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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_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 |