lib/52269: ctan(1+1000i) is incorrect

[coypu%sdf.org@localhost]

>Number:         52269
>Category:       lib
>Synopsis:       ctan(1+1000i) is incorrect
>Confidential:   no
>Severity:       serious
>Priority:       medium
>Responsible:    lib-bug-people
>State:          open
>Class:          sw-bug
>Submitter-Id:   net
>Arrival-Date:   Fri Jun 02 19:30:00 +0000 2017
>Originator:     coypu
>Release:        NetBSD 7.99.75
>Organization:
>Environment:
NetBSD loggy 7.99.75 NetBSD 7.99.75 (GENERIC) #61: Fri Jun  2 10:34:58 IDT 2017  fly@loggy:/home/fly/obj/sys/arch/amd64/compile/GENERIC amd64

>Description:
#include <complex.h>
#include <math.h>
#include <stdio.h>


int main() {
	printf("%f\n", ctan(1 + 1000*I));
}

$ gcc test2.c -lm
$ ./a.out
nan

expected: a number.
>How-To-Repeat:
Run R testsuite.
>Fix:
problem lies in using trigonometric functions which overflow in arg>=710.5 (some correctly)

maybe private taylor expansion is needed.