STD/Mathlib - Super Optimized Math Library

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Notes:

  • The following benchmarks figures between Sinectonalysis, the fastest third party software competitor, and TI’s rts.src library version 4.4 are in processor cycles, assuming 0-wait state SRAM for coefficients and a small memory compilation model. Parameters are passed on stack. Register model functions will run a few cycles faster, while large memory versions will have a 1-2 cycle penalty.
  • Two functions are provided with limited domain in order to enhance performance for [-¹/2,¹/2] subdomain, all other functions operate on full domains.
  • asin and acos are implemented differently on the C40 from Competitor’s or TI’s so that the faster path is used on a larger domain.STD/Mathlib asin and acos run in 26,27 cycles on the interval [-1/sqrt(2),+1/sqrt(2)] instead of interval [-1/2,+1/2]. Therefore the average time for Sinectonalysis functions is smaller than Competitor’s time although the minimum and maximum times for these functions are essentially the same.
  • Results with 7-9+ decimal digits of accuracy are maintained in STD/Mathlib as long as the results are kept in extended-precision registers. The competitor’s and TI’s libraries maintain 6-7 digits of accuracy.
  • The STD/Mathlib achieves maximum performance when “.const” section data is placed in 0WS RAM. If “.const” is placed in slow RAM the libraries incur only a minor performance penalty. For example, exp function will run 5 cycles slower if 1WS RAM is used.
  • No more than 15 words are needed by any one function for coefficient data.

Ordering Guide

STD/Mathlib™ is available in C30 and C40 versions for single user and multiple user PC and workstation hosts.

"X" specifies host and media.

  • STD/Mathlib-ASM-C30-X - TMS320C30 library compatible with TI C tools.
  • STD/Mathlib -ASM-C40-X - TMS320C40 library compatible with TI C tools.
  • STD/Mathlib-ASM-C40-HL-X - TMS320C40 library for Helios™ environment.
  • STD/Mathlib-UM - User manual, ~30 pp. 






PROCESSOR CYCLE COUNT

     

     FUNCTION      SINECTO C30     BEST 
 COMPETITOR C30 		     TI 
 C30 		     SINECTO C40     BEST 
 COMPETITOR C40 		     TI 
 C40 		
     


     

     ldexp   11-11 N/A  >20   9-9 N/A   >20 


     

     frexp  12-12 N/A  >20   9-9 N/A    >20 


     

     floor   6-6 N/A  >20   6-6 N/A   >20 
     

     

     ceiling    8-8 N/A   >20   7-7 N/A    >20 


     

     loge   26-26    39-41    109-109  27-27    39-41   77-79 


     

     log2   25-25  N/A    N/A  27-27    N/A    N/A 


     

     log10   26-26     40-42    114-114  27-27    39-41   82-84 


     

     exp   21-21  37-37    123-132  21-21    35-35    95-96 


     

     exp2   20-20   N/A    N/A  20-20    N/A  N/A 
     

     

     exp10   21-21    39-39    N/A  21-21    35-35    N/A 


     

     pow   43-43    124-129   197-262 44-44    96-100   169-234
     

     

     sin   22-23  32-37  66-82  21-22    31-31   65-82 
     

     

     fsin 16-16     26-26      N/A  15-15 26-26      N/A 


     

     cos  22-23    31-36   64-79  21-22    30-30   64-79 
     

     

     fcos 15-15      25-25      N/A  14-14    26-26      N/A 


     

     tan  40-40     55-60    110-128  28-28   37-37    82-99 


     

     cot   40-40    57-62    N/A  28-28    43-43    N/A 
     

     

     asin   26-56    26-73    93-151 26-43    26-41    62-84 


     

     acos   27-56    27-74    92-153  27-42    27-42    61-83 
     

     

     atan   27-37    37-67   84-175 27-29    37-44    55-92 


     

     atan2   56-59    81-111   151-259 39-45    57-66    97-151 


     

     acot   28-37   43-69    N/A  27-29    43-47    N/A
     

     

     acot2  56-59    83-113    N/A  39-45    57-66    N/A 




     sqrt   28-28    40-41    48-48  16-16    18-18    24-24 




     invsqrt 27-27  38-39    N/A  14-14   15-15  N/A
    



     sinh   14-41  52-87   75-176 14-35    30-61    48-122
    



     cosh  29-45    42-83    162-163 30-36    57-58    108-109
    



     tanh  13-49   57-86  77-210  13-38    33-61    50-147
    



     coth   42-49    91-120    N/A  29-37    53-81    N/A




asinh   17-56 23-97  N/A 16-46    57-61   N/A




acosh  38-56  57-93   N/A  44-44    57-61    N/A




atanh 16-49   29-89   N/A 15-43    30-67    N/A




acoth   35-51  62-92   N/A  22-44    41-63    N/A

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