diff options
| -rw-r--r-- | ChangeLog | 5 | ||||
| -rw-r--r-- | manual/Makefile | 14 | ||||
| -rwxr-xr-x | manual/libm-err-tab.pl (renamed from math/libm-err-tab.pl) | 0 | ||||
| -rw-r--r-- | manual/math.texi | 42 |
4 files changed, 59 insertions, 2 deletions
@@ -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 |