Error of tan/tanf in libm.

[J. Johnston]

Stephen L Moshier wrote:
> 
> On Sun, 15 Apr 2001, Tim Prince wrote:
> > I haven't looked that deeply; I simply ran elefunt tests on the
> > functions used by cygwin.  I think the results were consistent with your
> > assessment of 3 ulps relative error.
> 
> The cygwin configuration appears to use the fdlibm versions from
> libm/math.  Newlib's ef_asin.c there compares the same as glibc's
> e_asinf.c except for the spelling of a few labels.
> 
> Here is an example test case.  Using the stock library routine it prints
>     The relative error is 2.2746e-07.
> after applying the patch below it prints
>     The relative error is 0.0000e+00.
>

Thanks for the patch Stephen.

-- Jeff J.
 
> ----
> float asinf (float);
> 
> int
> main()
> {
>   float x, y, c, e;
> 
>   x = 5.00433922E-01f;
>   c = 5.24099886E-01f;
>   y = asinf(x);
>   e = (y-c)/c;
>   printf("The relative error is %1.4e.\n", (double) e);
>   exit(0);
> }
> -----
> 
> Here is the minimal patch to correct the excess function error.
> 
>         * newlib/libm/math/ef_asin.c (pio2_hi, pio2_lo, pio4_hi):
>          Correct the numerical values.
> 
> *** ef_asin.c   Sun Apr 15 14:23:52 2001
> --- ef_asin.c   Sun Apr 15 14:23:32 2001
> *************** static float
> *** 22,30 ****
>   #endif
>   one =  1.0000000000e+00, /* 0x3F800000 */
>   huge =  1.000e+30,
> ! pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
> ! pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
> ! pio4_hi =  7.8539818525e-01, /* 0x3f490fdb */
>         /* coefficient for R(x^2) */
>   pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
>   pS1 = -3.2556581497e-01, /* 0xbea6b090 */
> --- 22,30 ----
>   #endif
>   one =  1.0000000000e+00, /* 0x3F800000 */
>   huge =  1.000e+30,
> ! pio2_hi = 1.57079637050628662109375f,
> ! pio2_lo = -4.37113900018624283e-8f,
> ! pio4_hi = 0.785398185253143310546875f,
>         /* coefficient for R(x^2) */
>   pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
>   pS1 = -3.2556581497e-01, /* 0xbea6b090 */