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- W2736779729 abstract "Ada implementations have the option of supporting fixed-point arithmetic with arbitrary scale--that is, in which the safe numbers are of the form ma for a fixed, arbitrary rational rho<0, which m in some contiguous range of integers. The major difficulty with providing such support is the implementation of the mixed-type operations, multiplication and division. If x and y are the integer values representing the operands, these operations reduce to finding integer approximations of rho x y or Beta x/y with an absolute error less than 1 for a fixed-point result type, an absolute error less than or equal to 1/2 for an integer result type, or a relative error of less than one safe interval for a floating- point result type. The static constants alpha and Beta may be arbitrary positive rational numbers, depending on the scales of the two operand types and on the result type. I present reasonably fast ways to compute appropriate fixed-point results for all values of alpha or beta. For integer result types, I give algorithms for alpha and beta that have the form 2n a/b, where alpha and beta are positive, single-precision integer constants. Finally, I give algorithms to produce floating- point results for a variety of architectures, including the VAX, the IBM 370, and those conforming to IEEE 754." @default.
- W2736779729 created "2017-07-31" @default.
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- W2736779729 date "1990-06-01" @default.
- W2736779729 modified "2023-09-27" @default.
- W2736779729 title "Implementing Ada Fixed-point Types having Arbitrary Scales" @default.
- W2736779729 hasPublicationYear "1990" @default.
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