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This patch is updating soft-fp from glibc:
1. Add __extendhfxf2 to return an IEEE half converted to IEEE extended.
2. Add __truncxfhf2 to truncate IEEE extended into IEEE half.
These are needed by x86 _Float16 support.
* soft-fp/extendhfxf2.c: New file.
* soft-fp/truncxfhf2.c: Likewise.
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This patch enables support for TImode for AMD GCN, the lack of which
is currently causing a number of test failures for the target and which
is also needed to support "omp_depend_kind" for OpenMP 5.0, since that
is implemented as a 128-bit integer.
Several libgcc support routines are built by default for the "word size"
of a machine, and also for "2 * word size" of the machine. The libgcc
build for AMD GCN is changed so that it builds for a "word size" of 64
bits, in order to better match the (64-bit) host compiler. However it
isn't really true that we have 64-bit words -- GCN has 32-bit registers,
so changing UNITS_PER_WORD unconditionally would be the wrong thing to do.
Changing this setting for libgcc (only) means that support routines
are built for "single word" operations that are DImode (64 bits), and
those for "double word" operations are built for TImode (128 bits).
That leaves some gaps regarding previous operations that were built
for a "single word" size of 32 bits and a "double word" size of 64 bits
(generic code doesn't cover both alternatives for all operations that
might be needed). Those gaps are filled in by this patch, or by the
preceding patches in the series.
2021-06-18 Julian Brown <julian@codesourcery.com>
gcc/
* config/gcn/gcn.c (gcn_init_libfuncs): New function.
(TARGET_INIT_LIBFUNCS): Define target hook using above function.
* config/gcn/gcn.h (UNITS_PER_WORD): Define to 8 for IN_LIBGCC2, 4
otherwise.
(LIBGCC2_UNITS_PER_WORD, BITS_PER_WORD): Remove definitions.
(MAX_FIXED_MODE_SIZE): Change to 128.
libgcc/
* config/gcn/lib2-bswapti2.c: New file.
* config/gcn/lib2-divmod-di.c: New file.
* config/gcn/lib2-gcn.h (DItype, UDItype, TItype, UTItype): Add
typedefs.
(__divdi3, __moddi3, __udivdi3, __umoddi3): Add prototypes.
* config/gcn/t-amdgcn (LIB2ADD): Add lib2-divmod-di.c and
lib2-bswapti2.c.
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This patch changes the argument and return types for the libgcc __udivsi3
and __umodsi3 helper functions for GCN to USItype instead of SItype.
This is probably just cosmetic in practice.
2021-06-18 Julian Brown <julian@codesourcery.com>
libgcc/
* config/gcn/lib2-divmod.c (__udivsi3, __umodsi3): Change argument and
return types to USItype.
* config/gcn/lib2-gcn.h (__udivsi3, __umodsi3): Update prototypes.
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The recent float128 ISA3.1 support (r12-1340) has some typos,
it makes the libgcc build fail if it's with one binutils
(assembler) which doesn't support Power10 insns. The error
looks like:
Error: invalid switch -mpower10
Error: unrecognized option -mpower10
... [...libgcc/shared-object.mk:14: float128-p10.o] Error 1
What this patch does are:
- fix test target typo libgcc_cv_powerpc_3_1_float128_hw
(written wrongly as libgcc_cv_powerpc_float128_hw, so it's
going to build ISA3.1 stuffs just when detecting ISA3.0).
- fix test used for libgcc_cv_powerpc_3_1_float128_hw check.
- fix test option used for libgcc_cv_powerpc_3_1_float128_hw
check.
- remove the ISA3.1 related contents from t-float128-hw.
- add new macro FLOAT128_HW_INSNS_ISA3_1 to differentiate
ISA3.1 content from ISA3.0 part in ifunc support.
Bootstrapped/regtested on:
- powerpc64le-linux-gnu P10
- powerpc64le-linux-gnu P9 (w/i and w/o p10 supported as)
- powerpc64-linux-gnu P8 (w/i and w/o p10 supported as)
libgcc/ChangeLog:
* configure: Regenerate.
* configure.ac (test for libgcc_cv_powerpc_3_1_float128_hw): Fix
typos among the name, CFLAGS and the test.
* config/rs6000/t-float128-hw (fp128_3_1_hw_funcs, fp128_3_1_hw_src,
fp128_3_1_hw_static_obj, fp128_3_1_hw_shared_obj, fp128_3_1_hw_obj):
Remove.
* config/rs6000/t-float128-p10-hw (FLOAT128_HW_INSNS): Append
macro FLOAT128_HW_INSNS_ISA3_1.
(FP128_3_1_CFLAGS_HW): Fix option typo.
* config/rs6000/float128-ifunc.c (SW_OR_HW_ISA3_1): Guard this with
FLOAT128_HW_INSNS_ISA3_1.
(__floattikf_resolve): Likewise.
(__floatuntikf_resolve): Likewise.
(__fixkfti_resolve): Likewise.
(__fixunskfti_resolve): Likewise.
(__floattikf): Likewise.
(__floatuntikf): Likewise.
(__fixkfti): Likewise.
(__fixunskfti): Likewise.
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The current CMSE support in the multilib build for
"-march=armv8.1-m.main+mve -mfloat-abi=hard -mfpu=auto" is broken
as specified in PR99939 and this patch fixes the issue.
gcc/testsuite/ChangeLog:
2021-06-11 Srinath Parvathaneni <srinath.parvathaneni@arm.com>
PR target/99939
* gcc.target/arm/cmse/cmse-18.c: Add separate scan-assembler
directives check for target is v8.1-m.main+mve or not before
comparing the assembly output.
* gcc.target/arm/cmse/cmse-20.c: New test.
libgcc/ChangeLog:
2021-06-11 Srinath Parvathaneni <srinath.parvathaneni@arm.com>
PR target/99939
* config/arm/cmse_nonsecure_call.S: Add __ARM_FEATURE_MVE
macro.
* config/arm/t-arm: To link cmse.o and cmse_nonsecure_call.o
on passing -mcmse option.
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The *TItype_ppc definitions are guarded by _ARCH_PPC64, so all
declarations using it should do so as well.
2021-06-10 Segher Boessenkool <segher@kernel.crashing.org>
libgcc/
* config/rs6000/quad-float128.h: Guard all uses of [U]TItype_ppc by
_ARCH_PPC64 .
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The files fixkfti-sw.c and fixunskfti-sw.c are renamed versions of
fixkfti.c and fixunskfti.c respectively to do the conversions in software.
The function names in the files were updated with the rename as well as
some white spaces fixes. The file float128-p10.c contains the functions
for using the ISA 3.1 hardware instructions to perform the conversions.
2021-06-08 Carl Love <cel@us.ibm.com>
gcc/ChangeLog
* config/rs6000/rs6000.c (__fixkfti, __fixunskfti, __floattikf,
__floatuntikf): Names changed to __fixkfti_sw, __fixunskfti_sw,
__floattikf_sw, __floatuntikf_sw respectively.
* config/rs6000/rs6000.md (floatti<mode>2, floatunsti<mode>2,
fix_trunc<mode>ti2, fixuns_trunc<mode>ti2): Add
define_insn for mode IEEE 128.
gcc/testsuite/ChangeLog
* gcc.target/powerpc/fp128_conversions.c: New file.
* gcc.target/powerpc/int_128bit-runnable.c(vextsd2q,
vcmpuq, vcmpsq, vcmpequq, vcmpequq., vcmpgtsq, vcmpgtsq.
vcmpgtuq, vcmpgtuq.): Update scan-assembler-times.
(ppc_native_128bit): Remove dg-require-effective-target.
libgcc/ChangeLog
* config.host: Add if test and set for
libgcc_cv_powerpc_3_1_float128_hw.
* config/rs6000/fixkfti.c: Renamed to fixkfti-sw.c.
Change calls of __fixkfti to __fixkfti_sw.
* config/rs6000/fixunskfti.c: Renamed to fixunskfti-sw.c.
Change calls of __fixunskfti to __fixunskfti_sw.
* config/rs6000/float128-p10.c (__floattikf_hw,
__floatuntikf_hw, __fixkfti_hw, __fixunskfti_hw): New file.
* config/rs6000/float128-ifunc.c (SW_OR_HW_ISA3_1): New macro.
(__floattikf_resolve, __floatuntikf_resolve, __fixkfti_resolve,
__fixunskfti_resolve): Add resolve functions.
(__floattikf, __floatuntikf, __fixkfti, __fixunskfti): New functions.
* config/rs6000/float128-sed (floattitf, __floatuntitf,
__fixtfti, __fixunstfti): Add editor commands to change names.
* config/rs6000/float128-sed-hw (__floattitf,
__floatuntitf, __fixtfti, __fixunstfti): Add editor commands to
change names.
* config/rs6000/floattikf.c: Renamed to floattikf-sw.c.
* config/rs6000/floatuntikf.c: Renamed to floatuntikf-sw.c.
* config/rs6000/quad-float128.h (__floattikf_sw,
__floatuntikf_sw, __fixkfti_sw, __fixunskfti_sw, __floattikf_hw,
__floatuntikf_hw, __fixkfti_hw, __fixunskfti_hw, __floattikf,
__floatuntikf, __fixkfti, __fixunskfti): New extern declarations.
* config/rs6000/t-float128 (floattikf, floatuntikf,
fixkfti, fixunskfti): Remove file names from fp128_ppc_funcs.
(floattikf-sw, floatuntikf-sw, fixkfti-sw, fixunskfti-sw): Add
file names to fp128_ppc_funcs.
* config/rs6000/t-float128-hw(fp128_3_1_hw_funcs,
fp128_3_1_hw_src, fp128_3_1_hw_static_obj, fp128_3_1_hw_shared_obj,
fp128_3_1_hw_obj): Add variables for ISA 3.1 support.
* config/rs6000/t-float128-p10-hw: New file.
* configure: Update script for isa 3.1 128-bit float support.
* configure.ac: Add check for 128-bit float hardware support.
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This should help LD's --gc-sections feature to reduce final ELF size.
libgcc/ChangeLog:
* config/pru/mpyll.S (__pruabi_mpyll): Place into own section.
Signed-off-by: Dimitar Dimitrov <dimitar@dinux.eu>
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gcc/ChangeLog:
* gcov-io.c (gcov_write_block): Remove.
(gcov_write_words): Likewise.
(gcov_read_words): Re-implement using gcov_read_bytes.
(gcov_allocate): Remove.
(GCOV_BLOCK_SIZE): Likewise.
(struct gcov_var): Remove most of the fields.
(gcov_position): Implement with ftell.
(gcov_rewrite): Remove setting of start and offset fields.
(from_file): Re-format.
(gcov_open): Remove setbuf call. It should not be needed.
(gcov_close): Remove internal buffer handling.
(gcov_magic): Use __builtin_bswap32.
(gcov_write_counter): Use directly gcov_write_unsigned.
(gcov_write_string): Use direct fwrite and do not round
to 4 bytes.
(gcov_seek): Use directly fseek.
(gcov_write_tag): Use gcov_write_unsigned directly.
(gcov_write_length): Likewise.
(gcov_write_tag_length): Likewise.
(gcov_read_bytes): Use directly fread.
(gcov_read_unsigned): Use gcov_read_words.
(gcov_read_counter): Likewise.
(gcov_read_string): Use gcov_read_bytes.
* gcov-io.h (GCOV_WORD_SIZE): Adjust to reflect
that size is not in bytes, but words (4B).
(GCOV_TAG_FUNCTION_LENGTH): Likewise.
(GCOV_TAG_ARCS_LENGTH): Likewise.
(GCOV_TAG_ARCS_NUM): Likewise.
(GCOV_TAG_COUNTER_LENGTH): Likewise.
(GCOV_TAG_COUNTER_NUM): Likewise.
(GCOV_TAG_SUMMARY_LENGTH): Likewise.
libgcc/ChangeLog:
* libgcov-driver.c: Fix GNU coding style.
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c++tools/ChangeLog:
* Makefile.in: Include also ../gcc folder.
gcc/ChangeLog:
* Makefile.in: Rename gcov-iov to genversion and depend
on version.h (instead of gcov-iov.h).
* gcov-io.h: Include version.h instread of gcov-iov.h.
* gengtype-state.c (read_state_version): Likewise.
* gcov-iov.c: Moved to...
* genversion.c: ...here.
* lto-streamer.h (LTO_major_version): Define it with
GCC_major_version.
* version.c: Removed.
* version.h: Removed.
libgcc/ChangeLog:
* libgcov-driver.c (gcov_version): Use different name that does
not clash with newly introduced macro.
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If you attempt a profiled bootstrap on the MinGW platforms with -jN, N > 1,
it miserably fails because of profile mismatches all over the place, the
reason being that gcov has no support for parallelism on these platforms.
libgcc/
* libgcov.h: For the target, define GCOV_LOCKED_WITH_LOCKING
if __MSVCRT__ and, for the host, define it if HOST_HAS_LK_LOCK.
* libgcov-driver.c: Add directives if GCOV_LOCKED_WITH_LOCKING.
gcc/
* configure.ac: Check for the presence of sys/locking.h header and
for whether _LK_LOCK is supported by _locking.
* configure: Regenerate.
* config.in: Likewise.
* gcov-io.h: Define GCOV_LOCKED_WITH_LOCKING if HOST_HAS_LK_LOCK.
* gcov-io.c (gcov_open): Add support for GCOV_LOCKED_WITH_LOCKING.
* system.h: Include <sys/locking.h> if HAVE_SYS_LOCKING_H.
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Correctness and performance test programs used during development of
this project may be found in the attachment to:
https://www.mail-archive.com/gcc-patches@gcc.gnu.org/msg254210.html
Summary of Purpose
This patch to libgcc/libgcc2.c __divdc3 provides an
opportunity to gain important improvements to the quality of answers
for the default complex divide routine (half, float, double, extended,
long double precisions) when dealing with very large or very small exponents.
The current code correctly implements Smith's method (1962) [2]
further modified by c99's requirements for dealing with NaN (not a
number) results. When working with input values where the exponents
are greater than *_MAX_EXP/2 or less than -(*_MAX_EXP)/2, results are
substantially different from the answers provided by quad precision
more than 1% of the time. This error rate may be unacceptable for many
applications that cannot a priori restrict their computations to the
safe range. The proposed method reduces the frequency of
"substantially different" answers by more than 99% for double
precision at a modest cost of performance.
Differences between current gcc methods and the new method will be
described. Then accuracy and performance differences will be discussed.
Background
This project started with an investigation related to
https://gcc.gnu.org/bugzilla/show_bug.cgi?id=59714. Study of Beebe[1]
provided an overview of past and recent practice for computing complex
divide. The current glibc implementation is based on Robert Smith's
algorithm [2] from 1962. A google search found the paper by Baudin
and Smith [3] (same Robert Smith) published in 2012. Elen Kalda's
proposed patch [4] is based on that paper.
I developed two sets of test data by randomly distributing values over
a restricted range and the full range of input values. The current
complex divide handled the restricted range well enough, but failed on
the full range more than 1% of the time. Baudin and Smith's primary
test for "ratio" equals zero reduced the cases with 16 or more error
bits by a factor of 5, but still left too many flawed answers. Adding
debug print out to cases with substantial errors allowed me to see the
intermediate calculations for test values that failed. I noted that
for many of the failures, "ratio" was a subnormal. Changing the
"ratio" test from check for zero to check for subnormal reduced the 16
bit error rate by another factor of 12. This single modified test
provides the greatest benefit for the least cost, but the percentage
of cases with greater than 16 bit errors (double precision data) is
still greater than 0.027% (2.7 in 10,000).
Continued examination of remaining errors and their intermediate
computations led to the various tests of input value tests and scaling
to avoid under/overflow. The current patch does not handle some of the
rare and most extreme combinations of input values, but the random
test data is only showing 1 case in 10 million that has an error of
greater than 12 bits. That case has 18 bits of error and is due to
subtraction cancellation. These results are significantly better
than the results reported by Baudin and Smith.
Support for half, float, double, extended, and long double precision
is included as all are handled with suitable preprocessor symbols in a
single source routine. Since half precision is computed with float
precision as per current libgcc practice, the enhanced algorithm
provides no benefit for half precision and would cost performance.
Further investigation showed changing the half precision algorithm
to use the simple formula (real=a*c+b*d imag=b*c-a*d) caused no
loss of precision and modest improvement in performance.
The existing constants for each precision:
float: FLT_MAX, FLT_MIN;
double: DBL_MAX, DBL_MIN;
extended and/or long double: LDBL_MAX, LDBL_MIN
are used for avoiding the more common overflow/underflow cases. This
use is made generic by defining appropriate __LIBGCC2_* macros in
c-cppbuiltin.c.
Tests are added for when both parts of the denominator have exponents
small enough to allow shifting any subnormal values to normal values
all input values could be scaled up without risking overflow. That
gained a clear improvement in accuracy. Similarly, when either
numerator was subnormal and the other numerator and both denominator
values were not too large, scaling could be used to reduce risk of
computing with subnormals. The test and scaling values used all fit
within the allowed exponent range for each precision required by the C
standard.
Float precision has more difficulty with getting correct answers than
double precision. When hardware for double precision floating point
operations is available, float precision is now handled in double
precision intermediate calculations with the simple algorithm the same
as the half-precision method of using float precision for intermediate
calculations. Using the higher precision yields exact results for all
tested input values (64-bit double, 32-bit float) with the only
performance cost being the requirement to convert the four input
values from float to double. If double precision hardware is not
available, then float complex divide will use the same improved
algorithm as the other precisions with similar change in performance.
Further Improvement
The most common remaining substantial errors are due to accuracy loss
when subtracting nearly equal values. This patch makes no attempt to
improve that situation.
NOTATION
For all of the following, the notation is:
Input complex values:
a+bi (a= real part, b= imaginary part)
c+di
Output complex value:
e+fi = (a+bi)/(c+di)
For the result tables:
current = current method (SMITH)
b1div = method proposed by Elen Kalda
b2div = alternate method considered by Elen Kalda
new = new method proposed by this patch
DESCRIPTIONS of different complex divide methods:
NAIVE COMPUTATION (-fcx-limited-range):
e = (a*c + b*d)/(c*c + d*d)
f = (b*c - a*d)/(c*c + d*d)
Note that c*c and d*d will overflow or underflow if either
c or d is outside the range 2^-538 to 2^512.
This method is available in gcc when the switch -fcx-limited-range is
used. That switch is also enabled by -ffast-math. Only one who has a
clear understanding of the maximum range of all intermediate values
generated by an application should consider using this switch.
SMITH's METHOD (current libgcc):
if(fabs(c)<fabs(d) {
r = c/d;
denom = (c*r) + d;
e = (a*r + b) / denom;
f = (b*r - a) / denom;
} else {
r = d/c;
denom = c + (d*r);
e = (a + b*r) / denom;
f = (b - a*r) / denom;
}
Smith's method is the current default method available with __divdc3.
Elen Kalda's METHOD
Elen Kalda proposed a patch about a year ago, also based on Baudin and
Smith, but not including tests for subnormals:
https://gcc.gnu.org/legacy-ml/gcc-patches/2019-08/msg01629.html [4]
It is compared here for accuracy with this patch.
This method applies the most significant part of the algorithm
proposed by Baudin&Smith (2012) in the paper "A Robust Complex
Division in Scilab" [3]. Elen's method also replaces two divides by
one divide and two multiplies due to the high cost of divide on
aarch64. In the comparison sections, this method will be labeled
b1div. A variation discussed in that patch which does not replace the
two divides will be labeled b2div.
inline void improved_internal (MTYPE a, MTYPE b, MTYPE c, MTYPE d)
{
r = d/c;
t = 1.0 / (c + (d * r));
if (r != 0) {
x = (a + (b * r)) * t;
y = (b - (a * r)) * t;
} else {
/* Changing the order of operations avoids the underflow of r impacting
the result. */
x = (a + (d * (b / c))) * t;
y = (b - (d * (a / c))) * t;
}
}
if (FABS (d) < FABS (c)) {
improved_internal (a, b, c, d);
} else {
improved_internal (b, a, d, c);
y = -y;
}
NEW METHOD (proposed by patch) to replace the current default method:
The proposed method starts with an algorithm proposed by Baudin&Smith
(2012) in the paper "A Robust Complex Division in Scilab" [3]. The
patch makes additional modifications to that method for further
reductions in the error rate. The following code shows the #define
values for double precision. See the patch for #define values used
for other precisions.
#define RBIG ((DBL_MAX)/2.0)
#define RMIN (DBL_MIN)
#define RMIN2 (0x1.0p-53)
#define RMINSCAL (0x1.0p+51)
#define RMAX2 ((RBIG)*(RMIN2))
if (FABS(c) < FABS(d)) {
/* prevent overflow when arguments are near max representable */
if ((FABS (d) > RBIG) || (FABS (a) > RBIG) || (FABS (b) > RBIG) ) {
a = a * 0.5;
b = b * 0.5;
c = c * 0.5;
d = d * 0.5;
}
/* minimize overflow/underflow issues when c and d are small */
else if (FABS (d) < RMIN2) {
a = a * RMINSCAL;
b = b * RMINSCAL;
c = c * RMINSCAL;
d = d * RMINSCAL;
}
else {
if(((FABS (a) < RMIN) && (FABS (b) < RMAX2) && (FABS (d) < RMAX2)) ||
((FABS (b) < RMIN) && (FABS (a) < RMAX2) && (FABS (d) < RMAX2))) {
a = a * RMINSCAL;
b = b * RMINSCAL;
c = c * RMINSCAL;
d = d * RMINSCAL;
}
}
r = c/d; denom = (c*r) + d;
if( r > RMIN ) {
e = (a*r + b) / denom ;
f = (b*r - a) / denom
} else {
e = (c * (a/d) + b) / denom;
f = (c * (b/d) - a) / denom;
}
}
[ only presenting the fabs(c) < fabs(d) case here, full code in patch. ]
Before any computation of the answer, the code checks for any input
values near maximum to allow down scaling to avoid overflow. These
scalings almost never harm the accuracy since they are by 2. Values that
are over RBIG are relatively rare but it is easy to test for them and
allow aviodance of overflows.
Testing for RMIN2 reveals when both c and d are less than [FLT|DBL]_EPSILON.
By scaling all values by 1/EPSILON, the code converts subnormals to normals,
avoids loss of accuracy and underflows in intermediate computations
that otherwise might occur. If scaling a and b by 1/EPSILON causes either
to overflow, then the computation will overflow whatever method is used.
Finally, we test for either a or b being subnormal (RMIN) and if so,
for the other three values being small enough to allow scaling. We
only need to test a single denominator value since we have already
determined which of c and d is larger.
Next, r (the ratio of c to d) is checked for being near zero. Baudin
and Smith checked r for zero. This code improves that approach by
checking for values less than DBL_MIN (subnormal) covers roughly 12
times as many cases and substantially improves overall accuracy. If r
is too small, then when it is used in a multiplication, there is a
high chance that the result will underflow to zero, losing significant
accuracy. That underflow is avoided by reordering the computation.
When r is subnormal, the code replaces a*r (= a*(c/d)) with ((a/d)*c)
which is mathematically the same but avoids the unnecessary underflow.
TEST Data
Two sets of data are presented to test these methods. Both sets
contain 10 million pairs of complex values. The exponents and
mantissas are generated using multiple calls to random() and then
combining the results. Only values which give results to complex
divide that are representable in the appropriate precision after
being computed in quad precision are used.
The first data set is labeled "moderate exponents".
The exponent range is limited to -DBL_MAX_EXP/2 to DBL_MAX_EXP/2
for Double Precision (use FLT_MAX_EXP or LDBL_MAX_EXP for the
appropriate precisions.
The second data set is labeled "full exponents".
The exponent range for these cases is the full exponent range
including subnormals for a given precision.
ACCURACY Test results:
Note: The following accuracy tests are based on IEEE-754 arithmetic.
Note: All results reporteed are based on use of fused multiply-add. If
fused multiply-add is not used, the error rate increases, giving more
1 and 2 bit errors for both current and new complex divide.
Differences between using fused multiply and not using it that are
greater than 2 bits are less than 1 in a million.
The complex divide methods are evaluated by determining the percentage
of values that exceed differences in low order bits. If a "2 bit"
test results show 1%, that would mean that 1% of 10,000,000 values
(100,000) have either a real or imaginary part that differs from the
quad precision result by more than the last 2 bits.
Results are reported for differences greater than or equal to 1 bit, 2
bits, 8 bits, 16 bits, 24 bits, and 52 bits for double precision. Even
when the patch avoids overflows and underflows, some input values are
expected to have errors due to the potential for catastrophic roundoff
from floating point subtraction. For example, when b*c and a*d are
nearly equal, the result of subtraction may lose several places of
accuracy. This patch does not attempt to detect or minimize this type
of error, but neither does it increase them.
I only show the results for Elen Kalda's method (with both 1 and
2 divides) and the new method for only 1 divide in the double
precision table.
In the following charts, lower values are better.
current - current complex divide in libgcc
b1div - Elen Kalda's method from Baudin & Smith with one divide
b2div - Elen Kalda's method from Baudin & Smith with two divides
new - This patch which uses 2 divides
===================================================
Errors Moderate Dataset
gtr eq current b1div b2div new
====== ======== ======== ======== ========
1 bit 0.24707% 0.92986% 0.24707% 0.24707%
2 bits 0.01762% 0.01770% 0.01762% 0.01762%
8 bits 0.00026% 0.00026% 0.00026% 0.00026%
16 bits 0.00000% 0.00000% 0.00000% 0.00000%
24 bits 0% 0% 0% 0%
52 bits 0% 0% 0% 0%
===================================================
Table 1: Errors with Moderate Dataset (Double Precision)
Note in Table 1 that both the old and new methods give identical error
rates for data with moderate exponents. Errors exceeding 16 bits are
exceedingly rare. There are substantial increases in the 1 bit error
rates for b1div (the 1 divide/2 multiplys method) as compared to b2div
(the 2 divides method). These differences are minimal for 2 bits and
larger error measurements.
===================================================
Errors Full Dataset
gtr eq current b1div b2div new
====== ======== ======== ======== ========
1 bit 2.05% 1.23842% 0.67130% 0.16664%
2 bits 1.88% 0.51615% 0.50354% 0.00900%
8 bits 1.77% 0.42856% 0.42168% 0.00011%
16 bits 1.63% 0.33840% 0.32879% 0.00001%
24 bits 1.51% 0.25583% 0.24405% 0.00000%
52 bits 1.13% 0.01886% 0.00350% 0.00000%
===================================================
Table 2: Errors with Full Dataset (Double Precision)
Table 2 shows significant differences in error rates. First, the
difference between b1div and b2div show a significantly higher error
rate for the b1div method both for single bit errros and well
beyond. Even for 52 bits, we see the b1div method gets completely
wrong answers more than 5 times as often as b2div. To retain
comparable accuracy with current complex divide results for small
exponents and due to the increase in errors for large exponents, I
choose to use the more accurate method of two divides.
The current method has more 1.6% of cases where it is getting results
where the low 24 bits of the mantissa differ from the correct
answer. More than 1.1% of cases where the answer is completely wrong.
The new method shows less than one case in 10,000 with greater than
two bits of error and only one case in 10 million with greater than
16 bits of errors. The new patch reduces 8 bit errors by
a factor of 16,000 and virtually eliminates completely wrong
answers.
As noted above, for architectures with double precision
hardware, the new method uses that hardware for the
intermediate calculations before returning the
result in float precision. Testing of the new patch
has shown zero errors found as seen in Tables 3 and 4.
Correctness for float
=============================
Errors Moderate Dataset
gtr eq current new
====== ======== ========
1 bit 28.68070% 0%
2 bits 0.64386% 0%
8 bits 0.00401% 0%
16 bits 0.00001% 0%
24 bits 0% 0%
=============================
Table 3: Errors with Moderate Dataset (float)
=============================
Errors Full Dataset
gtr eq current new
====== ======== ========
1 bit 19.98% 0%
2 bits 3.20% 0%
8 bits 1.97% 0%
16 bits 1.08% 0%
24 bits 0.55% 0%
=============================
Table 4: Errors with Full Dataset (float)
As before, the current method shows an troubling rate of extreme
errors.
There very minor changes in accuracy for half-precision since the code
changes from Smith's method to the simple method. 5 out of 1 million
test cases show correct answers instead of 1 or 2 bit errors.
libgcc computes half-precision functions in float precision
allowing the existing methods to avoid overflow/underflow issues
for the allowed range of exponents for half-precision.
Extended precision (using x87 80-bit format on x86) and Long double
(using IEEE-754 128-bit on x86 and aarch64) both have 15-bit exponents
as compared to 11-bit exponents in double precision. We note that the
C standard also allows Long Double to be implemented in the equivalent
range of Double. The RMIN2 and RMINSCAL constants are selected to work
within the Double range as well as with extended and 128-bit ranges.
We will limit our performance and accurancy discussions to the 80-bit
and 128-bit formats as seen on x86 here.
The extended and long double precision investigations were more
limited. Aarch64 does not support extended precision but does support
the software implementation of 128-bit long double precision. For x86,
long double defaults to the 80-bit precision but using the
-mlong-double-128 flag switches to using the software implementation
of 128-bit precision. Both 80-bit and 128-bit precisions have the same
exponent range, with the 128-bit precision has extended mantissas.
Since this change is only aimed at avoiding underflow/overflow for
extreme exponents, I studied the extended precision results on x86 for
100,000 values. The limited exponent dataset showed no differences.
For the dataset with full exponent range, the current and new values
showed major differences (greater than 32 bits) in 567 cases out of
100,000 (0.56%). In every one of these cases, the ratio of c/d or d/c
(as appropriate) was zero or subnormal, indicating the advantage of
the new method and its continued correctness where needed.
PERFORMANCE Test results
In order for a library change to be practical, it is necessary to show
the slowdown is tolerable. The slowdowns observed are much less than
would be seen by (for example) switching from hardware double precison
to a software quad precision, which on the tested machines causes a
slowdown of around 100x).
The actual slowdown depends on the machine architecture. It also
depends on the nature of the input data. If underflow/overflow is
rare, then implementations that have strong branch prediction will
only slowdown by a few cycles. If underflow/overflow is common, then
the branch predictors will be less accurate and the cost will be
higher.
Results from two machines are presented as examples of the overhead
for the new method. The one labeled x86 is a 5 year old Intel x86
processor and the one labeled aarch64 is a 3 year old arm64 processor.
In the following chart, the times are averaged over a one million
value data set. All values are scaled to set the time of the current
method to be 1.0. Lower values are better. A value of less than 1.0
would be faster than the current method and a value greater than 1.0
would be slower than the current method.
================================================
Moderate set full set
x86 aarch64 x86 aarch64
======== =============== ===============
float 0.59 0.79 0.45 0.81
double 1.04 1.24 1.38 1.56
long double 1.13 1.24 1.29 1.25
================================================
Table 5: Performance Comparisons (ratio new/current)
The above tables omit the timing for the 1 divide and 2 multiply
comparison with the 2 divide approach.
The float results show clear performance improvement due to using the
simple method with double precision for intermediate calculations.
The double results with the newer method show less overhead for the
moderate dataset than for the full dataset. That's because the moderate
dataset does not ever take the new branches which protect from
under/overflow. The better the branch predictor, the lower the cost
for these untaken branches. Both platforms are somewhat dated, with
the x86 having a better branch predictor which reduces the cost of the
additional branches in the new code. Of course, the relative slowdown
may be greater for some architectures, especially those with limited
branch prediction combined with a high cost of misprediction.
The long double results are fairly consistent in showing the moderate
additional cost of the extra branches and calculations for all cases.
The observed cost for all precisions is claimed to be tolerable on the
grounds that:
(a) the cost is worthwhile considering the accuracy improvement shown.
(b) most applications will only spend a small fraction of their time
calculating complex divide.
(c) it is much less than the cost of extended precision
(d) users are not forced to use it (as described below)
Those users who find this degree of slowdown unsatisfactory may use
the gcc switch -fcx-fortran-rules which does not use the library
routine, instead inlining Smith's method without the C99 requirement
for dealing with NaN results. The proposed patch for libgcc complex
divide does not affect the code generated by -fcx-fortran-rules.
SUMMARY
When input data to complex divide has exponents whose absolute value
is less than half of *_MAX_EXP, this patch makes no changes in
accuracy and has only a modest effect on performance. When input data
contains values outside those ranges, the patch eliminates more than
99.9% of major errors with a tolerable cost in performance.
In comparison to Elen Kalda's method, this patch introduces more
performance overhead but reduces major errors by a factor of
greater than 4000.
REFERENCES
[1] Nelson H.F. Beebe, "The Mathematical-Function Computation Handbook.
Springer International Publishing AG, 2017.
[2] Robert L. Smith. Algorithm 116: Complex division. Commun. ACM,
5(8):435, 1962.
[3] Michael Baudin and Robert L. Smith. "A robust complex division in
Scilab," October 2012, available at http://arxiv.org/abs/1210.4539.
[4] Elen Kalda: Complex division improvements in libgcc
https://gcc.gnu.org/legacy-ml/gcc-patches/2019-08/msg01629.html
2020-12-08 Patrick McGehearty <patrick.mcgehearty@oracle.com>
gcc/c-family/
* c-cppbuiltin.c (c_cpp_builtins): Add supporting macros for new
complex divide
libgcc/
* libgcc2.c (XMTYPE, XCTYPE, RBIG, RMIN, RMIN2, RMINSCAL, RMAX2):
Define.
(__divsc3, __divdc3, __divxc3, __divtc3): Improve complex divide.
* config/rs6000/_divkc3.c (RBIG, RMIN, RMIN2, RMINSCAL, RMAX2):
Define.
(__divkc3): Improve complex divide.
gcc/testsuite/
* gcc.c-torture/execute/ieee/cdivchkd.c: New test.
* gcc.c-torture/execute/ieee/cdivchkf.c: Likewise.
* gcc.c-torture/execute/ieee/cdivchkld.c: Likewise.
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The test in the PowerPC 32-bit trampoline support is backwards. It aborts
if the trampoline size is greater than the expected size. It should abort
when the trampoline size is less than the expected size. I fixed the test
so the operands are reversed. I then folded the load immediate into the
compare instruction.
I verified this by creating a 32-bit trampoline program and manually
changing the size of the trampoline to be 48 instead of 40. The program
aborted with the larger size. I updated this code and ran the test again
and it passed.
I added a test case that runs on PowerPC 32-bit Linux systems and it calls
the __trampoline_setup function with a larger buffer size than the
compiler uses. The test is not run on 64-bit systems, since the function
__trampoline_setup is not called. I also limited the test to just Linux
systems, in case trampolines are handled differently in other systems.
libgcc/
2021-04-23 Michael Meissner <meissner@linux.ibm.com>
PR target/98952
* config/rs6000/tramp.S (__trampoline_setup, elfv1 #ifdef): Fix
trampoline size comparison in 32-bit by reversing test and
combining load immediate with compare.
(__trampoline_setup, elfv2 #ifdef): Fix trampoline size comparison
in 32-bit by reversing test and combining load immediate with
compare.
gcc/testsuite/
2021-04-23 Michael Meissner <meissner@linux.ibm.com>
PR target/98952
* gcc.target/powerpc/pr98952.c: New test.
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This patch fixes the problem that the Decimal <-> Float128 conversions
were built even if the user configured GCC with --disable-decimal-float.
libgcc/
2021-04-05 Florian Weimer <fweimer@redhat.com>
* config/rs6000/t-float128 (fp128_ppc_funcs): Add decimal floating
point functions for $(decimal_float) only.
Co-Authored-By: Michael Meissner <meissner@linux.ibm.com>
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[PR97653]
__floatunditf and __fixtfdi and a couple of other libgcc{.a,_s.so}
entrypoints for backwards compatibility should mean IBM double double
handling (i.e. IFmode), gcc emits such calls for that format and
form IEEE long double emits *kf* instead.
When gcc is configured without --with-long-double-format=ieee ,
everything is fine, but when it is not, we need to compile those
libgcc sources with -mno-gnu-attribute -mabi=ibmlongdouble.
The following snippet in libgcc/config/rs6000/t-linux was attempting
to ensure that, and for some routines it works fine (e.g. for _powitf2).
But, due to 4 different types of bugs it doesn't work for most of those
functions, which means that in --with-long-double-format=ieee
configured gcc those *tf* entrypoints instead handle the long double
arguments as if they were KFmode.
The bugs are:
1) the first few objs properly use $(objext) as suffix, but
several other contain a typo and use $(object) instead,
which is a variable that isn't set to anything, so we don't
add .o etc. extensions
2) while unsigned fix are properly called _fixuns*, unsigned float
are called _floatun* (without s), but the var was using there
the extra s and so didn't match
3) the variable didn't cover any of the TF <-> TI conversions,
only TF <-> DI conversions
4) nothing in libgcc_s.so was handled, as those object files are
called *_s.o rather than *.o and IBM128_SHARED_OBJS used wrong
syntax of the GNU make substitution reference, which should be
$(var:a=b) standing for $(patsubst a,b,$(var)) but it used
$(var:a:b) instead
2021-04-03 Jakub Jelinek <jakub@redhat.com>
PR target/97653
* config/rs6000/t-linux (IBM128_STATIC_OBJS): Fix spelling, use
$(objext) instead of $(object). Use _floatunditf instead of
_floatunsditf. Add tf <-> ti conversion objects.
(IBM128_SHARED_OBJS): Use proper substitution reference syntax.
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In the patch that I applied on March 2nd, I had code to provide support for
Decimal/_Float128 conversions if the user did not use at least GLIBC 2.32. It
did this by using __ibm128 as an intermediate type. The trouble is __ibm128
cannot represent all of the numbers that _Float128 can, and you lose if you do
this conversion.
This patch removes this support. The dfp-bit.c functions now call the the
__sprintfieee128 and __strtoieee128 functions to do the conversion. If the
user does not have GLIBC, they will get a linker error that these functions do
not exist.
The float128 support functions are only built into the static libgcc, so there
isn't an issue with having references to __strtoieee128 and __sprintfieee128
with older GLIBC libraries.
As an added bonus, this patch eliminates the __sprintfkf function which
included stdio.h to get a definition for the sprintf library function. This
allows for building cross compilers without having to have a target stdio.h
available.
libgcc/
2021-03-29 Michael Meissner <meissner@linux.ibm.com>
* config/rs6000/t-float128 (fp128_decstr_funcs): Delete.
(fp128_ppc_funcs): Do not add $(fp128_decstr_funcs).
(fp128_decstr_objs): Delete.
* dfp-bit.h: Call __sprintfieee128 to do conversions from
_Float128 to a Decimal type. Call __strtoieee128 to do
conversions from a Decimal type to _Float128.
* config/rs6000/_sprintfkf.c: Delete file.
* config/rs6000/_sprintfkf.h: Delete file.
* config/rs6000/_strtokf.c: Delete file.
* config/rs6000/_strtokf.h: Delete file.
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libgcc/
* config/riscv/sfp-machine.h (__BYTE_ORDER): Set according
to __BYTE_ORDER__.
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As reported, bootstrap currently fails on older Darwin because MAP_ANONYMOUS
is not defined.
The following is what gcc/system.h does, so I think it should work for
libgcov.
2021-03-06 Jakub Jelinek <jakub@redhat.com>
PR gcov-profile/99406
* libgcov.h (MAP_FAILED, MAP_ANONYMOUS): If HAVE_SYS_MMAN_H is
defined, define these macros if not defined already.
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libgcc/ChangeLog:
PR gcov-profile/99105
* libgcov-driver.c (write_top_counters): Rename to ...
(write_topn_counters): ... this.
(write_one_data): Pre-allocate buffer for number of items
in the corresponding linked lists.
* libgcov.h (malloc_mmap): New function.
(allocate_gcov_kvp): Use it.
gcc/testsuite/ChangeLog:
PR gcov-profile/99105
* gcc.dg/tree-prof/indir-call-prof-malloc.c: Use profile
correction as the wrapped malloc is called one more time
from libgcov.
* gcc.dg/tree-prof/pr97461.c: Likewise.
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libgcc/ChangeLog:
PR gcov-profile/99385
* libgcov.h (allocate_gcov_kvp): Call mmap with fd equal to -1.
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gcc/ChangeLog:
PR gcov-profile/97461
* gcov-io.h (GCOV_PREALLOCATED_KVP): Remove.
libgcc/ChangeLog:
PR gcov-profile/97461
* config.in: Regenerate.
* configure: Likewise.
* configure.ac: Check sys/mman.h header file
* libgcov-driver.c (struct gcov_kvp): Remove static
pre-allocated pool and use a dynamic one.
* libgcov.h (MMAP_CHUNK_SIZE): New.
(gcov_counter_add): Use mmap to allocate pool for struct
gcov_kvp.
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The prototype of __sprintfkf in _sprintfkf.h did not match the function in
_sprintfkf.c. This patch fixes the prototype. I also included the
_sprintfkf.h file in _sprintfkf.c to make sure the prototype is correct and to
eliminate a warning about declaring the function without a previous
declaration.
libgcc/
2021-03-01 Michael Meissner <meissner@linux.ibm.com>
* config/rs6000/_sprintfkf.h (__sprintfkf): Fix prototype to match
the function.
* config/rs6000/_sprintfkf.c: Include _sprintfkf.h.
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When these functions are called with integer minimum, there is UB on the libgcc
side. Fixed in the obvious way, the code in the end wants ABSU_EXPR behavior.
2021-02-24 Jakub Jelinek <jakub@redhat.com>
PR libgcc/99236
* libgcc2.c (__powisf2, __powidf2, __powitf2, __powixf2): Perform
negation of m in unsigned type.
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As discussed in the PR, the Makefile fragment lacks a double '$' to
get the return-code from GCC invocation, resulting is CMSE support
missing from multilibs.
I checked that the simple patch proposed in the PR fixes the problem.
2021-02-23 Christophe Lyon <christophe.lyon@linaro.org>
Hau Hsu <hsuhau617@gmail.com>
PR target/99157
libgcc/
* config/arm/t-arm: Fix cmse support detection.
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libgcc/
2021-02-22 Michael Meissner <meissner@linux.ibm.com>
* dfp-bit.c (BFP_TO_DFP): Fix a comment line that was too long.
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This patch implements conversions between _Float128 and the 3 Decimal floating
types. It does this by extendending the dfp-bit conversions to add a new
binary floating point type (KF), and doing the conversions in the same manner
as the other binary/decimal conversions.
For conversions from _Float128 to Decimal, this patch uses a function
(__sprintfkf) instead of the sprintf function to convert long double values to
strings. The __sprintfkf function determines if GLIBC 2.32 or newer is used
and calls the IEEE 128-bit version of sprintf (__sprintfieee128). If the GLIBC
is earlier than 2.32, the code will convert _Float128 to __ibm128 and then use
the normal sprintf to convert this value.
For conversions from Decimal to _Float128, this patch uses a function
(__strtokf) instead of strtold to convert the strings from the Decimal
conversion to long double. The __strtokf function determines if GLIBC 2.32 or
newer is used, and if it is, calls the IEEE 128-bit version (__strtoieee128).
If the GLIBC is earlier than 2.32, the code will call strtold and convert the
__ibm128 value to _Float128.
These functions will primarily be used if/when the default PowerPC long double
type is changed to IEEE 128-bit, but they could also be used if the user
explicitly converts _Float128 to/from a Decimal type.
libgcc/
2021-02-22 Michael Meissner <meissner@linux.ibm.com>
* config/rs6000/_dd_to_kf.c: New file.
* config/rs6000/_kf_to_dd.c: New file.
* config/rs6000/_kf_to_sd.c: New file.
* config/rs6000/_kf_to_td.c: New file.
* config/rs6000/_sd_to_kf.c: New file.
* config/rs6000/_sprintfkf.c: New file.
* config/rs6000/_sprintfkf.h: New file.
* config/rs6000/_strtokf.h: New file.
* config/rs6000/_strtokf.c: New file.
* config/rs6000/_td_to_kf.c: New file.
* config/rs6000/quad-float128.h: Add new declarations.
* config/rs6000/t-float128 (fp128_dec_funcs): New macro.
(fp128_decstr_funcs): New macro.
(ibm128_dec_funcs): New macro.
(fp128_ppc_funcs): Add the new conversions.
(fp128_dec_objs): Force Decimal <-> __float128 conversions to be
compiled with -mabi=ieeelongdouble.
(fp128_decstr_objs): Force __float128 <-> string conversions to be
compiled with -mabi=ibmlongdouble.
(ibm128_dec_objs): Force Decimal <-> __float128 conversions to be
compiled with -mabi=ieeelongdouble.
(FP128_CFLAGS_DECIMAL): New macro.
(IBM128_CFLAGS_DECIMAL): New macro.
* dfp-bit.c (DFP_TO_BFP): Add PowerPC _Float128 support.
(BFP_TO_DFP): Add PowerPC _Float128 support.
* dfp-bit.h (BFP_KIND): Add new binary floating point kind for
IEEE 128-bit floating point.
(DFP_TO_BFP): Add PowerPC _Float128 support.
(BFP_TO_DFP): Add PowerPC _Float128 support.
(BFP_SPRINTF): New macro.
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On Linux, GCC emits .note.GNU-stack sections when compiling code to mark
the code as not needing or needing executable stack, missing section means
unknown. But assembly files need to be marked manually. We already
mark various *.S files in libgcc manually, but the
avx_resms64f.o
avx_resms64fx.o
avx_resms64.o
avx_resms64x.o
avx_savms64f.o
avx_savms64.o
sse_resms64f.o
sse_resms64fx.o
sse_resms64.o
sse_resms64x.o
sse_savms64f.o
sse_savms64.o
files aren't marked, so when something links it in, it will require
executable stack. Nothing in the assembly requires executable stack though.
2021-01-27 Jakub Jelinek <jakub@redhat.com>
* config/i386/savms64.h: Add .note.GNU-stack section on Linux.
* config/i386/savms64f.h: Likewise.
* config/i386/resms64.h: Likewise.
* config/i386/resms64f.h: Likewise.
* config/i386/resms64x.h: Likewise.
* config/i386/resms64fx.h: Likewise.
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