Generation of mask-constrained floating-point addition and substraction test cases, and method and system therefor

A system for generating floating-point test-cases for verifying the operation of a floating-point arithmetic unit, the system comprising a processing unit which includes:

• (a) an exponent generator, for generating floating-point exponents;
• (b) a significand generator, for generating floating-point significands;
• and
• (c) a fixed-point generator coupled to said exponent generator and to said signficand generator;
• wherein said processing unit is configured to receive a specified arithmetic operation selected from a group that includes addition and subtraction, a specified rounding mode, a first input operand mask, a second input operand mask, and an output result mask;
• and wherein said processing unit is configured to output a set of floating-point numbers which includes a first input operand compatible with said first input operand mask, a second input operand compatible with said second input operand mask, and an output result compatible with said output result mask;
• and wherein said output result corresponds to said specified arithmetic operation on said first input operand and said second input operand for said specified rounding mode.

A method of seeking a solution, if a solution exists, to a specified mathematical condition, wherein the solution is used in constructing a floating-point test-case for verifying the operation of a floating-point arithmetic unit, wherein a complete generated test case is a set of floating-point numbers for a specified arithmetic operation and a specified rounding mode, and wherein a generated test case includes at least one input operand and an output result;

• and wherein an input operand is compatible with an operand mask, and the output result is compatible with an output result mask;
• the method comprising the steps of:
• (a) preparing a list of choices upon which the solution is based;
• (b) testing whether said list of choices is empty;
• (c) outputting, if said list of choices is empty, that no solution exists;
• (d) randomly choosing, if said list of choices is not empty, a choice of said list as a selection;
• (e) searching for a solution to the specified mathematical condition, based on said selection;
• (f) outputting, if said searching was successful, said solution;
• (g) erasing, if said searching was not successful, said selection from said list;
• and
• (h) repeating step (a) through step (g) until outputting occurs.

A method of seeking a solution, if a solution exists, to a specified mathematical condition, wherein the solution is used in constructing a floating-point test-case for verifying the operation of a floating-point arithmetic unit, wherein a complete generated test case is a set of floating-point numbers for a specified arithmetic operation selected from a group including addition and subtraction, and for a specified rounding mode, and wherein a generated test case includes a first input operand, a second input operand, and an output result;

• and wherein the first input operand is compatible with a first input operand mask, the second input operand is compatible with a second input operand mask, and the output result is compatible with an output result mask;
• the method comprising the steps of:
• (a) preparing a list of choices upon which the solution is based;
• (b) testing whether said list of choices is empty;
• (c) outputting, if said list of choices is empty, that no solution exists;
• (d) randomly choosing, if said list of choices is not empty, a choice of said list as a selection;
• (e) searching for a solution to the specified mathematical condition, based on said selection;
• (f) outputting, if said searching was successful, said solution;
• (g) erasing, if said searching was not successful, said selection from said list;
• and
• (h) repeating step (a) through step (g) until outputting occurs.

A method of generating a set of fixed-point numbers containing a first addend, a second addend, and a sum, wherein the first addend is compatible with a first addend mask, the second addend is compatible with a second addend mask, the sum is compatible with a sum mask, and wherein the addition of the first addend and the second addend results in a carry sequence of carry bits, wherein each carry bit has a unique index in the carry sequence, wherein the carry sequence is compatible with a carry sequence mask and wherein each carry bit has a value in the group consisting of 0, 1, and 2, and wherein there exists a boundary index in the carry sequence corresponding to the lowest index of a carry bit having the value 2;

• the method comprising the steps of:
• (a) constructing a list of possible boundary indices;
• (b) testing whether said list is empty;
• (c) outputting, if said list is empty, that no solution exists;
• (d) randomly choosing, if said list is not empty, a boundary index from said list as a selection;
• (e) searching for a carry sequence based on said selection, which is compatible with the carry sequence mask;
• (f) erasing, if said searching was not successful, said selection from said list;
• (g) constructing, if said searching was successful, a first addend compatible with the first addend mask, a second addend compatible with the second addend mask, and a sum compatible with the sum mask;
• (h) outputting said first addend, said second addend, said sum, and said carry sequence;
• and
• (i) repeating step (a) through step (h) until outputting occurs.