Fast, energy-efficient exponential computations in simd architectures

Patent metadata

Field	Value
Publication number	US-2016124709-A1
Application number	US-201414532312-A
Country	US
Kind code	A1
Filing date	Nov 4, 2014
Priority date	Nov 4, 2014
Publication date	May 5, 2016
Grant date	—

Abstract

In one embodiment, a computer-implemented method includes receiving as input a value of a variable x and receiving as input a degree n of a polynomial function being used to evaluate an exponential function e x . A first expression A*(x−ln(2)*K n (x f ))+B is evaluated, by one or more computer processors in a single instruction multiple data (SIMD) architecture, as an integer and is read as a double. In the first expression, K n (x f ) is a polynomial function of the degree n, x f is a fractional part of x/ln(2), A=2 52 /ln(2), and B=1023*2 52 . The result of reading the first expression as a double is returned as the value of the exponential function with respect to the variable x.

First claim

1 - 6 . (canceled)

7 . A system comprising:
a memory; and one or more processor cores, communicatively coupled to the memory, the one or more processor cores configured to:
receive as input a value of a variable x;
receive as input a degree n of a polynomial function being used to evaluate an exponential function e x ;
evaluate, in a single instruction multiple data (SIMD) architecture, a first expression A*(x−ln(2)*K n (x f ))+B as an integer and read the first expression as a double, wherein K n (x f ) is a polynomial function of the degree n, x f is a fractional part of x/ln(2), A=2 52 /ln(2), and B=1023*2 52 ; and
return, as the value of the exponential function with respect to the variable x, the result of reading the first expression as a double.

8 . The system of claim 7 , wherein the one or more processors are further configured to evaluate the exponential function using SIMD parallelism for two or more values of the variable x.

9 . The system of claim 7 , wherein the one or more processors perform the evaluating by, in a first SIMD instruction, multiplying the value of x by log 2 (e) to produce a first temporary result and by, in a second SIMD instruction, subtracting from the first temporary result the floor of the first temporary result.

10 . The system of claim 9 , wherein the one or more processors perform the evaluating by, in one or more additional SIMD instructions, evaluating the polynomial K n (x f ) to produce a second temporary result and subtracting the second temporary result from the first temporary result to product a third temporary result, wherein the one or more additional SIMD instructions comprise an SIMD instruction for each degree of the polynomial K n (x f ).

11 . The system of claim 10 , wherein the one or more processors perform the evaluating by, in a fourth SIMD instruction, computing a long integer as 2 52 +B.

12 . The system of claim 11 , wherein the one or more processors perform the reading the first expression as a double by reading the long integer as a double.

13 . The system of claim 7 , wherein the one or more processors are further configured to select a set of coefficients for the polynomial K n (x f ), wherein the selected coefficients are based on at least one of the Chebyshev polynomial and the Remez polynomial.

14 . A computer program product for evaluating an exponential function, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to perform a method comprising:
receiving as input a value of a variable x; receiving as input a degree n of a polynomial function being used to evaluate an exponential function e x ; evaluating, in a single instruction multiple data (SIMD) architecture, a first expression A*(x−ln(2)*K n (x f ))+B as an integer and reading the first expression as a double, wherein K n (x f ) is a polynomial function of the degree n, x f is a fractional part of x/ln(2), A=2 52 /ln(2), and B=1023*2 52 ; and returning, as the value of the exponential function with respect to the variable x, the result of reading the first expression as a double.

15 . The computer program product of claim 14 , the method further comprising evaluating the exponential function using SIMD parallelism for two or more values of the variable x.

16 . The computer program product of claim 14 , wherein the evaluating comprises computing x f by, in a first SIMD instruction, multiplying the value of x by log 2 (e) to produce a first temporary result and by, in a second SIMD instruction, subtracting from the first temporary result the floor of the first temporary result.

17 . The computer program product of claim 16 , wherein the evaluating comprises, one or more additional SIMD instructions, evaluating the polynomial K n (x f ) to produce a second temporary result and subtracting the second temporary result from the first temporary result to product a third temporary result, wherein the one or more additional SIMD instructions comprise an SIMD instruction for each degree of the polynomial K n (x f ).

18 . The computer program product of claim 17 , wherein the evaluating comprises, in a fourth SIMD instruction, computing a long integer as 2 52 +B.

19 . The computer program product of claim 18 , wherein reading the first expression as a double comprises reading the long integer as a double.

20 . The computer program product of claim 14 , the method further comprising selecting a set of coefficients for the polynomial K n (x f ), wherein the selected coefficients are based on at least one of the Chebyshev polynomial and the Remez polynomial.

Assignees

• IBM

Inventors

• Bekas Konstantinos
• Curioni Alessandro
• Ineichen Yves
• Malossi Adelmo Cristiano Innocenza

Classifications

• G06F7/556 Primary

  Logarithmic or exponential functions · CPC title

• G06F15/8007

  single instruction multiple data [SIMD] multiprocessors · CPC title

• G06F7/483 Primary

  Computations with numbers represented by a non-linear combination of denominational numbers, e.g. rational numbers, logarithmic number system or floating-point numbers {(G06F7/4806, G06F7/4824, G06F7/49, G06F7/491, G06F7/544 take precedence)} · CPC title

• G06F9/30036

  Instructions to perform operations on packed data, e.g. vector, tile or matrix operations · CPC title

• G06F9/3001

  Arithmetic instructions · CPC title