Add new log2 implementation

Similar algorithm is used as in log: log2(2^k x) = k + log2(c) + log2(x/c)
where the last term is approximated by a polynomial of x/c - 1, the first
order coefficient is about 1/ln2 in this case.

There is separate code path when fma instruction is not available for
computing x/c - 1 precisely, for which the table size is doubled.

The worst case error is 0.547 ULP (0.55 without fma), the read only
global data size is 1168 bytes (2192 without fma) on aarch64.  The
non-nearest rounding error is less than 1 ULP.

Improvements on Cortex-A72 compared to current glibc master:
log2 thruput: 2.00x in [0.01 11.1]
log2 latency: 2.04x in [0.01 11.1]
log2 thruput: 2.17x in [0.999 1.001]
log2 latency: 2.88x in [0.999 1.001]

Tested on
aarch64-linux-gnu (defined __FP_FAST_FMA)
arm-linux-gnueabihf (!defined __FP_FAST_FMA)
x86_64-linux-gnu (!defined __FP_FAST_FMA)
powerpc64le-linxu-gnu (defined __FP_FAST_FMA)
targets.

	* NEWS: Mention log2 improvements.
	* math/Makefile (type-double-routines): Add e_log2_data.
	* sysdeps/i386/fpu/e_log2_data.c: New file.
	* sysdeps/ia64/fpu/e_log2_data.c: New file.
	* sysdeps/ieee754/dbl-64/e_log2.c: Rewrite.
	* sysdeps/ieee754/dbl-64/e_log2_data.c: New file.
	* sysdeps/ieee754/dbl-64/math_config.h (__log2_data): Add.
	* sysdeps/ieee754/dbl-64/wordsize-64/e_log2.c: Remove.
	* sysdeps/m68k/m680x0/fpu/e_log2_data.c: New file.

1 files changed, 1 insertions, 1 deletions

diff --git a/NEWS b/NEWS
index 79bee8ee6b..04a0e89010 100644
--- a/NEWS
+++ b/NEWS
@@ -16,7 +16,7 @@ Major new features:
   to set the install root if you wish to install into a non-default
   configured location.
 
-* Optimized generic exp, exp2, log, sinf, cosf, sincosf and tanf.
+* Optimized generic exp, exp2, log, log2, sinf, cosf, sincosf and tanf.
 
 * The reallocarray function is now declared under _DEFAULT_SOURCE, not just
   for _GNU_SOURCE, to match BSD environments.