src/Tools/float.ML
author wenzelm
Sun, 11 Jan 2009 21:49:59 +0100
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(*  Title:      Tools/float.ML
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    ID:         $Id$
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    Author:     Steven Obua, Florian Haftmann, TU Muenchen
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Implementation of real numbers as mantisse-exponent pairs.
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*)
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signature FLOAT =
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sig
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  type float = int * int
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  val zero: float
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  val eq: float * float -> bool
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  val ord: float * float -> order
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  val sign: float -> order
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  val min: float -> float -> float
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  val max: float -> float -> float
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  val add: float -> float -> float
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  val sub: float -> float -> float
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  val neg: float -> float
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  val mult: float -> float -> float
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  val positive_part: float -> float
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  val negative_part: float -> float
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end;
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structure Float : FLOAT =
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struct
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type float = int * int;
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val zero: float = (0, 0);
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fun add (a1, b1) (a2, b2) =
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  if b1 < b2 then
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    (a1 + a2 * Integer.square (b2 - b1), b1)
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  else
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    (a1 * Integer.square (b1 - b2) + a2, b2);
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fun sub (a1, b1) (a2, b2) =
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  if b1 < b2 then
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    (a1 - a2 * Integer.square (b2 - b1), b1)
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  else
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    (a1 * Integer.square (b1 - b2) - a2, b2);
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fun neg (a, b) = (~ a, b);
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fun mult (a1, b1) (a2, b2) = (a1 * a2, b1 + b2);
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fun sign (a, b) = Integer.sign a;
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fun ord (r, s) = sign (sub r s);
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fun eq (r, s) = ord (r, s) = EQUAL;
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fun min r s = case ord (r, s) of LESS => r | _ => s;
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fun max r s = case ord (r, s) of LESS => s | _ => r;
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fun positive_part (a, b) = (Int.max (0, a), b);
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fun negative_part (a, b) = (Int.min (0, a), b);
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end;