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2d3b0a687b
patch to fix half-cycle trigonometric functions
Paul Zimmermann, a MPFR developer, contacted me about large errors in
the half-cycle trigonometric functions. I've have investigated these
issues and developed the attached patch. The float, double, and ld80
(long double) changes have been tested.
Caveat emptor: The ld128 changes have not been compiled. The ld128
changes have not been tested. I do not have access to a system that
uses ld128 floating point.
Here is an itemized list of changes:
* lib/msun/src/math_private.h:
. Add fast floor macros to compute the integer part of |x| for
0 <= |x| 01xp(N-1), where N is the precision of the type of x.
These macros are used in the half-cycle trigonometric functions
(e.g., sinpi(x)).
. The FFLOOR80 macros is used with the Intel 80-bit extended double
functions. This macors corrects an off-by-one error, which led to
enormous error for |x| > 0x1p32.
* lib/msun/src/s_cospif.c:
* lib/msun/src/s_cospi.c:
* lib/msun/ld80/s_cospil.c:
. Update Copyright years.
. Use FFLOOR*() macro to get integer part of |x|.
. Correct handle the range 0x1p(N-1) <= |x| < 0x1pN. Here, one needs
to determine if the integral value of |x| is even or odd to choose
+1 or -1. If |x| >= 0x1pN, always return +1.
* lib/msun/src/s_sinpif.c:
* lib/msun/src/s_sinpi.c:
* lib/msun/ld80/s_sinpil.c:
. Update Copyright years.
. Use FFLOOR*() macro to get integer part of |x|.
* lib/msun/src/s_tanpif.c:
* lib/msun/src/s_tanpi.c:
* lib/msun/ld80/s_tanpil.c:
. Update Copyright years.
. For +-0.5, return +-inf. Previously, tanpi[fl]() returned an NaN.
. Use FFLOOR*() to get integer part of |x|. Need to determine if the
integer part is even or odd. This is used to set +-0 for |x|
integral
and +-inf for (n+1/2).
. For 0x1p(N-1) <= |x| < 0x1pN need to determine if x is an even or
odd
integer to select +0 or -0. For |x| >= 0x1pN, it is always an even
integer, select 0.
. Note, tanpi[fl](x) is an odd function, so one needs to consider
tanpi[fl](-|x|) = - tanpi[fl](|x|).
* lib/msun/ld128/s_cospil.c:
* lib/msun/ld128/s_sinpil.c:
* lib/msun/ld128/s_tanpil.c:
. Update Copyright years.
. These routines use an FFLOOR128 macros, which likely should be
replaced by a bit twiddling algorithm.
. The same considerations above are applied to 0x1p112 <= |x| <
0x1p113,
and |x| >= 0x1p113 cases.
. Note, even and odd determination used fmodl(x,2.), which is likely
slow.
PR: 272742
MFC after: 1 week
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|---|---|---|
| .. | ||
| b_expl.c | ||
| b_logl.c | ||
| b_tgammal.c | ||
| e_lgammal_r.c | ||
| e_powl.c | ||
| e_rem_pio2l.h | ||
| invtrig.c | ||
| invtrig.h | ||
| k_cosl.c | ||
| k_cospil.h | ||
| k_expl.h | ||
| k_sinl.c | ||
| k_sinpil.h | ||
| k_tanl.c | ||
| s_cexpl.c | ||
| s_cospil.c | ||
| s_erfl.c | ||
| s_exp2l.c | ||
| s_expl.c | ||
| s_logl.c | ||
| s_nanl.c | ||
| s_sinpil.c | ||
| s_tanpil.c | ||