Algorithm 693: a FORTRAN package for floating-point multiple-precision arithmetic
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Contributions to a proposed standard for binary floating-point arithmetic (computer arithmetic)
Contributions to a proposed standard for binary floating-point arithmetic (computer arithmetic)
ACM Transactions on Mathematical Software (TOMS)
Standardization and testing of implementations of mathematical functions in floating point numbers
Programming and Computing Software
TAPIA '07 Proceedings of the 2007 conference on Diversity in computing
Validated computation of certain hypergeometric functions
ACM Transactions on Mathematical Software (TOMS)
FPGA paranoia: testing numerical properties of FPGA floating point IP-Cores
ARC'12 Proceedings of the 8th international conference on Reconfigurable Computing: architectures, tools and applications
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The IEEE 754 and 854 standards for floating-point arithmetic are essentially a specification of a programming environment, encompassing aspects from computer hardware, operating systems, and compilers to programming languages (see especially Section 8). Parts I and II of this paper together describe a tool to test floating-point implementations of arbitrary precision and exponent range (hardware as well as software) for compliance with the principles outlined in the IEEE standards. The tool consists of a driver program, together with a very large set of test vectors encoded in a precision-independent syntax. In Part I we have convered the testing of the basic operaitons +, −, ×, / and of the square root and remainder functions. In Part II we describe the extension of the test tool to deal with conversions between floating-point formats, conversions between floating-point and integer formats, the rounding of floating-point numbers to integral values, and binary-decimal conversions. Conversions can now be tested from a floating-point format of arbitrary precision and exponent range to another arbitrary smaller (larger) floating-point format as well as to and from fixed hardware integer formats. Conversion between the bases 2 and 10 can be tested for a number of precisions ranging from sing (24 bits), double (53 bits), long double or extended (64 bits) to quadruple (113 bits) precisioon and a proper multiprecision (240 bits) format. We conclude Part II with some applications of our test tool and report on the results of testing various floating-point implementations, meaning various language-compiler-hardware combinations as well as multiprecision libraries.