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authorUlrich Drepper <drepper@redhat.com>1999-10-30 06:56:10 +0000
committerUlrich Drepper <drepper@redhat.com>1999-10-30 06:56:10 +0000
commitaaa1276ee31ca872190cd097c7b4d845996fed39 (patch)
treed14e77b1744c5713f4cfff6e86c9417d7ddd8ce8
parent6491b8094e929133e3eb8793bb6296f69fb54a78 (diff)
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Update.
* manual/math.texi (Errors in Math Functions): New section. * math/libm-err-tab.pl: Moved to... * manual/libm-err-tab.pl: ...here. * manual/Makefile: Add rules for math function error table generation.
-rw-r--r--ChangeLog5
-rw-r--r--manual/Makefile14
-rwxr-xr-xmanual/libm-err-tab.pl (renamed from math/libm-err-tab.pl)0
-rw-r--r--manual/math.texi42
4 files changed, 59 insertions, 2 deletions
diff --git a/ChangeLog b/ChangeLog
index addc6c3bcb..e3e61ea52f 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,10 @@
1999-10-29 Ulrich Drepper <drepper@cygnus.com>
+ * manual/math.texi (Errors in Math Functions): New section.
+ * math/libm-err-tab.pl: Moved to...
+ * manual/libm-err-tab.pl: ...here.
+ * manual/Makefile: Add rules for math function error table generation.
+
* stdlib/tst-strtod.c: Add more hexadecimal tests.
* stdlib/strtod.c: Handle hexadecimal numbers with leading digit
diff --git a/manual/Makefile b/manual/Makefile
index 3c6640e8a7..4b88543129 100644
--- a/manual/Makefile
+++ b/manual/Makefile
@@ -69,7 +69,7 @@ examples = $(filter-out $(foreach d, $(add-ons), ../$d/%.c.texi), \
chapters.% top-menu.%: libc-texinfo.sh $(texis)
AWK=$(AWK) $(SHELL) $< '$(chapters)' '$(add-chapters)' '$(appendices)'
-libc.dvi libc.info: chapters.texi top-menu.texi
+libc.dvi libc.info: chapters.texi top-menu.texi libm-err.texi
libc.dvi: texinfo.tex
# Generate the summary from the Texinfo source files for each chapter.
@@ -89,6 +89,15 @@ dir-add.info: xtract-typefun.awk $(texis)
echo "END-INFO-DIR-ENTRY") > $@.new
mv -f $@.new $@
+# The table with the math errors is generated.
+libm-err.texi: stamp-libm-err
+stamp-libm-err: libm-err-tab.pl $(wildcard $(foreach dir,$(sysdirs),\
+ $(dir)/libm-test-ulps))
+ pwd=`pwd`; \
+ $(PERL) $< $$pwd/.. > libm-err-tmp
+ $(move-if-change) libm-err-tmp libm-err.texi
+ touch $@
+
# Generate Texinfo files from the C source for the example programs.
%.c.texi: examples/%.c
sed -e 's,[{}],@&,g' \
@@ -106,13 +115,14 @@ dir-add.info: xtract-typefun.awk $(texis)
# Distribution.
minimal-dist = summary.awk texis.awk tsort.awk libc-texinfo.sh libc.texinfo \
+ libm-err.texi stamp-libm-err \
$(filter-out summary.texi, $(nonexamples)) \
$(patsubst %.c.texi,examples/%.c, $(examples))
doc-only-dist = Makefile COPYING.LIB
distribute = $(minimal-dist) $(examples) stdio-fp.c \
libc.info* libc.?? libc.??s texinfo.tex \
- xtract-typefun.awk dir-add.info dir
+ xtract-typefun.awk dir-add.info dir libm-err-tab.pl
export distribute := $(distribute)
tar-it = tar chovf $@ $^
diff --git a/math/libm-err-tab.pl b/manual/libm-err-tab.pl
index 448bf801ab..448bf801ab 100755
--- a/math/libm-err-tab.pl
+++ b/manual/libm-err-tab.pl
diff --git a/manual/math.texi b/manual/math.texi
index f2736c2c45..c9a4c3a611 100644
--- a/manual/math.texi
+++ b/manual/math.texi
@@ -61,6 +61,7 @@ same as @code{double}.
* Exponents and Logarithms:: Also pow and sqrt.
* Hyperbolic Functions:: sinh, cosh, tanh, etc.
* Special Functions:: Bessel, gamma, erf.
+* Errors in Math Functions:: Known Maximum Errors in Math Functions.
* Pseudo-Random Numbers:: Functions for generating pseudo-random
numbers.
* FP Function Optimizations:: Fast code or small code.
@@ -1203,6 +1204,47 @@ is negative, @code{yn} signals a domain error; if it is zero,
@code{yn} signals overflow and returns @math{-@infinity}.
@end deftypefun
+@node Errors in Math Functions
+@section Known Maximum Errors in Math Functions
+@cindex math errors
+@cindex ulps
+
+This section lists the known errors of the functions in the math
+library. Errors are measured in ``units of the last place''. This is a
+measure for the relative error. For a number @math{z} with the
+representation @math{d.d@dots{}d@mul{}2^e} (we assume IEEE
+floating-point numbers with base 2) the ULP is represented by
+
+@tex
+$$\frac{|{\mathrm d.d\dots d - (z/2^e)|}{2^{p-1}}$$
+@end tex
+@ifnottex
+@smallexample
+|d.d...d - (z / 2^e)| / 2^(p - 1)
+@end smallexample
+@end ifnottex
+
+@noindent
+where @math{p} is the number of bits in the mantissa of the
+floating-point number representation. Ideally the error for all
+functions is always less than 0.5ulps. Using rounding bits this is also
+possible and normally implemented for the basic operations. To achieve
+the same for the complex math functions requires a lot more work and
+this was not spend so far.
+
+Therefore many of the functions in the math library have errors. The
+table lists the maximum error for each function which is exposed by one
+of the existing tests in the test suite. It is tried to cover as much
+as possible and really list the maximum error (or at least a ballpark
+figure) but this is often not achieved due to the large search space.
+
+The table lists the ULP values for different architectures. Different
+architectures have different results since their hardware support for
+floating-point operations varies and also the existing hardware support
+is different.
+
+@include libm-err.texi
+
@node Pseudo-Random Numbers
@section Pseudo-Random Numbers
@cindex random numbers