h&2(Y      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                                                                       Safe-InferredT Safe-Inferred 18; U rounded-hw(A type tagged with a rounding direction.*The rounding direction is effective for a single operation. You won't get the correctly-rounded result for a compound expression like ((a - b * c) :: Rounded 'TowardInf Double.'In particular, a negative literal like -0.1 :: Rounded r Double/ doesn't yield the correctly-rounded value for -0.1". To get the correct value, call  explicitly (i.e. 'fromRational (-0.1) :: Rounded r Double ) or use NegativeLiterals extension.X rounded-hwThis class allows you to recover the runtime value from a type-level rounding mode.See a.Y rounded-hw3The type for IEEE754 rounding-direction attributes.Z rounded-hw4Round to the nearest value (IEEE754 roundTiesToEven)[ rounded-hw,Round downward (IEEE754 roundTowardNegative)\ rounded-hw*Round upward (IEEE754 roundTowardPositive)] rounded-hw+Round toward zero (IEEE754 roundTowardZero)` rounded-hw(Returns the opposite rounding direction. TowardNegInf and  TowardInf are swapped.a rounded-hw1Recovers the value from type-level rounding mode.b rounded-hw$Lifts a rounding mode to type-level.R_S^UVWXYZ[\]`ab Safe-Inferred1 cdefg Safe-Inferred1i rounded-hw+\inftyj rounded-hw-\inftym rounded-hwThe correctly-rounded value of \pin rounded-hwThe correctly-rounded value of \pio rounded-hwThe correctly-rounded value of 3\pip rounded-hwThe correctly-rounded value of 3\piq rounded-hwThe correctly-rounded value of 5\pir rounded-hwThe correctly-rounded value of 5\pis rounded-hwThe correctly-rounded value of \log_e 2t rounded-hwThe correctly-rounded value of \log_e 2u rounded-hwThe correctly-rounded value of \exp(1)v rounded-hwThe correctly-rounded value of \exp(1)w rounded-hwThe correctly-rounded value of  \exp(1/2)x rounded-hwThe correctly-rounded value of  \exp(1/2)y rounded-hwThe correctly-rounded value of  \exp(-1/2)z rounded-hwThe correctly-rounded value of  \exp(-1/2){ rounded-hwThe correctly-rounded value of \sqrt{2}| rounded-hwThe correctly-rounded value of \sqrt{2}} rounded-hwThe correctly-rounded value of  \sqrt{2}-1~ rounded-hwThe correctly-rounded value of  \sqrt{2}-1 rounded-hwThe correctly-rounded value of  1/\sqrt{2} rounded-hwThe correctly-rounded value of  1/\sqrt{2} rounded-hwThe correctly-rounded value of  3-2\sqrt{2} rounded-hwThe correctly-rounded value of  3-2\sqrt{2} rounded-hwThe correctly-rounded value of  2-\sqrt{2} rounded-hwThe correctly-rounded value of  2-\sqrt{2}h~}|{zyxwvutsrqponmjikl Safe-Inferred 15 foldl ( r) 0 rounded-hwEquivalent to  zipWith .  rounded-hwEquivalent to  zipWith .  rounded-hwEquivalent to  zipWith .  rounded-hwEquivalent to  zipWith3 .  rounded-hwRounding-controlled version of . rounded-hwRounding-controlled version of . rounded-hwRounding-controlled version of . rounded-hw\x_lo x_hi y_lo y_hi -> intervalAdd (Rounded x_lo) (Rounded x_hi) (Rounded y_lo) (Rounded y_hi) == (Rounded (roundedAdd TowardNegInf x_lo y_lo), Rounded (roundedAdd TowardInf x_hi y_hi)) rounded-hw\x_lo x_hi y_lo y_hi -> intervalSub (Rounded x_lo) (Rounded x_hi) (Rounded y_lo) (Rounded y_hi) == (Rounded (roundedSub TowardNegInf x_lo y_hi), Rounded (roundedSub TowardInf x_hi y_lo)) rounded-hw(Returns the name of backend as a string.Example: >>> :m + Data.Proxy >>> ( (Proxy :: Proxy Double) "FastFFI+SSE2" 3R_S^UVWXY]\Z[`ab Safe-Inferred 1;dRSNone None None 1; rounded-hw-A wrapper providing particular instances for ,  and .This type is different from CDouble from Foreign.C.Types. rounded-hw-A wrapper providing particular instances for ,  and .This type is different from CFloat from Foreign.C.Types.RQPONMLKJIHGFEDCBA@?>=<;:9876543210/.,*)_S-+('&%$#"!  ^RQPONMLKJIHGFEDCBA@?>=<;:9876543210/.,*)_S-+('&%$#"!  ^None 15;? RS RS Safe-Inferred15? Safe-Inferred rounded-hw:binaryFloatToDecimalDigitsRn ToNearest 3 (0.125 :: Double) ([1,2,5],0)9binaryFloatToDecimalDigitsRn ToNearest 3 (12.5 :: Double) ([1,2,5],2) rounded-hw?binaryFloatToFixedDecimalDigitsRn ToNearest 3 (0.125 :: Double)[1,2,5]>binaryFloatToFixedDecimalDigitsRn ToNearest 3 (12.5 :: Double) [1,2,5,0,0] rounded-hw,binaryFloatToDecimalDigits (0.125 :: Double) ([1,2,5],0)+binaryFloatToDecimalDigits (12.5 :: Double) ([1,2,5],2) rounded-hw0showEFloatRn ToNearest (Just 0) (0 :: Double) """0e0"/showEFloatRn ToNearest Nothing (0 :: Double) """0.0e0"1showEFloatRn ToNearest Nothing (0.5 :: Double) """5.0e-1" rounded-hw0showFFloatRn ToNearest (Just 0) (0 :: Double) """0"/showFFloatRn ToNearest Nothing (0 :: Double) """0.0"0showFFloatRn ToNearest Nothing (-0 :: Double) """-0.0"2showFFloatRn ToNearest Nothing (-0.5 :: Double) """-0.5" rounded-hw rounding mode rounded-hwprec rounded-hw1a non-negative number (zero, normal or subnormal) rounded-hw rounding mode rounded-hwprec rounded-hw1a non-negative number (zero, normal or subnormal) rounded-hw1a non-negative number (zero, normal or subnormal) Safe-Inferred 'R_S^TUVWXY]\Z[`abcdefgh~}|{zyxwvutsrqponmjilkYZ[\]`XabUVWR_S^Tcdegfh~}|{zyxwvutsrqponmjiklYZ[\]`XabUVWR_S^ Safe-Inferred!|"" Safe-Inferred"* Safe-Inferred"T UVWXYZ[\] UVWYZ[\]X  Safe-Inferred1" rounded-hwa is a subset of b rounded-hw a rounded-hw b44444444 Safe-Inferred##  Safe-Inferred 1;$    Safe-Inferred 1;$| Safe-Inferred$ XYZ[\]`ab YZ[\]`Xab  Safe-Inferred&\ rounded-hwEquivalent to  rounded-hwEquivalent to  (+) rounded-hwEquivalent to  (-) rounded-hwEquivalent to  (*) rounded-hwEquivalent to  fusedMultiplyAdd rounded-hwEquivalent to  (/) rounded-hwEquivalent to  sqrt  Safe-Inferred1( rounded-hwEquivalent to  rounded-hwEquivalent to  (+) rounded-hwEquivalent to  (-) rounded-hwEquivalent to  (*) rounded-hwEquivalent to  fusedMultiplyAdd rounded-hwEquivalent to  (/) rounded-hwEquivalent to  sqrt ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o pqrrstuvwxyz{|}~                                                                                      'rounded-hw-0.4.0-3WAAI20vt2HBtLAkTAeX6n!Numeric.Rounded.Hardware.Internal"Numeric.Rounded.Hardware.Backend.CNumeric.Rounded.Hardware!Numeric.Rounded.Hardware.RoundingNumeric.Rounded.Hardware.Class Numeric.Rounded.Hardware.Backend,Numeric.Rounded.Hardware.Backend.ViaRational(Numeric.Rounded.Hardware.Backend.FastFFI'Numeric.Rounded.Hardware.Interval.Class*Numeric.Rounded.Hardware.Interval.NonEmpty!Numeric.Rounded.Hardware.Interval(Numeric.Rounded.Hardware.Vector.Storable'Numeric.Rounded.Hardware.Vector.Unboxed+Numeric.Rounded.Hardware.Internal.FloatUtil*Numeric.Rounded.Hardware.Internal.Rounding,Numeric.Rounded.Hardware.Internal.Conversion+Numeric.Rounded.Hardware.Internal.Constants'Numeric.Rounded.Hardware.Internal.ClassFFIWrapper.FloatFFIWrapper.Double(Numeric.Rounded.Hardware.Backend.Default&Numeric.Rounded.Hardware.Internal.Show5Numeric.Rounded.Hardware.Interval.ElementaryFunctions&fp-ieee-0.1.0.3-K5hnoEVPP67Ep0Ol1hSRCw"Numeric.Floating.IEEE.Internal.FMAfusedMultiplyAdd(Numeric.Floating.IEEE.Internal.NextFloatnextTowardZeronextDownnextUp%vector-0.13.1.0-2lCeeCyC2I3KCSVrGQfe2Data.Vector.Unboxed.BaseV_6V_5V_4V_3V_2 V_ComposeV_AltV_ConstV_AllV_AnyV_ArgV_WrappedMonoidV_LastV_FirstV_MaxV_Min V_ProductV_SumV_DualV_Down V_Identity V_ComplexV_BoolV_CharV_DoubleV_FloatV_Word64V_Word32V_Word16V_Word8V_WordV_Int64V_Int32V_Int16V_Int8V_IntV_UnitMV_UnitMV_UnboxViaPrimV_UnboxViaPrim MV_UnboxAs V_UnboxAsMV_IntMV_Int8MV_Int16MV_Int32MV_Int64MV_WordMV_Word8 MV_Word16 MV_Word32 MV_Word64MV_Float MV_DoubleMV_CharMV_Bool MV_Complex MV_IdentityMV_DownMV_DualMV_Sum MV_ProductMV_MinMV_MaxMV_FirstMV_LastMV_WrappedMonoidMV_ArgMV_AnyMV_AllMV_ConstMV_Alt MV_ComposeMV_2MV_3MV_4MV_5MV_6MVectorVector distanceUlpRounded getRoundedRounding RoundingMode ToNearest TowardNegInf TowardInf TowardZero V_Rounded MV_RoundedoppositeRoundingModerounding reifyRoundingroundedFromInteger_defaultroundedFromRational_defaultintervalFromInteger_defaultintervalFromRational_defaultintervalFromIntegralRealFloatConstantspositiveInfinitynegativeInfinity maxFinite minPositivepi_downpi_up three_pi_down three_pi_up five_pi_down five_pi_up log2_downlog2_up exp1_downexp1_up exp1_2_down exp1_2_up expm1_2_down expm1_2_up sqrt2_downsqrt2_up sqrt2m1_down sqrt2m1_up sqrt1_2_down sqrt1_2_upthree_minus_2sqrt2_downthree_minus_2sqrt2_uptwo_minus_sqrt2_downtwo_minus_sqrt2_upRoundedSqrt_Vectormap_roundedSqrtRoundedFractional_VectorzipWith_roundedDivRoundedRing_Vector roundedSumzipWith_roundedAddzipWith_roundedSubzipWith_roundedMul zipWith3_roundedFusedMultiplyAdd RoundedSqrt roundedSqrt intervalSqrtRoundedFractional roundedDiv roundedReciproundedFromRationalroundedFromRealFloat intervalDivintervalDivAdd intervalRecipintervalFromRational RoundedRing roundedAdd roundedSub roundedMulroundedFusedMultiplyAddroundedFromInteger intervalAdd intervalSub intervalMulintervalMulAddintervalFromInteger backendNameT backendName ViaRational$fUnboxViaRational$fVectorVectorViaRational$fMVectorMVectorViaRational%$fRoundedSqrt_VectorVectorViaRational+$fRoundedFractional_VectorVectorViaRational%$fRoundedRing_VectorVectorViaRational&$fRoundedSqrt_VectorVectorViaRational0,$fRoundedFractional_VectorVectorViaRational0&$fRoundedRing_VectorVectorViaRational0$fRoundedSqrtViaRational$fRoundedFractionalViaRational$fRoundedRingViaRational$fNFDataViaRational$fEqViaRational$fOrdViaRational$fShowViaRational$fGenericViaRational$fNumViaRational$fStorableViaRationalCDoubleCFloat V_CDouble MV_CDoubleV_CFloat MV_CFloatroundedFloatFromInt64roundedFloatFromWord64roundedDoubleFromInt64roundedDoubleFromWord64 $fUnboxCFloat$fVectorVectorCFloat$fMVectorMVectorCFloat $fRoundedSqrt_VectorVectorCFloat&$fRoundedFractional_VectorVectorCFloat $fRoundedRing_VectorVectorCFloat!$fRoundedSqrt_VectorVectorCFloat0'$fRoundedFractional_VectorVectorCFloat0!$fRoundedRing_VectorVectorCFloat0$fRoundedSqrtCFloat$fRoundedFractionalCFloat$fRoundedRingCFloat$fNFDataCFloat$fUnboxCDouble$fVectorVectorCDouble$fMVectorMVectorCDouble!$fRoundedSqrt_VectorVectorCDouble'$fRoundedFractional_VectorVectorCDouble!$fRoundedRing_VectorVectorCDouble"$fRoundedSqrt_VectorVectorCDouble0($fRoundedFractional_VectorVectorCDouble0"$fRoundedRing_VectorVectorCDouble0$fRoundedSqrtCDouble$fRoundedFractionalCDouble$fRoundedRingCDouble$fNFDataCDouble $fEqCDouble $fOrdCDouble $fShowCDouble$fGenericCDouble $fNumCDouble$fStorableCDouble $fEqCFloat $fOrdCFloat $fShowCFloat$fGenericCFloat $fNumCFloat$fStorableCFloatfastIntervalAddfastIntervalSubfastIntervalRecipbinaryFloatToDecimalDigitsRn!binaryFloatToFixedDecimalDigitsRnbinaryFloatToDecimalDigits showEFloatRn showFFloatRn showGFloatRn IsIntervalEndPoint withEndPoints singleton makeIntervalwidthhull intersectionmaybeIntersection equalAsSetsubset weaklyLessprecedesinterior strictLessstrictPrecedesdisjointIntervalI increasingmaxIminIpowIntnullinfsup$fIArrayUArrayInterval$fMArraySTUArrayIntervalST$fUnboxInterval$fVectorVectorInterval$fMVectorMVectorInterval$fIsIntervalInterval$fFloatingInterval$fFractionalInterval $fNumInterval$fNFDataInterval$fShowInterval$fGenericIntervalEmptywidthUlpcoercionfromVectorOfRoundedtoVectorOfRounded coercionMfromMVectorOfRoundedtoMVectorOfRoundedsum zipWith_add zipWith_sub zipWith_mulzipWith3_fusedMultiplyAdd zipWith_divmap_sqrtbaseGHC.Real fromRational GHC.Floatsqrt FractionalGHC.NumNumMV_ViaRational V_ViaRationalintervalDivAdd_upintervalDivAdd_downintervalMulAdd_upintervalMulAdd_downintervalDiv_upintervalDiv_downintervalMul_upintervalMul_down roundedFMAroundedFMAIfFastroundedFromInt64roundedFromWord64 vectorSumPtrvectorSumByteArray vectorAddPtrvectorAddByteArray vectorSubPtrvectorSubByteArray vectorMulPtrvectorMulByteArray vectorFMAPtrvectorFMAByteArray vectorDivPtrvectorDivByteArray vectorSqrtPtrvectorSqrtByteArraysqrtIexpPexpIexpm1Pexpm1IlogPlogIlog1pPlog1pI sin_small cos_smallsinPcosPsinIcosItanI atan_smallatanPatanIasinPasinIacosPacosIsinhPsinhIcoshPcoshItanhPtanhIasinhPasinhIacoshPacoshIatanhPatanhIData.Vector.StorablezipWithzipWith3mapData.Vector.Unboxed