This supersedes the fix for the old algorithm in rev.1.8 of k_cosf.c.
I want this change mainly because it is an optimization. It helps
make software cos[f](x) and sin[f](x) faster than the i387 hardware
versions for small x. It is also a simplification, and reduces the
maximum relative error for cosf() and sinf() on machines like amd64
from about 0.87 ulps to about 0.80 ulps. It was validated for cosf()
and sinf() by exhaustive testing. Exhaustive testing is not possible
for cos() and sin(), but ucbtest reports a similar reduction for the
worst case found by non-exhaustive testing. ucbtest's non-exhaustive
testing seems to be good enough to find problems in algorithms but not
maximum relative errors when there are spikes. E.g., short runs of
it find only 3 ulp error where the i387 hardware cos() has an error
of about 2**40 ulps near pi/2.
to floats (mainly i386's). All errors of more than 1 ulp for float
precision trig functions were supposed to have been fixed; however,
compiling with gcc -O2 uncovered 18250 more such errors for cosf(),
with a maximum error of 1.409 ulps.
Use essentially the same fix as in rev.1.8 of k_rem_pio2f.c (access a
non-volatile variable as a volatile). Here the -O1 case apparently
worked because the variable is in a 2-element array and it takes -O2
to mess up such a variable by putting it in a register.
The maximum error for cosf() on i386 with gcc -O2 is now 0.5467 (it
is still 0.5650 with gcc -O1). This shows that -O2 still causes some
extra precision, but the extra precision is now good.
Extra precision is harmful mainly for implementing extra precision in
software. We want to represent x+y as w+r where both "+" operations
are in infinite precision and r is tiny compared with w. There is a
standard algorithm for this (Knuth (1981) 4.2.2 Theorem C), and fdlibm
uses this routinely, but the algorithm requires w and r to have the
same precision as x and y. w is just x+y (calculated in the same
finite precision as x and y), and r is a tiny correction term. The
i386 gcc bugs tend to give extra precision in w, and then using this
extra precision in the calculation of r results in the correction
mostly staying in w and being missing from r. There still tends to
be no problem if the result is a simple expression involving w and r
-- modulo spills, w keeps its extra precision and r remains the right
correction for this wrong w. However, here we want to pass w and r
to extern functions. Extra precision is not retained in function args,
so w gets fixed up, but the change to the tiny r is tinier, so r almost
remains as a wrong correction for the right w.
{cos_sin}[f](x) so that x doesn't need to be reclassified in the
"kernel" functions to determine if it is tiny (it still needs to be
reclassified in the cosine case for other reasons that will go away).
This optimization is quite large for exponentially distributed x, since
x is tiny for almost half of the domain, but it is a pessimization for
uniformally distributed x since it takes a little time for all cases
but rarely applies. Arg reduction on exponentially distributed x
rarely gives a tiny x unless the reduction is null, so it is best to
only do the optimization if the initial x is tiny, which is what this
commit arranges. The imediate result is an average optimization of
1.4% relative to the previous version in a case that doesn't favour
the optimization (double cos(x) on all float x) and a large
pessimization for the relatively unimportant cases of lgamma[f][_r](x)
on tiny, negative, exponentially distributed x. The optimization should
be recovered for lgamma*() as part of fixing lgamma*()'s low-quality
arg reduction.
Fixed various wrong constants for the cutoff for "tiny". For cosine,
the cutoff is when x**2/2! == {FLT or DBL}_EPSILON/2. We round down
to an integral power of 2 (and for cos() reduce the power by another
1) because the exact cutoff doesn't matter and would take more work
to determine. For sine, the exact cutoff is larger due to the ration
of terms being x**2/3! instead of x**2/2!, but we use the same cutoff
as for cosine. We now use a cutoff of 2**-27 for double precision and
2**-12 for single precision. 2**-27 was used in all cases but was
misspelled 2**27 in comments. Wrong and sloppy cutoffs just cause
missed optimizations (provided the rounding mode is to nearest --
other modes just aren't supported).
broken assignment to floats (e.g., i386 with gcc -O, but not amd64 or
ia64; i386 with gcc -O0 worked accidentally).
Use an unnamed volatile temporary variable to trick gcc -O into clipping
extra precision on assignment. It's surprising that only 1 place needed
to be changed.
For tanf() on i386 with gcc -O, the bug caused errors > 1 ulp with a
density of 2.3% for args larger in magnitude than 128*pi/2, with a
maximum error of 1.624 ulps.
After this fix, exhaustive testing shows that range reduction for
floats works as intended assuming that it is in within a factor of
about 2^16 of working as intended for doubles. It provides >= 8
extra bits of precision for all ranges. On i386:
range max error in double/single ulps extra precision
----- ------------------------------- ---------------
0 to 3*pi/4 0x000d3132 / 0.0016 9+ bits
3*pi/4 to 128*pi/2 0x00160445 / 0.0027 8+
128*pi/2 to +Inf 0x00000030 / 0.00000009 23+
128*pi/2 up, -O0 before fix 0x00000030 / 0.00000009 23+
128*pi/2 up, -O1 before fix 0x10000000 / 0.5 1
The 23+ bits of extra precision for large multiples corresponds to almost
perfect reduction to a pair of floats (24 extra would be perfect).
After this fix, the maximum relative error (relative to the corresponding
fdlibm double precision function) is < 1 ulp for all basic trig functions
on all 2^32 float args on all machines tested:
amd64 ia64 i386-O0 i386-O1
------ ------ ------ ------
cosf: 0.8681 0.8681 0.7927 0.5650
sinf: 0.8733 0.8610 0.7849 0.5651
tanf: 0.9708 0.9329 0.9329 0.7035
of pi/2 (1 line) and expand a comment about related magic (many lines).
The bug was essentially the same as for the +-pi/2 case (a mistranslated
mask), but was smaller so it only significantly affected multiples
starting near +-13*pi/2. At least on amd64, for cosf() on all 2^32
float args, the bug caused 128 errors of >= 1 ulp, with a maximum error
of 1.2393 ulps.
and add a comment about related magic (many lines)).
__kernel_cos[f]() needs a trick to reduce the error to below 1 ulp
when |x| >= 0.3 for the range-reduced x. Modulo other bugs, naive
code that doesn't use the trick would have an error of >= 1 ulp
in about 0.00006% of cases when |x| >= 0.3 for the unreduced x,
with a maximum relative error of about 1.03 ulps. Mistransation
of the trick from the double precision case resulted in errors in
about 0.2% of cases, with a maximum relative error of about 1.3 ulps.
The mistranslation involved not doing implicit masking of the 32-bit
float word corresponding to to implicit masking of the lower 32-bit
double word by clearing it.
sinf() uses __kernel_cosf() for half of all cases so its errors from
this bug are similar. tanf() is not affected.
The error bounds in the above and in my other recent commit messages
are for amd64. Extra precision for floats on i386's accidentally masks
this bug, but only if k_cosf.c is compiled with -O. Although the extra
precision helps here, this is accidental and depends on longstanding
gcc precision bugs (not clipping extra precision on assignment...),
and the gcc bugs are mostly avoided by compiling without -O. I now
develop libm mainly on amd64 systems to simplify error detection and
debugging.
17+17+24 bit pi/2 must only be used when subtraction of the first 2
terms in it from the arg is exact. This happens iff the the arg in
bits is one of the 2**17[-1] values on each side of (float)(pi/2).
Revert to the algorithm in rev.1.7 and only fix its threshold for using
the 3-term pi/2. Use the threshold that maximizes the number of values
for which the 3-term pi/2 is used, subject to not changing the algorithm
for comparing with the threshold. The 3-term pi/2 ends up being used
for about half of its usable range (about 64K values on each side).
a maximum error of 2.905 ulps for cosf(), but the algorithm for cosf()
is good for < 1 ulps and happens to give perfect rounding (< 0.5 ulps)
near +-pi/2 except for the bug. The extra relative errors for tanf()
were similar (slightly larger). The bug didn't affect sinf() since
sinf'(+-pi/2) is 0.
For range reduction in ~[-3pi/4, -pi/4] and ~[pi/4, 3pi/4] we must
subtract +-pi/2 and the only complication is that this must be done
in extra precision. We have handy 17+24-bit and 17+17+24-bit
approximations to pi/2. If we always used the former then we would
lose up to 24 bits of accuracy due to cancelation of leading bits, but
we need to keep at least 24 bits plus a guard digit or 2, and should
keep as many guard bits as efficiency permits. So we used the
less-precise pi/2 not very near +-pi/2 and switched to using the
more-precise pi/2 very near +-pi/2. However, we got the threshold for
the switch wrong by allowing 19 bits to cancel, so we ended up with
only 21 or 22 bits of accuracy in some cases, which is even worse than
naively subtracting pi/2 would have done.
Exhaustive checking shows that allowing only 17 bits to cancel (min.
accuracy ~24 bits) is sufficient to reduce the maximum error for cosf()
near +-pi/2 to 0.726 ulps, but allowing only 6 bits to cancel (min.
accuracy ~35-bits) happens to give perfect rounding for cosf() at
little extra cost so we prefer that.
We actually (in effect) allow 0 bits to cancel and always use the
17+17+24-bit pi/2 (min. accuracy ~41 bits). This is simpler and
probably always more efficient too. Classifying args to avoid using
this pi/2 when it is not needed takes several extra integer operations
and a branch, but just using it takes only 1 FP operation.
The patch also fixes misspelling of 17 as 24 in many comments.
For the double-precision version, the magic numbers include 33+53 bits
for the less-precise pi/2 and (53-32-1 = 20) bits being allowed to
cancel, so there are ~33-20 = 13 guard bits. This is sufficient except
probably for perfect rounding. The more-precise pi/2 has 33+33+53
bits and we still waste time classifying args to avoid using it.
The bug is apparently from mistranslation of the magic 32 in 53-32-1.
The number of bits allowed to cancel is not critical and we use 32 for
double precision because it allows efficient classification using a
32-bit comparison. For float precision, we must use an explicit mask,
and there are fewer bits so there is less margin for error in their
allocation. The 32 got reduced to 4 but should have been reduced
almost in proportion to the reduction of mantissa bits.
to doubles as bits. fdlibm-1.1 had similar aliasing bugs, but these
were fixed by NetBSD or Cygnus before a modified version of fdlibm was
imported in 1994. TRUNC() is only used by tgamma() and some
implementation-detail functions. The aliasing bugs were detected by
compiling with gcc -O2 but don't seem to have broken tgamma() on i386's
or amd64's. They broke my modified version of tgamma().
Moved the definition of TRUNC() to mathimpl.h so that it can be fixed
in one place, although the general version is even slower than necessary
because it has to operate on pointers to volatiles to handle its arg
sometimes being volatile. Inefficiency of the fdlibm macros slows
down libm generally, and tgamma() is a relatively unimportant part of
libm. The macros act as if on 32-bit words in memory, so they are
hard to optimize to direct actions on 64-bit double registers for
(non-i386) machines where this is possible. The optimization is too
hard for gcc on amd64's, and declaring variables as volatile makes it
impossible.
floating-point arithmetic on i386. Now I'm going to make excuses
for why this code is kinda scary:
- To avoid breaking the ABI with 5.3-RELEASE, we can't change
sizeof(fenv_t). I stuck the saved mxcsr in some discontiguous
reserved bits in the existing structure.
- Attempting to access the mxcsr on older processors results
in an illegal instruction exception, so support for SSE must
be detected at runtime. (The extra baggage is optimized away
if either the application or libm is compiled with -msse{,2}.)
I didn't run tests to ensure that this doesn't SIGILL on older 486's
lacking the cpuid instruction or on other processors lacking SSE.
Results from running the fenv regression test on these processors
would be appreciated. (You'll need to compile the test with
-DNO_STRICT_DFL_ENV.) If you have an 80386, or if your processor
supports SSE but the kernel didn't enable it, then you're probably out
of luck.
Also, I un-inlined some of the functions that grew larger as a result
of this change, moving them from fenv.h to fenv.c.
fedisableexcept(), and fegetexcept(). These two sets of routines
provide the same functionality. I implemented the former as an
undocumented internal interface to make the regression test easier to
write. However, fe(enable|disable|get)except() is already part of
glibc, and I would like to avoid gratuitous differences. The only
major flaw in the glibc API is that there's no good way to report
errors on processors that don't support all the unmasked exceptions.
particularly good reason to do this, except that __strong_reference
does type checking, whereas __weak_reference does not.
On Alpha, the compiler won't accept a 'long double' parameter in
place of a 'double' parameter even thought the two types are
identical.
an invalid exception and return an NaN.
- If a long double has 113 bits of precision, implement fma in terms
of simple long double arithmetic instead of complicated double arithmetic.
- If a long double is the same as a double, alias fma as fmal.
identical to scalbnf, which is now aliased as ldexpf. Note that the
old implementations made the mistake of setting errno and were the
only libm routines to do so.
- Add nexttoward{,f,l} and nextafterl. On all platforms,
nexttowardl is an alias for nextafterl.
- Add fmal.
- Add man pages for new routines: fmal, nextafterl,
nexttoward{,f,l}, scalb{,l}nl.
Note that on platforms where long double is the same as double, we
generally just alias the double versions of the routines, since doing
so avoids extra work on the source code level and redundant code in
the binary. In particular:
ldbl53 ldbl64/113
fmal s_fma.c s_fmal.c
ldexpl s_scalbn.c s_scalbnl.c
nextafterl s_nextafter.c s_nextafterl.c
nexttoward s_nextafter.c s_nexttoward.c
nexttowardf s_nexttowardf.c s_nexttowardf.c
nexttowardl s_nextafter.c s_nextafterl.c
scalbnl s_scalbn.c s_scalbnl.c
sparc64's 128-bit long doubles.
- Define FP_FAST_FMAL for ia64.
- Prototypes for fmal, frexpl, ldexpl, nextafterl, nexttoward{,f,l},
scalblnl, and scalbnl.
- In scalbln and scalblnf, check the bounds of the second argument.
This is probably unnecessary, but strictly speaking, we should
report an error if someone tries to compute scalbln(x, INT_MAX + 1ll).
nexttowardl. These are not needed on machines where long doubles
look like IEEE-754 doubles, so the implementation only supports
the usual long double formats with 15-bit exponents.
Anything bizarre, such as machines where floating-point and integer
data have different endianness, will cause problems. This is the case
with big endian ia64 according to libc/ia64/_fpmath.h. Please contact
me if you managed to get a machine running this way.
that are intended to raise underflow and inexact exceptions.
- On systems where long double is the same as double, nextafter
should be aliased as nexttoward, nexttowardl, and nextafterl.
Symptoms of the problem included assembler warnings and
nondeterministic runtime behavior when a fe*() call that affects the
fpsr is closely followed by a float point op.
The bug (at least, I think it's a bug) is that gcc does not insert a
break between a volatile asm and a dependent instruction if the
volatile asm came from an inlined function. Volatile asms seem to be
fine in other circumstances, even without -mvolatile-asm-stop, so
perhaps the compiler adds the stop bits before inlining takes place.
The problem does not occur at -O0 because inlining is disabled, and it
doesn't happen at -O2 because -fschedule-insns2 knows better.
inputs. The trouble with replacing two floats with a double is that
the latter has 6 extra bits of precision, which actually hurts
accuracy in many cases. All of the constants are optimal when float
arithmetic is used, and would need to be recomputed to do this right.
Noticed by: bde (ucbtest)
results in a performance gain on the order of 10% for amd64 (sledge),
ia64 (pluto1), i386+SSE (Pentium 4), and sparc64 (panther), and a
negligible improvement for i386 without SSE. (The i386 port still
uses the hardware instruction, though.)
manpages. They are not very related, so separating them makes it
easier to add meaningful cross-references and extend some of the
descriptions.
- Move the part of math(3) that discusses IEEE 754 to the ieee(3)
manpage.
- Rearrange the list of functions into categories.
- Remove the ulps column. It was appropriate for only some
of the functions in the list, and correct for even fewer
of them.
- Add some new paragraphs, and remove some old ones about
NaNs that may do more harm than good.
- Document precisions other than double-precision.
flags, so they are not pure. Remove the __pure2 annotation from them.
I believe that the following routines and their float and long double
counterparts are the only ones here that can be __pure2:
copysign is* fabs finite fmax fmin fpclassify ilogb nan signbit
When gcc supports FENV_ACCESS, perhaps there will be a new annotation
that allows the other functions to be considered pure when FENV_ACCESS
is off.
Discussed with: bde
basically support this, subject to gcc's lack of FENV_ACCESS support.
In any case, the previous setting of math_errhandling to 0 is not
allowed by POSIX.
registers as volatile. Instructions that *wrote* to FP state were
already marked volatile, but apparently gcc has license to move
non-volatile asms past volatile asms. This broke amd64's feupdateenv
at -O2 due to a WAR conflict between fnstsw and fldenv there.
- Make some minor rearrangements in the introduction.
- Mention the problem with argument reduction on i386.
- Add recently-implemented functions to the table.
- Un-document the error bounds that only apply to the old 4BSD math
library, and fill in the correct values where I know them. No
attempt has been made to document bounds lower than 1 ulp, although
smaller bounds are usually achievable in round-to-nearest mode.
/lib/{libm,libreadline}
/usr/lib/{libhistory,libopie,libpcap}
in preparation for doing the same thing to RELENG_5. HUGE amounts of
help for determining what to bump provided by kris.
Discussed on: freebsd-current
Approved by: re (not required for commit but something like this should be)
libc. The externally-visible effect of this is to add __isnanl() to
libm, which means that libm.so.2 can once again link against libc.so.4
when LD_BIND_NOW is set. This was broken by the addition of fdiml(),
which calls __isnanl().
- It was added to libc instead of libm. Hopefully no programs rely
on this mistake.
- It didn't work properly on large long doubles because its argument
was converted to type double, resulting in undefined behavior.
- Unlike the builtin relational operators, builtin floating-point
constants were not available until gcc 3.3, so account for this.[1]
- Apparently some versions of the Intel C Compiler fallaciously define
__GNUC__ without actually being compatible with the claimed gcc
version. Account for this, too.[2]
[1] Noticed by: Christian Hiris <4711@chello.at>
[2] Submitted by: Alexander Leidinger <Alexander@Leidinger.net>
isnormal() the hard way, rather than relying on fpclassify(). This is
a lose in the sense that we need a total of 12 functions, but it is
necessary for binary compatibility because we have never bumped libm's
major version number. In particular, isinf(), isnan(), and isnanf()
were BSD libc functions before they were C99 macros, so we can't
reimplement them in terms of fpclassify() without adding a dependency
on libc.so.5. I have tried to arrange things so that programs that
could be compiled in FreeBSD 4.X will generate the same external
references when compiled in 5.X. At the same time, the new macros
should remain C99-compliant.
The isinf() and isnan() functions remain in libc for historical
reasons; however, I have moved the functions that implement the macros
isfinite() and isnormal() to libm where they belong. Moreover,
half a dozen MD versions of isinf() and isnan() have been replaced
with MI versions that work equally well.
Prodded by: kris
builtins are available: HUGE_VAL, HUGE_VALF, HUGE_VALL, INFINITY,
and NAN. These macros now expand to floating-point constant
expressions rather than external references, as required by C99.
Other compilers will retain the historical behavior. Note that
it is not possible say, e.g.
#define HUGE_VAL 1.0e9999
because the above may result in diagnostics at translation time
and spurious exceptions at runtime. Hence the need for compiler
support for these features.
Also use builtins to implement the macros isgreater(),
isgreaterequal(), isless(), islessequal(), islessgreater(),
and isunordered() when such builtins are available.
Although the old macros are correct, the builtin versions
are much faster, and they avoid double-expansion problems.
These trivial implementations are about 25 times slower than
rint{,f}() on x86 due to the FP environment save/restore.
They should eventually be redone in terms of fegetround() and
bit fiddling.
These routines are specified in C99 for the sake of
architectures where an int isn't big enough to represent
the full range of floating-point exponents. However,
even the 128-bit long double format has an exponent smaller
than 15 bits, so for all practical purposes, scalbln() and
scalblnf() are aliases for scalbn() and scalbnf(), respectively.
kicking and screaming into the 1980's. This change converts most of
the markup from man(7) to mdoc(7) format, and I believe it removes or
updates everything that was flat out wrong. However, much work is
still needed to sanitize the markup, improve coverage, and reduce
overlap with other manpages. Some of the sections would better belong
in a philosophy_of_w_kahan.3 manpage, but they are informative and
remain at least as reminders of topics to cover.
Reviewed by: doc@, trhodes@
on all inputs of the form x.75, where x is an even integer and
log2(x) = 21. A similar problem occurred when rounding upward.
The bug involves the following snippet copied from rint():
i>>=1;
if((i0&i)!=0) i0 = (i0&(~i))|((0x100000)>>j0);
The constant 0x100000 should be 0x200000. Apparently this case was
never tested.
It turns out that the bit manipulation is completely superfluous
anyway, so remove it. (It tries to simulate 90% of the rounding
process that the FPU does anyway.) Also, the special case of +-0 is
handled twice (in different ways), so remove the second instance.
Throw in some related simplifications from bde:
- Work around a bug where gcc fails to clip to float precision by
declaring two float variables as volatile. Previously, we
tricked gcc into generating correct code by declaring some
float constants as doubles.
- Remove additional superfluous bit manipulation.
- Minor reorganization.
- Include <sys/types.h> explicitly.
Note that some of the equivalent lines in rint() also appear to be
unnecessary, but I'll defer to the numerical analysts who wrote it,
since I can't test all 2^64 cases.
Discussed with: bde
It does not appear to be possible to cross-build arm from i386 at the
moment, and I have no ARM hardware anyway. Thus, I'm sure there are
bugs. I will gladly fix these when the arm port is more mature.
Reviewed by: standards@
features appear to work, subject to the caveat that you tell gcc you
want standard rather than recklessly fast behavior
(-mieee-with-inexact -mfp-rounding-mode=d).
The non-standard feature of delivering a SIGFPE when an application
raises an unmasked exception does not work, presumably due to a kernel
bug. This isn't so bad given that floating-point exceptions on the
Alpha architecture are not precise, so making them useful in userland
requires a significant amount of wizardry.
Reviewed by: standards@
We approximate pi with more than float precision using pi_hi+pi_lo in
the usual way (pi_hi is actually spelled pi in the source code), and
expect (float)0.5*pi_lo to give the low part of the corresponding
approximation for pi/2. However, the high part for pi/2 (pi_o_2) is
rounded to nearest, which happens to round up, while the high part for
pi was rounded down. Thus pi_o_2+(float)0.5*pi (in infinite precision)
was a very bad approximation for pi/2 -- the low term has the wrong
sign and increases the error drom less than half an ULP to a full ULP.
This fix rounds up instead of down for pi_hi. Consistently rounding
down instead of up should work, and is the method used in e_acosf.c
and e_asinf.c. The reason for the difference is that we sometimes
want to return precisely pi/2 in e_atan2f.c, so it is convenient to
have a correctly rounded (to nearest) value for pi/2 in a variable.
a_acosf.c and e_asinf.c also differ in directly approximating pi/2
instead pi; they multiply by 2.0 instead of dividing by 0.5 to convert
the approximation.
These complications are not directly visible in the double precision
versions because rounding to nearest happens to round down.
and not tanf() because float type can't represent numbers large enough
to trigger the problem. However, there seems to be a precedent that
the float versions of the fdlibm routines should mirror their double
counterparts.
Also update to the FDLIBM 5.3 license.
Obtained from: FDLIBM
Reviewed by: exhaustive comparison
where the exponent is an odd integer and the base is negative).
Obtained from: fdlibm-5.3
Sun finally released a new version of fdlibm just a coupe of weeks
ago. It only fixes 3 bugs (this one, another one in pow() that we
already have (rev.1.9), and one in tan(). I've learned too much about
powf() lately, so this fix was easy to merge. The patch is not verbatim,
because our base version has many differences for portability and I
didn't like global renaming of an unrelated variable to keep it separate
from the sign variable. This patch uses a new variable named sn for
the sign.
[t=p_l+p_h High]. We multiply t by lg2_h, and want the result to be
exact. For the bogus float case of the high-low decomposition trick,
we normally discard the lowest 12 bits of the fraction for the high
part, keeping 12 bits of precision. That was used for t here, but it
doesnt't work because for some reason we only discard the lowest 9
bits in the fraction for lg2_h. Discard another 3 bits of the fraction
for t to compensate.
This bug gave wrong results like:
powf(0.9999999, -2.9999995) = 1.0000002 (should be 1.0000001)
hex values: 3F7FFFFF C03FFFFE 3F800002 3F800001
As explained in the log for the previous commit, the bug is normally
masked by doing float calculations in extra precision on i386's, but
is easily detected by ucbtest on systems that don't have accidental
extra precision.
This completes fixing all the bugs in powf() that were routinely found
by ucbtest.
(1) The bit for the 1.0 part of bp[k] was right shifted by 4. This seems
to have been caused by a typo in converting e_pow.c to e_powf.c.
(2) The lower 12 bits of ax+bp[k] were not discarded, so t_h was actually
plain ax+bp[k]. This seems to have been caused by a logic error in
the conversion.
These bugs gave wrong results like:
powf(-1.1, 101.0) = -15158.703 (should be -15158.707)
hex values: BF8CCCCD 42CA0000 C66CDAD0 C66CDAD4
Fixing (1) gives a result wrong in the opposite direction (hex C66CDAD8),
and fixing (2) gives the correct result.
ucbtest has been reporting this particular wrong result on i386 systems
with unpatched libraries for 9 years. I finally figured out the extent
of the bugs. On i386's they are normally hidden by extra precision.
We use the trick of representing floats as a sum of 2 floats (one much
smaller) to get extra precision in intermediate calculations without
explicitly using more than float precision. This trick is just a
pessimization when extra precision is available naturally (as it always
is when dealing with IEEE single precision, so the float precision part
of the library is mostly misimplemented). (1) and (2) break the trick
in different ways, except on i386's it turns out that the intermediate
calculations are done in enough precision to mask both the bugs and
the limited precision of the float variables (as far as ucbtest can
check).
ucbtest detects the bugs because it forces float precision, but this
is not a normal mode of operation so the bug normally has little effect
on i386's.
On systems that do float arithmetic in float precision, e.g., amd64's,
there is no accidental extra precision and the bugs just give wrong
results.
constants the wrong way on the VAX. Instead, use C99 hexadecimal
floating-point constants, which are guaranteed to be exact on binary
IEEE machines. (The correct hexadecimal values were already provided
in the source, but not used.) Also, convert the constants to
lowercase to work around a gcc bug that wasn't fixed until gcc 3.4.0.
Prompted by: stefanf
namespaces are visible. Previously, math.h failed to hide some C99-,
XSI-, and BSD-specific symbols in certain compilation environments.
The referenced PR has a nice listing of the appropriate conditions for
making symbols visible in math.h. The only non-stylistic difference
between the patch in the PR and this commit is that I superfluously
test for __BSD_VISIBLE in a few places to be more explicit about which
symbols have historically been part of the FreeBSD environment.
PR: 65939
Submitted by: Stefan Farfeleder <stefan@fafoe.narf.at>
MATH_ERREXCEPTION and math_errhandling, so that C99 applications at
least have the possibility of determining that errno is not set for
math functions. Set math_errhandling to the non-standard-conforming
value of 0 for now to indicate that we don't support either method
of reporting errors. We intentionally don't support MATH_ERRNO
because errno is a mistake, and we are missing support for
MATH_ERREXCEPTION (<fenv.h>, compiler support for <fenv.h>, and
actually setting the exception flags correctly).
that are only in libc.so.5. This broke some 4.X applications linked
to libm and run under 5.X.
Background:
In C99, isinf() and isnan() cannot be implemented as regular
functions. We use macros that call libc functions in 5.X, but for
libm-internal use, we need to use the old versions until the next
time libm's major version number is bumped.
Submitted by: bde
Reported by: imp, kris
documented naming scheme (unfortunately the documentation isn't in the
tree as far as I can tell); no repocopy is required as there is no
history to preserve.
- replace simple and almost-correct implementation with slightly hackish
but definitely correct implementation (tested on i386, alpha, sparc64)
which requires pulling in fpmath.h and the MD _fpmath.h from libc.
- try not to make a mess of the Makefile in the process.
- enterprising minds are encouraged to implement more C99 long double
functions.
binaries in /bin and /sbin installed in /lib. Only the versioned files
reside in /lib, the .so symlink continues to live /usr/lib so the
toolchain doesn't need to be modified.
do not also provide a __generic_XXX version as well. This is how we
used to runtime select the generic vs i387 versions on the i386 platform.
This saves a pile of #defines in the src/math_private.h file to undo the
__generic_XXX renames in some of the *.c files.
fp emulator, stop doing the runtime selection of hardware or emulated
floating point operations on i386. Note that I have not suppressed the
duplicate compiles yet.
While here, fix the alpha. It has provided specific copysign/copysignf
functions since the beginning of time, but they have never been used.
in math.h; the consensus here was that __BSD_VISIBLE was correct instead.
- gamma_r, lgamma_r, gammaf_r, and lgammaf_r had no documentation in the
lgamma(3) manpage.
Reviewed by: standards@
Submitted by: Ben Mesander
isnormal(). The current isinf() and isnan() are perserved for
binary compatibility with 5.0, but new programs will use the macros.
o Implement C99 comparison macros isgreater(), isgreaterequal(),
isless(), islessequal(), islessgreater(), isunordered().
Submitted by: David Schultz <dschultz@uclink.Berkeley.EDU>
o Add a MD header private to libc called _fpmath.h; this header
contains bitfield layouts of MD floating-point types.
o Add a MI header private to libc called fpmath.h; this header
contains bitfield layouts of MI floating-point types.
o Add private libc variables to lib/libc/$arch/gen/infinity.c for
storing NaN values.
o Add __double_t and __float_t to <machine/_types.h>, and provide
double_t and float_t typedefs in <math.h>.
o Add some C99 manifest constants (FP_ILOGB0, FP_ILOGBNAN, HUGE_VALF,
HUGE_VALL, INFINITY, NAN, and return values for fpclassify()) to
<math.h> and others (FLT_EVAL_METHOD, DECIMAL_DIG) to <float.h> via
<machine/float.h>.
o Add C99 macro fpclassify() which calls __fpclassify{d,f,l}() based
on the size of its argument. __fpclassifyl() is never called on
alpha because (sizeof(long double) == sizeof(double)), which is good
since __fpclassifyl() can't deal with such a small `long double'.
This was developed by David Schultz and myself with input from bde and
fenner.
PR: 23103
Submitted by: David Schultz <dschultz@uclink.Berkeley.EDU>
(significant portions)
Reviewed by: bde, fenner (earlier versions)
HUGE_VAL is not properly aligned on some architectures. The previous
fix now works because the two versions of 'math.h' (include/math.h
and lib/msun/src/math.h) have since been merged into one.
PR: bin/43544
