Numeric processing algorithm.

Kragen Sitaker kragen at dnaco.net
Wed Sep 20 22:37:09 CEST 2000


In article <007001c01e35$b9c0e3a0$621aa7d1 at v1o9g4>,
The Majestic Moined Mogul <mogulNOSPAM at primus.ca> wrote:
>I know that Python is well known for its numeric processing power.  Does
>anyone know what algorithm it uses to do so.  Does it use the CORDIC?

It appears from web-searching that CORDIC is a clever set of algorithms
for computing trig and exponential functions using, among other things,
small lookup tables.

It looks like Python calculates these functions using the standard C
library math functions, which can use any algorithm whatsoever to
compute them, including CORDIC.  See Modules/mathmodule.c for details.

ISTR Plauger's book on the standard C library recommends using
Chebyshev polynomials to approximate trig functions; glibc 2.1.3
(sysdeps/libm-ieee754/k_sin.c) uses some kind of polynomial
approximation, which looks to me like a truncated Taylor series.

Glibc on my machine actually calls the hardware instructions in my FPU
to compute the trig functions, though --- according to objdump:

000096d0 <sin>:
    96d0:   dd 44 24 04             fldl   0x4(%esp,1)
    96d4:   d9 fe                   fsin   
    96d6:   df e0                   fnstsw 
    96d8:   a9 00 04 00 00          testl  $0x400,%eax
    96dd:   75 01                   jne    96e0 <sin+0x10>
    96df:   c3                      ret    
    96e0:   d9 eb                   fldpi  
    96e2:   d8 c0                   fadd   %st(0),%st
    96e4:   d9 c9                   fxch   %st(1)
    96e6:   d9 f5                   fprem1 
    96e8:   df e0                   fnstsw 
    96ea:   a9 00 04 00 00          testl  $0x400,%eax
    96ef:   75 f5                   jne    96e6 <sin+0x16>
    96f1:   dd d9                   fstp   %st(1)
    96f3:   d9 fe                   fsin   
    96f5:   c3                      ret    

I have no idea how the FPU on my machine calculates trig functions.
Probably not with CORDIC, though.

Does that answer your question?  
-- 
<kragen at pobox.com>       Kragen Sitaker     <http://www.pobox.com/~kragen/>
Perilous to all of us are the devices of an art deeper than we ourselves
possess.
                -- Gandalf the Grey [J.R.R. Tolkien, "Lord of the Rings"]



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