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.
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
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>
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>
The default implementation of the fenv.h methods return
-EOPNOTSUP. Some of these have implementations appropriate
for soft-float.
The intention of the new fenv.h is that it be portable
and that architectures provide their own implementation
of sys/fenv.h.
2019-07-09 Joern Rennecke <joern.rennecke@riscy-ip.com>
* libm/common/s_expm1.c ("math_config.h"): Include.
(expm1): Use __math_oflow to set errno.
* libm/common/s_log1p.c ("math_config.h"): Include.
(log1p): Use __math_divzero and __math_invalid to set errno.
* libm/common/sf_expm1.c ("math_config.h"): Include.
(expm1f): Use __math_oflow to set errno.
* libm/common/sf_log1p.c ("math_config.h"): Include.
(log1pf): Use __math_divzero and __math_invalid to set errno.
This patch removes the definitions of HUGE_VAL from some of the float math
functions. HUGE_VAL is defined in newlib/libc/include/math.h, so it is not
necessary to have a further definition in the math functions.
The threshold value at which powf overflows depends on the rounding mode
and the current check did not take this into account. So when the result
was rounded away from zero it could become infinity without setting
errno to ERANGE.
Example: pow(0x1.7ac7cp+5, 23) is 0x1.fffffep+127 + 0.1633ulp
If the result goes above 0x1.fffffep+127 + 0.5ulp then errno is set,
which is fine in nearest rounding mode, but
powf(0x1.7ac7cp+5, 23) is inf in upward rounding mode
powf(-0x1.7ac7cp+5, 23) is -inf in downward rounding mode
and the previous implementation did not set errno in these cases.
The fix tries to avoid affecting the common code path or calling a
function that may introduce a stack frame, so float arithmetics is used
to check the rounding mode and the threshold is selected accordingly.
Drop Cygwin-specific nanl in favor of a generic implementation
in newlib. Requires GCC 3.3 or later.
Signed-off-by: Corinna Vinschen <corinna@vinschen.de>
While working on the strstr patch I noticed several copyright headers
of the new math functions are missing closing quotes after ``AS IS.
I've added these. Also update spellings of Arm Ltd in a few places
(but still use ARM LTD in upper case portion). Finally add SPDX
identifiers to make everything consistent.
Improve comments in sincosf implementation to make the code easier
to understand. Rename the constant pi64 to pi63 since it's actually
PI * 2^-63. Add comments for fields of sincos_t structure. Add comments
describing implementation details to reduce_fast.
PREFER_FLOAT_COMPARISON setting was not correct as it could raise
spurious exceptions. Fixing it is easy: just use ISLESS(x, y) instead
of abstop12(x) < abstop12(y) with appropriate non-signaling definition
for ISLESS. However it seems this setting is not very useful (there is
only minor performance difference on various architectures), so remove
this option for now.
The !HAVE_FAST_FMA code path split r = z/c - 1 into r = rhi + rlo such
that when z = 1-tiny and c = 1 then rlo and rhi could have much larger
magnitude than r which later caused large rounding errors.
So do a nearest rounding instead of truncation at the split.
In newlib with default settings this was observable on some arm targets
that enable the new math code but has no fma.
The roundtoint and converttoint internal functions are only called with small
values, so 32 bit result is enough for converttoint and it is a signed int
conversion so the natural return type is int32_t.
The original idea was to help the compiler keeping the result in uint64_t,
then it's clear that no sign extension is needed and there is no accidental
undefined or implementation defined signed int arithmetics.
But it turns out gcc does a good job with inlining so changing the type has
no overhead and the semantics of the conversion is less surprising this way.
Since we want to allow the asuint64 (x + 0x1.8p52) style conversion, the top
bits were never usable and the existing code ensures that only the bottom
32 bits of the conversion result are used.
In newlib with default settings only aarch64 is affected and there is no
significant code generation change with gcc after the patch.
Synchronize code style and comments with Arm Optimized Routines, there
are no code changes in this patch. This ensures different projects using
the same code have consistent code style so bug fix patches can be applied
more easily.
The new implementation is provided under !__OBSOLETE_MATH, it uses
ISO C99 code. With default settings the worst case error in nearest
rounding mode is 0.54 ULP with inlined fma and fma contraction. It uses
a 4 KB lookup table in addition to the table in exp_data.c, on aarch64
.text+.rodata size of libm.a is increased by 2295 bytes.
Improvements on Cortex-A72:
latency: 3.3x
thruput: 4.9x
The new implementation is provided under !__OBSOLETE_MATH, it uses
ISO C99 code. With default settings the worst case error in nearest
rounding mode is 0.547 ULP with inlined fma and fma contraction. It uses
a 1 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased
by 1584 bytes.
Note that the math.h header defines log2(x) to be log(x)/Ln2, this is
not changed, so the new code is only used if that macro is suppressed.
Improvements on Cortex-A72:
latency: 2.0x
thruput: 2.2x
The new implementations are provided under !__OBSOLETE_MATH, it uses
ISO C99 code. With default settings the worst case error in nearest
rounding mode is 0.519 ULP with inlined fma and fma contraction. It uses
a 2 KB lookup table, on aarch64 .text+.rodata size of libm.a is increased
by 1703 bytes. The w_log.c wrapper is disabled since error handling is
inline in the new code.
New __HAVE_FAST_FMA and __HAVE_FAST_FMA_DEFAULT feature macros were
added to enable selecting between the code path that uses fma and the
one that does not. Targets supposed to set __HAVE_FAST_FMA_DEFAULT
if they have single instruction fma and the compiler can actually
inline it (gcc has __FP_FAST_FMA macro but that does not guarantee
inlining with -fno-builtin-fma).
Improvements on Cortex-A72:
latency: 1.9x
thruput: 2.3x
The new implementations are provided under !__OBSOLETE_MATH, they use
ISO C99 code. There are several settings, with the default one the
worst case error in nearest rounding mode is 0.509 ULP for exp and
0.507 ULP for exp2 when a multiply and add is contracted into an fma.
They use a shared 2 KB lookup table, on aarch64 .text+.rodata size
of libm.a is increased by 1868 bytes. The w_*.c wrappers are disabled
for the new code as it takes care of error handling inline.
The old exp2(x) code used to be just pow(2,x) so the speedup there
is more significant.
The file name has no special prefix to avoid any name collision with
existing files.
Improvements on Cortex-A72:
exp latency: 3.2x
exp thruput: 4.1x
exp2 latency: 7.8x
exp2 thruput: 18.8x
This change is equivalent to the commit
c65db17340
and only affects code that is from the Arm optimized-routines project.
It does not affect the observable behaviour, but the code generation
can be different on 64bit targets. The intention is to make the
portable semantics of the code obvious by using a fixed size type.
Here is the correct patch with both filenames and int cast fixed:
This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
Simple benchmark showing speedup factor on AArch64 for various ranges:
range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
ChangeLog:
2018-05-18 Wilco Dijkstra <wdijkstr@arm.com>
* newlib/libm/common/Makefile.in: Regenerated.
* newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
sincosf.h, sincosf_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
* newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
eval_as_double, likely, unlikely.
* newlib/libm/common/cosf.c: New file.
* newlib/libm/common/sinf.c: Likewise.
* newlib/libm/common/sincosf.h: Likewise.
* newlib/libm/common/sincosf.c: Likewise.
* newlib/libm/common/sincosf_data.c: Likewise.
* newlib/libm/math/sf_cos.c: Add #if to build conditionally.
* newlib/libm/math/sf_sin.c: Likewise.
* newlib/libm/math/wf_sincos.c: Likewise.
--
This patch is a complete rewrite of sinf, cosf and sincosf. The new version
is significantly faster, as well as simple and accurate.
The worst-case ULP is 0.56072, maximum relative error is 0.5303p-23 over all
4 billion inputs. In non-nearest rounding modes the error is 1ULP.
The algorithm uses 3 main cases: small inputs which don't need argument
reduction, small inputs which need a simple range reduction and large inputs
requiring complex range reduction. The code uses approximate integer
comparisons to quickly decide between these cases - on some targets this may
be slow, so this can be configured to use floating point comparisons.
The small range reducer uses a single reduction step to handle values up to
120.0. It is fastest on targets which support inlined round instructions.
The large range reducer uses integer arithmetic for simplicity. It does a
32x96 bit multiply to compute a 64-bit modulo result. This is more than
accurate enough to handle the worst-case cancellation for values close to
an integer multiple of PI/4. It could be further optimized, however it is
already much faster than necessary.
Simple benchmark showing speedup factor on AArch64 for various ranges:
range 0.7853982 sinf 1.7 cosf 2.2 sincosf 2.8
range 1.570796 sinf 1.9 cosf 1.9 sincosf 2.7
range 3.141593 sinf 2.0 cosf 2.0 sincosf 3.5
range 6.283185 sinf 2.3 cosf 2.3 sincosf 4.2
range 125.6637 sinf 2.9 cosf 3.0 sincosf 5.1
range 1.1259e15 sinf 26.8 cosf 26.8 sincosf 45.2
ChangeLog:
2018-06-18 Wilco Dijkstra <wdijkstr@arm.com>
* newlib/libm/common/Makefile.in: Regenerated.
* newlib/libm/common/Makefile.am: Add sinf.c, cosf.c, sincosf.c
sincosf.h, sincosf_data.c. Add -fbuiltin -fno-math-errno to CFLAGS.
* newlib/libm/common/math_config.h: Add HAVE_FAST_ROUND, HAVE_FAST_LROUND,
roundtoint, converttoint, force_eval_float, force_eval_double, eval_as_float,
eval_as_double, likely, unlikely.
* newlib/libm/common/cosf.c: New file.
* newlib/libm/common/sinf.c: Likewise.
* newlib/libm/common/sincosf.h: Likewise.
* newlib/libm/common/sincosf.c: Likewise.
* newlib/libm/common/sincosf_data.c: Likewise.
* newlib/libm/math/sf_cos.c: Add #if to build conditionally.
* newlib/libm/math/sf_sin.c: Likewise.
* newlib/libm/math/wf_sincos.c: Likewise.
--
- From: Cesar Philippidis <cesar@codesourcery.com>
Date: Tue, 10 Apr 2018 14:43:42 -0700
Subject: [PATCH] nvptx port
This port adds support for Nvidia GPU's, which are primarily used as
offload accelerators in OpenACC and OpenMP.
Updated patch to use 0.0f in addition to calling rintf.
Tested same way as before, with a testcase that triggers the code and
make check.
OK?
newlib/
* libm/math/wf_pow.c (powf): Call rintf instead of rint. Use 0.0f
for compare.
Discard QUICKREF sections, rather than writing them to stderr
Discard MATHREF sections, rather than discarding as an error
Pass NOTES sections through to texinfo, rather than discarding as an error
Don't redirect makedoc stderr to .ref file
Remove makedoc output on error
Remove .ref files from CLEANFILES
Regenerate Makefile.ins
Signed-off-by: Jon Turney <jon.turney@dronecode.org.uk>
The recently added new math code inlines error handling instead of using
error handling wrappers around __ieee754* internal symbols, and thus the
__ieee754* symbols are no longer provided.
However __ieee754_expf and __ieee754_logf are used in the implementation
of a number of other math functions. These symbols are safe to redirect
to the external expf and logf symbols, because those names are always
reserved when single precision math functions are reserved and the
additional error handling code is either not reached or there will be
an error in the final result that will override an internal spurious
errno setting.
For consistency all of __ieee754_expf, __ieee754_logf and __ieee754_powf
are redirected using a macro.
Based on code from https://github.com/ARM-software/optimized-routines/
This patch adds a highly optimized generic implementation of expf,
exp2f, logf, log2f and powf. The new functions are not only
faster (6x for powf!), but are also smaller and more accurate.
In order to achieve this, the algorithm uses double precision
arithmetic for accuracy, avoids divisions and uses small table
lookups to minimize the polynomials. Special cases are handled
inline to avoid the unnecessary overhead of wrapper functions and
set errno to POSIX requirements.
The new functions are added under newlib/libm/common, but the old
implementations are kept (in newlib/libm/math) for non-IEEE or
pre-C99 systems. Targets can enable the new math code by defining
__OBSOLETE_MATH_DEFAULT to 0 in newlib/libc/include/machine/ieeefp.h,
users can override the default by defining __OBSOLETE_MATH.
Currently the new code is enabled for AArch64 and AArch32 with VFP.
Targets with a single precision FPU may still prefer the old
implementation.
libm.a size changes:
arm: -1692
arm/thumb/v7-a/nofp: -878
arm/thumb/v7-a+fp/hard: -864
arm/thumb/v7-a+fp/softfp: -908
aarch64: -1476
Joseph S. Myers
Fabian Schriever
Joel Sherrill
Nicolas Brunie
Keith Packard
Jeff Johnston
Dimitar Dimitrov
Jon Turney
Jozef Lawrynowicz
Szabolcs Nagy
Corinna Vinschen
Wilco Dijkstra
Jon Beniston
Matthias Kannwischer
Yaakov Selkowitz
Jim Wilson
Brian Inglis
Kito Cheng
Aditya Upadhyay