Bug 772592

Summary: tan(pi/2) eval requires too much time
Product: [Fedora] Fedora Reporter: Gerard Torrent <gerard>
Component: glibcAssignee: Jeff Law <law>
Status: CLOSED NOTABUG QA Contact: Fedora Extras Quality Assurance <extras-qa>
Severity: low Docs Contact:
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Version: 16CC: fweimer, jakub, law, schwab
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Last Closed: 2012-02-07 18:24:32 UTC Type: ---
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tan(pi/2) eval requires too much time none

Description Gerard Torrent 2012-01-09 11:18:15 UTC
Created attachment 551534 [details]
tan(pi/2) eval requires too much time

Description of problem: tan(x) evaluated at x = k*M_PI/2 where k=1,2,3,... or k=-1,-2,-3,... requires 2 orders of magnitude more time than in the other cases.

Version-Release number of selected component (if applicable):
gcc (GCC) 4.6.2 20111027 (Red Hat 4.6.2-1)
glibc-2.14.90-24.fc16.4.x86_64

How reproducible: compiling and executing the attached source code

Steps to Reproduce:
1. gcc -O2 tan-pi-div-2.c -lm
2. ./a.out > data.txt
3. gnuplot (plot "data.txt" using 1:2 with lines)

Actual results: peaks at pi/2 multiples

Expected results: all values in the same range

Additional info: see attached file

Comment 1 Jeff Law 2012-02-07 18:24:32 UTC
This is the same as:

http://sources.redhat.com/bugzilla/show_bug.cgi?id=3783

In a nutshell, glibc's tan implementation first computes the result using FPU instructions.  if the maximum error is sufficiently low that result is returned.  Obviously this is fast.  If the error is potentially > than 0.5ulp, then glibc falls back to a more expensive algorithm to compute the result.

For tan, values such as pi/2 multiples will trigger the need to use the slower algorithm, thus the significantly longer times.