úÎO5KD      Safe-Inferred6%The type of fixed-precision numbers. (Add 1000 digits to the given precision. 'Add 100 digits to the given precision. &Add 10 digits to the given precision. %Add 3 digits to the given precision. $Add 1 digit to the given precision. Precision of 2000 digits. Precision of 1000 digits. Precision of 100 digits. Precision of 10 digits. Precision of 1 digit. Precision of 0 digits. <A type class for type-level integers, capturing a precision 5 parameter. Precision is measured in decimal digits. &Get the precision, in decimal digits. >Integer division with rounding to the closest. Note: rounding D could be improved. Right now, we always round up in case of a tie. >Shift the integer to the right by the given number of decimal  digits, with rounding. >Shift the integer to the right by the given number of decimal + digits, without rounding (i.e., truncate) =Shift the integer to the left by the given number of decimal  digits. For n- "e 0, return the floor of the square root of n . This is A done using integer arithmetic, so there are no rounding errors. Given positive numbers b and x , return (n, r ) such that  x = r b[sup n] and  1 "d r < b$. In other words, let n = # log[sub b] x# and  r = x b[sup "n]". This can be more efficient than   ( b x1) depending on the type; moreover, it also works  for exact types such as  and EReal. 2A version of the natural logarithm that returns a . The 2 logarithm of just about any value can fit into a ; so if C not a lot of precision is required in the mantissa, this function  is often faster than . BGet the precision of a fixed-precision number, in decimal digits. Cast from any  type to another. ECast to a fixed-point type with three additional digits of accuracy. @Cast to a fixed-point type with three fewer digits of accuracy.  The function  d f x evaluates f(x ), adding  d digits of accuracy to x during the computation. 9Multiply an integer by a fixed-precision number. This is @ marginally more efficient than multiplying two fixed-precision  numbers. !BDivide a fixed-precision number by an integer. This is marginally ; more efficient than dividing two fixed-precision numbers. 9Return the positive fractional part of a fixed-precision B number. The result is always in [0,1), regardless of the sign of  the input. "?Define a list of rational numbers (i.e., the coefficients of a ) power series) from a recursive formula. #>The power series stops when the last term is smaller than the D precision. This is accurate for alternating and decreasing series,  and provided |x| "d 1. $The Taylor series for sin x%, centered at 0. This implementation  works for |x| "d 1. %The Taylor series for cos x%, centered at 0. This implementation  works for |x| "d 1. &The Taylor series for [exp x], centered at 0. This  implementation works for |x| "d 1. 'The Taylor series for log x, centered at 1. This  implementation works for |x " 1| "d 1/4. (The Taylor series for atan x, centered at 0. This  implementation works for |x | "d 0.44. )The Taylor series for atan x, centered at 0. This  implementation works for |x'| "d 0.2, and is faster, in that range,  than (. *The Taylor series for atan x, centered at 0. This  implementation works for |x| "d 1/239, and is faster, in that  range, than ). +)Raw implementation of the sine function. ,+Raw implementation of the cosine function. -BRaw implementation of the exponential function. Note: the loss of ? precision is much more substantial than that of the other raw A functions in this section. This is due to the multiplication of 7 fixed-precision values by numbers much larger than 1. .-Raw implementation of the natural logarithm. /=Raw implementation of the power function. This is subject to " similar loss of precision as the - function. 0Raw implementation of the  function. This is subject to " similar loss of precision as the - function. 1'Raw implementation of the square root. 2+Raw implementation of the inverse tangent. 3Raw implementation of À. 41Raw implementation of the inverse sine function. 53Raw implementation of the inverse cosine function. 6+Raw implementation of the hyperbolic sine. 7-Raw implementation of the hyperbolic cosine. 86Raw implementation of the inverse hyperbolic tangent. 93Raw implementation of the inverse hyperbolic sine. :5Raw implementation of the inverse hyperbolic cosine. H;   !"#$%&'()*+,-./0123456789:<=>?@ABCDEFGHIJKL   F;   !"#$%&'()*+,-./0123456789:<=>?@ABCDEFGHIJKLM      !"#$% &'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRST fixedprec-0.2Data.Number.FixedPrec FixedPrec PPlus1000PPlus100PPlus10PPlus3PPlus1P2000P1000P100P10P1P0 Precision log_doublegetpreccastupcastdowncastwith_added_digits fractionaldigitsdivi decshiftR dectruncR decshiftLintsqrtfloorlogbaseGHC.Realfloor GHC.FloatlogBaseRationalghc-prim GHC.TypesDoublelog..*/..accs powerseriessin_pcos_pexp_plog_patan_patan_p2atan_p3sin_rawcos_rawexp_rawlog_raw power_raw logBase_rawsqrt_rawatan_rawpi_rawasin_rawacos_rawsinh_rawcosh_raw atanh_raw asinh_raw acosh_rawF$fFloatingFixedPrec$fRealFracFixedPrec$fRealFixedPrec$fFractionalFixedPrec$fNumFixedPrec$fShowFixedPrec$fPrecisionPPlus1000$fPrecisionPPlus100$fPrecisionPPlus10$fPrecisionPPlus3$fPrecisionPPlus1$fPrecisionP2000$fPrecisionP1000$fPrecisionP100$fPrecisionP10 $fPrecisionP1 $fPrecisionP0