Execution of a conditional statement by an arithmetic and/or bitwise unit
Methods, systems, and apparatus, including computer programs encoded on computer storage media, for execution of a conditional statement by an arithmetic and/or bitwise unit. A computer program that comprises a conditional statement that comprises a boolean condition is accessed. The boolean condition is transformed into an arithmetic and/or bitwise expression of the boolean condition. An arithmetic and/or bitwise expression of the computer program comprises the arithmetic and/or bitwise expression of the boolean condition in place of the boolean condition. The arithmetic and/or bitwise expression of the computer program is executed by an arithmetic and/or bitwise operation unit of a processor.
1. A method comprising:
accessing a computer program, wherein the computer program comprises a conditional statement that comprises a boolean condition;
transforming the boolean condition into an arithmetic and/or bitwise expression of the boolean condition;
generating an arithmetic and/or bitwise expression of the computer program comprising the arithmetic and/or bitwise expression of the boolean condition in place of the boolean condition;
providing the arithmetic and/or bitwise expression of the computer program, wherein the arithmetic and/or bitwise expression of the computer program is configured to be executed by an arithmetic and/or bitwise operation unit of a processor; and
executing, by the arithmetic and/or bitwise operation unit, the arithmetic and/or bitwise expression of the computer program;
wherein the boolean condition takes a first variable A and a second variable B, wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
subtracting B from A;
computing an absolute value of a result of the subtracting B from A;
computing an exponent based on the absolute value of the result of the subtracting B from A;
computing an exponential by exponentiation of a base number by the computed exponent; and
computing the arithmetic and/or bitwise expression of the boolean condition based on a remainder of a division of the exponential by the base number.
2. The method of claim 1 , wherein the arithmetic and/or bitwise expression of the boolean condition verifies the following:
if the boolean condition is verified, the arithmetic and/or bitwise expression of the boolean condition is equal to 1; and
if the boolean condition is not verified, the arithmetic and/or bitwise expression of the boolean condition is equal to 0.
3. The method of claim 2 , wherein the boolean condition comprises a consequent task that is formulated as an arithmetic statement, and wherein generating the arithmetic and/or bitwise expression of the computer program comprises:
multiplying the consequent task with the arithmetic and/or bitwise expression of the boolean condition.
4. The method of claim 3 , wherein the boolean condition comprises an alternative task that is formulated as an arithmetic statement, and wherein generating the arithmetic and/or bitwise expression of the computer program comprises:
multiplying the alternative task with a 1 minus the arithmetic and/or bitwise expression of the boolean condition.
5. The method of claim 2 , wherein the boolean condition comprises a consequent task that is formulated as a non-arithmetic statement, and wherein generating the arithmetic and/or bitwise expression of the computer program comprises:
including in the arithmetic and/or bitwise expression of the computer program an unconditional jump to a label associated with the arithmetic and/or bitwise expression of the boolean condition.
6. The method of claim 5 , wherein the label is equal to a start of a statement of the consequent task when a value of the arithmetic and/or bitwise expression of the boolean condition is equal to 1.
7. The method of claim 6 , wherein the boolean condition comprises an alternative task that is formulated as a non-arithmetic statement, wherein the label is equal to a start of a statement of the alternative task when the value of the arithmetic and/or bitwise expression of the boolean condition is equal to 0.
8. The method of claim 1 , wherein the boolean condition is A=B, and wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
computing the exponent as the absolute value of the result of the subtracting B from A; and
computing the arithmetic and/or bitwise expression of the boolean condition as the remainder of the division of the exponential by the base number.
9. The method of claim 1 , wherein the boolean condition is A≥B, wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A;
computing the exponent as an absolute value of a result of the subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A; and
computing the arithmetic and/or bitwise expression of the boolean condition as the remainder of the division of the exponential by the base number.
10. The method of claim 1 , wherein the boolean condition is A<B, wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A;
computing the exponent as an absolute value of a result of the subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A;
computing the exponential by exponentiation of the base number by the exponent; and
computing the arithmetic and/or bitwise expression of the boolean condition as 1 minus the remainder of the division of the exponential by the base number.
11. The method of claim 1 , wherein the base number is equal to 2, wherein the processor uses a binary system, and wherein the remainder of the division of the exponential by the base number is extracted by taking a last bit of the exponential.
12. The method of claim 1 , wherein the processor uses a binary system, and wherein the exponentiation of the base number by the computed exponent is performed by shifting a bit, which is equal to 1, left by a number of places equal to the computed exponent.
13. The method of claim 1 , wherein providing the arithmetic and/or bitwise expression of the computer program comprises:
fragmenting the arithmetic and/or bitwise expression of the computer program into multiple fragments of arithmetic and/or bitwise expression; and
wherein the fragments of arithmetic and/or bitwise expression are configured to be executed in parallel.
14. A system comprising:
one or more instruction processing units comprising at least one control unit, at least one arithmetic and/or bitwise operation unit, and at least one register unit; and
one or more memory units coupled with the one or more instruction processing units;
wherein the at least one control unit is configured to perform operations comprising:
accessing a computer program, wherein the computer program comprises a conditional statement that comprises a boolean condition;
transforming the boolean condition into an arithmetic and/or bitwise expression of the boolean condition;
generating an arithmetic and/or bitwise expression of the computer program comprising the arithmetic and/or bitwise expression of the boolean condition in place of the boolean condition; and
providing the arithmetic and/or bitwise expression of the computer program, wherein the arithmetic and/or bitwise expression of the computer program is configured to be executed by the at least one arithmetic and/or bitwise operation unit of the one or more instruction processing units, thereby causing execution, by the at least one arithmetic and/or bitwise operation unit, the arithmetic and/or bitwise expression of the computer program;
wherein the boolean condition takes a first variable A and a second variable B, wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
subtracting B from A;
computing an absolute value of a result of the subtracting B from A;
computing an exponent based on the absolute value of the result of the subtracting B from A;
computing an exponential by exponentiation of a base number by the computed exponent; and
computing the arithmetic and/or bitwise expression of the boolean condition based on a remainder of a division of the exponential by the base number.
15. The system of claim 14 , wherein the at least one arithmetic and/or bitwise operation unit comprises one or more of an arithmetic block, a bitwise shift block, and a bitwise logical block, and wherein the at least one arithmetic and/or bitwise operation unit does not include any digital comparator.
16. The system of claim 14 , wherein the boolean condition is A=B, and wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
computing the exponent as the absolute value of the result of the subtracting B from A; and
computing the arithmetic and/or bitwise expression of the boolean condition as the remainder of the division of the exponential by the base number.
17. The system of claim 14 , wherein the boolean condition is A≥B, wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A;
computing the exponent as an absolute value of a result of the subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A; and
computing the arithmetic and/or bitwise expression of the boolean condition as the remainder of the division of the exponential by the base number.
18. The system of claim 14 , wherein the boolean condition is A<B, wherein transforming the boolean condition into the arithmetic and/or bitwise expression of the boolean condition comprises:
subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A;
computing the exponent as an absolute value of a result of the subtracting the result of the subtracting B from A from the absolute value of the result of the subtracting B from A;
computing the exponential by exponentiation of the base number by the exponent; and
computing the arithmetic and/or bitwise expression of the boolean condition as 1 minus the remainder of the division of the exponential by the base number.
19. The system of claim 14 , wherein the base number is equal to 2, wherein the one or more instruction processing units use a binary system, wherein the remainder of the division of the exponential by the base number is extracted by taking a last bit of the exponential; and wherein the exponentiation of the base number by the computed exponent is performed by shifting a bit, which is equal to 1, left by a number of places equal to the computed exponent.
20. The system of claim 14 , wherein providing the arithmetic and/or bitwise expression of the computer program comprises:
fragmenting the arithmetic and/or bitwise expression of the computer program into multiple fragments of arithmetic and/or bitwise expression; and
wherein the fragments of arithmetic and/or bitwise expression are configured to be executed in parallel.