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Data.Scientific provides a space efficient and arbitrary precision scientific number type.

Scientific numbers are represented using scientific notation. It uses a coefficient c :: Integer and a base-10 exponent e :: Int (do note that since we're using an Int to represent the exponent these numbers aren't truly arbitrary precision. I intend to change this to Integer in the future!). A scientific number corresponds to the Fractional number: fromInteger c * 10 ^^ e.

The main application of Scientific is to be used as the target of parsing arbitrary precision numbers coming from an untrusted source. The advantages over using Rational for this are that:

  • A Scientific is more efficient to construct. Rational numbers need to be constructed using % which has to compute the gcd of the numerator and denominator.

  • Scientific is safe against numbers with huge exponents. For example: 1e1000000000 :: Rational will fill up all space and crash your program. Scientific works as expected:

 > read "1e1000000000" :: Scientific
 1.0e1000000000
  • Also, the space usage of converting scientific numbers with huge exponents to Integral's (like: Int) or RealFloats (like: Double or Float) will always be bounded by the target type.

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Arbitrary-precision floating-point numbers represented using scientific notation

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