Unified computation systems and methods for iterative multiplication and division, efficient overflow detection systems and methods for integer division, and tree-based addition systems and methods for single-cycle multiplication

A method, comprising:

• receiving, by a hardware division overflow detection circuit, a size, sign, and value of a dividend x for a division operation as a part of an instruction;
• receiving, by the hardware division overflow detection circuit, a size, sign, and value of a divisor d for the division operation as a part of the instruction;
• and
• executing the instruction, by the hardware division overflow detection circuit, by:
• separating the dividend x into a first part Y and a second part Z based on the sign of the dividend x and the sign of the divisor d;
• and
• evaluating whether an overflow situation for the division operation exists by:
• when the dividend x and the divisor d are each greater than or equal to zero, generating a first K value by subtracting the dividend x from the first part Y, determining that no overflow situation exists when the first K value is less than zero, and determining that an overflow situation does exist when the first K value is greater than or equal to zero;
• when the dividend x is less than zero and the divisor d is greater than or equal to zero, generating a second K value by subtracting the dividend x from an inversion of the first part Y, determining that no overflow situation exists when the second K value is less than zero, determining that an overflow situation does exist when the second K value is greater than or equal to zero, and determining that special processing is to be conducted when the second K value equals zero;
• when the dividend x is greater than or equal to zero and the divisor d is less than zero, generating a third K value by adding the dividend x to the first part Y, determining that no overflow situation exists when the third K value is less than zero, and determining that an overflow situation does exist when the third K value is greater than or equal to zero, and determining that special processing is to be conducted when the third K value equals zero;
• and
• when the dividend x and the divisor d are each less than zero, generating a fourth K value by subtracting the dividend x from the first part Y, determining that no overflow situation exists when the fourth K value is less than zero, determining that an overflow situation does exist when the fourth K value is greater than or equal to zero, and determining that special processing is to be conducted when the fourth K value equals zero.