Efficiently determining a floor for a floating-point number

A apparatus for determining the floating-point floor of a floating-point number, the apparatus comprising:

• means for identifying a binary floating-point number including a sign bit, exponent bits, and mantissa bits, wherein the binary floating-point number is negative when the sign bit is a one (“1”);
• means for concatenating an implicit bit and the mantissa bits, thereby producing a first binary number such that the implicit bit is the most significant bit (MSB) of the first binary number;
• a decrementer configured to decrement the first binary number when the sign bit is a one (“1”) and do nothing when the sign bit is a zero (“0”), thereby producing a second binary number;
• a fraction mask table configured to identify a fraction portion of the second binary number based at least on the exponent bits;
• a multiplexer operative to receive the fraction portion from the fraction mask table and configured to replace each bit of the fraction portion with the sign bit thereby producing a third binary number;
• an exclusive-OR configured to perform an exclusive-OR operation between each bit of the third binary number and the sign bit thereby producing a fourth binary number;
• means for concatenating the sign bit, the fourth binary number, and a first predetermined number of zeros, thereby producing a fifth binary number such that the sign bit is the MSB of the fifth binary number, and the zeros are the least significant bits of the fifth binary number;
• and
• a signed-right-shift configured to perform, upon the fifth binary number, a signed-right-shift operation by a number of bits equivalent to the difference between the exponent and a second predetermined number, thereby producing the floor of the binary floating-point number in integer format.

A method for determining the floating-point floor of a floating-point number, the method comprising:

• identifying a binary floating-point number including a sign bit, exponent bits, and mantissa bits, wherein the binary floating-point number is negative when the sign bit is a one (“1”);
• concatenating an implicit bit and the mantissa bits, thereby producing a first binary number such that the implicit bit is the most significant bit (MSB) of the first binary number;
• decrementing the first binary number when the sign bit is a one (“1”) and doing nothing when the sign bit is a zero (“0”), thereby producing a second binary number;
• identifying a fraction portion of the second binary number based at least on the exponent bits;
• replacing each bit of the fraction portion with the sign bit thereby producing a third binary number;
• performing an exclusive-OR operation between each bit of the third binary number and the sign bit thereby producing a fourth binary number;
• concatenating the sign bit, the fourth binary number, and a first predetermined number of zeros, thereby producing a fifth binary number such that the sign bit is the MSB of the fifth binary number, and the zeros are the least significant bits of the fifth binary number;
• and
• performing, upon the fifth binary number, a signed-right-shift operation by a number of bits equivalent to the difference between the exponent and a second predetermined number, thereby producing the floor of the binary floating-point number in integer format.

A computer program product, tangibly stored on a computer-readable

• medium, for determining the floating-point floor of a floating-point number, comprising instructions operable to cause a programmable processor to:
• identify a binary floating-point number including a sign bit, exponent bits, and mantissa bits, wherein the binary floating-point number is negative when the sign bit is a one (“1”);
• concatenate an implicit bit and the mantissa bits, thereby producing a first binary number such that the implicit bit is the most significant bit (MSB) of the first binary number;
• decrement the first binary number when the sign bit is a one (“1”) and doing nothing when the sign bit is a zero (“0”), thereby producing a second binary number;
• identify a fraction portion of the second binary number based at least on the exponent bits;
• replace each bit of the fraction portion with the sign bit thereby producing a third binary number;
• perform an exclusive-OR operation between each bit of the third binary number and the sign bit thereby producing a four binary number;
• concatenate the sign bit, the fourth binary number, and a first predetermined number of zeros, thereby producing a fifth binary number such that the sign bit is the MSB of the
• fifth binary number, and the zeros are the least significant bits of the fifth binary number;
• and
• perform, upon the fifth binary number, a signed-right-shift operation by a number of bits equivalent to the difference between the exponent and a second predetermined number, thereby producing the floor of the binary floating-point number in integer format.