Improve accuracy and range of tgamma*(3)

[markm]

Summary

• lib/msun/bsdsrc/b_exp.c: . Replace scalb() usage with C99's ldexp(). . Replace finite(x) usage with C99's isfinite(). . Whitespace changes towards style(9). . Remove include of "mathimpl.h". It is no longer needed. . Remove #if 0 ... #endif code, which has been present since svn r93211 (2002-03-26). . New minimax polynomial coefficients. . Add comments to explain origins of some constants. . Use ansi-C prototype. Remove K&R prototype. Add static to prototype.

• lib/msun/bsdsrc/b_log.c: . Remove include of "mathimpl.h". It is no longer needed. . Fix comments to actually describe the code. . Reduce minimax polynomial from degree 4 to degree 3. This uses newly computed coefficients. . Use ansi-C prototype. Remove K&R prototype. Add static to prototype. . Remove volatile in declaration of u1. . Alphabetize decalaration list. . Whitespace changes towards style(9). . In argument reduction of x to g and m, replace use of logb() and ldexp() with a single call to frexp(). Add code to get 1 <= g < 2. . Remove #if 0 ... #endif code, which has been present since svn r93211 (2002-03-26). . The special case m == -1022, replace logb() with ilogb().

• lib/msun/bsdsrc/b_tgamma.c: . Update comments. Fix comments where needed. . Add float.h to get LDBL_MANT_DIG for weak reference of tgammal to tgamma. . Remove include of "mathimpl.h". It is no longer needed. . Use "math.h" instead of <math.h>. . Add '#include math_private.h" . Add struct Double from mathimpl.h and include b_log.c and b_exp.c. . Remove forward declarations of neg_gam(), small_gam(), smaller_gam, large_gam() and ratfun_gam() by re-arranging the code to move these function above their first reference. . New minimax coefficients for polynomial in large_gam(). . New splitting of a0 into a0hi nd a0lo, which include additional bits of precision. . Use ansi-C prototype. Remove K&R prototype. . Replace the TRUNC() macro with a simple cast of a double entities to float before assignment (functional changes). . Replace sin(M_PI*z) with sinpi(z) and cos(M_PI*(0.5-z)) with cospi(0.5-z).

Submitted-by: Steve Kargl

• lib/msun/Makefile b/lib/msun/Makefile: . Disconnect imprecise.c from the build. This file can be deleted. . Add b_tgammal.c to the build for ld80 and ld128 targets. The ld128 is a 'git mv' of imprecise.c to ld128/b_tgammal.c.

• lib/msun/ld80/b_expl.c: . New file. Implement expD for ld80 targets. This is based on bsdsrc/b_exp.c.

• lib/msun/ld80/b_logl.c: . New file. Implement logD for ld80 targets. This is based on bsdsrc/b_log.c.

• lib/msun/ld80/b_tgammal.c b/lib/msun/ld80/b_tgammal.c . New file. Implement tgammal(x) for ld80 targets.

Submitted-By: Steve Kargl

[markm]

This is two git commits - see the commit message.

[imp]

the structural parts of this are good. I'm not enough of a numeric computation person to know if the math is still good (or improved), though it looks like it should be.

[markm]

I missed the move of imprecise.c to its new, temporary home in ld128.

[pfg]

I appreciate this effort going on. Getting good implementations of these functions is tough.,

For the record: I once tried to replace the OpenOffice implementations of the gamma functions with Boost and the results were so different that all tests failed.