EXTENDED FLOATING-POINT RANGE ADDITION AND MULTIPLICATION
A first storage location is to store a first floating-point data element. The first data element has a sign bit, an N-bit first exponent value, and M bits. A second storage location is to store a second floating-point data element that is to have a same number of bits as the first floating-point data element. The second data element has a sign bit, an N-bit first exponent value, and M bits. The N-bit first exponent value of the second data element is all zeroes and the M bits of the second data element include a significand and a second exponent value. A floating-point arithmetic unit is coupled with the first and second storage locations. The floating-point arithmetic unit is to perform either multiplication or addition on the first and second data elements to generate a result data element based at least in part on the second exponent value.
1 . An apparatus comprising:
a first storage location to store a first floating-point data element, the first floating-point data element having a sign bit, an N-bit first exponent value, and M bits;
a second storage location to store a second floating-point data element that is to have a same total number of bits as the first floating-point data element, the second floating-point data element having a sign bit, an N-bit first exponent value, and M bits, wherein the N-bit first exponent value of the second floating-point data element is all zeroes and the M bits of the second floating-point data element include a significand and a second exponent value; and
a floating-point arithmetic unit coupled with the first storage location and the second storage location, the floating-point arithmetic unit to perform either multiplication or addition on the first floating-point data element and the second floating-point data element to generate a result floating-point data element based at least in part on the second exponent value of the second floating-point data element.
2 . The apparatus of claim 1 , wherein the M bits of the first floating-point data element is an M-bit significand when the N-bit first exponent value is not all zeros and when the N-bit first exponent value is not all ones.
3 . The apparatus of claim 1 , wherein the floating-point arithmetic unit is to perform the multiplication, including subtracting the second exponent value from a sum of the N-bit first exponent value of the first floating-point data element and the N-bit first exponent value of the second floating-point data element.
4 . The apparatus of claim 1 , wherein the N-bit first exponent value of the first floating-point data element is all zeroes and the M bits of the first floating-point data element include a significand and a second exponent value, and wherein the floating-point arithmetic unit is to perform the multiplication, including subtracting a sum of the second exponent value of the first floating-point data element and the second exponent value of the second floating-point data element from a sum of the N-bit first exponent value of the first floating-point data element and the N-bit first exponent value of the second floating-point data element.
5 . The apparatus of claim 1 , wherein the floating-point arithmetic unit is to perform the addition, including using the N-bit first exponent value of the first floating-point data element as a base exponent for the addition, and determining a right shift amount, to be used to right shift the significand of the second floating-point data element, to be a sum of the N-bit first exponent value of the first floating-point data element and the second exponent value of the second floating-point data element.
6 . The apparatus of claim 1 , wherein the N-bit first exponent value of the first floating-point data element is all zeroes and the M bits of the first floating-point data element include a significand and a second exponent value, and wherein the floating-point arithmetic unit is to perform the addition, including using a base exponent of zero for the addition, and determining a right shift amount, to be used to right shift a significand, to be an absolute value of a difference between the second exponent value of the first floating-point data element and the second exponent value of the second floating-point data element.
7 . The apparatus of claim 1 , wherein the floating-point arithmetic unit, to generate the result floating-point data element, is to use the second exponent value to identify a position of a binary point relative to the significand of the second floating-point data element.
8 . The apparatus of claim 7 , wherein the floating-point arithmetic unit, to generate the result floating-point data element, is to use the second exponent value to represent the second floating-point data element.
9 . The apparatus of claim 1 , wherein the significand of the second floating-point data element and the second exponent value of the second floating-point data element together include all the M bits of the second floating-point data element, and wherein the second exponent value comprises a plurality of least significant bits of the M bits of the second floating-point data element.
10 . The apparatus of claim 1 , wherein the total number of bits is 64-bits, wherein the N-bit first exponent value of the first floating-point data element is an 11-bit value, wherein the M bits of the first floating-point data element is fifty-two bits, wherein the significand of the second floating-point data element includes from forty-six to fifty bits, and wherein the second exponent value includes from two to six bits.
11 . The apparatus of claim 1 , wherein the total number of bits is 32-bits, wherein the N-bit first exponent value of the first floating-point data element is an 8-bit value, wherein the M bits of the first floating-point data element is twenty-three bits, wherein the significand of the second floating-point data element includes from eighteen to twenty-one bits, and wherein the second exponent value includes from two to five bits.
12 . A method executed by a computer processor, the method comprising:
accessing a first floating-point data element from a first storage location, the first floating-point data element having a sign bit, an N-bit first exponent value that is not all zeroes and that is not all ones, and an M-bit significand;
accessing a second floating-point data element, having a same total number of bits as the first floating-point data element, from a second storage location, the second floating-point data element having a sign bit, an N-bit first exponent value that is all zeroes, and M bits including a significand and a second exponent value; and
performing either multiplication or addition, with circuitry of the computer processor, on the first floating-point data element and the second floating-point data element to generate a result floating-point data element based at least in part on the second exponent value of the second floating-point data element.
13 . The method of claim 12 , wherein said performing either the multiplication or the addition comprises performing the multiplication, and wherein performing the multiplication includes subtracting the second exponent value of the second floating-point data element from a sum of the N-bit first exponent value of the first floating-point data element and the N-bit first exponent value of the second floating-point data element.
14 . The method of claim 12 , wherein said performing either the multiplication or the addition comprises performing the addition, and wherein performing the addition includes using the N-bit first exponent value of the first floating-point data element as a base exponent for the addition, and determining a right shift amount, to right shift the significand of the second floating-point data element, to be a sum of the N-bit first exponent value of the first floating-point data element and the second exponent value of the second floating-point data element.
15 . The method of claim 12 , wherein generating the result floating-point data element includes using the second exponent value to represent the second floating-point data element.
16 . The method of claim 12 , wherein the significand of the second floating-point data element and the second exponent value of the second floating-point data element together include all of the M bits of the second floating-point data element, and wherein the second exponent value of the second floating-point data element comprises a plurality of least significant bits of the M bits of the second floating-point data element.
17 . The method of claim 12 , wherein the total number of bits is 32-bits, wherein the N-bit first exponent value of the first floating-point data element is an 8-bit value, wherein the M bits of the first floating-point data element is twenty-three bits, wherein the significand of the second floating-point data element includes from eighteen to twenty-one bits, and wherein the second exponent value of the second floating-point data element includes from two to five bits.
18 . A non-transitory machine-readable storage medium comprising instructions that, when executed, cause processor circuitry to at least:
access a first floating-point data element from a first storage location, the first floating-point data element to have a sign bit, an N-bit first exponent value that is not all zeroes and that is not all ones, and an M-bit significand;
access a second floating-point data element, having a same total number of bits as the first floating-point data element, from a second storage location, the second floating-point data element to have a sign bit, an N-bit first exponent value that is all zeroes, and M bits including a significand and a second exponent value; and
perform either multiplication or addition on the first floating-point data element and the second floating-point data element to generate a result floating-point data element based at least in part on the second exponent value of the second floating-point data element.
19 . The non-transitory machine-readable storage medium of claim 18 , wherein the instructions, when executed, cause the processor circuitry to perform the multiplication, and wherein performing the multiplication includes subtracting the second exponent value from a sum of the N-bit first exponent value of the first floating-point data element and the N-bit first exponent value of the second floating-point data element
20 . The non-transitory machine-readable storage medium of claim 18 , wherein the total number of bits is 32-bits, wherein the N-bit first exponent value of the first floating-point data element is an 8-bit value, wherein the M bits of the first floating-point data element is twenty-three bits, wherein the significand of the second floating-point data element includes from eighteen to twenty-one bits, and wherein the second exponent value includes from two to five bits.