Improve __ieee754_exp() performance by greater than 5x on sparc/x86.

These changes will be active for all platforms that don't provide
their own exp() routines. They will also be active for ieee754
versions of ccos, ccosh, cosh, csin, csinh, sinh, exp10, gamma, and
erf.

Typical performance gains is typically around 5x when measured on
Sparc s7 for common values between exp(1) and exp(40).

Using the glibc perf tests on sparc,
      sparc (nsec)    x86 (nsec)
      old     new     old     new
max   17629   395    5173     144
min     399    54      15      13
mean   5317   200    1349      23

The extreme max times for the old (ieee754) exp are due to the
multiprecision computation in the old algorithm when the true value is
very near 0.5 ulp away from an value representable in double
precision. The new algorithm does not take special measures for those
cases. The current glibc exp perf tests overrepresent those values.
Informal testing suggests approximately one in 200 cases might
invoke the high cost computation. The performance advantage of the new
algorithm for other values is still large but not as large as indicated
by the chart above.

Glibc correctness tests for exp() and expf() were run. Within the
test suite 3 input values were found to cause 1 bit differences (ulp)
when "FE_TONEAREST" rounding mode is set. No differences in exp() were
seen for the tested values for the other rounding modes.
Typical example:
exp(-0x1.760cd2p+0)  (-1.46113312244415283203125)
 new code:    2.31973271630014299393707e-01   0x1.db14cd799387ap-3
 old code:    2.31973271630014271638132e-01   0x1.db14cd7993879p-3
    exp    =  2.31973271630014285508337 (high precision)
Old delta: off by 0.49 ulp
New delta: off by 0.51 ulp

In addition, because ieee754_exp() is used by other routines, cexp()
showed test results with very small imaginary input values where the
imaginary portion of the result was off by 3 ulp when in upward
rounding mode, but not in the other rounding modes.  For x86, tgamma
showed a few values where the ulp increased to 6 (max ulp for tgamma
is 5). Sparc tgamma did not show these failures.  I presume the tgamma
differences are due to compiler optimization differences within the
gamma function.The gamma function is known to be difficult to compute
accurately.

	* sysdeps/ieee754/dbl-64/e_exp.c: Include <math-svid-compat.h> and
	<errno.h>.  Include "eexp.tbl".
	(half): New constant.
	(one): Likewise.
	(__ieee754_exp): Rewrite.
	(__slowexp): Remove prototype.
	* sysdeps/ieee754/dbl-64/eexp.tbl: New file.
	* sysdeps/ieee754/dbl-64/slowexp.c: Remove file.
	* sysdeps/i386/fpu/slowexp.c: Likewise.
	* sysdeps/ia64/fpu/slowexp.c: Likewise.
	* sysdeps/m68k/m680x0/fpu/slowexp.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowexp-avx.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowexp-fma.c: Likewise.
	* sysdeps/x86_64/fpu/multiarch/slowexp-fma4.c: Likewise.
	* sysdeps/generic/math_private.h (__slowexp): Remove prototype.
	* sysdeps/ieee754/dbl-64/e_pow.c: Remove mention of slowexp.c in
	comment.
	* sysdeps/powerpc/power4/fpu/Makefile [$(subdir) = math]
	(CPPFLAGS-slowexp.c): Remove variable.
	* sysdeps/x86_64/fpu/multiarch/Makefile (libm-sysdep_routines):
	Remove slowexp-fma, slowexp-fma4 and slowexp-avx.
	(CFLAGS-slowexp-fma.c): Remove variable.
	(CFLAGS-slowexp-fma4.c): Likewise.
	(CFLAGS-slowexp-avx.c): Likewise.
	* sysdeps/x86_64/fpu/multiarch/e_exp-avx.c (__slowexp): Do not
	define as macro.
	* sysdeps/x86_64/fpu/multiarch/e_exp-fma.c (__slowexp): Likewise.
	* sysdeps/x86_64/fpu/multiarch/e_exp-fma4.c (__slowexp): Likewise.
	* math/Makefile (type-double-routines): Remove slowexp.
	* manual/probes.texi (slowexp_p6): Remove.
	(slowexp_p32): Likewise.

1 files changed, 3 insertions, 6 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile
index 0825340c0c..bec45e073c 100644
--- a/sysdeps/x86_64/fpu/multiarch/Makefile
+++ b/sysdeps/x86_64/fpu/multiarch/Makefile
@@ -10,7 +10,7 @@ libm-sysdep_routines += s_ceil-sse4_1 s_ceilf-sse4_1 s_floor-sse4_1 \
 
 libm-sysdep_routines += e_exp-fma e_log-fma e_pow-fma s_atan-fma \
 			e_asin-fma e_atan2-fma s_sin-fma s_tan-fma \
-			mplog-fma mpa-fma slowexp-fma slowpow-fma \
+			mplog-fma mpa-fma slowpow-fma \
 			sincos32-fma doasin-fma dosincos-fma \
 			halfulp-fma mpexp-fma \
 			mpatan2-fma mpatan-fma mpsqrt-fma mptan-fma
@@ -32,7 +32,6 @@ CFLAGS-mpsqrt-fma.c = -mfma -mavx2
 CFLAGS-mptan-fma.c = -mfma -mavx2
 CFLAGS-s_atan-fma.c = -mfma -mavx2
 CFLAGS-sincos32-fma.c = -mfma -mavx2
-CFLAGS-slowexp-fma.c = -mfma -mavx2
 CFLAGS-slowpow-fma.c = -mfma -mavx2
 CFLAGS-s_sin-fma.c = -mfma -mavx2
 CFLAGS-s_tan-fma.c = -mfma -mavx2
@@ -52,7 +51,7 @@ CFLAGS-s_cosf-fma.c = -mfma -mavx2
 
 libm-sysdep_routines += e_exp-fma4 e_log-fma4 e_pow-fma4 s_atan-fma4 \
 			e_asin-fma4 e_atan2-fma4 s_sin-fma4 s_tan-fma4 \
-			mplog-fma4 mpa-fma4 slowexp-fma4 slowpow-fma4 \
+			mplog-fma4 mpa-fma4 slowpow-fma4 \
 			sincos32-fma4 doasin-fma4 dosincos-fma4 \
 			halfulp-fma4 mpexp-fma4 \
 			mpatan2-fma4 mpatan-fma4 mpsqrt-fma4 mptan-fma4
@@ -74,14 +73,13 @@ CFLAGS-mpsqrt-fma4.c = -mfma4
 CFLAGS-mptan-fma4.c = -mfma4
 CFLAGS-s_atan-fma4.c = -mfma4
 CFLAGS-sincos32-fma4.c = -mfma4
-CFLAGS-slowexp-fma4.c = -mfma4
 CFLAGS-slowpow-fma4.c = -mfma4
 CFLAGS-s_sin-fma4.c = -mfma4
 CFLAGS-s_tan-fma4.c = -mfma4
 
 libm-sysdep_routines += e_exp-avx e_log-avx s_atan-avx \
 			e_atan2-avx s_sin-avx s_tan-avx \
-			mplog-avx mpa-avx slowexp-avx \
+			mplog-avx mpa-avx \
 			mpexp-avx
 
 CFLAGS-e_atan2-avx.c = -msse2avx -DSSE2AVX
@@ -92,7 +90,6 @@ CFLAGS-mpexp-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-mplog-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_atan-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_sin-avx.c = -msse2avx -DSSE2AVX
-CFLAGS-slowexp-avx.c = -msse2avx -DSSE2AVX
 CFLAGS-s_tan-avx.c = -msse2avx -DSSE2AVX
 endif