let9-Floating Point Arithmetic

# Computer Arithmetic: Algorithms and Hardware Designs

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CSE 246: Computer Arithmetic  Algorithms and Hardware Design Instructor: Prof. Chung-Kuan Cheng Fall 2006 Lecture 9: Floating Point Numbers

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CSE 246 2 Motivation Maximal information with given bit  numbers. Arithmetic with proper precision. Fairness of rounding. Features at the expenses of the complexity  of the operations.
CSE 246 3 Topics: Floating Point Numbers (IEEE P754) Standard Operations Exceptional Situations Rounding Modes Numerical Computing with IEEE Floating Point  Arithmetic, Michael L. Overton, SIAM

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CSE 246 4 Standard 2 32    Typically Goal: Dynamic Range: largest #/ smallest # If too large, holes between #’s
CSE 246 5 Standard  ulp ( unit in the last place ) Difference between two consecutive values of the  significand. 3 Parts  x = ~s b e :sign, significand, exponent Sign Bit 8-bit exponent 23-bit Significand

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CSE 246 6 Standard    ~ e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 s 1 s 2 s 3 …s 22 s
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