libm for 68881 and Sun fpa is incredibly slow

[prl at eiger.uucp]

I have constructed a replacement for libm.a in which most of the C library
routines have had their code replaced by code out of the inline
replacement library.

I will be making this code available in sun-spots or in comp.sources.sun
(as appropriate), in a form which requires no distribution of Sun source
or binaries, as soon as it has been tested locally.

You can expect sqrt() to be more than 10 times faster in this library than
in the standard -lm!

The speedups are as follows (Sun3/280, SunOS 4.0.1):

Motorola 68881

Func	-lm	-lmfast		libm.il
	secs	secs	rel	secs	rel	rel
			-lm		-lm	-lmfast

cos()	9.43	1.85	5.10	1.67	5.65	1.11
sin()	8.87	1.77	5.01	1.65	5.38	1.07
tan()	12.98	1.97	6.59	1.83	7.09	1.08
acos()	5.13	2.37	2.16	2.27	2.26	1.04
asin()	6.40	2.37	2.70	2.20	2.91	1.08
atan()	9.22	1.82	5.07	1.70	5.42	1.07
log()	10.25	2.25	4.56	2.10	4.88	1.07
log10()	6.47	2.35	2.75	2.22	2.91	1.06
log2()	5.33	2.33	2.29	1.48	3.60	1.57
exp()	8.42	1.95	4.32	1.80	4.68	1.08
exp10()	9.37	2.12	4.42	2.02	4.64	1.05
exp2()	6.50	2.10	3.10	1.97	3.30	1.07
sqrt()	14.32	1.20	11.93	1.03	13.90	1.17
cosh()	4.82	2.23	2.16	2.10	2.30	1.06
sinh()	5.32	2.15	2.47	1.98	2.69	1.09
tanh()	5.57	2.33	2.39	2.23	2.50	1.04
atanh()	3.95	2.52	1.57	1.63	2.42	1.55



Weitek FPA

Func	-lm	-lmfast		libm.il
	secs	secs	rel	secs	rel	rel
			-lm		-lm	-lmfast

cos()	3.45	0.83	4.16	0.82	4.21	1.01
sin()	3.23	0.75	4.31	0.73	4.42	1.03
tan()	4.60	1.63	2.82	1.57	2.93	1.04
acos()	3.55	2.00	1.77	1.97	1.80	1.02
asin()	3.95	2.05	1.93	1.90	2.08	1.08
atan()	2.97	1.23	2.41	1.23	2.41	1.00
log()	4.42	1.27	3.48	1.28	3.45	0.99
log10()	4.17	2.07	2.01	1.93	2.16	1.07
log2()	3.43	1.93	1.78	1.95	1.76	0.99
exp()	3.15	1.42	2.22	1.25	2.52	1.14
exp10()	4.90	1.75	2.80	1.67	2.93	1.05
exp2()	3.32	1.75	1.90	1.68	1.98	1.04
sqrt()	12.37	1.18	10.48	1.18	10.48	1.00
cosh()	2.75	1.95	1.41	1.82	1.51	1.07
sinh()	3.03	1.75	1.73	1.68	1.80	1.04
tanh()	3.33	2.00	1.67	1.93	1.73	1.04
atanh()	2.32	2.12	1.09	2.10	1.10	1.01

NOTES:

1) -lmfast is my modified libm.a, libm.il is with the use
   of the Sun-supplied inline code file.

2) Columns entitled `rel' are the speedup relative to the named column.

3) The times for each routine are for 50000 calls, with parameter values in the
   range from slightly more than 0.0 to slightly more than 1.0, spaced linearly
   by 1.0/50000.0.

4) Loop overhead has been subtracted, but not subroutine call overhead.


Peter Lamb
uucp:  uunet!mcvax!ethz!prl	eunet: prl at ethz.uucp	Tel:   +411 256 5241
Integrated Systems Laboratory
ETH-Zentrum, 8092 Zurich