- - - -
New in version 6: Due to an oversight (i.e. coding error), version 5
changed the use of __LIBGCC_TF_EPSILON__ to __LIBGCC_DF_EPSILON__ but
not the other LIBGCC_TF values. For correct execution of the long
double test case it is necessary to also switch to using
__LIBGCC_DF_MIN__. For consistency we also switch to using
__LIBGCC_DF_MAX__. LDBL_MIN is 2**53 times as larger than DBL_MIN.
The larger value causes the code to switch the order of computation
when it is not optimal, resulting in failure for one of the values
in the cdivchk_ld.c test. Using DBL_MIN does not cause that failure..
There may be opportunity for further refinement of IBM128 format
Long Double complex divide, but that's beyond the scope of this
patch.
- - - -
This revision adds a test in libgcc/libgcc2.c for when
"__LIBGCC_TF_MANT_DIG__ == 106" to use __LIBGCC_DF_EPSILON__ instead
of __LIBGCC_TF_EPSILON__. That is specific to IBM 128-bit format long
doubles where EPSILON is very, very small and 1/EPSILON oveflows to
infinity. This change avoids the overflow without affecting any other
platform. Discussion in the patch is adjusted to reflect this
limitation.
It does not make any changes to .../rs6000/_divkc3.c, leaving it to
use __LIBGCC_KF__*. That means the upstream gcc will not build in
older IBM environments that do not recognize the KF floating point
mode properly. Environments that do not need IBM longdouble support
do build cleanly.
- - - -
This patch addresses the failure of powerpc64 long double complex divide
in native ibm long double format after the patch "Practical improvement
to libgcc complex divide".
The new code uses the following macros which are intended to be mapped
to appropriate values according to the underlying hardware representation.
See https://gcc.gnu.org/bugzilla/show_bug.cgi?id=101104
RBIG a value near the maximum representation
RMIN a value near the minimum representation
(but not in the subnormal range)
RMIN2 a value moderately less than 1
RMINSCAL the inverse of RMIN2
RMAX2 RBIG * RMIN2 - a value to limit scaling to not overflow
When "long double" values were not using the IEEE 128-bit format but
the traditional IBM 128-bit, the previous code used the LDBL values
which caused overflow for RMINSCAL. The new code uses the DBL values.
RBIG LDBL_MAX = 0x1.fffffffffffff800p+1022
DBL_MAX = 0x1.fffffffffffff000p+1022
RMIN LDBL_MIN = 0x1.0000000000000000p-969
RMIN DBL_MIN = 0x1.0000000000000000p-1022
RMIN2 LDBL_EPSILON = 0x0.0000000000001000p-1022 = 0x1.0p-1074
RMIN2 DBL_EPSILON = 0x1.0000000000000000p-52
[ORMINSCAL 1/LDBL_EPSILON = inf (1.0p+1074 does not fit in IBM 128-bit).
1/DBL_EPSILON = 0x1.0000000000000000p+52
RMAX2 = RBIG * RMIN2 = 0x1.fffffffffffff800p-52
RBIG * RMIN2 = 0x1.fffffffffffff000p+970
The MAX and MIN values have only modest changes since the maximum and
minimum values are about the same as for double precision. The
EPSILON field is considerably different. Due to how very small values
can be represented in the lower 64 bits of the IBM 128-bit floating
point, EPSILON is extremely small, so far beyond the desired value
that inversion of the value overflows and even without the overflow,
the RMAX2 is so small as to eliminate most usage of the test.
The change has been tested on gcc135.fsffrance.org and gains the
expected improvements in accuracy for long double complex divide.
libgcc/
PR target/101104
* libgcc2.c (RMIN2, RMINSCAL, RMAX2):
Use more correct values for native IBM 128-bit.
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.
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.
FSTYPE FUNC (DWtype u) in libgcc2.c, which converts DI/TI to SF/DF, has
/* No leading bits means u == minimum. */
if (count == 0)
return -(Wtype_MAXp1_F * (Wtype_MAXp1_F / 2));
in the third case (where actually count == 0 only means the high part is
minimum). It should be:
/* No leading bits means u == minimum. */
if (count == 0)
return Wtype_MAXp1_F * (FSTYPE) (hi | ((UWtype) u != 0));
instead.
gcc/testsuite/
2019-01-23 H.J. Lu <hongjiu.lu@intel.com>
PR libgcc/88931
* gcc.dg/torture/fp-int-convert-timode-1.c: New test.
* gcc.dg/torture/fp-int-convert-timode-2.c: Likewise.
* gcc.dg/torture/fp-int-convert-timode-3.c: Likewise.
* gcc.dg/torture/fp-int-convert-timode-4.c: Likewise.
libgcc/
2019-01-23 Joseph Myers <joseph@codesourcery.com>
PR libgcc/88931
* libgcc2.c (FSTYPE FUNC (DWtype u)): Correct no leading bits
case.
From-SVN: r268216
PR target/82274
* internal-fn.c (expand_mul_overflow): If both operands have
the same highpart of -1 or 0 and the topmost bit of lowpart
is different, overflow is if res <= 0 rather than res < 0.
* libgcc2.c (__mulvDI3): If both operands have
the same highpart of -1 and the topmost bit of lowpart is 0,
multiplication overflows even if both lowparts are 0.
* gcc.dg/pr82274-1.c: New test.
* gcc.dg/pr82274-2.c: New test.
From-SVN: r253734
This patch arranges for half-precision complex multiply and divide
routines to be built if __LIBGCC_HAS_HF_MODE__. This will be true
if the target supports the _Float16 type.
libgcc/
PR target/63250
* Makefile.in (lib2funcs): Build _mulhc3 and _divhc3.
* libgcc2.h (LIBGCC_HAS_HF_MODE): Conditionally define.
(HFtype): Likewise.
(HCtype): Likewise.
(__divhc3): Likewise.
(__mulhc3): Likewise.
* libgcc2.c: Support _mulhc3 and _divhc3.
From-SVN: r240043
libgcc complex multiply is meant to eliminate excess
precision from certain internal values by forcing them to memory in
exactly those cases where the type has excess precision. But in
https://gcc.gnu.org/ml/gcc-patches/2014-09/msg01894.html I
accidentally inverted the logic so that values get forced to memory in
exactly the cases where it's not needed. (This is a pessimization in
the no-excess-precision case, in principle could lead to bad results
depending on code generation in the excess-precision case. Note: I do
not have a test demonstrating bad results.)
Bootstrapped with no regressions on x86_64-pc-linux-gnu. Code size
went down on x86_64 as expected; old sizes:
text data bss dec hex filename
887 0 0 887 377 _muldc3.o
810 0 0 810 32a _mulsc3.o
2032 0 0 2032 7f0 _multc3.o
983 0 0 983 3d7 _mulxc3.o
New sizes:
847 0 0 847 34f _muldc3.o
770 0 0 770 302 _mulsc3.o
2032 0 0 2032 7f0 _multc3.o
951 0 0 951 3b7 _mulxc3.o
PR libgcc/77519
* libgcc2.c (NOTRUNC): Invert settings.
From-SVN: r240033
The last target to use this was i386-interix, so since that is gone we
don't need this anymore.
libgcc/ChangeLog:
2016-07-06 Trevor Saunders <tbsaunde+gcc@tbsaunde.org>
* libgcc2.c (SYMBOL__MAIN): Remove checks for
CTOR_LISTS_DEFINED_EXTERNALLY.
From-SVN: r238067
This patch removes the target macro LIBGCC2_LONG_DOUBLE_TYPE_SIZE.
After recent changes, this macro was used in two ways in libgcc: to
determine the mode of long double in dfp-bit.h, and to determine
whether a particular mode has excess precision for use in complex
multiplication.
The former is concerned specifically with long double: it relates to
use of strtold for converting between decimal and binary floating
point. This is replaced by comparing __LDBL_MANT_DIG__ with the
appropriate __LIBGCC_*_MANT_DIG__ macro. The latter is replaced
__LIBGCC_*_EXCESS_PRECISION__ predefined macros.
Remarks:
* Comparing (__LDBL_MANT_DIG__ == __LIBGCC_XF_MANT_DIG__) is more
fragile than it looks; it's possible for XFmode to have 53-bit
mantissa (TARGET_96_ROUND_53_LONG_DOUBLE, on FreeBSD and
DragonFlyBSD 32-bit), in which case such a comparison would not
distinguish XFmode and DFmode as possible modes for long double.
Fortunately, no target supporting that form of XFmode also supports
long double = double (but if some target did, we'd need e.g. an
additional macro giving the exponent range of each mode).
Furthermore, this code doesn't actually get used for x86 (or any
other target with XFmode support), because x86 uses BID not DPD and
BID has its own conversion code (which handles conversions for both
XFmode and TFmode without needing to go via strtold). And FreeBSD
and DragonFlyBSD aren't among the targets with DFP support. So
while in principle this code is fragile and it's a deficiency that
it can't support both XFmode and TFmode at once (something that
can't be solved with the string conversion approach without libc
having TS 18661 functions such as strtof128), all these issues
should not be a problem in practice.
* If other cases of excess precision are supported in future, the code
for defining __LIBGCC_*_EXCESS_PRECISION__ may need updating.
Although the most likely such cases might not actually involve
excess precision for any mode used in libgcc - FLT_EVAL_METHOD being
32 to do _Float16 arithmetic on _Float32 should have the effect of
_Complex _Float16 arithmetic using __mulsc3 and __divsc3, rather
than currently nonexistent __mulhc3 and __divhc3 as in bug 63250 for
ARM.
* As has been noted in the context of simultaneous support for
__float128 and __ibm128 on Power, the semantics of macros such as
LONG_DOUBLE_TYPE_SIZE are problematic because they rely on a
poorly-defined precision value for floating-point modes (which seems
to be intended as the number of significant bits in the
representation, e.g. 80 for XFmode which may be either 12 or 16
bytes) uniquely identifying a mode (although defining an arbitrarily
different value for one of the modes you wish to distinguish may
work as a hack). It would be cleaner to have a target hook that
gives a machine mode directly for float, double and long double,
rather than going via these precision values. By eliminating all
use of these macros (FLOAT_TYPE_SIZE, DOUBLE_TYPE_SIZE,
LONG_DOUBLE_TYPE_SIZE) from code built for the target, this patch
facilitates such a conversion to a hook (which I suppose would take
some suitable enum as an argument to identify which of the three
types to return a mode for).
(The issue of multiple type support for DFP conversions would apply
in that Power case.
<https://gcc.gnu.org/ml/gcc-patches/2014-07/msg01084.html> doesn't
seem to touch on it, but it would seem reasonable to punt on it
initially as hard to fix. There would also be the issue of getting
functions such as __powikf2, __mulkc3, __divkc3 defined, but that's
rather easier to address.)
Bootstrapped with no regressions on x86_64-unknown-linux-gnu.
gcc:
* doc/tm.texi.in (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* doc/tm.texi: Regenerate.
* system.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Poison.
* config/alpha/alpha.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/i386/i386-interix.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE):
Remove.
* config/i386/i386.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/i386/rtemself.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/ia64/ia64.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/m68k/m68k.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/m68k/netbsd-elf.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE):
Remove.
* config/mips/mips.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/mips/n32-elf.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/msp430/msp430.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/rl78/rl78.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/rs6000/rs6000.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/rx/rx.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/s390/s390.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/sparc/freebsd.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/sparc/linux.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/sparc/linux64.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
* config/sparc/netbsd-elf.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE):
Remove.
gcc/c-family:
* c-cppbuiltin.c (c_cpp_builtins): Define
__LIBGCC_*_EXCESS_PRECISION__ macros for supported floating-point
modes.
libgcc:
* dfp-bit.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
(__LIBGCC_XF_MANT_DIG__): Define if not already defined.
(LONG_DOUBLE_HAS_XF_MODE): Define in terms of
__LIBGCC_XF_MANT_DIG__.
(__LIBGCC_TF_MANT_DIG__): Define if not already defined.
(LONG_DOUBLE_HAS_TF_MODE): Define in terms of
__LIBGCC_TF_MANT_DIG__.
* libgcc2.c (NOTRUNC): Define in terms of
__LIBGCC_*_EXCESS_PRECISION__, not LIBGCC2_LONG_DOUBLE_TYPE_SIZE.
* libgcc2.h (LIBGCC2_LONG_DOUBLE_TYPE_SIZE): Remove.
From-SVN: r215491
This patch removes the (undocumented) LIBGCC2_TF_CEXT target macro,
replacing it by -fbuilding-libgcc predefines (and thereby gets rid of
another LIBGCC2_LONG_DOUBLE_TYPE_SIZE conditional, though some more
patches are needed before that target macro can be eliminated). This
macro indicated the suffix used on __builtin_huge_val,
__builtin_copysign, __builtin_fabs built-in function names to produce
the names for a given floating-point mode.
Predefines are added for all floating-point modes supported for
libgcc, not just TFmode. These are fully accurate for modes
corresponding to float, double and long double. For other modes, the
suffix for *constants* is determined by the targetm.c.mode_for_suffix
hook (the limit to two possible suffixes 'w' and 'q' being hardcoded
in various places). This is in fact the suffix for built-in functions
as well where such functions exist.
* For i386, the *q functions always exist (whether or not TFmode is
used for long double). The *w functions never exist (but this
doesn't matter for libgcc, since no i386 configuration treats XFmode
as a supported scalar mode if long double is TFmode; if __float80
were to be supported for 64-bit Android, properly such functions
ought to be added).
* For ia64, the *q functions exist for non-HP-UX (under HP-UX, long
double is TFmode, so they aren't needed). The *w functions never
exist. This is an issue for this libgcc code for the XFmode complex
functions in libgcc on HP-UX; as I understand it, right now those
will accidentally be using TFmode versions of those three functions,
so involving unnecessary conversions, while the sanity check on CEXT
accidentally passes because all it tests is the sizes of the types.
Because of the lack of 'w' functions, the patch uses 'l' when the
constant suffix is 'w', matching what the existing libgcc code would
do for IA64 HP-UX in that case.
Ideally there would be generic code to create such built-in functions
for all supported floating-point types. That may be something to
consider if support for TS 18661-3 (standard bindings for IEEE
754-2008, defining names such as _Float128, and function names such as
copysignf128) is added in future.
Bootstrapped with no regressions on x86_64-unknown-linux-gnu.
gcc:
* system.h (LIBGCC2_TF_CEXT): Poison.
* config/i386/cygming.h (LIBGCC2_TF_CEXT): Remove.
* config/i386/darwin.h (LIBGCC2_TF_CEXT): Likewise.
* config/i386/dragonfly.h (LIBGCC2_TF_CEXT): Likewise.
* config/i386/freebsd.h (LIBGCC2_TF_CEXT): Likewise.
* config/i386/gnu-user-common.h (LIBGCC2_TF_CEXT): Likewise.
* config/i386/openbsdelf.h (LIBGCC2_TF_CEXT): Likewise.
* config/i386/sol2.h (LIBGCC2_TF_CEXT): Likewise.
* config/ia64/ia64.h (LIBGCC2_TF_CEXT): Likewise.
* config/ia64/linux.h (LIBGCC2_TF_CEXT): Likewise.
gcc/c-family:
* c-cppbuiltin.c (c_cpp_builtins): Define __LIBGCC_*_FUNC_EXT__
for supported floating-point modes.
libgcc:
* libgcc2.c (CEXT): Define using __LIBGCC_*_FUNC_EXT__.
From-SVN: r215368
gcc:
* config/i386/cygming.h (TF_SIZE): Remove.
* config/i386/darwin.h (TF_SIZE): Remove.
* config/i386/dragonfly.h (TF_SIZE): Remove.
* config/i386/freebsd.h (TF_SIZE): Remove.
* config/i386/gnu-user-common.h (TF_SIZE): Remove.
* config/i386/openbsdelf.h (TF_SIZE): Remove.
* config/i386/sol2.h (TF_SIZE): Remove.
* config/ia64/hpux.h (XF_SIZE, TF_SIZE): Remove.
* config/ia64/linux.h (TF_SIZE): Remove.
* doc/tm.texi.in (SF_SIZE, DF_SIZE, XF_SIZE, TF_SIZE): Remove.
* doc/tm.texi: Regenerate.
* system.h (SF_SIZE, DF_SIZE, XF_SIZE, TF_SIZE): Poison.
gcc/c-family:
* c-cppbuiltin.c (c_cpp_builtins): Define macros for mantissa
digits of floating-point modes if -fbuilding-libgcc.
libgcc:
* libgcc2.c (SF_SIZE): Change all uses to __LIBGCC_SF_MANT_DIG__.
(DF_SIZE): Change all uses to __LIBGCC_DF_MANT_DIG__.
(XF_SIZE): Change all uses to __LIBGCC_XF_MANT_DIG__.
(TF_SIZE): Change all uses to __LIBGCC_TF_MANT_DIG__.
* libgcc2.h (SF_SIZE): Change to __LIBGCC_SF_MANT_DIG__. Give
error if not defined and LIBGCC2_HAS_SF_MODE is defined.
(DF_SIZE): Change to __LIBGCC_DF_MANT_DIG__. Give error if not
defined and LIBGCC2_HAS_DF_MODE is defined.
(XF_SIZE): Change to __LIBGCC_XF_MANT_DIG__. Give error if not
defined and LIBGCC2_HAS_XF_MODE is defined.
(TF_SIZE): Change to __LIBGCC_TF_MANT_DIG__. Give error if not
defined and LIBGCC2_HAS_TF_MODE is defined.
From-SVN: r215014
gcc/c-family:
* c-cppbuiltin.c (c_cpp_builtins): Also define
__LIBGCC_EH_TABLES_CAN_BE_READ_ONLY__,
__LIBGCC_EH_FRAME_SECTION_NAME__, __LIBGCC_JCR_SECTION_NAME__,
__LIBGCC_CTORS_SECTION_ASM_OP__, __LIBGCC_DTORS_SECTION_ASM_OP__,
__LIBGCC_TEXT_SECTION_ASM_OP__, __LIBGCC_INIT_SECTION_ASM_OP__,
__LIBGCC_INIT_ARRAY_SECTION_ASM_OP__,
__LIBGCC_STACK_GROWS_DOWNWARD__,
__LIBGCC_DONT_USE_BUILTIN_SETJMP__,
__LIBGCC_DWARF_ALT_FRAME_RETURN_COLUMN__,
__LIBGCC_DWARF_FRAME_REGISTERS__,
__LIBGCC_EH_RETURN_STACKADJ_RTX__, __LIBGCC_JMP_BUF_SIZE__,
__LIBGCC_STACK_POINTER_REGNUM__ and
__LIBGCC_VTABLE_USES_DESCRIPTORS__ for -fbuilding-libgcc.
(builtin_define_with_value): Handle backslash-escaping in string
macro values.
libgcc:
* Makefile.in (CRTSTUFF_CFLAGS): Add -fbuilding-libgcc.
* config/aarch64/linux-unwind.h (STACK_POINTER_REGNUM): Change all
uses to __LIBGCC_STACK_POINTER_REGNUM__.
(DWARF_ALT_FRAME_RETURN_COLUMN): Change all uses to
__LIBGCC_DWARF_ALT_FRAME_RETURN_COLUMN__.
* config/alpha/vms-unwind.h (DWARF_ALT_FRAME_RETURN_COLUMN):
Change use to __LIBGCC_DWARF_ALT_FRAME_RETURN_COLUMN__.
* config/cr16/unwind-cr16.c (STACK_GROWS_DOWNWARD): Change all
uses to __LIBGCC_STACK_GROWS_DOWNWARD__.
(DWARF_FRAME_REGISTERS): Change all uses to
__LIBGCC_DWARF_FRAME_REGISTERS__.
(EH_RETURN_STACKADJ_RTX): Change all uses to
__LIBGCC_EH_RETURN_STACKADJ_RTX__.
* config/cr16/unwind-dw2.h (DWARF_FRAME_REGISTERS): Change use to
__LIBGCC_DWARF_FRAME_REGISTERS__. Remove conditional definition.
* config/i386/cygming-crtbegin.c (EH_FRAME_SECTION_NAME): Change
use to __LIBGCC_EH_FRAME_SECTION_NAME__.
(JCR_SECTION_NAME): Change use to __LIBGCC_JCR_SECTION_NAME__.
* config/i386/cygming-crtend.c (EH_FRAME_SECTION_NAME): Change use
to __LIBGCC_EH_FRAME_SECTION_NAME__.
(JCR_SECTION_NAME): Change use to __LIBGCC_JCR_SECTION_NAME__
* config/mips/linux-unwind.h (STACK_POINTER_REGNUM): Change use to
__LIBGCC_STACK_POINTER_REGNUM__.
(DWARF_ALT_FRAME_RETURN_COLUMN): Change all uses to
__LIBGCC_DWARF_ALT_FRAME_RETURN_COLUMN__.
* config/nios2/linux-unwind.h (STACK_POINTER_REGNUM): Change use
to __LIBGCC_STACK_POINTER_REGNUM__.
* config/pa/hpux-unwind.h (DWARF_ALT_FRAME_RETURN_COLUMN): Change
all uses to __LIBGCC_DWARF_ALT_FRAME_RETURN_COLUMN__.
* config/pa/linux-unwind.h (DWARF_ALT_FRAME_RETURN_COLUMN): Change
all uses to __LIBGCC_DWARF_ALT_FRAME_RETURN_COLUMN__.
* config/rs6000/aix-unwind.h (DWARF_ALT_FRAME_RETURN_COLUMN):
Change all uses to __LIBGCC_DWARF_ALT_FRAME_RETURN_COLUMN__.
(STACK_POINTER_REGNUM): Change all uses to
__LIBGCC_STACK_POINTER_REGNUM__.
* config/rs6000/darwin-fallback.c (STACK_POINTER_REGNUM): Change
use to __LIBGCC_STACK_POINTER_REGNUM__.
* config/rs6000/linux-unwind.h (STACK_POINTER_REGNUM): Change all
uses to __LIBGCC_STACK_POINTER_REGNUM__.
* config/sparc/linux-unwind.h (DWARF_FRAME_REGISTERS): Change use
to __LIBGCC_DWARF_FRAME_REGISTERS__.
* config/sparc/sol2-unwind.h (DWARF_FRAME_REGISTERS): Change use
to __LIBGCC_DWARF_FRAME_REGISTERS__.
* config/tilepro/linux-unwind.h (STACK_POINTER_REGNUM): Change use
to __LIBGCC_STACK_POINTER_REGNUM__.
* config/xtensa/unwind-dw2-xtensa.h (DWARF_FRAME_REGISTERS):
Remove conditional definition.
* crtstuff.c (TEXT_SECTION_ASM_OP): Change all uses to
__LIBGCC_TEXT_SECTION_ASM_OP__.
(EH_FRAME_SECTION_NAME): Change all uses to
__LIBGCC_EH_FRAME_SECTION_NAME__.
(EH_TABLES_CAN_BE_READ_ONLY): Change all uses to
__LIBGCC_EH_TABLES_CAN_BE_READ_ONLY__.
(CTORS_SECTION_ASM_OP): Change all uses to
__LIBGCC_CTORS_SECTION_ASM_OP__.
(DTORS_SECTION_ASM_OP): Change all uses to
__LIBGCC_DTORS_SECTION_ASM_OP__.
(JCR_SECTION_NAME): Change all uses to
__LIBGCC_JCR_SECTION_NAME__.
(INIT_SECTION_ASM_OP): Change all uses to
__LIBGCC_INIT_SECTION_ASM_OP__.
(INIT_ARRAY_SECTION_ASM_OP): Change all uses to
__LIBGCC_INIT_ARRAY_SECTION_ASM_OP__.
* generic-morestack.c (STACK_GROWS_DOWNWARD): Change all uses to
__LIBGCC_STACK_GROWS_DOWNWARD__.
* libgcc2.c (INIT_SECTION_ASM_OP): Change all uses to
__LIBGCC_INIT_SECTION_ASM_OP__.
(INIT_ARRAY_SECTION_ASM_OP): Change all uses to
__LIBGCC_INIT_ARRAY_SECTION_ASM_OP__.
(EH_FRAME_SECTION_NAME): Change all uses to
__LIBGCC_EH_FRAME_SECTION_NAME__.
* libgcov-profiler.c (VTABLE_USES_DESCRIPTORS): Remove conditional
definitions. Change all uses to
__LIBGCC_VTABLE_USES_DESCRIPTORS__.
* unwind-dw2.c (STACK_GROWS_DOWNWARD): Change all uses to
__LIBGCC_STACK_GROWS_DOWNWARD__.
(DWARF_FRAME_REGISTERS): Change all uses to
__LIBGCC_DWARF_FRAME_REGISTERS__.
(EH_RETURN_STACKADJ_RTX): Change all uses to
__LIBGCC_EH_RETURN_STACKADJ_RTX__.
* unwind-dw2.h (DWARF_FRAME_REGISTERS): Remove conditional
definition. Change use to __LIBGCC_DWARF_FRAME_REGISTERS__.
* unwind-sjlj.c (DONT_USE_BUILTIN_SETJMP): Change all uses to
__LIBGCC_DONT_USE_BUILTIN_SETJMP__.
(JMP_BUF_SIZE): Change use to __LIBGCC_JMP_BUF_SIZE__.
From-SVN: r214954
Jakub Jelinek
Patrick McGehearty
Stefan Kanthak
Jeff Law
Jakub Jelinek
Martin Sebor
H.J. Lu
Uros Bizjak
Bernd Edlinger
Uros Bizjak
James Greenhalgh
Joseph Myers
Trevor Saunders
Eric Botcazou
Richard Sandiford
Kugan Vivekanandarajah
Matthias Klose
Rainer Orth