Solving the generalized mask constraint for test generation of binary floating point add operation

Solving constraints on the invisible bits of the intermediate result for floating-point verification

“…Find a random solution for the fixed point add operation using the fixed point generator (see [12]). …”

“…One example can be found in [12], which describes a test generator for the add instruction, where the input and result operands are described as masks. Another example is found in [11], which describes a test generator for the add, subtract, divide, and multiply instructions, where the input and result operands are constrained to given ranges.…”

“…The algorithms presented in this paper, and the algorithms in [12], [11], have been implemented in FPgen [2]. FPgen is an automatic floating-point test-generator that receives as input the description of a floating-point subspace and generates a random test case out of this subspace.…”

Solving range constraints for binary floating-point instructions

“…This occurs, for example, when there is a significant cancellation of bits; in other words, when the exponent of the result is smaller than the input exponents. We illustrate this point by an example using binary floating-point numbers with a three bit significand: 2 , with round to nearest mode. Clearly the set A x,y in this example, is not empty.…”

“…Many interesting sets of numbers can be efficiently represented as a union of ranges. Test generation for the FP-ADD instruction, where the input sets are described as masks, is discussed in [2]. Examples of other algorithms that may be used for test generation may be found in [3], [4], and [5].…”