Date: Fri, 4 Feb 2005 22:00:52 GMT From: David Schultz <das@FreeBSD.ORG> To: freebsd-i386@FreeBSD.org Subject: Re: i386/67469: src/lib/msun/i387/s_tan.S gives incorrect results for large inputs Message-ID: <200502042200.j14M0q0w030598@freefall.freebsd.org>
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The following reply was made to PR i386/67469; it has been noted by GNATS. From: David Schultz <das@FreeBSD.ORG> To: FreeBSD-gnats-submit@FreeBSD.ORG, freebsd-i386@FreeBSD.ORG Cc: bde@FreeBSD.ORG Subject: Re: i386/67469: src/lib/msun/i387/s_tan.S gives incorrect results for large inputs Date: Fri, 4 Feb 2005 16:59:13 -0500 On Wed, Jun 02, 2004, Bruce Evans wrote: > On Tue, 1 Jun 2004, David Schultz wrote: > > > >Description: > > src/lib/msun/i387/s_tan.S returns wildly inaccuate results when > > its input has a large magnitude (>> 2*pi). For example: > > > > input s_tan.S k_tan.c > > 1.776524190754802e+269 1.773388446261095e+16 -1.367233274980565e+01 > > 1.182891728897420e+57 -1.9314539773999572e-01 1.0020569035866138e+03 > > 2.303439778835110e+202 2.8465460220132694e+00 3.5686329695133922e+00 Here is a patch to fix the problem for tan(). See caveats below... Index: s_tan.S =================================================================== RCS file: /cvs/src/lib/msun/i387/s_tan.S,v retrieving revision 1.6 diff -u -r1.6 s_tan.S --- s_tan.S 28 Aug 1999 00:06:14 -0000 1.6 +++ s_tan.S 4 Feb 2005 21:43:32 -0000 @@ -45,14 +45,21 @@ jnz 1f fstp %st(0) ret -1: fldpi - fadd %st(0) - fxch %st(1) -2: fprem1 - fstsw %ax - andw $0x400,%ax - jnz 2b - fstp %st(1) - fptan - fstp %st(0) + +/* Use the fdlibm routines for accuracy with large arguments. */ +1: pushl %ebp + movl %esp,%ebp + subl $32,%esp + leal 12(%esp),%eax + movl %eax,8(%esp) + fstpl (%esp) + call __ieee754_rem_pio2 + addl $12,%esp + andl $1,%eax /* compute (eax & 1) ? -1 : 1 */ + sall %eax + subl $1,%eax + neg %eax + movl %eax,16(%esp) + call __kernel_tan + leave ret Unfortunately, I'm still getting the wrong answer for large values that are *supposed* to be handled by the fptan instruction. The error seems to increase towards the end of the range of fptan, (-2^63,2^63). For instance, tan(0x1.3dea2a2c29172p+22) is only off by the least significant 15 binary digits or so, but tan(0x1.2c95e550f1635p+62) is off by about 5%. Is fptan simply inherently inaccurate, or did I screw up somewhere? I would be interested in results from an AMD processor.
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