementBit :: Word64 -> Int -> Word64 # testBit :: Word64 -> Int -> Bool # bitSizeMaybe :: Word64 -> Maybe Int # bitSize :: Word64 -> Int # isSigned :: Word64 -> Bool # shiftL :: Word64 -> Int -> Word64 # unsafeShiftL :: Word64 -> Int -> Word64 # shiftR :: Word64 -> Int -> Word64 # unsafeShiftR :: Word64 -> Int -> Word64 # rotateL :: Word64 -> Int -> Word64 # rotateR :: Word64 -> Int -> Word64 # popCount :: Word64 -> Int #
FiniteBits Word64	Since: base-4.6.0.0
Instance details Defined in GHC.Internal.Word Methods finiteBitSize :: Word64 -> Int # countLeadingZeros :: Word64 -> Int # countTrailingZeros :: Word64 -> Int #
Bounded Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods minBound :: Word64 # maxBound :: Word64 #
Enum Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods succ :: Word64 -> Word64 # pred :: Word64 -> Word64 # toEnum :: Int -> Word64 # fromEnum :: Word64 -> Int # enumFrom :: Word64 -> [Word64] # enumFromThen :: Word64 -> Word64 -> [Word64] # enumFromTo :: Word64 -> Word64 -> [Word64] # enumFromThenTo :: Word64 -> Word64 -> Word64 -> [Word64] #
Storable Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Word64 -> Int # alignment :: Word64 -> Int # peekElemOff :: Ptr Word64 -> Int -> IO Word64 # pokeElemOff :: Ptr Word64 -> Int -> Word64 -> IO () # peekByteOff :: Ptr b -> Int -> IO Word64 # pokeByteOff :: Ptr b -> Int -> Word64 -> IO () # peek :: Ptr Word64 -> IO Word64 # poke :: Ptr Word64 -> Word64 -> IO () #
Ix Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods range :: (Word64, Word64) -> [Word64] # index :: (Word64, Word64) -> Word64 -> Int # unsafeIndex :: (Word64, Word64) -> Word64 -> Int # inRange :: (Word64, Word64) -> Word64 -> Bool # rangeSize :: (Word64, Word64) -> Int # unsafeRangeSize :: (Word64, Word64) -> Int #
Num Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (+) :: Word64 -> Word64 -> Word64 # (-) :: Word64 -> Word64 -> Word64 # (*) :: Word64 -> Word64 -> Word64 # negate :: Word64 -> Word64 # abs :: Word64 -> Word64 # signum :: Word64 -> Word64 # fromInteger :: Integer -> Word64 #
Read Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Word64 # readList :: ReadS [Word64] # readPrec :: ReadPrec Word64 # readListPrec :: ReadPrec [Word64] #
Integral Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods quot :: Word64 -> Word64 -> Word64 # rem :: Word64 -> Word64 -> Word64 # div :: Word64 -> Word64 -> Word64 # mod :: Word64 -> Word64 -> Word64 # quotRem :: Word64 -> Word64 -> (Word64, Word64) # divMod :: Word64 -> Word64 -> (Word64, Word64) # toInteger :: Word64 -> Integer #
Real Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods toRational :: Word64 -> Rational #
Show Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods showsPrec :: Int -> Word64 -> ShowS # show :: Word64 -> String # showList :: [Word64] -> ShowS #
Eq Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods (==) :: Word64 -> Word64 -> Bool # (/=) :: Word64 -> Word64 -> Bool #
Ord Word64	Since: base-2.1
Instance details Defined in GHC.Internal.Word Methods compare :: Word64 -> Word64 -> Ordering # (<) :: Word64 -> Word64 -> Bool # (<=) :: Word64 -> Word64 -> Bool # (>) :: Word64 -> Word64 -> Bool # (>=) :: Word64 -> Word64 -> Bool # max :: Word64 -> Word64 -> Word64 # min :: Word64 -> Word64 -> Word64 #
Element Word64 Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy Word64 -> DType Source # putElement :: Endian -> Word64 -> Put Source # getElement :: Endian -> Get Word64 Source #
IArray UArray Word64
Instance details Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word64 -> (i, i) # numElements :: Ix i => UArray i Word64 -> Int # unsafeArray :: Ix i => (i, i) -> [(Int, Word64)] -> UArray i Word64 # unsafeAt :: Ix i => UArray i Word64 -> Int -> Word64 # unsafeReplace :: Ix i => UArray i Word64 -> [(Int, Word64)] -> UArray i Word64 # unsafeAccum :: Ix i => (Word64 -> e' -> Word64) -> UArray i Word64 -> [(Int, e')] -> UArray i Word64 # unsafeAccumArray :: Ix i => (Word64 -> e' -> Word64) -> Word64 -> (i, i) -> [(Int, e')] -> UArray i Word64 #
MArray IOUArray Word64 IO
Instance details Defined in Data.Array.IO.Internals Methods getBounds :: Ix i => IOUArray i Word64 -> IO (i, i) # getNumElements :: Ix i => IOUArray i Word64 -> IO Int # newArray :: Ix i => (i, i) -> Word64 -> IO (IOUArray i Word64) # newArray_ :: Ix i => (i, i) -> IO (IOUArray i Word64) # unsafeNewArray_ :: Ix i => (i, i) -> IO (IOUArray i Word64) # unsafeRead :: Ix i => IOUArray i Word64 -> Int -> IO Word64 # unsafeWrite :: Ix i => IOUArray i Word64 -> Int -> Word64 -> IO () #
MArray (STUArray s) Word64 (ST s)
Instance details Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word64 -> ST s (i, i) # getNumElements :: Ix i => STUArray s i Word64 -> ST s Int # newArray :: Ix i => (i, i) -> Word64 -> ST s (STUArray s i Word64) # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word64) # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word64) # unsafeRead :: Ix i => STUArray s i Word64 -> Int -> ST s Word64 # unsafeWrite :: Ix i => STUArray s i Word64 -> Int -> Word64 -> ST s () #

Float32

type Float32 = Float Source #

Alias for Haskell Float (IEEE binary32 on supported targets).

Float64

type Float64 = Double Source #

Alias for Haskell Double (IEEE binary64 on supported targets).

Complex

data Complex a #

A data type representing complex numbers.

You can read about complex numbers on wikipedia.

In haskell, complex numbers are represented as a :+ b which can be thought of as representing \(a + bi\). For a complex number z, abs z is a number with the magnitude of z, but oriented in the positive real direction, whereas signum z has the phase of z, but unit magnitude. Apart from the loss of precision due to IEEE754 floating point numbers, it holds that z == abs z * signum z.

Note that Complex's instances inherit the deficiencies from the type parameter's. For example, Complex Float's Ord instance has similar problems to Float's.

As can be seen in the examples, the Foldable and Traversable instances traverse the real part first.

Examples

Expand

>>> (5.0 :+ 2.5) + 6.5
11.5 :+ 2.5

>>> abs (1.0 :+ 1.0) - sqrt 2.0
0.0 :+ 0.0

>>> abs (signum (4.0 :+ 3.0))
1.0 :+ 0.0

>>> foldr (:) [] (1 :+ 2)
[1,2]

>>> mapM print (1 :+ 2)
1
2

Constructors

!a :+ !a infix 6

forms a complex number from its real and imaginary rectangular components.

Instances

Instances details

MonadZip Complex	Since: base-4.15.0.0
Instance details Defined in Data.Complex Methods mzip :: Complex a -> Complex b -> Complex (a, b) # mzipWith :: (a -> b -> c) -> Complex a -> Complex b -> Complex c # munzip :: Complex (a, b) -> (Complex a, Complex b) #
Foldable1 Complex	Since: base-4.18.0.0
Instance details Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Complex m -> m # foldMap1 :: Semigroup m => (a -> m) -> Complex a -> m # foldMap1' :: Semigroup m => (a -> m) -> Complex a -> m # toNonEmpty :: Complex a -> NonEmpty a # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # head :: Complex a -> a # last :: Complex a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Complex a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Complex a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Complex a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Complex a -> b #
Eq1 Complex	>>> eq1 (1 :+ 2) (1 :+ 2) True >>> eq1 (1 :+ 2) (1 :+ 3) False Since: base-4.16.0.0
Instance details Defined in Data.Functor.Classes Methods liftEq :: (a -> b -> Bool) -> Complex a -> Complex b -> Bool #
Read1 Complex	>>> readPrec_to_S readPrec1 0 "(2 % 3) :+ (3 % 4)" :: [(Complex Rational, String)] [(2 % 3 :+ 3 % 4,"")] Since: base-4.16.0.0
Instance details Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Complex a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Complex a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Complex a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Complex a] #
Show1 Complex	>>> showsPrec1 0 (2 :+ 3) "" "2 :+ 3" Since: base-4.16.0.0
Instance details Defined in Data.Functor.Classes Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Complex a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Complex a] -> ShowS #
Applicative Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods pure :: a -> Complex a # (<*>) :: Complex (a -> b) -> Complex a -> Complex b # liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c # (*>) :: Complex a -> Complex b -> Complex b # (<*) :: Complex a -> Complex b -> Complex a #
Functor Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Monad Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods (>>=) :: Complex a -> (a -> Complex b) -> Complex b # (>>) :: Complex a -> Complex b -> Complex b # return :: a -> Complex a #
MonadFix Complex	Since: base-4.15.0.0
Instance details Defined in Data.Complex Methods mfix :: (a -> Complex a) -> Complex a #
Foldable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Traversable Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Generic1 Complex
Instance details Defined in Data.Complex Associated Types type Rep1 Complex Since: base-4.9.0.0 Instance details Defined in Data.Complex type Rep1 Complex = D1 ('MetaData "Complex" "Data.Complex" "base" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1)) Methods from1 :: Complex a -> Rep1 Complex a # to1 :: Rep1 Complex a -> Complex a #
Data a => Data (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Complex a -> c (Complex a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Complex a) # toConstr :: Complex a -> Constr # dataTypeOf :: Complex a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Complex a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Complex a)) # gmapT :: (forall b. Data b => b -> b) -> Complex a -> Complex a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r # gmapQ :: (forall d. Data d => d -> u) -> Complex a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Complex a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) #
RealFloat a => Floating (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods pi :: Complex a # exp :: Complex a -> Complex a # log :: Complex a -> Complex a # sqrt :: Complex a -> Complex a # (**) :: Complex a -> Complex a -> Complex a # logBase :: Complex a -> Complex a -> Complex a # sin :: Complex a -> Complex a # cos :: Complex a -> Complex a # tan :: Complex a -> Complex a # asin :: Complex a -> Complex a # acos :: Complex a -> Complex a # atan :: Complex a -> Complex a # sinh :: Complex a -> Complex a # cosh :: Complex a -> Complex a # tanh :: Complex a -> Complex a # asinh :: Complex a -> Complex a # acosh :: Complex a -> Complex a # atanh :: Complex a -> Complex a # log1p :: Complex a -> Complex a # expm1 :: Complex a -> Complex a # log1pexp :: Complex a -> Complex a # log1mexp :: Complex a -> Complex a #
Storable a => Storable (Complex a)	Since: base-4.8.0.0
Instance details Defined in Data.Complex Methods sizeOf :: Complex a -> Int # alignment :: Complex a -> Int # peekElemOff :: Ptr (Complex a) -> Int -> IO (Complex a) # pokeElemOff :: Ptr (Complex a) -> Int -> Complex a -> IO () # peekByteOff :: Ptr b -> Int -> IO (Complex a) # pokeByteOff :: Ptr b -> Int -> Complex a -> IO () # peek :: Ptr (Complex a) -> IO (Complex a) # poke :: Ptr (Complex a) -> Complex a -> IO () #
Generic (Complex a)
Instance details Defined in Data.Complex Associated Types type Rep (Complex a) Since: base-4.9.0.0 Instance details Defined in Data.Complex type Rep (Complex a) = D1 ('MetaData "Complex" "Data.Complex" "base" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))) Methods from :: Complex a -> Rep (Complex a) x # to :: Rep (Complex a) x -> Complex a #
RealFloat a => Num (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a # (-) :: Complex a -> Complex a -> Complex a # (*) :: Complex a -> Complex a -> Complex a # negate :: Complex a -> Complex a # abs :: Complex a -> Complex a # signum :: Complex a -> Complex a # fromInteger :: Integer -> Complex a #
Read a => Read (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods readsPrec :: Int -> ReadS (Complex a) # readList :: ReadS [Complex a] # readPrec :: ReadPrec (Complex a) # readListPrec :: ReadPrec [Complex a] #
RealFloat a => Fractional (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (/) :: Complex a -> Complex a -> Complex a # recip :: Complex a -> Complex a # fromRational :: Rational -> Complex a #
Show a => Show (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
Eq a => Eq (Complex a)	Since: base-2.1
Instance details Defined in Data.Complex Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
Field (Complex Double) Source #
Instance details Defined in HMath.API.Algebra Methods invert :: Complex Double -> Either MathError (Complex Double) Source #
FloatingPoint (Complex Double) Source #
Instance details Defined in HMath.API.Algebra Methods machineEpsilon :: proxy (Complex Double) -> Double Source # finiteScalar :: Complex Double -> Bool Source #
Numeric (Complex Double) Source #
Instance details Defined in HMath.API.Algebra Methods rational :: Rational -> Either MathError (Complex Double) Source #
Ring (Complex Double) Source #
Instance details Defined in HMath.API.Algebra Methods zero :: Complex Double Source # one :: Complex Double Source # plus :: Complex Double -> Complex Double -> Complex Double Source # times :: Complex Double -> Complex Double -> Complex Double Source # negative :: Complex Double -> Complex Double Source # integer :: Integer -> Complex Double Source #
Scalar (Complex Double) Source #
Instance details Defined in HMath.API.Algebra Methods conjugateScalar :: Complex Double -> Complex Double Source #
Element (Complex Double) Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy (Complex Double) -> DType Source # putElement :: Endian -> Complex Double -> Put Source # getElement :: Endian -> Get (Complex Double) Source #
Element (Complex Float) Source #
Instance details Defined in HMath.Interchange.Array Methods elementType :: proxy (Complex Float) -> DType Source # putElement :: Endian -> Complex Float -> Put Source # getElement :: Endian -> Get (Complex Float) Source #
type Rep1 Complex	Since: base-4.9.0.0
Instance details Defined in Data.Complex type Rep1 Complex = D1 ('MetaData "Complex" "Data.Complex" "base" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))
type Rep (Complex a)	Since: base-4.9.0.0
Instance details Defined in Data.Complex type Rep (Complex a) = D1 ('MetaData "Complex" "Data.Complex" "base" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))

Rational

type Rational = Ratio Integer #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

RoundingMode

data RoundingMode Source #

Software rounding direction: nearest-even,toward zero,toward positive infinity,or toward negative infinity. Host CPU rounding mode is unchanged.

Constructors

NearestEven
TowardZero
TowardPositive
TowardNegative

Instances

Instances details

Show RoundingMode Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> RoundingMode -> ShowS # show :: RoundingMode -> String # showList :: [RoundingMode] -> ShowS #
Eq RoundingMode Source #
Instance details Defined in HMath.Numeric Methods (==) :: RoundingMode -> RoundingMode -> Bool # (/=) :: RoundingMode -> RoundingMode -> Bool #

NumericException

data NumericException Source #

Software operation flags: invalid operation,division by zero,overflow,underflow,or inexact conversion.

Constructors

InvalidOperation
DivisionByZero
NumericOverflow
NumericUnderflow
Inexact

Instances

Instances details

Show NumericException Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> NumericException -> ShowS # show :: NumericException -> String # showList :: [NumericException] -> ShowS #
Eq NumericException Source #
Instance details Defined in HMath.Numeric Methods (==) :: NumericException -> NumericException -> Bool # (/=) :: NumericException -> NumericException -> Bool #

Rounded

data Rounded a Source #

Rounded numeric result paired with software exception flags. Inspect flags when intentional precision loss matters.

Constructors

Rounded
Fields roundedValue :: a Value produced by the explicitly selected software rounding operation. numericalExceptions :: [NumericException] Software rounding flags; these do not modify the host IEEE exception environment.

Instances

Instances details

Show a => Show (Rounded a) Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> Rounded a -> ShowS # show :: Rounded a -> String # showList :: [Rounded a] -> ShowS #
Eq a => Eq (Rounded a) Source #
Instance details Defined in HMath.Numeric Methods (==) :: Rounded a -> Rounded a -> Bool # (/=) :: Rounded a -> Rounded a -> Bool #

roundRational

roundRational :: RoundingMode -> Rational -> Integer Source #

Given software rounding mode then exact Rational, return Integer rounded by nearest-even, toward zero, toward positive infinity, or toward negative infinity. No host rounding flags are changed.

IEEEClass

data IEEEClass Source #

IEEE classification distinguishing NaN,signed infinity,signed zero,subnormal,and normal finite values.

Constructors

NotANumber
PositiveInfinity
NegativeInfinity
PositiveZero
NegativeZero
Subnormal
Normal

Instances

Instances details

Show IEEEClass Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> IEEEClass -> ShowS # show :: IEEEClass -> String # showList :: [IEEEClass] -> ShowS #
Eq IEEEClass Source #
Instance details Defined in HMath.Numeric Methods (==) :: IEEEClass -> IEEEClass -> Bool # (/=) :: IEEEClass -> IEEEClass -> Bool #

classify

classify :: RealFloat a => a -> IEEEClass Source #

Classify a RealFloat value as NaN, signed infinity, signed zero, subnormal, or normal. Signed zero is distinguished with isNegativeZero.

NumericLimits

data NumericLimits a Source #

Format limits and precision metadata derived from RealFloat or the explicit 16-bit format definition.

Constructors

NumericLimits

Fields minimumNormal :: a Smallest positive normal value of the represented floating format. minimumSubnormal :: a Smallest positive subnormal value of the represented floating format. maximumFinite :: a Largest finite positive value of the represented floating format. machineEpsilon :: a Gap between one and its next larger representable value. significandDigits :: Int Number of radix digits in the floating significand. minimumExponent :: Int Lower exponent bound returned by RealFloat.floatRange. maximumExponent :: Int Upper exponent bound returned by RealFloat.floatRange.

Instances

Instances details

Show a => Show (NumericLimits a) Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> NumericLimits a -> ShowS # show :: NumericLimits a -> String # showList :: [NumericLimits a] -> ShowS #
Eq a => Eq (NumericLimits a) Source #
Instance details Defined in HMath.Numeric Methods (==) :: NumericLimits a -> NumericLimits a -> Bool # (/=) :: NumericLimits a -> NumericLimits a -> Bool #

numericLimits

numericLimits :: RealFloat a => a -> NumericLimits a Source #

Derived from RealFloat radixdigitsrange, not hardcoded for Double.

integerLimits

integerLimits :: (Integral a, Bounded a) => a -> (Integer, Integer) Source #

Given a bounded integral type witness, return its exact (minimum,maximum) as Integers. The witness value is used only to select the type.

float16Limits

float16Limits :: NumericLimits Double Source #

Limits returned as exact binary64 values for the two 16-bit storage formats.

bfloat16Limits

bfloat16Limits :: NumericLimits Double Source #

Limits returned as exact binary64 values for the two 16-bit storage formats.

nextAfter

nextAfter :: RealFloat a => a -> a -> a Source #

Adjacent representable value toward target, including gradual underflow. Equal signed zeros return the target; NaN propagates. Supports binary formats.

frexp

frexp :: RealFloat a => a -> (a, Int) Source #

x=m*2^e, with abs m in [1/2,1) for nonzero finite binary inputs.

ldexp

ldexp :: RealFloat a => a -> Int -> a Source #

Given real value then Int exponent, scale by the numeric radix to that power using scaleFloat (binary types use powers of two). IEEE overflow/underflow follows the host type; no Either check is added.

ulpDistance

ulpDistance :: Double -> Double -> Either MathError Integer Source #

IEEE binary64 distance. Signed zeros compare equal; NaN is rejected.

withinULPs

withinULPs :: Integer -> Double -> Double -> Bool Source #

Given nonnegative allowed ULP distance then two Doubles, test their binary64 representable-value distance. Signed zeros compare equal. Negative tolerance or NaN gives False.

safeIntegralCast

safeIntegralCast :: (Integral a, Integral b, Bounded b) => a -> Either MathError b Source #

Convert an integral value to a bounded integral destination only if in range. Return Left DomainError rather than wrap or truncate out-of-range input.

saturatingCast

saturatingCast :: (Integral a, Integral b, Bounded b) => a -> b Source #

Convert an integral value to a bounded integral destination, clamping to minBound/maxBound when out of range. No error result is produced.

realToIntegral

realToIntegral :: (RealFloat a, Integral b, Bounded b) => RoundingMode -> a -> Either MathError b Source #

Given software rounding mode then finite real value, round exactly through Rational then range-check the bounded integral destination. Non-finite or out-of-range input returns Left DomainError.

narrowFloat

narrowFloat :: (RealFloat a, RealFloat b) => a -> Either MathError b Source #

A narrowing conversion must be finite and exact; choose explicit quantized Float16/BigFloat rounding APIs when loss of precision is intentional.

Float16

data Float16 Source #

IEEE binary16 and bfloat16 storage. Conversion rounds directly from the exact binary64 value (no intermediate binary32 rounding), preserving signed zero and infinity. NaNs are canonical quiet NaNs. All four rounding modes report inexact, overflow and tininess-after-rounding underflow flags.

Instances

Instances details

Show Float16 Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> Float16 -> ShowS # show :: Float16 -> String # showList :: [Float16] -> ShowS #
Eq Float16 Source #
Instance details Defined in HMath.Numeric Methods (==) :: Float16 -> Float16 -> Bool # (/=) :: Float16 -> Float16 -> Bool #

float16

float16 :: RoundingMode -> Double -> Rounded Float16 Source #

Given rounding mode then Double, round directly to IEEE binary16 and return Rounded storage plus software flags. Preserve signed zero/infinity; canonicalize NaN. Flags report inexact, overflow, and tininess-after-rounding underflow.

fromFloat16

fromFloat16 :: Float16 -> Double Source #

Decode binary16 storage to Double, preserving finite values, signed zero, infinity and NaN classification. Every finite binary16 value is exactly representable as Double.

float16Bits

float16Bits :: Float16 -> Word16 Source #

Return raw IEEE binary16 storage bits, including sign, exponent and fraction, as Word16.

float16FromBits

float16FromBits :: Word16 -> Float16 Source #

Construct binary16 storage from raw Word16 without validation or rounding; all bit patterns, including NaNs, are representable.

BFloat16

data BFloat16 Source #

Opaque bfloat16 storage with 8 exponent and 7 explicit fraction bits. Use bfloat16 for rounded conversion or bfloat16FromBits for exact storage construction.

Instances

Instances details

Show BFloat16 Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> BFloat16 -> ShowS # show :: BFloat16 -> String # showList :: [BFloat16] -> ShowS #
Eq BFloat16 Source #
Instance details Defined in HMath.Numeric Methods (==) :: BFloat16 -> BFloat16 -> Bool # (/=) :: BFloat16 -> BFloat16 -> Bool #

bfloat16

bfloat16 :: RoundingMode -> Double -> Rounded BFloat16 Source #

Given rounding mode then Double, round directly to bfloat16 without an intermediate binary32 rounding. Return Rounded storage and software flags, preserving signed zero/infinity and canonicalizing NaN.

fromBFloat16

fromBFloat16 :: BFloat16 -> Double Source #

Decode bfloat16 storage to Double, preserving finite values, signed zero and non-finite classification.

bfloat16Bits

bfloat16Bits :: BFloat16 -> Word16 Source #

Return raw bfloat16 storage bits as Word16.

bfloat16FromBits

bfloat16FromBits :: Word16 -> BFloat16 Source #

Construct bfloat16 storage from raw Word16 without conversion; all bit patterns are retained.

BigFloat

data BigFloat Source #

An unbounded-exponent binary floating value backed by an exact Rational, rounded to a runtime number of significant bits (2..1,000,000). Unlike Double, this is genuinely configurable precision. No NaN/infinity or hidden CPU flags. Algebraic operations round once, nearest-even; explicit construction can select any RoundingMode. Transcendentals use guard bits and rational series.

Instances

Instances details

Show BigFloat Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> BigFloat -> ShowS # show :: BigFloat -> String # showList :: [BigFloat] -> ShowS #
Eq BigFloat Source #
Instance details Defined in HMath.Numeric Methods (==) :: BigFloat -> BigFloat -> Bool # (/=) :: BigFloat -> BigFloat -> Bool #

bigFloat

bigFloat :: Int -> RoundingMode -> Rational -> Either MathError (Rounded BigFloat) Source #

Given precision in [2,1000000] bits, rounding mode, then Rational, construct configurable-precision BigFloat plus Inexact flag if rounded. Invalid precision returns Left InvalidArgument. Exponents are unbounded; no IEEE NaN/infinity is stored.

bigPrecision

bigPrecision :: BigFloat -> Int Source #

Return the runtime number of significant binary bits retained by a BigFloat.

bigRational

bigRational :: BigFloat -> Rational Source #

Return the exact Rational value of the already-rounded BigFloat, without another conversion or rounding.

bigToDouble

bigToDouble :: BigFloat -> Double Source #

Round BigFloat to host Double through fromRational. This may overflow/underflow or lose precision; it returns no software flags or Either validation.

bigAdd

bigAdd :: BigFloat -> BigFloat -> Either MathError BigFloat Source #

Add two BigFloats exactly then round once to the larger operand precision, nearest-even. Return the new BigFloat in Either.

bigSubtract

bigSubtract :: BigFloat -> BigFloat -> Either MathError BigFloat Source #

Subtract the second BigFloat from the first, rounding once nearest-even at the larger operand precision.

bigMultiply

bigMultiply :: BigFloat -> BigFloat -> Either MathError BigFloat Source #

Multiply two BigFloats exactly then round once nearest-even to the larger operand precision.

bigDivide

bigDivide :: BigFloat -> BigFloat -> Either MathError BigFloat Source #

Divide two BigFloats and round once nearest-even to the larger precision. Zero divisor returns Left DomainError.

bigSqrt

bigSqrt :: BigFloat -> Either MathError BigFloat Source #

Compute nonnegative BigFloat square root using integer/rational guard precision then round to the input precision. Negative input returns Left DomainError; zero succeeds.

bigExp

bigExp :: BigFloat -> Either MathError BigFloat Source #

Absolute tail controlled rational series; final rounding is accurate to the requested precision up to one final ulp, not a correctly-rounded promise.

bigLog

bigLog :: BigFloat -> Either MathError BigFloat Source #

Compute natural logarithm at the BigFloat precision using rational series and guard bits. Require positive input; invalid domain/resource limits return Left MathError. Final rounding has the module's documented accuracy limits.

extended

extended :: Rational -> Either MathError BigFloat Source #

Software extended precision: 64 significant bits, unbounded exponent.

mixedAdd

mixedAdd :: BigFloat -> Double -> Either MathError BigFloat Source #

Given BigFloat then finite Double, add via exact Rational intermediates at max(BigFloat precision,53) bits, nearest-even. Non-finite Double fails.

mixedMultiply

mixedMultiply :: BigFloat -> Double -> Either MathError BigFloat Source #

Given BigFloat then finite Double, multiply at max(BigFloat precision,53) bits using exact intermediates and nearest-even. Non-finite Double fails.

Fixed

data Fixed Source #

Runtime-scale base-ten fixed point: coefficient * 10^(-scale). All constructors and arithmetic use explicit rounding and report inexactness.

Instances

Instances details

Show Fixed Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> Fixed -> ShowS # show :: Fixed -> String # showList :: [Fixed] -> ShowS #
Eq Fixed Source #
Instance details Defined in HMath.Numeric Methods (==) :: Fixed -> Fixed -> Bool # (/=) :: Fixed -> Fixed -> Bool #

fixed

fixed :: Int -> RoundingMode -> Rational -> Either MathError (Rounded Fixed) Source #

Given decimal scale in [0,10000], rounding mode, then Rational, return Rounded Fixed and Inexact when required. Invalid scale fails. This scale counts decimal fractional places, not significant digits.

fixedScale

fixedScale :: Fixed -> Int Source #

Return nonnegative decimal scale s of a Fixed value; its exact value is coefficient / 10^s.

fixedCoefficient

fixedCoefficient :: Fixed -> Integer Source #

Return exact stored Integer coefficient of a Fixed value, before division by 10^fixedScale.

fixedRational

fixedRational :: Fixed -> Rational Source #

Return exact coefficient/10^scale represented by a Fixed value, without rounding.

fixedAdd

fixedAdd :: Fixed -> Fixed -> Either MathError (Rounded Fixed) Source #

Add two Fixed values using the larger decimal scale, nearest-even, returning Rounded result and software flags.

fixedMultiply

fixedMultiply :: RoundingMode -> Fixed -> Fixed -> Either MathError (Rounded Fixed) Source #

Given rounding mode then two Fixed values, multiply and round to their larger scale, returning Rounded result and flags.

fixedDivide

fixedDivide :: RoundingMode -> Fixed -> Fixed -> Either MathError (Rounded Fixed) Source #

Given rounding mode then Fixed numerator and denominator, divide and round to their larger scale. Zero divisor returns Left DomainError; successful rounding flags are retained.

Decimal

data Decimal Source #

Opaque decimal fixed-point value with fractional-place scale, built through decimal with explicit rounding. This is not an implicit significant-digit decimal context.

Instances

Instances details

Show Decimal Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> Decimal -> ShowS # show :: Decimal -> String # showList :: [Decimal] -> ShowS #
Eq Decimal Source #
Instance details Defined in HMath.Numeric Methods (==) :: Decimal -> Decimal -> Bool # (/=) :: Decimal -> Decimal -> Bool #

decimal

decimal :: Int -> RoundingMode -> Rational -> Either MathError (Rounded Decimal) Source #

Given decimal fractional-place scale, rounding mode, then Rational, construct Rounded Decimal through fixed. Scale must lie in [0,10000]; no significant-digit interpretation is implied.

decimalRational

decimalRational :: Decimal -> Rational Source #

Return exact Rational value stored in a Decimal without further rounding.

decimalAdd

decimalAdd :: Decimal -> Decimal -> Either MathError (Rounded Decimal) Source #

Add two Decimals at their larger decimal scale, nearest-even, returning Rounded result and software flags.

decimalMultiply

decimalMultiply :: RoundingMode -> Decimal -> Decimal -> Either MathError (Rounded Decimal) Source #

Given rounding mode then two Decimals, multiply at the larger fractional-place scale and return Rounded result with flags.

decimalDivide

decimalDivide :: RoundingMode -> Decimal -> Decimal -> Either MathError (Rounded Decimal) Source #

Given rounding mode then two Decimals, divide at their larger scale and return Rounded result. Zero divisor returns Left DomainError.

Interval

data Interval Source #

Finite closed binary64 intervals. Arithmetic endpoints are rounded outward using exact rationals, so results enclose exact real arithmetic. Unbounded output is rejected; division rejects denominators containing zero.

Instances

Instances details

Show Interval Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> Interval -> ShowS # show :: Interval -> String # showList :: [Interval] -> ShowS #
Eq Interval Source #
Instance details Defined in HMath.Numeric Methods (==) :: Interval -> Interval -> Bool # (/=) :: Interval -> Interval -> Bool #

interval

interval :: Double -> Double -> Either MathError Interval Source #

Given finite lower and upper bounds in increasing order, construct a closed binary64 Interval. Reversed or non-finite bounds fail. Equal endpoints are valid.

intervalBounds

intervalBounds :: Interval -> (Double, Double) Source #

Return (lower,upper) binary64 endpoints of a validated closed interval.

intervalAdd

intervalAdd :: Interval -> Interval -> Either MathError Interval Source #

Add finite intervals with exact Rational endpoint arithmetic rounded outward, enclosing the exact sum. Results requiring unbounded endpoints fail.

intervalSubtract

intervalSubtract :: Interval -> Interval -> Either MathError Interval Source #

Subtract intervals with endpoints [a-d,b-c], rounding outward. Non-finite/unbounded resulting endpoints return Left MathError.

intervalMultiply

intervalMultiply :: Interval -> Interval -> Either MathError Interval Source #

Multiply intervals using the minimum/maximum of all four endpoint products and outward rounding. Reject unbounded output.

intervalDivide

intervalDivide :: Interval -> Interval -> Either MathError Interval Source #

Divide intervals using endpoint quotients with outward rounding. A divisor interval containing zero returns Left DomainError; unbounded output also fails.

intervalContains

intervalContains :: Interval -> Double -> Bool Source #

Given interval then Double, test closed-bound membership lower<=x<=upper. NaN comparisons give False.

Dual

data Dual a Source #

Forward-mode automatic differentiation, f(a+b epsilon), epsilon^2=0. Elementary functions follow host IEEE domains; checked algorithms can inspect both components. abs at zero uses derivative zero (a chosen subgradient).

Constructors

Dual
Fields primal :: a Primal component of a forward-mode Dual number. tangent :: a Directional derivative component of a forward-mode Dual number.

Instances

Instances details

Floating a => Floating (Dual a) Source #
Instance details Defined in HMath.Numeric Methods pi :: Dual a # exp :: Dual a -> Dual a # log :: Dual a -> Dual a # sqrt :: Dual a -> Dual a # (**) :: Dual a -> Dual a -> Dual a # logBase :: Dual a -> Dual a -> Dual a # sin :: Dual a -> Dual a # cos :: Dual a -> Dual a # tan :: Dual a -> Dual a # asin :: Dual a -> Dual a # acos :: Dual a -> Dual a # atan :: Dual a -> Dual a # sinh :: Dual a -> Dual a # cosh :: Dual a -> Dual a # tanh :: Dual a -> Dual a # asinh :: Dual a -> Dual a # acosh :: Dual a -> Dual a # atanh :: Dual a -> Dual a # log1p :: Dual a -> Dual a # expm1 :: Dual a -> Dual a # log1pexp :: Dual a -> Dual a # log1mexp :: Dual a -> Dual a #
Num a => Num (Dual a) Source #
Instance details Defined in HMath.Numeric Methods (+) :: Dual a -> Dual a -> Dual a # (-) :: Dual a -> Dual a -> Dual a # (*) :: Dual a -> Dual a -> Dual a # negate :: Dual a -> Dual a # abs :: Dual a -> Dual a # signum :: Dual a -> Dual a # fromInteger :: Integer -> Dual a #
Fractional a => Fractional (Dual a) Source #
Instance details Defined in HMath.Numeric Methods (/) :: Dual a -> Dual a -> Dual a # recip :: Dual a -> Dual a # fromRational :: Rational -> Dual a #
Show a => Show (Dual a) Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> Dual a -> ShowS # show :: Dual a -> String # showList :: [Dual a] -> ShowS #
Eq a => Eq (Dual a) Source #
Instance details Defined in HMath.Numeric Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #

derivative

derivative :: Num a => (Dual a -> Dual a) -> a -> a Source #

Given a function on Dual numbers then primal input x, seed Dual x 1 and extract the output tangent. Arithmeticdomains follow Dual's NumFloating instances; no Either validation is added.

Quaternion

data Quaternion a Source #

Hamilton quaternion (real, i, j, k); multiplication is noncommutative.

Constructors

Quaternion a a a a

Instances

Instances details

RealFloat a => Num (Quaternion a) Source #
Instance details Defined in HMath.Numeric Methods (+) :: Quaternion a -> Quaternion a -> Quaternion a # (-) :: Quaternion a -> Quaternion a -> Quaternion a # (*) :: Quaternion a -> Quaternion a -> Quaternion a # negate :: Quaternion a -> Quaternion a # abs :: Quaternion a -> Quaternion a # signum :: Quaternion a -> Quaternion a # fromInteger :: Integer -> Quaternion a #
Show a => Show (Quaternion a) Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> Quaternion a -> ShowS # show :: Quaternion a -> String # showList :: [Quaternion a] -> ShowS #
Eq a => Eq (Quaternion a) Source #
Instance details Defined in HMath.Numeric Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #

quaternionConjugate

quaternionConjugate :: Num a => Quaternion a -> Quaternion a Source #

For Quaternion real i j k, negate the three imaginary components and preserve the real part.

quaternionNorm

quaternionNorm :: RealFloat a => Quaternion a -> a Source #

Return scaled Euclidean norm of four quaternion components, reducing avoidable intermediate overflow. Empty/zero-component quaternion has norm zero.

quaternionInverse

quaternionInverse :: RealFloat a => Quaternion a -> Either MathError (Quaternion a) Source #

Invert a finite nonzero quaternion using scaled norm arithmetic. Zero/non-finite input returns DomainError; non-finite inverse returns NonFiniteResult.

rotateVector

rotateVector :: RealFloat a => Quaternion a -> (a, a, a) -> Either MathError (a, a, a) Source #

Given nonzero finite quaternion q then (x,y,z), return imaginary part of q*(0,x,y,z)*inverse(q). Normalization of q is implicit in the inverse; invalid input/result returns Left MathError.

DualQuaternion

data DualQuaternion a Source #

Real and dual quaternion pair, commonly representing a rigid rotation/translation. Construct normalized rigid transforms with rigidTransform.

Constructors

DualQuaternion (Quaternion a) (Quaternion a)

Instances

Instances details

Show a => Show (DualQuaternion a) Source #
Instance details Defined in HMath.Numeric Methods showsPrec :: Int -> DualQuaternion a -> ShowS # show :: DualQuaternion a -> String # showList :: [DualQuaternion a] -> ShowS #
Eq a => Eq (DualQuaternion a) Source #
Instance details Defined in HMath.Numeric Methods (==) :: DualQuaternion a -> DualQuaternion a -> Bool # (/=) :: DualQuaternion a -> DualQuaternion a -> Bool #

dualQuaternionMultiply

dualQuaternionMultiply :: RealFloat a => DualQuaternion a -> DualQuaternion a -> DualQuaternion a Source #

Multiply real/dual quaternion pairs as (a,b)*(c,d)=(a*c,a*d+b*c). Return the product using host quaternion arithmetic; no validation or normalization is added.

dualQuaternionInverse

dualQuaternionInverse :: RealFloat a => DualQuaternion a -> Either MathError (DualQuaternion a) Source #

Invert the real quaternion a, returning (inverse(a), -inverse(a)*b*inverse(a)). Invalid real part propagates quaternionInverse failure.

rigidTransform

rigidTransform :: RealFloat a => Quaternion a -> (a, a, a) -> Either MathError (DualQuaternion a) Source #

Construct a rigid transform from a nonzero rotation quaternion and translation.

transformPoint

transformPoint :: RealFloat a => DualQuaternion a -> (a, a, a) -> Either MathError (a, a, a) Source #

Given dual-quaternion transform then point tuple, rotate by its real part and add translation from twice the dual part times the real inverse. Invalid inverse or non-finite result fails.

kahanSum

kahanSum :: Num a => [a] -> a Source #

Sum a finite list using Kahan compensation; empty input yields zero. Arithmetic follows Num and compensation does not promise exact rounding or reject non-finite values.

neumaierSum

neumaierSum :: (Num a, Ord a) => [a] -> a Source #

Sum a finite list with Neumaier compensation, correcting for differing term magnitudes. Empty input gives zero; arithmetic follows the chosen ordered Num type.

pairwiseSum

pairwiseSum :: Num a => [a] -> a Source #

Recursively split and sum a finite list to reduce sequential rounding accumulation. Empty input gives zero. Arithmetic remains that of the chosen Num type.

logsumexp

logsumexp :: RealFloat a => [a] -> Either MathError a Source #

Empty input is -infinity; +infinity dominates finite/-infinite inputs. NaN is rejected, and an all -infinity input is -infinity.

sumErrorBound

sumErrorBound :: RealFloat a => [a] -> Either MathError a Source #

Conservative sequential sum bound gamma_(n-1) * sum abs x. Returns infinity when n*u >= 1 or finite inputs overflow the bound. Does not claim bounds in the presence of underflow; an extra (n-1)*minimumSubnormal term covers it.