Techniques for performing square root or reciprocal square root calculations on BF16 data elements in response to an instruction are described. An example of an instruction is one that includes fields for an opcode, an identification of a location of a packed data source operand, and an identification of a packed data destination operand, wherein the opcode is to indicate that execution circuitry is to perform, for each data element position of the packed data source operand, a calculation of a square root value of a BF16 data element in that position and store a result of each square root into a corresponding data element position of the packed data destination operand.

A field programmable gate array (FPGA) including a configurable interconnect fabric connecting a plurality of logic blocks configured to implement a reciprocal function data path including: a mantissa computation stage including a mantissa portion of the reciprocal function data path configured to: partition an M-bit mantissa component of an input floating-point value into L most-significant bits and M-L least significant bits; lookup a slope value and an offset value, based on the L most significant bits, from a reciprocal lookup table; and compute an output mantissa component of an output floating-point value by multiplying the slope value by the M-L least significant bits to compute a product and adding the offset value to the product; and an exponent computation stage configured to compute an output exponent component of the output floating-point value, the computing the output exponent component including negating an exponent component of the input floating-point value.

A function estimation hardware logic unit may be implemented as part of an execution pipeline in a processor. The function estimation hardware logic unit is arranged to calculate, in hardware logic, an improved estimate of a function of an input value, d, where the function is given by

[00001]$1/\sqrt[i]{d}.$

The hardware logic comprises a plurality of multipliers and adders arranged to implement a m.sup.th-order polynomial with coefficients that are rational numbers, where m is not equal to two and in various examples m is not equal to a power of two. In various examples i=1, i=2 or i=3. In various examples m=3.

A function estimation hardware logic unit may be implemented as part of an execution pipeline in a processor. The function estimation hardware logic unit is arranged to calculate, in hardware logic, an improved estimate of a function of an input value, d, where the function is given by $1\text{/}\sqrt[i]{d}.$
The hardware logic comprises a plurality of multipliers and adders arranged to implement a m.sup.th-order polynomial with coefficients that are rational numbers, where m is not equal to two and in various examples m is not equal to a power of two. In various examples i=1, i=2 or i=3. In various examples m=3.

Methods and systems for determining whether an infinitely precise result of a reciprocal square root operation performed on an input floating point number is greater than a particular number in a first floating point precision. The method includes calculating the square of the particular number in a second lower floating point precision; calculating an error in the calculated square due to the second floating point precision; calculating a first delta value in the first floating point precision by calculating the square multiplied by the input floating point number less one; calculating a second delta value by calculating the error multiplied by the input floating point number plus the first delta value; and outputting an indication of whether the infinitely precise result of the reciprocal square root operation is greater than the particular number based on the second delta term.

Methods and systems for determining whether an infinitely precise result of a reciprocal square root operation performed on an input floating point number is greater than a particular number in a first floating point precision. The method includes calculating the square of the particular number in a second lower floating point precision; calculating an error in the calculated square due to the second floating point precision; calculating a first delta value in the first floating point precision by calculating the square multiplied by the input floating point number less one; calculating a second delta value by calculating the error multiplied by the input floating point number plus the first delta value; and outputting an indication of whether the infinitely precise result of the reciprocal square root operation is greater than the particular number based on the second delta term.

Methods and systems for determining whether an infinitely precise result of a reciprocal square root operation performed on an input floating point number is greater than a particular number in a first floating point precision. The method includes calculating the square of the particular number in a second lower floating point precision; calculating an error in the calculated square due to the second floating point precision; calculating a first delta value in the first floating point precision by calculating the square multiplied by the input floating point number less one; calculating a second delta value by calculating the error multiplied by the input floating point number plus the first delta value; and outputting an indication of whether the infinitely precise result of the reciprocal square root operation is greater than the particular number based on the second delta term.

A function estimation hardware logic unit may be implemented as part of an execution pipeline in a processor. The function estimation hardware logic unit is arranged to calculate, in hardware logic, an improved estimate of a function of an input value, d, where the function is given by

[00001]$1.Math.\text{/}.Math.\sqrt[i]{d}.$

The hardware logic comprises a plurality of multipliers and adders arranged to implement a m.sup.th-order polynomial with coefficients that are rational numbers, where m is not equal to two and in various examples m is not equal to a power of two. In various examples i=1, i=2 or i=3. In various examples m=3.

An apparatus and method for performing a reciprocal square root. For example one embodiment of a processor comprises: a decoder to decode a reciprocal square root instruction to generate a decoded reciprocal square root instruction; a source register to store at least one packed input data element; a destination register to store a result data element; and reciprocal square root execution circuitry to execute the decoded reciprocal square root instruction, the reciprocal square root execution circuitry to use a first portion of the packed input data element as an index to a data structure containing a plurality of sets of coefficients to identify a first set of coefficients from the plurality of sets, the reciprocal square root execution circuitry to generate a reciprocal square root of the packed input data element using a combination of the coefficients and a second portion of the packed input data element.

An apparatus and method for performing a reciprocal. For example one embodiment of a processor comprises: a decoder to decode a reciprocal instruction to generate a decoded reciprocal instruction; a source register to store at least one packed input data element; a destination register to store a result data element; and reciprocal execution circuitry to execute the decoded reciprocal instruction, the reciprocal execution circuitry to use a first portion of the packed input data element as an index to a data structure containing a plurality of sets of coefficients to identify a first set of coefficients from the plurality of sets, the reciprocal execution circuitry to generate a reciprocal of the packed input data element using a combination of the coefficients and a second portion of the packed input data element.