Math circuit for estimating a transcendental function

• US 9,465,580 B2
• Filed: 12/21/2011
• Issued: 10/11/2016
• Est. Priority Date: 12/21/2011
• Status: Active Grant

• Current Assignee: Intel Corporation
• Original Assignee: Intel Corporation
• Inventors: Pineiro, Jose-Alejandro, Rubanovich, Simon, Eitan, Benny, Gradstein, Amit, Fletcher, Thomas D.
• Primary Examiner(s): Ngo, Chuong D
• Application Number:
  US13/991,892
• Publication Number:
  US 20140222883A1
• Time in Patent Office: 1,756 Days
• Field of Search: 708200-490, 708/523
• US Class Current: 1/1
• CPC Class Codes: G06F 1/02 Digital function generators
• CPC Class Codes: G06F 1/03 working, at least partly, by table look-up G06F1/025 takes precedence
• CPC Class Codes: G06F 1/0356 by using two or more smaller tables, e.g. addressed by parts of the argument
• CPC Class Codes: G06F 2101/08 Powers or roots
• CPC Class Codes: G06F 2101/10 Logarithmic or exponential functions
• CPC Class Codes: G06F 2101/12 Reciprocal functions
• CPC Class Codes: G06F 2207/5521 Inverse root of a number or a function, e.g. the reciprocal of a Pythagorean sum
• CPC Class Codes: G06F 7/544 for evaluating functions by calculation G06F7/4824 takes precedence
• CPC Class Codes: G06F 7/552 Powers or roots , e.g. Pythagorean sums
• CPC Class Codes: G06F 7/57 Arithmetic logic units [ALU], i.e. arrangements or devices for performing two or more of the operations covered by groups G06F7/483 – G06F7/556 or for performing logical operations G06F7/49, G06F7/491 take precedence
• CPC Class Codes: G06F 9/30014 with variable precision
• CPC Class Codes: G06F 9/3832 Value prediction for operands; operand history buffers

Abstract

A math circuit for computing an estimate of a transcendental function is described. A lookup table storage circuit has stored therein several groups of binary values, where each group of values represents a respective coefficient of a first polynomial that estimates the function to a high precision. A computing circuit uses a portion of a binary value, that is also taken from one of the groups of values, to evaluate a second polynomial that estimates the function to a low precision. Other embodiments are also described and claimed.

Claims

1. A circuit for computing an estimate of a transcendental function, comprising:

a lookup table storage circuit having stored therein a plurality of groups of values, each group of values representing a respective coefficient of a first polynomial that estimates the transcendental function to a first precision; and

a first computing circuit coupled to the lookup table storage circuit to use portions of two groups of values representing two lowest-order coefficients of the first polynomial to evaluate a second polynomial that estimates the transcendental function to a second precision, wherein the second precision is lower than the first precision and the order of the second polynomial is lower than the order of the first polynomial, wherein the first computing circuit comprises;

an adjustment circuit to adjust the portion of the value representing the lowest-order coefficient that is taken from the lookup table storage circuit into an adjusted lowest-order coefficient of the second polynomial by adding an offset value, and

a multiply add circuit to use the adjusted lowest-order coefficient and the portion of the value representing the first-order coefficient of the first polynomial to evaluate the second polynomial;

wherein the circuit uses the lookup table storage circuit to evaluate both the first polynomial and the second polynomial.

2. The circuit of claim 1 further comprising a second computing circuit coupled to the lookup table storage circuit to use a value taken from each of the plurality of groups of values, to evaluate the first polynomial.

3. The circuit of claim 1 wherein the adjustment circuit comprises a further lookup table storage circuit having stored therein a plurality of offset values.

4. The circuit of claim 3 wherein the lookup table storage circuit outputs a value from each group, and the further lookup table circuit outputs the offset value, both in response to an instance of an input operand for the function,

wherein a first group of bits of the input operand are used as input to the lookup table storage circuit, and a second group of bits of the input operand are used as input to the further lookup table storage circuit.

5. The circuit of claim 4 wherein the first and second group of bits are the same.

6. The circuit of claim 1 wherein the second polynomial has a lower order than the first polynomial.

7. The circuit of claim 6 wherein the second polynomial is linear and the first polynomial is quadratic.

8. A processor device comprising:

an instruction decoder to receive a first instruction that is to evaluate a transcendental function; and

an execution unit having first lookup table circuitry that contains a plurality of values representing coefficients of a first polynomial that estimates the transcendental function to a first precision, the execution unit having an adjustment circuit that, in response to a decode of the first instruction, adjusts portions of the values that represent two lowest-order coefficients of the first polynomial and that are output by the first lookup table circuitry by adding an offset, and wherein the execution unit is to use the adjusted portion of the value to evaluate a second polynomial that estimates the transcendental function to a second precision, wherein the second precision is lower than the first precision and the order of the second polynomial is lower than the order of the first polynomial;

wherein the execution unit uses the lookup table circuitry to evaluate both the first polynomial and the second polynomial.

9. The processor device of claim 8 wherein the instruction decoder is to receive a second instruction that is to evaluate the transcendental function at a higher precision than the first instruction, and wherein the first lookup table circuitry, in response to a decode of the second instruction, outputs the plurality of values representing coefficients of the first polynomial, and the execution unit is to evaluate the first polynomial using the plurality of values output by the first lookup table circuitry.

10. The processor device of claim 9 wherein the execution unit comprises first multiplier adder logic to evaluate the first polynomial, with input from a) the plurality of values representing coefficients of the first polynomial and b) an instance of an input operand of the second instruction,

and second multiplier adder logic to evaluate the second polynomial, with input from a) the adjusted portion of the value that represents a coefficient of the first polynomial and b) an instance of an input operand of the first instruction.

11. The processor device of claim 8 wherein the adjustment circuit comprises second lookup table circuitry having stored therein a plurality of offset values, and wherein the execution unit comprises multiplier adder logic to evaluate the second polynomial, by adding one of the plurality of offset values to the portion of the value taken from the first lookup table circuitry.

12. The processor device of claim 11 wherein a first group of bits of an input operand of the first instruction are used as input to the first lookup table circuit, and a second group of bits of the input operand are used as input to the second lookup table circuit.

13. The processor device of claim 12 wherein the first and second group of bits are the same.

14. A machine-implemented method for computing an estimate of a transcendental function in a processor device, comprising:

fetching an instruction that is to estimate a transcendental function;

decoding the instruction and in response accessing a lookup table to obtain a value, wherein the value output by the lookup table represents coefficients of a first polynomial that estimates the transcendental function to a first precision;

adjusting a portion of the the lowest-order coefficient output by the lookup table by adding an offset; and

evaluating a second polynomial that estimates the transcendental function to a second precision, using the adjusted value, wherein the second precision is lower than the first precision and the order of the second polynomial is lower than the order of the first polynomial;

wherein the processor device uses the lookup table to evaluate both the first polynomial and the second polynomial; and

wherein the offset is selected such that a result of evaluating the second polynomial is substantially the same as a result of the transcendental function as executed by a legacy processor belonging to a different processor family than the processor device.

15. The method of claim 14 wherein adjusting a portion of the value output by the lookup table comprises:

in response to decoding of the low precision instruction, accessing a further lookup table to obtain the offset value, and wherein the lower order polynomial is evaluated using the offset value.

16. The method of claim 15 wherein accessing a further lookup table comprises consulting the further lookup table using the same group of bits of an input operand of the instruction as was used for accessing the lookup table to obtain said value.

17. A computer system comprising:

storage to store software; and

a processor device coupled to the storage, the processor device having an instruction set architecture that includes an instruction that is to evaluate a transcendental function, the processor device having a plurality of cores wherein each core of the processor has a math circuit to compute an estimate of the transcendental function, the math circuit includes a) a lookup table storage circuit having stored therein a plurality of groups of values, each group of values representing a respective coefficient of a first polynomial to estimate the transcendental function to a first precision, and b) a computing circuit coupled to the lookup table storage circuit to use values from two groups of values representing two lowest-order coefficients to evaluate a second polynomial that estimates the function to a second precision, wherein the second precision is lower than the first precision and the order of the second polynomial is lower than the order of the first polynomial, wherein the computing circuit comprises;

an adjustment circuit that adjusts a portion of the value representing the lowest-order coefficient that is taken from the lookup table storage circuit into an adjusted lowest-order coefficient of the second polynomial by adding an offset value; and

a multiply add circuit that uses the adjusted lowest-order coefficient and a portion of the value representing the first-order coefficient of the first polynomial to evaluate the second polynomial;

wherein the processor device uses the lookup table storage circuit to evaluate both the first polynomial and the second polynomial; and

wherein the processor device belongs to a first processor family, and the offset value is selected such that a result of evaluating the second polynomial is substantially the same as a result of the transcendental function as executed by a processor device belonging to a second processor family.

18. The computer system of claim 17 wherein the math circuit is to produce a result of an evaluation of the transcendental function, for said instruction, that is essentially equal, on a per bit basis, to a result produced by a second processor device executing the same instruction.

19. The computer system of claim 17 wherein the adjustment circuit comprises a further lookup table storage circuit having stored therein a plurality of offset values, and wherein the multiply add circuit adds one of the plurality of offset values to the portion of the value taken from the lookup table, when evaluating the second polynomial.