This fixes a loss of precision that occurs when the first input is
very close to 1, so that its logarithm is very small.
Formerly, during the initial low-precision calculation to estimate the
result weight, the logarithm was computed to a local rscale that was
capped to NUMERIC_MAX_DISPLAY_SCALE (1000). However, the base may be
as close as 1e-16383 to 1, hence its logarithm may be as small as
1e-16383, and so the local rscale needs to be allowed to exceed 16383,
otherwise all precision is lost, leading to a poor choice of rscale
for the full-precision calculation.
Fix this by removing the cap on the local rscale during the initial
low-precision calculation, as we already do in the full-precision
calculation. This doesn't change the fact that the initial calculation
is a low-precision approximation, computing the logarithm to around 8
significant digits, which is very fast, especially when the base is
very close to 1.
Patch by me, reviewed by Alvaro Herrera.
Discussion: https://postgr.es/m/CAEZATCV-Ceu%2BHpRMf416yUe4KKFv%3DtdgXQAe5-7S9tD%3D5E-T1g%40mail.gmail.com
Formerly, the numeric code tested whether an integer value of a larger
type would fit in a smaller type by casting it to the smaller type and
then testing if the reverse conversion produced the original value.
That's perfectly fine, except that it caused a test failure on
buildfarm animal castoroides, most likely due to a compiler bug.
Instead, do these tests by comparing against PG_INT16/32_MIN/MAX. That
matches existing code in other places, such as int84(), which is more
widely tested, and so is less likely to go wrong.
While at it, add regression tests covering the numeric-to-int8/4/2
conversions, and adjust the recently added tests to the style of
434ddfb79a (on the v11 branch) to make failures easier to diagnose.
Per buildfarm via Tom Lane, reviewed by Tom Lane.
Discussion: https://postgr.es/m/2394813.1628179479%40sss.pgh.pa.us
This fixes a long-standing bug when using to_char() to format a
numeric value in scientific notation -- if the value's exponent is
less than -NUMERIC_MAX_DISPLAY_SCALE-1 (-1001), it produced a
division-by-zero error.
The reason for this error was that get_str_from_var_sci() divides its
input by 10^exp, which it produced using power_var_int(). However, the
underflow test in power_var_int() causes it to return zero if the
result scale is too small. That's not a problem for power_var_int()'s
only other caller, power_var(), since that limits the rscale to 1000,
but in get_str_from_var_sci() the exponent can be much smaller,
requiring a much larger rscale. Fix by introducing a new function to
compute 10^exp directly, with no rscale limit. This also allows 10^exp
to be computed more efficiently, without any numeric multiplication,
division or rounding.
Discussion: https://postgr.es/m/CAEZATCWhojfH4whaqgUKBe8D5jNHB8ytzemL-PnRx+KCTyMXmg@mail.gmail.com
This fixes a couple of related problems that arise when raising
numbers to very large powers.
Firstly, when raising a negative number to a very large integer power,
the result should be well-defined, but the previous code would only
cope if the exponent was small enough to go through power_var_int().
Otherwise it would throw an internal error, attempting to take the
logarithm of a negative number. Fix this by adding suitable handling
to the general case in power_var() to cope with negative bases,
checking for integer powers there.
Next, when raising a (positive or negative) number whose absolute
value is slightly less than 1 to a very large power, the result should
approach zero as the power is increased. However, in some cases, for
sufficiently large powers, this would lose all precision and return 1
instead of 0. This was due to the way that the local_rscale was being
calculated for the final full-precision calculation:
local_rscale = rscale + (int) val - ln_dweight + 8
The first two terms on the right hand side are meant to give the
number of significant digits required in the result ("val" being the
estimated result weight). However, this failed to account for the fact
that rscale is clipped to a maximum of NUMERIC_MAX_DISPLAY_SCALE
(1000), and the result weight might be less then -1000, causing their
sum to be negative, leading to a loss of precision. Fix this by
forcing the number of significant digits calculated to be nonnegative.
It's OK for it to be zero (when the result weight is less than -1000),
since the local_rscale value then includes a few extra digits to
ensure an accurate result.
Finally, add additional underflow checks to exp_var() and power_var(),
so that they consistently return zero for cases like this where the
result is indistinguishable from zero. Some paths through this code
already returned zero in such cases, but others were throwing overflow
errors.
Dean Rasheed, reviewed by Yugo Nagata.
Discussion: http://postgr.es/m/CAEZATCW6Dvq7+3wN3tt5jLj-FyOcUgT5xNoOqce5=6Su0bCR0w@mail.gmail.com
This fixes an overflow error when using the numeric * operator if the
result has more than 16383 digits after the decimal point by rounding
the result. Overflow errors should only occur if the result has too
many digits *before* the decimal point.
Discussion: https://postgr.es/m/CAEZATCUmeFWCrq2dNzZpRj5+6LfN85jYiDoqm+ucSXhb9U2TbA@mail.gmail.com
In power_var_int(), the computation of the number of significant
digits to use in the computation used log(Abs(exp)), which isn't safe
because Abs(exp) returns INT_MIN when exp is INT_MIN. Use fabs()
instead of Abs(), so that the exponent is cast to a double before the
absolute value is taken.
Back-patch to 9.6, where this was introduced (by 7d9a4737c2).
Discussion: https://postgr.es/m/CAEZATCVd6pMkz=BrZEgBKyqqJrt2xghr=fNc8+Z=5xC6cgWrWA@mail.gmail.com
float8_numeric() and float4_numeric() failed to consider the possibility
that the input is an IEEE infinity. The results depended on the
platform-specific behavior of sprintf(): on most platforms you'd get
something like
ERROR: invalid input syntax for type numeric: "inf"
but at least on Windows it's possible for the conversion to succeed and
deliver a finite value (typically 1), due to a nonstandard output format
from sprintf and lack of syntax error checking in these functions.
Since our numeric type lacks the concept of infinity, a suitable conversion
is impossible; the best thing to do is throw an explicit error before
letting sprintf do its thing.
While at it, let's use snprintf not sprintf. Overrunning the buffer
should be impossible if sprintf does what it's supposed to, but this
is cheap insurance against a stack smash if it doesn't.
Problem reported by Taiki Kondo. Patch by me based on fix suggestion
from KaiGai Kohei. Back-patch to all supported branches.
Discussion: https://postgr.es/m/12A9442FBAE80D4E8953883E0B84E088C8C7A2@BPXM01GP.gisp.nec.co.jp
This introduces a numeric sum accumulator, which performs better than
repeatedly calling add_var(). The performance comes from using wider digits
and delaying carry propagation, tallying positive and negative values
separately, and avoiding a round of palloc/pfree on every value. This
speeds up SUM(), as well as other standard aggregates like AVG() and
STDDEV() that also calculate a sum internally.
Reviewed-by: Andrey Borodin
Discussion: <c0545351-a467-5b76-6d46-4840d1ea8aa4@iki.fi>
Set the "rscales" for intermediate-result calculations to ensure that
suitable numbers of significant digits are maintained throughout. The
previous coding hadn't thought this through in any detail, and as a result
could deliver results with many inaccurate digits, or in the worst cases
even fail with divide-by-zero errors as a result of losing all nonzero
digits of intermediate results.
In exp_var(), get rid entirely of the logic that separated the calculation
into integer and fractional parts: that was neither accurate nor
particularly fast. The existing range-reduction method of dividing by 2^n
can be applied across the full input range instead of only 0..1, as long as
we are careful to set an appropriate rscale for each step.
Also fix the logic in mul_var() for shortening the calculation when the
caller asks for fewer output digits than an exact calculation would
require. This bug doesn't affect simple multiplications since that code
path asks for an exact result, but it does contribute to accuracy issues
in the transcendental math functions.
In passing, improve performance of mul_var() a bit by forcing the shorter
input to be on the left, thus reducing the number of iterations of the
outer loop and probably also reducing the number of carry-propagation
steps needed.
This is arguably a bug fix, but in view of the lack of field complaints,
it does not seem worth the risk of back-patching.
Dean Rasheed
mul_var() postpones propagating carries until it risks overflow in its
internal digit array. However, the logic failed to account for the
possibility of overflow in the carry propagation step, allowing wrong
results to be generated in corner cases. We must slightly reduce the
when-to-propagate-carries threshold to avoid that.
Discovered and fixed by Dean Rasheed, with small adjustments by me.
This has been wrong since commit d72f6c75038d8d37e64a29a04b911f728044d83b,
so back-patch to all supported branches.
Revert "to_char(float4/8): zero pad to specified length". There are
too many platform-specific problems, and the proper rounding is missing.
Also revert companion patch 9d61b9953c1489cbb458ca70013cf5fca1bb7710.
Commit cc0d90b73b2e6dd2f301d46818a7265742c41a14 also avoids printing
junk digits, which are digits that are beyond the precision of the
underlying type.
Previously, zero padding was limited to the internal length, rather than
the specified length. This allows it to match to_char(int/numeric), which
always padded to the specified length.
Regression tests added.
BACKWARD INCOMPATIBILITY
In generate_series_step_numeric(), the variables "start_num"
and "stop_num" may be potentially freed until the next call.
So they should be put in the location which can survive across calls.
But previously they were not, and which could cause incorrect
behavior of generate_series(numeric, numeric). This commit fixes
this problem by copying them on multi_call_memory_ctx.
Andrew Gierth
The code for raising a NUMERIC value to an integer power wasn't very
careful about large powers. It got an outright wrong answer for an
exponent of INT_MIN, due to failure to consider overflow of the Abs(exp)
operation; which is fixable by using an unsigned rather than signed
exponent value after that point. Also, even though the number of
iterations of the power-computation loop is pretty limited, it's easy for
the repeated squarings to result in ridiculously enormous intermediate
values, which can take unreasonable amounts of time/memory to process,
or even overflow the internal "weight" field and so produce a wrong answer.
We can forestall misbehaviors of that sort by bailing out as soon as the
weight value exceeds what will fit in int16, since then the final answer
must overflow (if exp > 0) or underflow (if exp < 0) the packed numeric
format.
Per off-list report from Pavel Stehule. Back-patch to all supported
branches.
Trailing-zero stripping applied by the FM specifier could strip zeroes
to the left of the decimal point, for a format with no digit positions
after the decimal point (such as "FM999.").
Reported and diagnosed by Marti Raudsepp, though I didn't use his patch.
algorithm. This is a good deal slower than our old roundoff-error-prone
code for long inputs, so we keep the old code for use in the transcendental
functions, where everything is approximate anyway. Also create a
user-accessible function div(numeric, numeric) to provide access to the
exact result of trunc(x/y) --- since the regular numeric / operator will
round off its result, simply computing that expression in SQL doesn't
reliably give the desired answer. This fixes bug #3387 and various related
corner cases, and improves the usefulness of PG for high-precision integer
arithmetic.
The implementation is somewhat ugly logic-wise, but I don't see an
easy way to make it more concise.
When writing this, I noticed that my previous implementation of
width_bucket() doesn't handle NaN correctly:
postgres=# select width_bucket('NaN', 1, 5, 5);
width_bucket
--------------
6
(1 row)
AFAICS SQL:2003 does not define a NaN value, so it doesn't address how
width_bucket() should behave here. The patch changes width_bucket() so
that ereport(ERROR) is raised if NaN is specified for the operand or the
lower or upper bounds to width_bucket(). For float8, NaN is disallowed
for any of the floating-point inputs, and +/- infinity is disallowed
for the histogram bounds (but allowed for the operand).
Update docs and regression tests, bump the catversion.
literally.
Add GUC variables:
"escape_string_warning" - warn about backslashes in non-E strings
"escape_string_syntax" - supports E'' syntax?
"standard_compliant_strings" - treats backslashes literally in ''
Update code to use E'' when escapes are used.
a variant of the function for the 'numeric' datatype; it would be possible
to add additional variants for other datatypes, but I haven't done so yet.
This commit includes regression tests and minimal documentation; if we
want developers to actually use this function in applications, we'll
probably need to document what it does more fully.
Regression tests and documentation have both been updated.
SQL2003 requires that both ceiling() and ceil() be present, so I have
documented both spellings. SQL2003 doesn't mention pow() as far as I
can see, so I decided to replace pow() with power() in the documentation:
there is little reason to encourage the continued usage of a function
that isn't compliant with the standard, given a standard-compliant
alternative.
RELEASE NOTES: should state that pow() is considered deprecated
(although I don't see the need to ever remove it.)
any amount of leading or trailing whitespace (where "whitespace"
is defined by isspace()). This is for SQL conformance, as well
as consistency with other numeric types (e.g. oid, numeric).
Also refactor pg_atoi() to avoid looking at errno where not
necessary, and add a bunch of regression tests for the input
to these types.
Implement TIME WITH TIME ZONE type (timetz internal type).
Remap length() for character strings to CHAR_LENGTH() for SQL92
and to remove the ambiguity with geometric length() functions.
Keep length() for character strings for backward compatibility.
Shrink stored views by removing internal column name list from visible rte.
Implement min(), max() for time and timetz data types.
Implement conversion of TIME to INTERVAL.
Implement abs(), mod(), fac() for the int8 data type.
Rename some math functions to generic names:
round(), sqrt(), cbrt(), pow(), etc.
Rename NUMERIC power() function to pow().
Fix int2 factorial to calculate result in int4.
Enhance the Oracle compatibility function translate() to work with string
arguments (from Edwin Ramirez).
Modify pg_proc system table to remove OID holes.
the to_char() source code is large, here are regression tests for
numeric/timestamp/int8 part. It is probably enough test for formatting
code in the formatting.c module. The others (float4/float8/int4) types
share this formatting code and eventual bugs for these types aren't
few probable.
Patch fix timestamp_to_char() for infinity/invalid timestamp too.
Karel
1. Using 100 digits after decimal point on the default
make runtest.
2. Using 1000 digits after decimal point in a new target
make bigtest.
At the end of 'make runtest', a hint about the new bigtest is
printed.
Jan
