Dr. Dobb's Journal - April 2008 - (Page 40) d04will_p3ds 2/13/08 9:39 AM Page 40 Core Technology OPTIMIZING MATH-INTENSIVE APPLICATIONS WITH FIXED-POINT ARITHMETIC The single biggest gain was achieved by optimizing the trigonometric and exponential functions continued from page 38 cosines from the Taylor series, for example) gave me hope—by improving the implementation of these functions, there was potential for much greater improvements, so I pressed on with renewed vigor. Eventually, the whole fixed-point library was rewritten from scratch, but the final performance gain was enough to justify the time spent in doing so, and it was easier than anticipated. (The com- plete source code for the fixed-point library and profiling code is available online.) Don’t Forget the Constants! Having changed over to fixed point, the next easy gain came from replacing floating-point and integer constants involved in fixedpoint calculations with fixed-point ones. It’s easy just to use M_PI or 40 Dr. Dobb’s Journal l www.ddj.com l April 2008 http://www.imagix.com http://www.mcobject.com http://www.mcobject.com/enterprise http://www.ddj.com
Table of Contents Feed for the Digital Edition of Dr. Dobb's Journal - April 2008 Dr. Dobb's Journal - April 2008 Contents Hmmmm Alia Vox Developer Diaries Dr. Dobb's Excellence in Programming Award Conversations Fast String Search on Multicore Processors The Byzantine Generals Problem Optimizing Math-Intensive Applications with Fixed-Point Arithmetic Random Numbers in a Range Using Generic Programming The Agile Edge Effective Concurrency Swaine's Flames Dr. Dobb's Journal - April 2008 Dr. Dobb's Journal - April 2008 - Dr. Dobb's Journal - April 2008 (Page Cover1) Dr. Dobb's Journal - April 2008 - Dr. Dobb's Journal - April 2008 (Page Cover2) Dr. Dobb's Journal - April 2008 - Dr. Dobb's Journal - April 2008 (Page 1) Dr. Dobb's Journal - April 2008 - Dr. Dobb's Journal - April 2008 (Page 2) Dr. Dobb's Journal - April 2008 - Dr. Dobb's Journal - April 2008 (Page 3) Dr. Dobb's Journal - April 2008 - Contents (Page 4) Dr. Dobb's Journal - April 2008 - Contents (Page 5) Dr. Dobb's Journal - April 2008 - Hmmmm (Page 6) Dr. Dobb's Journal - April 2008 - Hmmmm (Page 7) Dr. Dobb's Journal - April 2008 - Hmmmm (Page 8) Dr. Dobb's Journal - April 2008 - Hmmmm (Page 9) Dr. Dobb's Journal - April 2008 - Alia Vox (Page 10) Dr. Dobb's Journal - April 2008 - Alia Vox (Page 11) Dr. Dobb's Journal - April 2008 - Developer Diaries (Page 12) Dr. Dobb's Journal - April 2008 - Developer Diaries (Page 13) Dr. Dobb's Journal - April 2008 - Developer Diaries (Page 14) Dr. Dobb's Journal - April 2008 - Developer Diaries (Page 15) Dr. Dobb's Journal - April 2008 - Dr. Dobb's Excellence in Programming Award (Page 16) Dr. Dobb's Journal - April 2008 - Dr. Dobb's Excellence in Programming Award (Page 17) Dr. Dobb's Journal - April 2008 - Conversations (Page 18) Dr. Dobb's Journal - April 2008 - Conversations (Page 19) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 20) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 21) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 22) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 23) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 24) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 25) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 26) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 27) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 28) Dr. Dobb's Journal - April 2008 - Fast String Search on Multicore Processors (Page 29) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 30) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 31) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 32) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 33) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 34) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 35) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 36) Dr. Dobb's Journal - April 2008 - The Byzantine Generals Problem (Page 37) Dr. Dobb's Journal - April 2008 - Optimizing Math-Intensive Applications with Fixed-Point Arithmetic (Page 38) Dr. Dobb's Journal - April 2008 - Optimizing Math-Intensive Applications with Fixed-Point Arithmetic (Page 39) Dr. Dobb's Journal - April 2008 - Optimizing Math-Intensive Applications with Fixed-Point Arithmetic (Page 40) Dr. Dobb's Journal - April 2008 - Optimizing Math-Intensive Applications with Fixed-Point Arithmetic (Page 41) Dr. Dobb's Journal - April 2008 - Optimizing Math-Intensive Applications with Fixed-Point Arithmetic (Page 42) Dr. Dobb's Journal - April 2008 - Optimizing Math-Intensive Applications with Fixed-Point Arithmetic (Page 43) Dr. Dobb's Journal - April 2008 - Random Numbers in a Range Using Generic Programming (Page 44) Dr. Dobb's Journal - April 2008 - Random Numbers in a Range Using Generic Programming (Page 45) Dr. Dobb's Journal - April 2008 - Random Numbers in a Range Using Generic Programming (Page 46) Dr. Dobb's Journal - April 2008 - Random Numbers in a Range Using Generic Programming (Page 47) Dr. Dobb's Journal - April 2008 - Random Numbers in a Range Using Generic Programming (Page 48) Dr. Dobb's Journal - April 2008 - The Agile Edge (Page 49) Dr. Dobb's Journal - April 2008 - The Agile Edge (Page 50) Dr. Dobb's Journal - April 2008 - The Agile Edge (Page 51) Dr. Dobb's Journal - April 2008 - Effective Concurrency (Page 52) Dr. Dobb's Journal - April 2008 - Effective Concurrency (Page 53) Dr. Dobb's Journal - April 2008 - Effective Concurrency (Page 54) Dr. Dobb's Journal - April 2008 - Effective Concurrency (Page 55) Dr. Dobb's Journal - April 2008 - Swaine's Flames (Page 56) Dr. Dobb's Journal - April 2008 - Swaine's Flames (Page Cover3) Dr. Dobb's Journal - April 2008 - Swaine's Flames (Page Cover4)
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