!q     Constructible real numbers Anders Kaseorg, 2013 BSD-style Anders Kaseorg <andersk@mit.edu> experimentalNon-portable (GHC extensions)None&'.2=?@AHV  constructible,The type of exceptions thrown by impossible  operations. constructible. was given an irrational constructible number. constructible+ was given a negative constructible number. constructible^ was given an exponent that is not a dyadic rational, or a transcendental function was called. constructible'The type of constructible real numbers. constructible1Deconstruct a rational constructible number as a 4, or an irrational constructible number as a triple  (a, b, r)/ of simpler constructible numbers representing  a + b*sqrt r (with b /= 0 and r > 0). Recursively calling < on all triples will yield a finite tree that terminates in  leaves.\Note that two constructible numbers that compare as equal may deconstruct in different ways. constructibleThis   instance only supports ( on numbers that are in fact rational. ( on an irrational number will throw the  exception. constructible This partial ! instance only supports  and H where the exponent is a dyadic rational. Passing a negative number to  will throw the 1 exception. All other operations will throw the  exception. constructibleCEvaluate a floating-point approximation for a constructible number.pTo improve numerical stability, addition of numbers with different signs is avoided using quadratic conjugation.hfromConstruct $ sum (map sqrt [7, 14, 39, 70, 72, 76, 85]) - sum (map sqrt [13, 16, 46, 55, 67, 73, 79])1.8837969820815017e-19"6#6$7%7&      !"!#$%!&'()*+*constructible-0.1.1-K9cbl7lA6svBA7SDqgQA70Data.Real.ConstructibleConstructExceptionConstructIrrationalConstructSqrtNegativeUnconstructible Construct deconstruct $fShowField$fEnumConstruct$fRealFracConstruct$fReadConstruct$fShowConstruct$fFractionalConstruct$fNumConstruct$fOrdConstruct $fEqConstruct$fRealConstruct$fFloatingConstruct$fExceptionConstructException$fShowConstructException$fShowFieldShape$fEqConstructException$fOrdConstructException fromConstruct$fFloatingComplex$fFractionalComplex $fNumComplex$fComplexPolarComplexConstruct$fComplexRectComplexConstructbaseGHC.Real toRational GHC.Floatsqrt**RationalRealFloating+!-!*!/!