This fix comes from glibc, from files which originated from
the same place as the newlib files. Those files in glibc carry
the same license as the newlib files.
Bug 14155 is spurious underflow exceptions from Bessel functions for
large arguments. (The correct results for large x are roughly
constant * sin or cos (x + constant) / sqrt (x), so no underflow
exceptions should occur based on the final result.)
There are various places underflows may occur in the intermediate
calculations that cause the failures listed in that bug. This patch
fixes problems for the double version where underflows occur in
calculating the intermediate functions P and Q (in particular, x**-12
gets computed while calculating Q). Appropriate approximations are
used for P and Q for arguments at least 0x1p28 and above to avoid the
underflows.
For sufficiently large x - 0x1p129 and above - the code already has a
cut-off to avoid calculating P and Q at all, which means the
approximations -0.125 / x and 0.375 / x can't themselves cause
underflows calculating Q. This cut-off is heuristically reasonable
for the point beyond which Q can be neglected (based on expecting
around 0x1p-64 to be the least absolute value of sin or cos for large
arguments representable in double).
The float versions use a cut-off 0x1p17, which is less heuristically
justifiable but should still only affect values near zeroes of the
Bessel functions where these implementations are intrinsically
inaccurate anyway (bugs 14469-14472), and should serve to avoid
underflows (the float underflow for jn in bug 14155 probably comes
from the recurrence to compute jn). ldbl-96 uses 0x1p129, which may
not really be enough heuristically (0x1p143 or so might be safer - 143
= 64 + 79, number of mantissa bits plus total number of significant
bits in representation) but again should avoid underflows and only
affect values where the code is substantially inaccurate anyway.
ldbl-128 and ldbl-128ibm share a completely different implementation
with no such cut-off, which I propose to fix separately.
Signed-off-by: Keith Packard <keithp@keithp.com>
Add the missing mask for the decomposition of hi+lo which caused some
errors of 1-2 ULP.
This change is taken over from FreeBSD:
95436ce20d
Additionally I've removed some variable assignments which were never
read before being overwritten again in the next 2 lines.
This fix for k_tan.c is a copy from fdlibm version 5.3 (see also
http://www.netlib.org/fdlibm/readme), adjusted to use the macros
available in newlib (SET_LOW_WORD).
This fix reduces the ULP error of the value shown in the fdlibm readme
(tan(1.7765241907548024E+269)) to 0.45 (thereby reducing the error by
1).
This issue only happens for large numbers that get reduced by the range
reduction to a value smaller in magnitude than 2^-28, that is also
reduced an uneven number of times. This seems rather unlikely given that
one ULP is (much) larger than 2^-28 for the values that may cause an
issue. Although given the sheer number of values a double can
represent, it is still possible that there are more affected values,
finding them however will be quite hard, if not impossible.
We also took a look at how another library (libm in FreeBSD) handles the
issue: In FreeBSD the complete if branch which checks for values smaller
than 2^-28 (or rather 2^-27, another change done by FreeBSD) is moved
out of the kernel function and into the external function. This means
that the value that gets checked for this condition is the unreduced
value. Therefore the input value which caused a problem in the
fdlibm/newlib kernel tan will run through the full polynomial, including
the careful calculation of -1/(x+r). So the difference is really whether
r or y is used. r = y + p with p being the result of the polynomial with
1/3*x^3 being the largest (and magnitude defining) value. With x being
<2^-27 we therefore know that p is smaller than y (y has to be at least
the size of the value of x last mantissa bit divided by 2, which is at
least x*2^-51 for doubles) by enough to warrant saying that r ~ y. So
we can conclude that the general implementation of this special case is
the same, FreeBSD simply has a different philosophy on when to handle
especially small numbers.
Make line 47 in sf_trunc.c reachable. While converting the double
precision function trunc to the single precision version truncf an error
was introduced into the special case. This special case is meant to
catch both NaNs and infinities, however qNaNs and infinities work just
fine with the simple return of x (line 51). The only error occurs for
sNaNs where the same sNaN is returned and no invalid exception is
raised.
The comparison c == FP_INFINITE causes the function to return +inf as it
expects x = +inf to always be larger than y. This shortcut causes
several issues as it also returns +inf for the following cases:
- fdim(+inf, +inf), expected (as per C99): +0.0
- fdim(-inf, any non NaN), expected: +0.0
I don't see a reason to keep the comparison as all the infinity cases
return the correct result using just the ternary operation.
While testing the exp function we noticed some errors at the specified
magnitude. Within this range the exp function returns the input value +1
as an output. We chose to run a test of 1m exponentially spaced values
in the ranges [-2^-27,-2^-32] and [2^-32,2^-27] which showed 7603 and
3912 results with an error of >=0.5 ULP (compared with MPFR in 128 bit)
with the highest being 0.56 ULP and 0.53 ULP.
It's easy to fix by changing the magnitude at which the input value +1
is returned from <2^-28 to <2^-32 and using the polynomial instead. This
reduces the number of results with an error of >=0.5 ULP to 485 and 479
in above tests, all of which are exactly 0.5 ULP.
As we were already checking on exp we also took a look at expf. For expf
the magnitude where the input value +1 is returned can be increased from
<2^-28 to <2^-23 without accuracy loss for a slight performance
improvement. To ensure this was the correct value we tested all values
in the ranges [-2^-17,-2^-28] and [2^-28,2^-17] (~92.3m values each).
The single-precision trigonometric functions show rather high errors in
specific ranges starting at about 30000 radians. For example the sinf
procedure produces an error of 7626.55 ULP with the input
5.195880078125e+04 (0x474AF6CD) (compared with MPFR in 128bit
precision). For the test we used 100k values evenly spaced in the range
of [30k, 70k]. The issues are periodic at higher ranges.
This error was introduced when the double precision range reduction was
first converted to float. The shift by 8 bits always returns 0 as iq is
never higher than 255.
The fix reduces the error of the example above to 0.45 ULP, highest
error within the test set fell to 1.31 ULP, which is not perfect, but
still a significant improvement. Testing other previously erroneous
ranges no longer show particularly large accuracy errors.
Most code in newlib already uses unified syntax, but just a couple of
laggards remain. This patch removes these and means the the entire
code base has now been converted.
Having symlinks for these files led to an issue reported to the RTEMS
Project that showed up using some tar for native Windows to unpack the
newlib sources. It creates symlinks in the tar file as copies of the
files the symlinks point to. If the links appear in the tar file before
the source exists, it cannot copy the file.
The solution in this patch is to convert the files that are symbolic
links into simple files which include the file they were linked to.
This should be more portable and avoids the symbolinc link problem.
I think I may have encountered a bug in the implementation of pow:
pow(-1.0, NaN) returns 1.0 when it should return NaN.
Because ix is used to check input vs 1.0 rather than hx, -1.0 is
mistaken for 1.0
This edits licenses held by Berkeley and NetBSD, both of which
have removed the advertising requirement from their licenses.
Signed-off-by: Keith Packard <keithp@keithp.com>
This reverts commit 59362c80e3.
This breaks gnulib's autoconf test for POSIX compatibility of
fflush/fseek. After fflush/fseek, ftello and lseek are out of
sync, with lseek having the wrong offset. This breaks backward
compatibility with Cygwin applications.
Signed-off-by: Corinna Vinschen <corinna@vinschen.de>
- also change the handling of default_newlib_reent_check_verify to
be the same as other default variables in configure.host
- regenerate newlib/configure
If we had architecture-specific exception bits, we could just set them
to match the processor, but instead ieeefp.h is shared by all targets
so we need to map between the public values and the register contents.
Signed-off-by: Keith Packard <keithp@keithp.com>
This makes the fpsetround function actually do something rather than
just return -1 due to the default 'fall-through' behavior of the switch
statement.
Signed-off-by: Keith Packard <keithp@keithp.com>
In the two helper functions that _dcvt calls for 'f' and 'e' mode, if
there are no digits to display after the decimal point, don't add one.
Signed-off-by: Keith Packard <keithp@keithp.com>
Leading zeros after the decimal point should not count
towards the 'ndigits' limit.
This makes gcvt match glibc and the posix gcvt man page.
Signed-off-by: Keith Packard <keithp@keithp.com>
Even if the number is really small and this means showing *no* digits.
This makes newlib match glibc, and the fcvt posix man page.
Signed-off-by: Keith Packard <keithp@keithp.com>
sf_log1p was using __math_divzero and __math_invalid, which
drag in a pile of double-precision code. Switch to using the
single-precision variants. This also required making those
available in __OBSOLETE_MATH mode.
Signed-off-by: Keith Packard <keithp@keithp.com>
newlib wide char conversion functions were updated to
Unicode 11 on 2019-01-12
update standard symbol __STDC_ISO_10646__ to
Unicode 11 release date 2018-06-05 for Cygwin
The call to fflush was invalidating the read buffer, preventing relative
seeks to positions that would have been inside the read buffer from
being optimized. The call to srefill would then re-read mostly the same
data that was initially in the read buffer.
s[0:3] contain a descriptor used to set up the initial value of the
stack, but only the lower 48 bits of s[0:1] are currently used.
The reent marker is currently set in s3, but by stashing it in the
upper 16 bits of s[0:1] instead, s3 can be freed up for other purposes.
This change is based on the FreeBSD commit:
Author: asomers <asomers@FreeBSD.org>
Date: Mon Jul 30 15:46:40 2018 +0000
Make timespecadd(3) and friends public
The timespecadd(3) family of macros were imported from NetBSD back in
r35029. However, they were initially guarded by #ifdef _KERNEL. In the
meantime, we have grown at least 28 syscalls that use timespecs in some
way, leading many programs both inside and outside of the base system to
redefine those macros. It's better just to make the definitions public.
Our kernel currently defines two-argument versions of timespecadd and
timespecsub. NetBSD, OpenBSD, and FreeDesktop.org's libbsd, however, define
three-argument versions. Solaris also defines a three-argument version, but
only in its kernel. This revision changes our definition to match the
common three-argument version.
Bump _FreeBSD_version due to the breaking KPI change.
Discussed with: cem, jilles, ian, bde
Differential Revision: https://reviews.freebsd.org/D14725
The TI proprietary toolchain uses nonstandard names for some math
library functions. In order to achieve ABI compatibility between
GNU and TI toolchains, add support for the TI function names.
Signed-off-by: Dimitar Dimitrov <dimitar@dinux.eu>
Joseph S. Myers
Fabian Schriever
Sebastian Huber
Joel Sherrill
Richard Earnshaw
Thomas Wolff
Nicolas Brunie
Keith Packard
Corinna Vinschen
Jeff Johnston
Jon Turney
Anthony Green
Bruno Haible
Brian Inglis
Bastien Bouclet
Kwok Cheung Yeung
imp
Dimitar Dimitrov