Unlock instant, AI-driven research and patent intelligence for your innovation.

Fast computation of products by dyadic fractions with sign-symmetric rounding errors

A product-vector technique, applied in the field of fast calculation of the product of the union-vector fraction and the sign-symmetric rounding error, which can solve problems such as increasing rounding error

Active Publication Date: 2011-05-18
QUALCOMM INC
View PDF3 Cites 0 Cited by
  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Since right shifting is a non-linear operation, arithmetic right shifting can increase rounding errors and produce results that may not be equal to the result of multiplication after the right shift

Method used

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
View more

Image

Smart Image Click on the blue labels to locate them in the text.
Viewing Examples
Smart Image
  • Fast computation of products by dyadic fractions with sign-symmetric rounding errors
  • Fast computation of products by dyadic fractions with sign-symmetric rounding errors
  • Fast computation of products by dyadic fractions with sign-symmetric rounding errors

Examples

Experimental program
Comparison scheme
Effect test

Embodiment Construction

[0012] Discrete Cosine Transform (DCT) and Inverse Discrete Cosine Transform (IDCT) perform multiplication operations with respect to irrational constants (ie, cosine). In the design of an implementation of the DCT / IDCT, the approximation of the computed product of these irrational constants can be performed using fixed-point arithmetic. One technique for converting floating-point values ​​to fixed-point values ​​is based on finding the irrational factor α by merging vector fractions i approximation:

[0013] alpha i ≈a i / 2 k (1)

[0014] where a i and k are both integers. x and factor α i The multiplication of provides an approximate implementation in integer arithmetic, as follows:

[0015] xα i ≈(x*a i )>>k (2)

[0016] Where >> indicates a bitwise right shift operation.

[0017] The number k of exact bits can affect the complexity of the union-vector rational approximation. In a software implementation, the exact parameter k may be constrained by the wi...

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to View More

PUM

No PUM Login to View More

Abstract

A product of an integer value and an irrational value may be determined by a sign-symmetric algorithm. A process may determine possible algorithms that minimize metrics such as mean asymmetry, mean error, variance of error, and magnitude of error. Given an integer variable x and rational dyadic constants that approximate the irrational fraction, a series of intermediate values may be produced that are sign-symmetric. The intermediate values may include a sequence of addition, subtraction and right shift operations the when summed together approximate the product of the integer and irrational value. Other operations, such as additions or subtractions of Os or shifts by 0 bits may be removed.

Description

technical field [0001] The subject matter herein relates generally to processing, and in particular to approximation techniques for use in hardware and software processing. Background technique [0002] Arithmetic shifts can be used to perform signed integer multiplication or division by powers of 2. Shifting a signed or unsigned binary number to the left by n bits has the effect of multiplying it by 2n. Right shifting a 2's complement signed binary number by n bits has the effect of dividing it by 2n, but it usually rounds (ie, towards negative infinity). Since right shifting is a non-linear operation, arithmetic right shifting can increase rounding errors and produce results that may not be equal to the multiplication result after the right shifting. [0003] In some implementations, sign symmetric algorithms can be used in IDCT transform architectures or other digital filters. [0004] An example of the use of arithmetic shifts is in fixed-point implementations of some...

Claims

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to View More

Application Information

Patent Timeline
no application Login to View More
Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/14G06F7/499
CPCG06F7/533H04N7/26702H04N7/30H04N19/00775G06F7/49942G06F17/147H04N19/00478H04N19/42H04N19/60G06F7/483
Inventor 尤里娅·列兹尼克
Owner QUALCOMM INC
Features
  • R&D
  • Intellectual Property
  • Life Sciences
  • Materials
  • Tech Scout
Why Patsnap Eureka
  • Unparalleled Data Quality
  • Higher Quality Content
  • 60% Fewer Hallucinations
Social media
Patsnap Eureka Blog
Learn More

Browse by: Latest US Patents, China's latest patents, Technical Efficacy Thesaurus, Application Domain, Technology Topic, Popular Technical Reports.

© 2025 PatSnap. All rights reserved.Legal|Privacy policy|Modern Slavery Act Transparency Statement|Sitemap|About US| Contact US: help@patsnap.com