Xref: utzoo comp.sys.m68k:738 comp.arch:3359
Path: utzoo!mnetor!uunet!seismo!sundc!pitstop!sun!decwrl!pyramid!prls!mips!earl
From: earl@mips.COM (Earl Killian)
Newsgroups: comp.sys.m68k,comp.arch
Subject: Re: Motorola MC68881/68882 Manual published by Prentice-Hall
Message-ID: <1519@gumby.mips.COM>
Date: 8 Feb 88 07:22:11 GMT
References: <41174@sun.uucp>
Lines: 42
Keywords: CISC RISC

In article <41174@sun.uucp> dgh%dgh@Sun.COM (David Hough) writes:

   From a practical point of view, most chip vendors probably would
   not be smart enough to give away the software elementary
   transcendental function implementations for their chips.  They'd
   try to make money by selling the code which hardly anybody would
   buy (why not just take the stuff that comes "free" with System V or
   4.2?) and the result would be that their customers, the system
   integrators, would produce systems with inaccurate transcendental
   functions that aren't much faster than the 68881's.

Why not take the stuff that comes "free" with 4.3 instead of ancient
4.2?  The accuracy is quite good.  Consider Zliu's test suite on
4.3bsd libm and the 68881:

 NME  =  Negative Maximum Error observed in ULPs
 PME  =  Positive Maximum Error observed in ULPs
 NMC  =  Non-monotonicity count.

                [      From     ,      to       )       N.M.E.       P.M.E. NMC

4.3bsd libm:

SIN(X)      ALL [ +0.0000000e+00, +1.5707960e+00)      -0.6730      +1.0640  0
EXP(X)      ALL [ -1.0371094e+00, +1.0087891e+00)      -0.7630      +0.7720  0
EXPM1(X)    ALL [ -1.0371094e+00, +1.0087891e+00)      -0.8070      +0.8630  0
LOG1P(X)    ALL [ -2.9289320e-01, +4.1421360e-01)      -0.8430      +0.8110  0
ATAN(X)     ALL [ -6.5536000e+04, +6.5536000e+04)      -1.0610      +1.0680  0
LOG(X)      ALL [ +7.0710680e-01, +1.2851563e+00)      -0.8100      +0.8030  0

68881:

SIN(X)      ALL [ +0.0000000e+00, +1.5707960e+00)      -0.5500      +0.5540  0
EXP(X)      ALL [ -1.0371094e+00, +1.0087891e+00)      -0.5100      +0.5110  0
EXPM1(X)    ALL [ -1.0371094e+00, +1.0087891e+00)      -0.5560      +0.5550  0
LOG1P(X)    ALL [ -2.9289320e-01, +4.1421360e-01)      -0.5930      +0.5560  0
ATAN(X)     ALL [ -6.5536000e+04, +6.5536000e+04)      -0.5450      +0.5460  0
LOG(X)      ALL [ +7.0710680e-01, +1.4142136e+00)      -0.5930      +0.5610  0

What's more, because the 68881 is so slow, I'd guess that the 4.3 libm
is likely to be faster, given a decent implementation of add,
multiply, and divide.