úÎYÂQLĄ      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abc d e f g h i j k l m n o p q r s t u v w x y z { | } ~  €  ‚ ƒ „ … † ‡ ˆ ‰ Š ‹ Œ  Ž   ‘ ’ “ ” • – — ˜ ™ š › œ  ž Ÿ    Safe-Inferred0Base 2 logarithm of argument, rounded downwards.+Converts precisions from decimal to binary.UOperator allowing function expecting binary precision to be applied to decimal ditto. Safe-Inferred†Common functions collected to allow for instances which handle dependency problems for intervals, and for automatic differentiation. Safe-Inferred          Safe-Inferred Scaling.  scale x n computes x * 2^n using bit shifts.dCorrectly rounded result for negative n. Rounds upwards when decimal part of unrounded result is .5  None2Memoizing a function which satisfies the property f (p-r) = scale (f p) (-r) for all r > 0=. Unsafe; based on ideas from Lennart Augustsson's uglymemo. Safe-Inferred A  ā value is an infinite list consisting of the values of an infinitely differentiable function and all its derivatives, all evaluated at a common point. Polynomials are represented by finite lists, omitting zero derivatives.)Kderiv n f is the n'th derivative of f (with derivative information omitted)*>derivs f a is the list of allderivatives of f, evaluated at a. !"#$%&'()*+,-./012345678 !"#$%&'()*+,-. !"#$%&'()*+,-876543210/. !"#$%&'()*+,-./012345678None9†A real number/interval is a function from required precision to an integer interval; for numbers the interval is thin (has radius 1).<USmart constructor; uses an (unfortunately unsafe) memoizing technique for efficiency.=8Selector; computes integer interval for given precision.>6prec n x is an interval of width 10^(-n) containing x.9:;<=>9:;<=;9:<=>9:;<=>None?0Constructs an interval from midpoint and radius.@IConstructs an interval from end points (which can be given in any order).AReturns midpoint of argument.BReturns radius of argument.C#Returns left end point of argument.D$Returns right end point of argument.E#Convex hull of a list of intervals.FUTests whether first arg is contained in second, using total tests of given precision.G4Intersection of intervals; empty intersection gives ĄJ%Total, approximate equality test. If x =?= y  d returns Ē, then x and y* are definitely not equal. If it returns Ģ;, then the absolute value of their difference is less than 10^(-d) (but they may be non-equal).K'Total, approximate inequality test. If x <! y  d returns Ģ, then x is definitely smaller than y, If it returns Ē, x may still be smaller than y', but their difference is then at most 10^(-d). Lx >! y is the same as y <! x.N Prints an 9V with given number of decimals. Rounding error is up to one unit in the last position.O Prints an 9k in scientific notation with given number of digits. Rounding error is up to one unit in the last position.PZForces evaluation of second argument to given number of decimals; returns second argument.WIReal is an instance of Ī3 but it should be avoided; see introduction. Use x ? n to print x with n decimals.Z8Equality test for overlapping values is non-terminating.a$Division by zero is non-terminating.$?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`ab?@ABCDEFGHIJKLMNOPQRSTUV$?@CBADEFGba`_^H]\[ZYIXJKLMWNOPQRSTVU$?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`ab?@JKLNO NonerEGenerates real numbers uniformly distributed over the given interval.seGenerates real intervals of varying width, with midpoints uniformly distributed over given interval.t{Generates random expressions built from values generated by argument generator, arithmetic operators and applications of Ĩ functions.v_Basic test that the argument is a proper real number (is thin and satisfies Cauchy criterion).w™Basic test that argument is a proper interval (the end points are proper numbers, with left end smaller than right end). cdefghijklmnopqrstuvwxyzcdefghijklmnopqrstuvwxehgfcdijklmnozpqyrstuvwxcdehgfijklmnopqrstuvwxyz None{‚Balanced fold, minimizing depth of call tree. Assumes associative operator. Often much more efficient than foldl/foldr when type a is 9 and the list is long.|;Balanced fold for associative operator over non-empty list.}ABalanced sum, reorganized for (much) better efficiency when type a is 9 and the list is long.€$1st arg should be length of 2nd arg.{|}~€{|}~€{|}~€{|}~€ None0 !"#%')*9?@ABCDEFGHJKLMNOPrstvw{|}~€09HNOMKLJ?@EGCDABF{|}~€ !)*"#'%rstvwP None'(24= ‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•– ƒ„… Ÿ‚ž†‡œ›š™˜—ˆ‰ŠŒ‹Ž“’‘”•–‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ˆ‰Š‹ŒŽĶ  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmno p p q r s t u v w x y z { | } ~  €  ‚ ƒ „ … † ‡ ˆ ‰ Š ‹ Œ H  Ž   ‘ ’ [ \ W X Y L M Z N O P Q R S T “ ” • – — ˜ ™ š › œžŸ ĄĒ ĄĢĪĨĶ§Ļ ireal-0.2Data.Number.IReal.AuxiliaryData.Number.IReal.Powers!Data.Number.IReal.IntegerIntervalData.Number.IReal.ScalableData.Number.IReal.UnsafeMemoData.Number.IReal.FADData.Number.IReal.IReal!Data.Number.IReal.IRealOperationsData.Number.IReal.GeneratorsData.Number.IReal.FoldBData.Number.IReal.RoundedData.Number.IReallg2dec2bits atDecimalsPowerssqpow$fPowersInteger$fPowersDoubleIntegerIntervalIuptomidIradIlowerIupperIisThinivalCase$fPowersIntegerInterval$fNumIntegerIntervalVarPrecprecprecBScalablescale$fVarPrecDouble $fVarPrec[]$fScalableDouble$fScalableIntegerInterval$fScalableRatio$fScalableInteger unsafeMemomemoIODifDconvarmkDifvalfromDifunDifdfderivderivschainrchainr2chainconvs$fRealFloatDif $fRealFracDif $fRealDif $fPowersDif $fFloatingDif$fFractionalDif$fNumDif$fOrdDif$fEqDif $fVarPrecDifIRealIR Precisionirappr$fVarPrecIReal+--+-midradlowerupperhull containedIn intersectiontoDoublecomp=?=! showIReal???force powerSeriesg0pshalfPi quarterPilog2 $fShowIReal $fEnumIReal $fOrdIReal $fEqIReal$fScalableIReal $fPowersIReal$fRealFloatIReal$fRealFracIReal $fRealIReal$fFloatingIReal$fFractionalIReal $fNumIRealFracDigPZMmzpftailfracnfracpfracexpandgenIReal uniformNum uniformIvalexprGenisCauchy propIsRealNumpropIsRealIvalforAllI$fArbitraryIReal$fArbitraryFracfoldbfoldb1bsumfoldb'isum'isumN' precisionRoundedRunRoundrproxyPrecision$fScalableRounded $fOrdRounded $fEqRounded$fFloatingRounded $fShowRounded$fFractionalRounded $fNumRounded$fPrecisionNatn$fPowersRounded$fVarPrecRoundedbase Data.MaybeNothingghc-prim GHC.TypesFalseTrueGHC.ShowShow GHC.FloatFloating