=[4=      !"#$%&'()*+,-./012345678 9 : ; <  Safe-InferredClass of vector spaces v with scalar s.  Safe-InferredThe infinite natural number. =>?@ABCDEF >=?@ABCDEF Safe-Inferred G HIJKL  G HIJKL Safe-Inferred  !  !  !  !NoneM500 decimals. $ 50 decimals. %Ten decimals. &AA type construct that gives one more decimals than the argument. '$An epsilon of 1, i.e., no decimals. (The (< class contains the types that can be used to determine the  precision of a " number. *5Convert between two arbitrary fixed precision types. , The call with_added_precision r f v evaluates f v, while * temporarily multiplying the precision of v by r. "N#M$%&'(O)PQ*RST+,UVWXYZ[\]^_` "#$%&'()*+, "('&%$#*+),"N#M$%&'(O)PQ*RST+,UVWXYZ[\]^_`None-DFloating point number where the precision is determined by the type e. -abcdefghijkl#$%&'(--('&%$# -abcdefghijkl Safe-Inferred.The .. type implements (constructive) real numbers. 'Note that the comparison operations on . may diverge < since it is (by necessity) impossible to implementent them # correctly and always terminating. *This implementation is really David Lester's ERA package. /The / function connverts a . to a m. ".nopqrstuvwxyz{|}/The number of decimals The real number The resulting string ~././!.nopqrstuvwxyz{|}/~ Safe-Inferred0The 0- type is the type of differentiable numbers.  It'0s an instance of all the usual numeric classes. 5 The computed derivative of a function is is correct = except where the function is discontinuous, at these points 3 the derivative should be a Dirac pulse, but it isn't. The 0+ numbers are printed with a trailing ~~ to  indicate that there is a "tail" of derivatives. 1The 1' function turns a normal number into a 0 8 number with the same value. Not that numeric literals 6 do not need an explicit conversion due to the normal " Haskell overloading of literals. 2The 2) function turns a number into a variable 8 number. This is the number with with respect to which  the derivaticve is computed. 3The 3 takes a 0 number and returns its first 5 derivative. The function can be iterated to to get  higher derivaties. 4The 4 function takes a 0 number back to a normal 4 number, thus forgetting about all the derivatives. 5The 5 takes a value and 0 value and makes  a 0/ number that has the given value as its normal  value, and the 0 number as its derivatives. 6The 6* function is a simple utility to take the - derivative of a (single argument) function.  It is simply defined as  deriv f = val . df . f . dVar 7 Convert a 0# function to an ordinary function. 01234567012345670435126701234567  Safe-Inferred87Symbolic numbers over some base type for the literals. 9Create a variable. :5Create a constant (useful when it is not a literal). ;The expression  subst x v e substitutes the expression v for each  occurence of the variable x in e. 89:;<89:;<89:;<89:;<     !"#$%&'()*+,-./0123456789:;<=>?@A B C D E FGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstukvwxyz{|}~   numbers-3000.2.0.0Data.Number.VectorspaceData.Number.NaturalData.Number.IntervalData.Number.FixedFunctionsData.Number.FixedData.Number.BigFloatData.Number.CRealData.Number.DifData.Number.Symbolic Vectorspace*><+>vnegatevzeroNaturalinfinityIntervalivalgetIvalCFapproxfromCFtoCFapproxCFfromTaylorToCFfac integerRoot2pitansincosatanasinacossqrtexpcoshsinhtanhatanhasinhacoshlogFixed PrecPlus20Prec50Prec10EpsDiv10Eps1Epsilon precision convertFixed dynamicEpswith_added_precisionBigFloatCReal showCRealDifdCondVardfvalmkDifderivunDifSymvarconsubstunSymSZ maybeSubtract $fEnumNatural $fRealNatural$fIntegralNatural $fNumNatural $fOrdNatural $fEqNatural $fShowNaturalI$fFractionalInterval $fNumInterval$fShowInterval $fOrdInterval $fEqIntervalPrec500Fepslift2getEpstoFixed0toFixed1$fRealFloatFixed$fFloatingFixed $fReadFixed $fShowFixed$fFractionalFixed $fNumFixed$fEpsilonPrecPlus20$fEpsilonPrec500$fEpsilonPrec50$fEpsilonPrec10$fEpsilonEpsDiv10 $fEpsilonEps1BFbasebftoFloat1$fRealFloatBigFloat$fFloatingBigFloat$fRealFracBigFloat$fFractionalBigFloat $fOrdBigFloat$fRealBigFloat $fNumBigFloat$fShowBigFloatGHC.BaseStringCRdiv2nmul2nacc_seqexp_drlog_drlog_drxsin_drcos_dratan_dratan_drx power_seriespiBy2piBy4log2sqrt1By2 digitsToBitsdigits sizeinbase floorsqrtround_uk $fShowCReal $fReadCReal$fRealFloatCReal$fRealFracCReal $fRealCReal $fEnumCReal$fFloatingCReal$fFractionalCReal $fNumCReal $fOrdCReal $fEqCRealCDlift$fRealFloatDif $fRealFracDif $fRealDif $fFloatingDif$fFractionalDif$fNumDif$fOrdDif$fEqDif $fReadDif $fShowDifAppConbinOpunOpisCon$fRealFloatSym $fFloatingSym $fRealFracSym $fRealSym $fEnumSym $fIntegralSym$fFractionalSym$fNumSym $fShowSym$fOrdSym$fEqSym