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Change floating-point output format for improved performance.

Browse Source 
Previously, floating-point output was done by rounding to a specific
decimal precision; by default, to 6 or 15 decimal digits (losing
information) or as requested using extra_float_digits. Drivers that
wanted exact float values, and applications like pg_dump that must
preserve values exactly, set extra_float_digits=3 (or sometimes 2 for
historical reasons, though this isn't enough for float4).

Unfortunately, decimal rounded output is slow enough to become a
noticable bottleneck when dealing with large result sets or COPY of
large tables when many floating-point values are involved.

Floating-point output can be done much faster when the output is not
rounded to a specific decimal length, but rather is chosen as the
shortest decimal representation that is closer to the original float
value than to any other value representable in the same precision. The
recently published Ryu algorithm by Ulf Adams is both relatively
simple and remarkably fast.

Accordingly, change float4out/float8out to output shortest decimal
representations if extra_float_digits is greater than 0, and make that
the new default. Applications that need rounded output can set
extra_float_digits back to 0 or below, and take the resulting
performance hit.

We make one concession to portability for systems with buggy
floating-point input: we do not output decimal values that fall
exactly halfway between adjacent representable binary values (which
would rely on the reader doing round-to-nearest-even correctly). This
is known to be a problem at least for VS2013 on Windows.

Our version of the Ryu code originates from
https://github.com/ulfjack/ryu/ at commit c9c3fb1979, but with the
following (significant) modifications:

 - Output format is changed to use fixed-point notation for small
   exponents, as printf would, and also to use lowercase 'e', a
   minimum of 2 exponent digits, and a mandatory sign on the exponent,
   to keep the formatting as close as possible to previous output.

 - The output of exact midpoint values is disabled as noted above.

 - The integer fast-path code is changed somewhat (since we have
   fixed-point output and the upstream did not).

 - Our project style has been largely applied to the code with the
   exception of C99 declaration-after-statement, which has been
   retained as an exception to our present policy.

 - Most of upstream's debugging and conditionals are removed, and we
   use our own configure tests to determine things like uint128
   availability.

Changing the float output format obviously affects a number of
regression tests. This patch uses an explicit setting of
extra_float_digits=0 for test output that is not expected to be
exactly reproducible (e.g. due to numerical instability or differing
algorithms for transcendental functions).

Conversions from floats to numeric are unchanged by this patch. These
may appear in index expressions and it is not yet clear whether any
change should be made, so that can be left for another day.

This patch assumes that the only supported floating point format is
now IEEE format, and the documentation is updated to reflect that.

Code by me, adapting the work of Ulf Adams and other contributors.

References:
https://dl.acm.org/citation.cfm?id=3192369

Reviewed-by: Tom Lane, Andres Freund, Donald Dong
Discussion: https://postgr.es/m/87r2el1bx6.fsf@news-spur.riddles.org.uk
pull/38/head
Andrew Gierth 6 years ago
parent f397e08599
commit 02ddd49932
50 changed files with 5466 additions and 368 deletions
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
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  1. 10
      configure
  2. 9
      configure.in
  3. 12
      contrib/btree_gist/expected/float4.out
  4. 12
      contrib/btree_gist/expected/float8.out
  5. 24
      contrib/cube/expected/cube.out
  6. 12
      contrib/cube/expected/cube_sci.out
  7. 8
      contrib/cube/sql/cube.sql
  8. 2
      contrib/pg_trgm/expected/pg_strict_word_trgm.out
  9. 2
      contrib/pg_trgm/expected/pg_trgm.out
  10. 2
      contrib/pg_trgm/expected/pg_word_trgm.out
  11. 3
      contrib/pg_trgm/sql/pg_strict_word_trgm.sql
  12. 3
      contrib/pg_trgm/sql/pg_trgm.sql
  13. 3
      contrib/pg_trgm/sql/pg_word_trgm.sql
  14. 6
      contrib/seg/expected/seg.out
  15. 37
      doc/src/sgml/config.sgml
  16. 89
      doc/src/sgml/datatype.sgml
  17. 1
      src/Makefile.global.in
  18. 24
      src/backend/utils/adt/float.c
  19. 7
      src/backend/utils/misc/guc.c
  20. 3
      src/backend/utils/misc/postgresql.conf.sample
  21. 15
      src/common/Makefile
  22. 1076
      src/common/d2s.c
  23. 358
      src/common/d2s_full_table.h
  24. 202
      src/common/d2s_intrinsics.h
  25. 21
      src/common/digit_table.h
  26. 804
      src/common/f2s.c
  27. 133
      src/common/ryu_common.h
  28. 63
      src/include/common/shortest_dec.h
  29. 2
      src/test/regress/expected/aggregates.out
  30. 2
      src/test/regress/expected/circle.out
  31. 574
      src/test/regress/expected/float4-misrounded-input.out
  32. 574
      src/test/regress/expected/float4.out
  33. 447
      src/test/regress/expected/float8-small-is-zero.out
  34. 447
      src/test/regress/expected/float8.out
  35. 24
      src/test/regress/expected/int8.out
  36. 4
      src/test/regress/expected/jsonb.out
  37. 4
      src/test/regress/expected/line.out
  38. 2
      src/test/regress/expected/point.out
  39. 8
      src/test/regress/expected/rules.out
  40. 4
      src/test/regress/expected/tsearch.out
  41. 46
      src/test/regress/expected/tstypes.out
  42. 2
      src/test/regress/expected/updatable_views.out
  43. 10
      src/test/regress/expected/window.out
  44. 3
      src/test/regress/sql/aggregates.sql
  45. 3
      src/test/regress/sql/circle.sql
  46. 219
      src/test/regress/sql/float4.sql
  47. 210
      src/test/regress/sql/float8.sql
  48. 3
      src/test/regress/sql/point.sql
  49. 3
      src/test/regress/sql/updatable_views.sql
  50. 2
      src/tools/msvc/Mkvcbuild.pm

10
configure vendored
Unescape View File

@ -732,6 +732,7 @@ CPP
BITCODE_CXXFLAGS
BITCODE_CFLAGS
CFLAGS_VECTOR
PERMIT_DECLARATION_AFTER_STATEMENT
LLVM_BINPATH
LLVM_CXXFLAGS
LLVM_CFLAGS
@ -5261,6 +5262,7 @@ if test "$GCC" = yes -a "$ICC" = no; then
CFLAGS="-Wall -Wmissing-prototypes -Wpointer-arith"
CXXFLAGS="-Wall -Wpointer-arith"
# These work in some but not all gcc versions
save_CFLAGS=$CFLAGS
{ $as_echo "$as_me:${as_lineno-$LINENO}: checking whether ${CC} supports -Wdeclaration-after-statement, for CFLAGS" >&5
$as_echo_n "checking whether ${CC} supports -Wdeclaration-after-statement, for CFLAGS... " >&6; }
@ -5301,7 +5303,13 @@ if test x"$pgac_cv_prog_CC_cflags__Wdeclaration_after_statement" = x"yes"; then
fi
# -Wdeclaration-after-statement isn't applicable for C++
# -Wdeclaration-after-statement isn't applicable for C++. Specific C files
# disable it, so AC_SUBST the negative form.
PERMIT_DECLARATION_AFTER_STATEMENT=
if test x"save_$CFLAGS" != x"$CFLAGS"; then
PERMIT_DECLARATION_AFTER_STATEMENT=-Wno-declaration-after-statement
fi
# Really don't want VLAs to be used in our dialect of C
{ $as_echo "$as_me:${as_lineno-$LINENO}: checking whether ${CC} supports -Werror=vla, for CFLAGS" >&5

9
configure.in
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@ -476,8 +476,15 @@ if test "$GCC" = yes -a "$ICC" = no; then
CFLAGS="-Wall -Wmissing-prototypes -Wpointer-arith"
CXXFLAGS="-Wall -Wpointer-arith"
# These work in some but not all gcc versions
save_CFLAGS=$CFLAGS
PGAC_PROG_CC_CFLAGS_OPT([-Wdeclaration-after-statement])
# -Wdeclaration-after-statement isn't applicable for C++
# -Wdeclaration-after-statement isn't applicable for C++. Specific C files
# disable it, so AC_SUBST the negative form.
PERMIT_DECLARATION_AFTER_STATEMENT=
if test x"save_$CFLAGS" != x"$CFLAGS"; then
PERMIT_DECLARATION_AFTER_STATEMENT=-Wno-declaration-after-statement
fi
AC_SUBST(PERMIT_DECLARATION_AFTER_STATEMENT)
# Really don't want VLAs to be used in our dialect of C
PGAC_PROG_CC_CFLAGS_OPT([-Werror=vla])
# -Wvla is not applicable for C++

12
contrib/btree_gist/expected/float4.out
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@ -34,10 +34,10 @@ SELECT count(*) FROM float4tmp WHERE a > -179.0;
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
a | ?column?
----------+----------
------------+-----------
-179 | 0
-189.024 | 10.0239
-158.177 | 20.8226
-189.02386 | 10.023865
-158.17741 | 20.822586
(3 rows)
CREATE INDEX float4idx ON float4tmp USING gist ( a );
@ -83,9 +83,9 @@ SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
a | ?column?
----------+----------
------------+-----------
-179 | 0
-189.024 | 10.0239
-158.177 | 20.8226
-189.02386 | 10.023865
-158.17741 | 20.822586
(3 rows)

12
contrib/btree_gist/expected/float8.out
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@ -34,10 +34,10 @@ SELECT count(*) FROM float8tmp WHERE a > -1890.0;
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
a | ?column?
--------------+------------
--------------+--------------------
-1890 | 0
-2003.634512 | 113.634512
-1769.73634 | 120.26366
-2003.634512 | 113.63451200000009
-1769.73634 | 120.26366000000007
(3 rows)
CREATE INDEX float8idx ON float8tmp USING gist ( a );
@ -83,9 +83,9 @@ SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
a | ?column?
--------------+------------
--------------+--------------------
-1890 | 0
-2003.634512 | 113.634512
-1769.73634 | 120.26366
-2003.634512 | 113.63451200000009
-1769.73634 | 120.26366000000007
(3 rows)

24
contrib/cube/expected/cube.out
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@ -82,20 +82,20 @@ SELECT 'NaN'::cube AS cube;
SELECT '.1234567890123456'::cube AS cube;
cube
---------------------
(0.123456789012346)
----------------------
(0.1234567890123456)
(1 row)
SELECT '+.1234567890123456'::cube AS cube;
cube
---------------------
(0.123456789012346)
----------------------
(0.1234567890123456)
(1 row)
SELECT '-.1234567890123456'::cube AS cube;
cube
----------------------
(-0.123456789012346)
-----------------------
(-0.1234567890123456)
(1 row)
-- simple lists (points)
@ -944,8 +944,8 @@ SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
cube_distance
------------------
140.762210837994
--------------------
140.76221083799445
(1 row)
-- Test of cube function (text to cube)
@ -1356,8 +1356,9 @@ SELECT cube_size('(42,137)'::cube);
0
(1 row)
-- Test of distances
-- Test of distances (euclidean distance may not be bit-exact)
--
SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
cube_distance
---------------
@ -1370,6 +1371,7 @@ SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
5
(1 row)
RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
distance_chebyshev
--------------------
@ -1557,6 +1559,7 @@ RESET enable_bitmapscan;
INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases
SET enable_seqscan = false;
-- Test different metrics
SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@ -1567,6 +1570,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------
@ -1751,6 +1755,7 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------------------
@ -1761,6 +1766,7 @@ SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c
(1444, 403),(1346, 344) | 846
(5 rows)
RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
c | dist
-------------------------+------

12
contrib/cube/expected/cube_sci.out
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@ -88,19 +88,19 @@ SELECT '-1e-300'::cube AS cube;
SELECT '1234567890123456'::cube AS cube;
cube
------------------------
(1.23456789012346e+15)
-------------------------
(1.234567890123456e+15)
(1 row)
SELECT '+1234567890123456'::cube AS cube;
cube
------------------------
(1.23456789012346e+15)
-------------------------
(1.234567890123456e+15)
(1 row)
SELECT '-1234567890123456'::cube AS cube;
cube
-------------------------
(-1.23456789012346e+15)
--------------------------
(-1.234567890123456e+15)
(1 row)

8
contrib/cube/sql/cube.sql
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@ -336,10 +336,12 @@ SELECT cube_inter('(1,2,3)'::cube, '(5,6,3)'::cube); -- point args
SELECT cube_size('(4,8),(15,16)'::cube);
SELECT cube_size('(42,137)'::cube);
-- Test of distances
-- Test of distances (euclidean distance may not be bit-exact)
--
SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
RESET extra_float_digits;
SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <=> '(4,5)'::cube as d_c;
SELECT distance_taxicab('(1,1)'::cube, '(4,5)'::cube);
@ -395,7 +397,9 @@ INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some c
SET enable_seqscan = false;
-- Test different metrics
SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
@ -412,7 +416,9 @@ SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upp
-- Same queries with sequential scan (should give the same results as above)
RESET enable_seqscan;
SET enable_indexscan = OFF;
SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
RESET extra_float_digits;
SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound

2
contrib/pg_trgm/expected/pg_strict_word_trgm.out
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@ -1,6 +1,8 @@
DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
ERROR: relation "test_trgm3" does not exist
-- reduce noise
set extra_float_digits = 0;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
t | sml
-------------------------------------+----------

2
contrib/pg_trgm/expected/pg_trgm.out
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@ -10,6 +10,8 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--backslash is used in tests below, installcheck will fail if
--standard_conforming_string is off
set standard_conforming_strings=on;
-- reduce noise
set extra_float_digits = 0;
select show_trgm('');
show_trgm
-----------

2
contrib/pg_trgm/expected/pg_word_trgm.out
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@ -1,5 +1,7 @@
CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
-- reduce noise
set extra_float_digits = 0;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
t | sml
-------------------------------------+----------

3
contrib/pg_trgm/sql/pg_strict_word_trgm.sql
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@ -2,6 +2,9 @@ DROP INDEX trgm_idx2;
\copy test_trgm3 from 'data/trgm2.data'
-- reduce noise
set extra_float_digits = 0;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <<% t order by sml desc, t;
select t,strict_word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <<% t order by sml desc, t;
select t,strict_word_similarity('Baykal',t) as sml from test_trgm2 where t %>> 'Baykal' order by sml desc, t;

3
contrib/pg_trgm/sql/pg_trgm.sql
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@ -9,6 +9,9 @@ WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
--standard_conforming_string is off
set standard_conforming_strings=on;
-- reduce noise
set extra_float_digits = 0;
select show_trgm('');
select show_trgm('(*&^$@%@');
select show_trgm('a b c');

3
contrib/pg_trgm/sql/pg_word_trgm.sql
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@ -2,6 +2,9 @@ CREATE TABLE test_trgm2(t text COLLATE "C");
\copy test_trgm2 from 'data/trgm2.data'
-- reduce noise
set extra_float_digits = 0;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where 'Baykal' <% t order by sml desc, t;
select t,word_similarity('Kabankala',t) as sml from test_trgm2 where 'Kabankala' <% t order by sml desc, t;
select t,word_similarity('Baykal',t) as sml from test_trgm2 where t %> 'Baykal' order by sml desc, t;

6
contrib/seg/expected/seg.out
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@ -1127,7 +1127,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
2.1 | 6.95 | 11.8
2.3 | Infinity | Infinity
2.3 | Infinity | Infinity
2.4 | 6.85 | 11.3
2.4 | 6.8500004 | 11.3
2.5 | 7 | 11.5
2.5 | 7.15 | 11.8
2.6 | Infinity | Infinity
@ -1155,7 +1155,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
4.5 | 59.75 | 115
4.7 | 8.25 | 11.8
4.8 | 8.15 | 11.5
4.8 | 8.2 | 11.6
4.8 | 8.200001 | 11.6
4.8 | 8.65 | 12.5
4.8 | Infinity | Infinity
4.9 | 8.45 | 12
@ -1244,7 +1244,7 @@ FROM test_seg WHERE s @> '11.2..11.3' OR s IS NULL ORDER BY s;
9 | 10.5 | 12
9 | Infinity | Infinity
9.2 | 10.6 | 12
9.4 | 10.8 | 12.2
9.4 | 10.799999 | 12.2
9.5 | 10.75 | 12
9.5 | 10.85 | 12.2
9.5 | Infinity | Infinity

37
doc/src/sgml/config.sgml
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@ -7871,16 +7871,37 @@ SET XML OPTION { DOCUMENT | CONTENT };
</term>
<listitem>
<para>
This parameter adjusts the number of digits displayed for
This parameter adjusts the number of digits used for textual output of
floating-point values, including <type>float4</type>, <type>float8</type>,
and geometric data types. The parameter value is added to the
standard number of digits (<literal>FLT_DIG</literal> or <literal>DBL_DIG</literal>
as appropriate). The value can be set as high as 3, to include
partially-significant digits; this is especially useful for dumping
float data that needs to be restored exactly. Or it can be set
negative to suppress unwanted digits.
See also <xref linkend="datatype-float"/>.
and geometric data types.
</para>
<para>
If the value is 1 (the default) or above, float values are output in
shortest-precise format; see <xref linkend="datatype-float"/>. The
actual number of digits generated depends only on the value being
output, not on the value of this parameter. At most 17 digits are
required for <type>float8</type> values, and 9 for <type>float4</type>
values. This format is both fast and precise, preserving the original
binary float value exactly when correctly read. For historical
compatibility, values up to 3 are permitted.
</para>
<para>
If the value is zero or negative, then the output is rounded to a
given decimal precision. The precision used is the standard number of
digits for the type (<literal>FLT_DIG</literal>
or <literal>DBL_DIG</literal> as appropriate) reduced according to the
value of this parameter. (For example, specifying -1 will cause float4
values to be output rounded to 5 significant digits, and float8 values
rounded to 14 digits.) This format is slower and does not preserve all
the bits of the binary float value, but may be more human-readable.
</para>
<note>
<para>
The meaning of this parameter, and its default value, changed
in <productname>PostgreSQL</productname> 12;
see <xref linkend="datatype-float"/> for further discussion.
</para>
</note>
</listitem>
</varlistentry>

89
doc/src/sgml/datatype.sgml
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@ -671,13 +671,12 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</indexterm>
<para>
The data types <type>real</type> and <type>double
precision</type> are inexact, variable-precision numeric types.
In practice, these types are usually implementations of
<acronym>IEEE</acronym> Standard 754 for Binary Floating-Point
Arithmetic (single and double precision, respectively), to the
extent that the underlying processor, operating system, and
compiler support it.
The data types <type>real</type> and <type>double precision</type> are
inexact, variable-precision numeric types. On all currently supported
platforms, these types are implementations of <acronym>IEEE</acronym>
Standard 754 for Binary Floating-Point Arithmetic (single and double
precision, respectively), to the extent that the underlying processor,
operating system, and compiler support it.
</para>
<para>
@ -715,24 +714,57 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</para>
<para>
On most platforms, the <type>real</type> type has a range of at least
1E-37 to 1E+37 with a precision of at least 6 decimal digits. The
<type>double precision</type> type typically has a range of around
1E-307 to 1E+308 with a precision of at least 15 digits. Values that
are too large or too small will cause an error. Rounding might
take place if the precision of an input number is too high.
Numbers too close to zero that are not representable as distinct
from zero will cause an underflow error.
On all currently supported platforms, the <type>real</type> type has a
range of around 1E-37 to 1E+37 with a precision of at least 6 decimal
digits. The <type>double precision</type> type has a range of around
1E-307 to 1E+308 with a precision of at least 15 digits. Values that are
too large or too small will cause an error. Rounding might take place if
the precision of an input number is too high. Numbers too close to zero
that are not representable as distinct from zero will cause an underflow
error.
</para>
<para>
By default, floating point values are output in text form in their
shortest precise decimal representation; the decimal value produced is
closer to the true stored binary value than to any other value
representable in the same binary precision. (However, the output value is
currently never <emphasis>exactly</emphasis> midway between two
representable values, in order to avoid a widespread bug where input
routines do not properly respect the round-to-even rule.) This value will
use at most 17 significant decimal digits for <type>float8</type>
values, and at most 9 digits for <type>float4</type> values.
</para>
<note>
<para>
The <xref linkend="guc-extra-float-digits"/> setting controls the
number of extra significant digits included when a floating point
value is converted to text for output. With the default value of
<literal>0</literal>, the output is the same on every platform
supported by PostgreSQL. Increasing it will produce output that
more accurately represents the stored value, but may be unportable.
This shortest-precise output format is much faster to generate than the
historical rounded format.
</para>
</note>
<para>
For compatibility with output generated by older versions
of <productname>PostgreSQL</productname>, and to allow the output
precision to be reduced, the <xref linkend="guc-extra-float-digits"/>
parameter can be used to select rounded decimal output instead. Setting a
value of 0 restores the previous default of rounding the value to 6
(for <type>float4</type>) or 15 (for <type>float8</type>)
significant decimal digits. Setting a negative value reduces the number
of digits further; for example -2 would round output to 4 or 13 digits
respectively.
</para>
<para>
Any value of <xref linkend="guc-extra-float-digits"/> greater than 0
selects the shortest-precise format.
</para>
<note>
<para>
Applications that wanted precise values have historically had to set
<xref linkend="guc-extra-float-digits"/> to 3 obtain them. For maximum
compatibility between versions, they should continue to do so.
</para>
</note>
@ -751,9 +783,7 @@ FROM generate_series(-3.5, 3.5, 1) as x;
</literallayout>
These represent the IEEE 754 special values
<quote>infinity</quote>, <quote>negative infinity</quote>, and
<quote>not-a-number</quote>, respectively. (On a machine whose
floating-point arithmetic does not follow IEEE 754, these values
will probably not work as expected.) When writing these values
<quote>not-a-number</quote>, respectively. When writing these values
as constants in an SQL command, you must put quotes around them,
for example <literal>UPDATE table SET x = '-Infinity'</literal>. On input,
these strings are recognized in a case-insensitive manner.
@ -786,17 +816,6 @@ FROM generate_series(-3.5, 3.5, 1) as x;
<type>double precision</type>.
</para>
<note>
<para>
The assumption that <type>real</type> and
<type>double precision</type> have exactly 24 and 53 bits in the
mantissa respectively is correct for IEEE-standard floating point
implementations. On non-IEEE platforms it might be off a little, but
for simplicity the same ranges of <replaceable>p</replaceable> are used
on all platforms.
</para>
</note>
</sect2>
<sect2 id="datatype-serial">

1
src/Makefile.global.in
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@ -261,6 +261,7 @@ CFLAGS = @CFLAGS@
CFLAGS_VECTOR = @CFLAGS_VECTOR@
CFLAGS_SSE42 = @CFLAGS_SSE42@
CFLAGS_ARMV8_CRC32C = @CFLAGS_ARMV8_CRC32C@
PERMIT_DECLARATION_AFTER_STATEMENT = @PERMIT_DECLARATION_AFTER_STATEMENT@
CXXFLAGS = @CXXFLAGS@
LLVM_CPPFLAGS = @LLVM_CPPFLAGS@

24
src/backend/utils/adt/float.c
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@ -21,6 +21,7 @@
#include "catalog/pg_type.h"
#include "common/int.h"
#include "common/shortest_dec.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "utils/array.h"
@ -30,8 +31,15 @@
#include "utils/timestamp.h"
/* Configurable GUC parameter */
int extra_float_digits = 0; /* Added to DBL_DIG or FLT_DIG */
/*
* Configurable GUC parameter
*
* If >0, use shortest-decimal format for output; this is both the default and
* allows for compatibility with clients that explicitly set a value here to
* get round-trip-accurate results. If 0 or less, then use the old, slow,
* decimal rounding method.
*/
int extra_float_digits = 1;
/* Cached constants for degree-based trig functions */
static bool degree_consts_set = false;
@ -282,6 +290,12 @@ float4out(PG_FUNCTION_ARGS)
char *ascii = (char *) palloc(32);
int ndig = FLT_DIG + extra_float_digits;
if (extra_float_digits > 0)
{
float_to_shortest_decimal_buf(num, ascii);
PG_RETURN_CSTRING(ascii);
}
(void) pg_strfromd(ascii, 32, ndig, num);
PG_RETURN_CSTRING(ascii);
}
@ -498,6 +512,12 @@ float8out_internal(double num)
char *ascii = (char *) palloc(32);
int ndig = DBL_DIG + extra_float_digits;
if (extra_float_digits > 0)
{
double_to_shortest_decimal_buf(num, ascii);
return ascii;
}
(void) pg_strfromd(ascii, 32, ndig, num);
return ascii;
}

7
src/backend/utils/misc/guc.c
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@ -2667,11 +2667,12 @@ static struct config_int ConfigureNamesInt[] =
{"extra_float_digits", PGC_USERSET, CLIENT_CONN_LOCALE,
gettext_noop("Sets the number of digits displayed for floating-point values."),
gettext_noop("This affects real, double precision, and geometric data types. "
"The parameter value is added to the standard number of digits "
"(FLT_DIG or DBL_DIG as appropriate).")
"A zero or negative parameter value is added to the standard "
"number of digits (FLT_DIG or DBL_DIG as appropriate). "
"Any value greater than zero selects precise output mode.")
},
&extra_float_digits,
0, -15, 3,
1, -15, 3,
NULL, NULL, NULL
},

3
src/backend/utils/misc/postgresql.conf.sample
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@ -651,7 +651,8 @@
# India
# You can create your own file in
# share/timezonesets/.
#extra_float_digits = 0 # min -15, max 3
#extra_float_digits = 1 # min -15, max 3; any value >0 actually
# selects precise output mode
#client_encoding = sql_ascii # actually, defaults to database
# encoding

15
src/common/Makefile
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@ -44,9 +44,11 @@ override CPPFLAGS += -DVAL_LIBS="\"$(LIBS)\""
override CPPFLAGS := -DFRONTEND -I. -I$(top_srcdir)/src/common $(CPPFLAGS)
LIBS += $(PTHREAD_LIBS)
OBJS_COMMON = base64.o config_info.o controldata_utils.o exec.o file_perm.o \
ip.o keywords.o kwlookup.o link-canary.o md5.o pg_lzcompress.o \
pgfnames.o psprintf.o relpath.o \
# If you add objects here, see also src/tools/msvc/Mkvcbuild.pm
OBJS_COMMON = base64.o config_info.o controldata_utils.o d2s.o exec.o f2s.o \
file_perm.o ip.o keywords.o kwlookup.o link-canary.o md5.o \
pg_lzcompress.o pgfnames.o psprintf.o relpath.o \
rmtree.o saslprep.o scram-common.o string.o unicode_norm.o \
username.o wait_error.o
@ -130,6 +132,13 @@ kwlist_d.h: $(top_srcdir)/src/include/parser/kwlist.h $(GEN_KEYWORDLIST_DEPS)
# that you don't get broken parsing code, even in a non-enable-depend build.
keywords.o keywords_shlib.o keywords_srv.o: kwlist_d.h
# The code imported from Ryu gets a pass on declaration-after-statement,
# in order to keep it more closely aligned with its upstream.
RYU_FILES = d2s.o f2s.o
RYU_OBJS = $(RYU_FILES) $(RYU_FILES:%.o=%_shlib.o) $(RYU_FILES:%.o=%_srv.o)
$(RYU_OBJS): CFLAGS += $(PERMIT_DECLARATION_AFTER_STATEMENT)
# kwlist_d.h is in the distribution tarball, so it is not cleaned here.
clean distclean:
rm -f libpgcommon.a libpgcommon_shlib.a libpgcommon_srv.a

1076
src/common/d2s.c
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358
src/common/d2s_full_table.h
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@ -0,0 +1,358 @@
/*---------------------------------------------------------------------------
*
* Ryu floating-point output for double precision.
*
* Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
*
* IDENTIFICATION
* src/common/d2s_full_table.h
*
* This is a modification of code taken from github.com/ulfjack/ryu under the
* terms of the Boost license (not the Apache license). The original copyright
* notice follows:
*
* Copyright 2018 Ulf Adams
*
* The contents of this file may be used under the terms of the Apache
* License, Version 2.0.
*
* (See accompanying file LICENSE-Apache or copy at
* http://www.apache.org/licenses/LICENSE-2.0)
*
* Alternatively, the contents of this file may be used under the terms of the
* Boost Software License, Version 1.0.
*
* (See accompanying file LICENSE-Boost or copy at
* https://www.boost.org/LICENSE_1_0.txt)
*
* Unless required by applicable law or agreed to in writing, this software is
* distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied.
*
*---------------------------------------------------------------------------
*/
#ifndef RYU_D2S_FULL_TABLE_H
#define RYU_D2S_FULL_TABLE_H
/*
* These tables are generated (by the upstream) using PrintDoubleLookupTable
* from the upstream sources at github.com/ulfjack/ryu, and then modified (by
* us) by adding UINT64CONST.
*/
static const uint64 DOUBLE_POW5_INV_SPLIT[292][2] = {
{UINT64CONST(1), UINT64CONST(288230376151711744)}, {UINT64CONST(3689348814741910324), UINT64CONST(230584300921369395)},
{UINT64CONST(2951479051793528259), UINT64CONST(184467440737095516)}, {UINT64CONST(17118578500402463900), UINT64CONST(147573952589676412)},
{UINT64CONST(12632330341676300947), UINT64CONST(236118324143482260)}, {UINT64CONST(10105864273341040758), UINT64CONST(188894659314785808)},
{UINT64CONST(15463389048156653253), UINT64CONST(151115727451828646)}, {UINT64CONST(17362724847566824558), UINT64CONST(241785163922925834)},
{UINT64CONST(17579528692795369969), UINT64CONST(193428131138340667)}, {UINT64CONST(6684925324752475329), UINT64CONST(154742504910672534)},
{UINT64CONST(18074578149087781173), UINT64CONST(247588007857076054)}, {UINT64CONST(18149011334012135262), UINT64CONST(198070406285660843)},
{UINT64CONST(3451162622983977240), UINT64CONST(158456325028528675)}, {UINT64CONST(5521860196774363583), UINT64CONST(253530120045645880)},
{UINT64CONST(4417488157419490867), UINT64CONST(202824096036516704)}, {UINT64CONST(7223339340677503017), UINT64CONST(162259276829213363)},
{UINT64CONST(7867994130342094503), UINT64CONST(259614842926741381)}, {UINT64CONST(2605046489531765280), UINT64CONST(207691874341393105)},
{UINT64CONST(2084037191625412224), UINT64CONST(166153499473114484)}, {UINT64CONST(10713157136084480204), UINT64CONST(265845599156983174)},
{UINT64CONST(12259874523609494487), UINT64CONST(212676479325586539)}, {UINT64CONST(13497248433629505913), UINT64CONST(170141183460469231)},
{UINT64CONST(14216899864323388813), UINT64CONST(272225893536750770)}, {UINT64CONST(11373519891458711051), UINT64CONST(217780714829400616)},
{UINT64CONST(5409467098425058518), UINT64CONST(174224571863520493)}, {UINT64CONST(4965798542738183305), UINT64CONST(278759314981632789)},
{UINT64CONST(7661987648932456967), UINT64CONST(223007451985306231)}, {UINT64CONST(2440241304404055250), UINT64CONST(178405961588244985)},
{UINT64CONST(3904386087046488400), UINT64CONST(285449538541191976)}, {UINT64CONST(17880904128604832013), UINT64CONST(228359630832953580)},
{UINT64CONST(14304723302883865611), UINT64CONST(182687704666362864)}, {UINT64CONST(15133127457049002812), UINT64CONST(146150163733090291)},
{UINT64CONST(16834306301794583852), UINT64CONST(233840261972944466)}, {UINT64CONST(9778096226693756759), UINT64CONST(187072209578355573)},
{UINT64CONST(15201174610838826053), UINT64CONST(149657767662684458)}, {UINT64CONST(2185786488890659746), UINT64CONST(239452428260295134)},
{UINT64CONST(5437978005854438120), UINT64CONST(191561942608236107)}, {UINT64CONST(15418428848909281466), UINT64CONST(153249554086588885)},
{UINT64CONST(6222742084545298729), UINT64CONST(245199286538542217)}, {UINT64CONST(16046240111861969953), UINT64CONST(196159429230833773)},
{UINT64CONST(1768945645263844993), UINT64CONST(156927543384667019)}, {UINT64CONST(10209010661905972635), UINT64CONST(251084069415467230)},
{UINT64CONST(8167208529524778108), UINT64CONST(200867255532373784)}, {UINT64CONST(10223115638361732810), UINT64CONST(160693804425899027)},
{UINT64CONST(1599589762411131202), UINT64CONST(257110087081438444)}, {UINT64CONST(4969020624670815285), UINT64CONST(205688069665150755)},
{UINT64CONST(3975216499736652228), UINT64CONST(164550455732120604)}, {UINT64CONST(13739044029062464211), UINT64CONST(263280729171392966)},
{UINT64CONST(7301886408508061046), UINT64CONST(210624583337114373)}, {UINT64CONST(13220206756290269483), UINT64CONST(168499666669691498)},
{UINT64CONST(17462981995322520850), UINT64CONST(269599466671506397)}, {UINT64CONST(6591687966774196033), UINT64CONST(215679573337205118)},
{UINT64CONST(12652048002903177473), UINT64CONST(172543658669764094)}, {UINT64CONST(9175230360419352987), UINT64CONST(276069853871622551)},
{UINT64CONST(3650835473593572067), UINT64CONST(220855883097298041)}, {UINT64CONST(17678063637842498946), UINT64CONST(176684706477838432)},
{UINT64CONST(13527506561580357021), UINT64CONST(282695530364541492)}, {UINT64CONST(3443307619780464970), UINT64CONST(226156424291633194)},
{UINT64CONST(6443994910566282300), UINT64CONST(180925139433306555)}, {UINT64CONST(5155195928453025840), UINT64CONST(144740111546645244)},
{UINT64CONST(15627011115008661990), UINT64CONST(231584178474632390)}, {UINT64CONST(12501608892006929592), UINT64CONST(185267342779705912)},
{UINT64CONST(2622589484121723027), UINT64CONST(148213874223764730)}, {UINT64CONST(4196143174594756843), UINT64CONST(237142198758023568)},
{UINT64CONST(10735612169159626121), UINT64CONST(189713759006418854)}, {UINT64CONST(12277838550069611220), UINT64CONST(151771007205135083)},
{UINT64CONST(15955192865369467629), UINT64CONST(242833611528216133)}, {UINT64CONST(1696107848069843133), UINT64CONST(194266889222572907)},
{UINT64CONST(12424932722681605476), UINT64CONST(155413511378058325)}, {UINT64CONST(1433148282581017146), UINT64CONST(248661618204893321)},
{UINT64CONST(15903913885032455010), UINT64CONST(198929294563914656)}, {UINT64CONST(9033782293284053685), UINT64CONST(159143435651131725)},
{UINT64CONST(14454051669254485895), UINT64CONST(254629497041810760)}, {UINT64CONST(11563241335403588716), UINT64CONST(203703597633448608)},
{UINT64CONST(16629290697806691620), UINT64CONST(162962878106758886)}, {UINT64CONST(781423413297334329), UINT64CONST(260740604970814219)},
{UINT64CONST(4314487545379777786), UINT64CONST(208592483976651375)}, {UINT64CONST(3451590036303822229), UINT64CONST(166873987181321100)},
{UINT64CONST(5522544058086115566), UINT64CONST(266998379490113760)}, {UINT64CONST(4418035246468892453), UINT64CONST(213598703592091008)},
{UINT64CONST(10913125826658934609), UINT64CONST(170878962873672806)}, {UINT64CONST(10082303693170474728), UINT64CONST(273406340597876490)},
{UINT64CONST(8065842954536379782), UINT64CONST(218725072478301192)}, {UINT64CONST(17520720807854834795), UINT64CONST(174980057982640953)},
{UINT64CONST(5897060404116273733), UINT64CONST(279968092772225526)}, {UINT64CONST(1028299508551108663), UINT64CONST(223974474217780421)},
{UINT64CONST(15580034865808528224), UINT64CONST(179179579374224336)}, {UINT64CONST(17549358155809824511), UINT64CONST(286687326998758938)},
{UINT64CONST(2971440080422128639), UINT64CONST(229349861599007151)}, {UINT64CONST(17134547323305344204), UINT64CONST(183479889279205720)},
{UINT64CONST(13707637858644275364), UINT64CONST(146783911423364576)}, {UINT64CONST(14553522944347019935), UINT64CONST(234854258277383322)},
{UINT64CONST(4264120725993795302), UINT64CONST(187883406621906658)}, {UINT64CONST(10789994210278856888), UINT64CONST(150306725297525326)},
{UINT64CONST(9885293106962350374), UINT64CONST(240490760476040522)}, {UINT64CONST(529536856086059653), UINT64CONST(192392608380832418)},
{UINT64CONST(7802327114352668369), UINT64CONST(153914086704665934)}, {UINT64CONST(1415676938738538420), UINT64CONST(246262538727465495)},
{UINT64CONST(1132541550990830736), UINT64CONST(197010030981972396)}, {UINT64CONST(15663428499760305882), UINT64CONST(157608024785577916)},
{UINT64CONST(17682787970132668764), UINT64CONST(252172839656924666)}, {UINT64CONST(10456881561364224688), UINT64CONST(201738271725539733)},
{UINT64CONST(15744202878575200397), UINT64CONST(161390617380431786)}, {UINT64CONST(17812026976236499989), UINT64CONST(258224987808690858)},
{UINT64CONST(3181575136763469022), UINT64CONST(206579990246952687)}, {UINT64CONST(13613306553636506187), UINT64CONST(165263992197562149)},
{UINT64CONST(10713244041592678929), UINT64CONST(264422387516099439)}, {UINT64CONST(12259944048016053467), UINT64CONST(211537910012879551)},
{UINT64CONST(6118606423670932450), UINT64CONST(169230328010303641)}, {UINT64CONST(2411072648389671274), UINT64CONST(270768524816485826)},
{UINT64CONST(16686253377679378312), UINT64CONST(216614819853188660)}, {UINT64CONST(13349002702143502650), UINT64CONST(173291855882550928)},
{UINT64CONST(17669055508687693916), UINT64CONST(277266969412081485)}, {UINT64CONST(14135244406950155133), UINT64CONST(221813575529665188)},
{UINT64CONST(240149081334393137), UINT64CONST(177450860423732151)}, {UINT64CONST(11452284974360759988), UINT64CONST(283921376677971441)},
{UINT64CONST(5472479164746697667), UINT64CONST(227137101342377153)}, {UINT64CONST(11756680961281178780), UINT64CONST(181709681073901722)},
{UINT64CONST(2026647139541122378), UINT64CONST(145367744859121378)}, {UINT64CONST(18000030682233437097), UINT64CONST(232588391774594204)},
{UINT64CONST(18089373360528660001), UINT64CONST(186070713419675363)}, {UINT64CONST(3403452244197197031), UINT64CONST(148856570735740291)},
{UINT64CONST(16513570034941246220), UINT64CONST(238170513177184465)}, {UINT64CONST(13210856027952996976), UINT64CONST(190536410541747572)},
{UINT64CONST(3189987192878576934), UINT64CONST(152429128433398058)}, {UINT64CONST(1414630693863812771), UINT64CONST(243886605493436893)},
{UINT64CONST(8510402184574870864), UINT64CONST(195109284394749514)}, {UINT64CONST(10497670562401807014), UINT64CONST(156087427515799611)},
{UINT64CONST(9417575270359070576), UINT64CONST(249739884025279378)}, {UINT64CONST(14912757845771077107), UINT64CONST(199791907220223502)},
{UINT64CONST(4551508647133041040), UINT64CONST(159833525776178802)}, {UINT64CONST(10971762650154775986), UINT64CONST(255733641241886083)},
{UINT64CONST(16156107749607641435), UINT64CONST(204586912993508866)}, {UINT64CONST(9235537384944202825), UINT64CONST(163669530394807093)},
{UINT64CONST(11087511001168814197), UINT64CONST(261871248631691349)}, {UINT64CONST(12559357615676961681), UINT64CONST(209496998905353079)},
{UINT64CONST(13736834907283479668), UINT64CONST(167597599124282463)}, {UINT64CONST(18289587036911657145), UINT64CONST(268156158598851941)},
{UINT64CONST(10942320814787415393), UINT64CONST(214524926879081553)}, {UINT64CONST(16132554281313752961), UINT64CONST(171619941503265242)},
{UINT64CONST(11054691591134363444), UINT64CONST(274591906405224388)}, {UINT64CONST(16222450902391311402), UINT64CONST(219673525124179510)},
{UINT64CONST(12977960721913049122), UINT64CONST(175738820099343608)}, {UINT64CONST(17075388340318968271), UINT64CONST(281182112158949773)},
{UINT64CONST(2592264228029443648), UINT64CONST(224945689727159819)}, {UINT64CONST(5763160197165465241), UINT64CONST(179956551781727855)},
{UINT64CONST(9221056315464744386), UINT64CONST(287930482850764568)}, {UINT64CONST(14755542681855616155), UINT64CONST(230344386280611654)},
{UINT64CONST(15493782960226403247), UINT64CONST(184275509024489323)}, {UINT64CONST(1326979923955391628), UINT64CONST(147420407219591459)},
{UINT64CONST(9501865507812447252), UINT64CONST(235872651551346334)}, {UINT64CONST(11290841220991868125), UINT64CONST(188698121241077067)},
{UINT64CONST(1653975347309673853), UINT64CONST(150958496992861654)}, {UINT64CONST(10025058185179298811), UINT64CONST(241533595188578646)},
{UINT64CONST(4330697733401528726), UINT64CONST(193226876150862917)}, {UINT64CONST(14532604630946953951), UINT64CONST(154581500920690333)},
{UINT64CONST(1116074521063664381), UINT64CONST(247330401473104534)}, {UINT64CONST(4582208431592841828), UINT64CONST(197864321178483627)},
{UINT64CONST(14733813189500004432), UINT64CONST(158291456942786901)}, {UINT64CONST(16195403473716186445), UINT64CONST(253266331108459042)},
{UINT64CONST(5577625149489128510), UINT64CONST(202613064886767234)}, {UINT64CONST(8151448934333213131), UINT64CONST(162090451909413787)},
{UINT64CONST(16731667109675051333), UINT64CONST(259344723055062059)}, {UINT64CONST(17074682502481951390), UINT64CONST(207475778444049647)},
{UINT64CONST(6281048372501740465), UINT64CONST(165980622755239718)}, {UINT64CONST(6360328581260874421), UINT64CONST(265568996408383549)},
{UINT64CONST(8777611679750609860), UINT64CONST(212455197126706839)}, {UINT64CONST(10711438158542398211), UINT64CONST(169964157701365471)},
{UINT64CONST(9759603424184016492), UINT64CONST(271942652322184754)}, {UINT64CONST(11497031554089123517), UINT64CONST(217554121857747803)},
{UINT64CONST(16576322872755119460), UINT64CONST(174043297486198242)}, {UINT64CONST(11764721337440549842), UINT64CONST(278469275977917188)},
{UINT64CONST(16790474699436260520), UINT64CONST(222775420782333750)}, {UINT64CONST(13432379759549008416), UINT64CONST(178220336625867000)},
{UINT64CONST(3045063541568861850), UINT64CONST(285152538601387201)}, {UINT64CONST(17193446092222730773), UINT64CONST(228122030881109760)},
{UINT64CONST(13754756873778184618), UINT64CONST(182497624704887808)}, {UINT64CONST(18382503128506368341), UINT64CONST(145998099763910246)},
{UINT64CONST(3586563302416817083), UINT64CONST(233596959622256395)}, {UINT64CONST(2869250641933453667), UINT64CONST(186877567697805116)},
{UINT64CONST(17052795772514404226), UINT64CONST(149502054158244092)}, {UINT64CONST(12527077977055405469), UINT64CONST(239203286653190548)},
{UINT64CONST(17400360011128145022), UINT64CONST(191362629322552438)}, {UINT64CONST(2852241564676785048), UINT64CONST(153090103458041951)},
{UINT64CONST(15631632947708587046), UINT64CONST(244944165532867121)}, {UINT64CONST(8815957543424959314), UINT64CONST(195955332426293697)},
{UINT64CONST(18120812478965698421), UINT64CONST(156764265941034957)}, {UINT64CONST(14235904707377476180), UINT64CONST(250822825505655932)},
{UINT64CONST(4010026136418160298), UINT64CONST(200658260404524746)}, {UINT64CONST(17965416168102169531), UINT64CONST(160526608323619796)},
{UINT64CONST(2919224165770098987), UINT64CONST(256842573317791675)}, {UINT64CONST(2335379332616079190), UINT64CONST(205474058654233340)},
{UINT64CONST(1868303466092863352), UINT64CONST(164379246923386672)}, {UINT64CONST(6678634360490491686), UINT64CONST(263006795077418675)},
{UINT64CONST(5342907488392393349), UINT64CONST(210405436061934940)}, {UINT64CONST(4274325990713914679), UINT64CONST(168324348849547952)},
{UINT64CONST(10528270399884173809), UINT64CONST(269318958159276723)}, {UINT64CONST(15801313949391159694), UINT64CONST(215455166527421378)},
{UINT64CONST(1573004715287196786), UINT64CONST(172364133221937103)}, {UINT64CONST(17274202803427156150), UINT64CONST(275782613155099364)},
{UINT64CONST(17508711057483635243), UINT64CONST(220626090524079491)}, {UINT64CONST(10317620031244997871), UINT64CONST(176500872419263593)},
{UINT64CONST(12818843235250086271), UINT64CONST(282401395870821749)}, {UINT64CONST(13944423402941979340), UINT64CONST(225921116696657399)},
{UINT64CONST(14844887537095493795), UINT64CONST(180736893357325919)}, {UINT64CONST(15565258844418305359), UINT64CONST(144589514685860735)},
{UINT64CONST(6457670077359736959), UINT64CONST(231343223497377177)}, {UINT64CONST(16234182506113520537), UINT64CONST(185074578797901741)},
{UINT64CONST(9297997190148906106), UINT64CONST(148059663038321393)}, {UINT64CONST(11187446689496339446), UINT64CONST(236895460861314229)},
{UINT64CONST(12639306166338981880), UINT64CONST(189516368689051383)}, {UINT64CONST(17490142562555006151), UINT64CONST(151613094951241106)},
{UINT64CONST(2158786396894637579), UINT64CONST(242580951921985771)}, {UINT64CONST(16484424376483351356), UINT64CONST(194064761537588616)},
{UINT64CONST(9498190686444770762), UINT64CONST(155251809230070893)}, {UINT64CONST(11507756283569722895), UINT64CONST(248402894768113429)},
{UINT64CONST(12895553841597688639), UINT64CONST(198722315814490743)}, {UINT64CONST(17695140702761971558), UINT64CONST(158977852651592594)},
{UINT64CONST(17244178680193423523), UINT64CONST(254364564242548151)}, {UINT64CONST(10105994129412828495), UINT64CONST(203491651394038521)},
{UINT64CONST(4395446488788352473), UINT64CONST(162793321115230817)}, {UINT64CONST(10722063196803274280), UINT64CONST(260469313784369307)},
{UINT64CONST(1198952927958798777), UINT64CONST(208375451027495446)}, {UINT64CONST(15716557601334680315), UINT64CONST(166700360821996356)},
{UINT64CONST(17767794532651667857), UINT64CONST(266720577315194170)}, {UINT64CONST(14214235626121334286), UINT64CONST(213376461852155336)},
{UINT64CONST(7682039686155157106), UINT64CONST(170701169481724269)}, {UINT64CONST(1223217053622520399), UINT64CONST(273121871170758831)},
{UINT64CONST(15735968901865657612), UINT64CONST(218497496936607064)}, {UINT64CONST(16278123936234436413), UINT64CONST(174797997549285651)},
{UINT64CONST(219556594781725998), UINT64CONST(279676796078857043)}, {UINT64CONST(7554342905309201445), UINT64CONST(223741436863085634)},
{UINT64CONST(9732823138989271479), UINT64CONST(178993149490468507)}, {UINT64CONST(815121763415193074), UINT64CONST(286389039184749612)},
{UINT64CONST(11720143854957885429), UINT64CONST(229111231347799689)}, {UINT64CONST(13065463898708218666), UINT64CONST(183288985078239751)},
{UINT64CONST(6763022304224664610), UINT64CONST(146631188062591801)}, {UINT64CONST(3442138057275642729), UINT64CONST(234609900900146882)},
{UINT64CONST(13821756890046245153), UINT64CONST(187687920720117505)}, {UINT64CONST(11057405512036996122), UINT64CONST(150150336576094004)},
{UINT64CONST(6623802375033462826), UINT64CONST(240240538521750407)}, {UINT64CONST(16367088344252501231), UINT64CONST(192192430817400325)},
{UINT64CONST(13093670675402000985), UINT64CONST(153753944653920260)}, {UINT64CONST(2503129006933649959), UINT64CONST(246006311446272417)},
{UINT64CONST(13070549649772650937), UINT64CONST(196805049157017933)}, {UINT64CONST(17835137349301941396), UINT64CONST(157444039325614346)},
{UINT64CONST(2710778055689733971), UINT64CONST(251910462920982955)}, {UINT64CONST(2168622444551787177), UINT64CONST(201528370336786364)},
{UINT64CONST(5424246770383340065), UINT64CONST(161222696269429091)}, {UINT64CONST(1300097203129523457), UINT64CONST(257956314031086546)},
{UINT64CONST(15797473021471260058), UINT64CONST(206365051224869236)}, {UINT64CONST(8948629602435097724), UINT64CONST(165092040979895389)},
{UINT64CONST(3249760919670425388), UINT64CONST(264147265567832623)}, {UINT64CONST(9978506365220160957), UINT64CONST(211317812454266098)},
{UINT64CONST(15361502721659949412), UINT64CONST(169054249963412878)}, {UINT64CONST(2442311466204457120), UINT64CONST(270486799941460606)},
{UINT64CONST(16711244431931206989), UINT64CONST(216389439953168484)}, {UINT64CONST(17058344360286875914), UINT64CONST(173111551962534787)},
{UINT64CONST(12535955717491360170), UINT64CONST(276978483140055660)}, {UINT64CONST(10028764573993088136), UINT64CONST(221582786512044528)},
{UINT64CONST(15401709288678291155), UINT64CONST(177266229209635622)}, {UINT64CONST(9885339602917624555), UINT64CONST(283625966735416996)},
{UINT64CONST(4218922867592189321), UINT64CONST(226900773388333597)}, {UINT64CONST(14443184738299482427), UINT64CONST(181520618710666877)},
{UINT64CONST(4175850161155765295), UINT64CONST(145216494968533502)}, {UINT64CONST(10370709072591134795), UINT64CONST(232346391949653603)},
{UINT64CONST(15675264887556728482), UINT64CONST(185877113559722882)}, {UINT64CONST(5161514280561562140), UINT64CONST(148701690847778306)},
{UINT64CONST(879725219414678777), UINT64CONST(237922705356445290)}, {UINT64CONST(703780175531743021), UINT64CONST(190338164285156232)},
{UINT64CONST(11631070584651125387), UINT64CONST(152270531428124985)}, {UINT64CONST(162968861732249003), UINT64CONST(243632850284999977)},
{UINT64CONST(11198421533611530172), UINT64CONST(194906280227999981)}, {UINT64CONST(5269388412147313814), UINT64CONST(155925024182399985)},
{UINT64CONST(8431021459435702103), UINT64CONST(249480038691839976)}, {UINT64CONST(3055468352806651359), UINT64CONST(199584030953471981)},
{UINT64CONST(17201769941212962380), UINT64CONST(159667224762777584)}, {UINT64CONST(16454785461715008838), UINT64CONST(255467559620444135)},
{UINT64CONST(13163828369372007071), UINT64CONST(204374047696355308)}, {UINT64CONST(17909760324981426303), UINT64CONST(163499238157084246)},
{UINT64CONST(2830174816776909822), UINT64CONST(261598781051334795)}, {UINT64CONST(2264139853421527858), UINT64CONST(209279024841067836)},
{UINT64CONST(16568707141704863579), UINT64CONST(167423219872854268)}, {UINT64CONST(4373838538276319787), UINT64CONST(267877151796566830)},
{UINT64CONST(3499070830621055830), UINT64CONST(214301721437253464)}, {UINT64CONST(6488605479238754987), UINT64CONST(171441377149802771)},
{UINT64CONST(3003071137298187333), UINT64CONST(274306203439684434)}, {UINT64CONST(6091805724580460189), UINT64CONST(219444962751747547)},
{UINT64CONST(15941491023890099121), UINT64CONST(175555970201398037)}, {UINT64CONST(10748990379256517301), UINT64CONST(280889552322236860)},
{UINT64CONST(8599192303405213841), UINT64CONST(224711641857789488)}, {UINT64CONST(14258051472207991719), UINT64CONST(179769313486231590)}
};
static const uint64 DOUBLE_POW5_SPLIT[326][2] = {
{UINT64CONST(0), UINT64CONST(72057594037927936)}, {UINT64CONST(0), UINT64CONST(90071992547409920)},
{UINT64CONST(0), UINT64CONST(112589990684262400)}, {UINT64CONST(0), UINT64CONST(140737488355328000)},
{UINT64CONST(0), UINT64CONST(87960930222080000)}, {UINT64CONST(0), UINT64CONST(109951162777600000)},
{UINT64CONST(0), UINT64CONST(137438953472000000)}, {UINT64CONST(0), UINT64CONST(85899345920000000)},
{UINT64CONST(0), UINT64CONST(107374182400000000)}, {UINT64CONST(0), UINT64CONST(134217728000000000)},
{UINT64CONST(0), UINT64CONST(83886080000000000)}, {UINT64CONST(0), UINT64CONST(104857600000000000)},
{UINT64CONST(0), UINT64CONST(131072000000000000)}, {UINT64CONST(0), UINT64CONST(81920000000000000)},
{UINT64CONST(0), UINT64CONST(102400000000000000)}, {UINT64CONST(0), UINT64CONST(128000000000000000)},
{UINT64CONST(0), UINT64CONST(80000000000000000)}, {UINT64CONST(0), UINT64CONST(100000000000000000)},
{UINT64CONST(0), UINT64CONST(125000000000000000)}, {UINT64CONST(0), UINT64CONST(78125000000000000)},
{UINT64CONST(0), UINT64CONST(97656250000000000)}, {UINT64CONST(0), UINT64CONST(122070312500000000)},
{UINT64CONST(0), UINT64CONST(76293945312500000)}, {UINT64CONST(0), UINT64CONST(95367431640625000)},
{UINT64CONST(0), UINT64CONST(119209289550781250)}, {UINT64CONST(4611686018427387904), UINT64CONST(74505805969238281)},
{UINT64CONST(10376293541461622784), UINT64CONST(93132257461547851)}, {UINT64CONST(8358680908399640576), UINT64CONST(116415321826934814)},
{UINT64CONST(612489549322387456), UINT64CONST(72759576141834259)}, {UINT64CONST(14600669991935148032), UINT64CONST(90949470177292823)},
{UINT64CONST(13639151471491547136), UINT64CONST(113686837721616029)}, {UINT64CONST(3213881284082270208), UINT64CONST(142108547152020037)},
{UINT64CONST(4314518811765112832), UINT64CONST(88817841970012523)}, {UINT64CONST(781462496279003136), UINT64CONST(111022302462515654)},
{UINT64CONST(10200200157203529728), UINT64CONST(138777878078144567)}, {UINT64CONST(13292654125893287936), UINT64CONST(86736173798840354)},
{UINT64CONST(7392445620511834112), UINT64CONST(108420217248550443)}, {UINT64CONST(4628871007212404736), UINT64CONST(135525271560688054)},
{UINT64CONST(16728102434789916672), UINT64CONST(84703294725430033)}, {UINT64CONST(7075069988205232128), UINT64CONST(105879118406787542)},
{UINT64CONST(18067209522111315968), UINT64CONST(132348898008484427)}, {UINT64CONST(8986162942105878528), UINT64CONST(82718061255302767)},
{UINT64CONST(6621017659204960256), UINT64CONST(103397576569128459)}, {UINT64CONST(3664586055578812416), UINT64CONST(129246970711410574)},
{UINT64CONST(16125424340018921472), UINT64CONST(80779356694631608)}, {UINT64CONST(1710036351314100224), UINT64CONST(100974195868289511)},
{UINT64CONST(15972603494424788992), UINT64CONST(126217744835361888)}, {UINT64CONST(9982877184015493120), UINT64CONST(78886090522101180)},
{UINT64CONST(12478596480019366400), UINT64CONST(98607613152626475)}, {UINT64CONST(10986559581596820096), UINT64CONST(123259516440783094)},
{UINT64CONST(2254913720070624656), UINT64CONST(77037197775489434)}, {UINT64CONST(12042014186943056628), UINT64CONST(96296497219361792)},
{UINT64CONST(15052517733678820785), UINT64CONST(120370621524202240)}, {UINT64CONST(9407823583549262990), UINT64CONST(75231638452626400)},
{UINT64CONST(11759779479436578738), UINT64CONST(94039548065783000)}, {UINT64CONST(14699724349295723422), UINT64CONST(117549435082228750)},
{UINT64CONST(4575641699882439235), UINT64CONST(73468396926392969)}, {UINT64CONST(10331238143280436948), UINT64CONST(91835496157991211)},
{UINT64CONST(8302361660673158281), UINT64CONST(114794370197489014)}, {UINT64CONST(1154580038986672043), UINT64CONST(143492962746861268)},
{UINT64CONST(9944984561221445835), UINT64CONST(89683101716788292)}, {UINT64CONST(12431230701526807293), UINT64CONST(112103877145985365)},
{UINT64CONST(1703980321626345405), UINT64CONST(140129846432481707)}, {UINT64CONST(17205888765512323542), UINT64CONST(87581154020301066)},
{UINT64CONST(12283988920035628619), UINT64CONST(109476442525376333)}, {UINT64CONST(1519928094762372062), UINT64CONST(136845553156720417)},
{UINT64CONST(12479170105294952299), UINT64CONST(85528470722950260)}, {UINT64CONST(15598962631618690374), UINT64CONST(106910588403687825)},
{UINT64CONST(5663645234241199255), UINT64CONST(133638235504609782)}, {UINT64CONST(17374836326682913246), UINT64CONST(83523897190381113)},
{UINT64CONST(7883487353071477846), UINT64CONST(104404871487976392)}, {UINT64CONST(9854359191339347308), UINT64CONST(130506089359970490)},
{UINT64CONST(10770660513014479971), UINT64CONST(81566305849981556)}, {UINT64CONST(13463325641268099964), UINT64CONST(101957882312476945)},
{UINT64CONST(2994098996302961243), UINT64CONST(127447352890596182)}, {UINT64CONST(15706369927971514489), UINT64CONST(79654595556622613)},
{UINT64CONST(5797904354682229399), UINT64CONST(99568244445778267)}, {UINT64CONST(2635694424925398845), UINT64CONST(124460305557222834)},
{UINT64CONST(6258995034005762182), UINT64CONST(77787690973264271)}, {UINT64CONST(3212057774079814824), UINT64CONST(97234613716580339)},
{UINT64CONST(17850130272881932242), UINT64CONST(121543267145725423)}, {UINT64CONST(18073860448192289507), UINT64CONST(75964541966078389)},
{UINT64CONST(8757267504958198172), UINT64CONST(94955677457597987)}, {UINT64CONST(6334898362770359811), UINT64CONST(118694596821997484)},
{UINT64CONST(13182683513586250689), UINT64CONST(74184123013748427)}, {UINT64CONST(11866668373555425458), UINT64CONST(92730153767185534)},
{UINT64CONST(5609963430089506015), UINT64CONST(115912692208981918)}, {UINT64CONST(17341285199088104971), UINT64CONST(72445432630613698)},
{UINT64CONST(12453234462005355406), UINT64CONST(90556790788267123)}, {UINT64CONST(10954857059079306353), UINT64CONST(113195988485333904)},
{UINT64CONST(13693571323849132942), UINT64CONST(141494985606667380)}, {UINT64CONST(17781854114260483896), UINT64CONST(88434366004167112)},
{UINT64CONST(3780573569116053255), UINT64CONST(110542957505208891)}, {UINT64CONST(114030942967678664), UINT64CONST(138178696881511114)},
{UINT64CONST(4682955357782187069), UINT64CONST(86361685550944446)}, {UINT64CONST(15077066234082509644), UINT64CONST(107952106938680557)},
{UINT64CONST(5011274737320973344), UINT64CONST(134940133673350697)}, {UINT64CONST(14661261756894078100), UINT64CONST(84337583545844185)},
{UINT64CONST(4491519140835433913), UINT64CONST(105421979432305232)}, {UINT64CONST(5614398926044292391), UINT64CONST(131777474290381540)},
{UINT64CONST(12732371365632458552), UINT64CONST(82360921431488462)}, {UINT64CONST(6692092170185797382), UINT64CONST(102951151789360578)},
{UINT64CONST(17588487249587022536), UINT64CONST(128688939736700722)}, {UINT64CONST(15604490549419276989), UINT64CONST(80430587335437951)},
{UINT64CONST(14893927168346708332), UINT64CONST(100538234169297439)}, {UINT64CONST(14005722942005997511), UINT64CONST(125672792711621799)},
{UINT64CONST(15671105866394830300), UINT64CONST(78545495444763624)}, {UINT64CONST(1142138259283986260), UINT64CONST(98181869305954531)},
{UINT64CONST(15262730879387146537), UINT64CONST(122727336632443163)}, {UINT64CONST(7233363790403272633), UINT64CONST(76704585395276977)},
{UINT64CONST(13653390756431478696), UINT64CONST(95880731744096221)}, {UINT64CONST(3231680390257184658), UINT64CONST(119850914680120277)},
{UINT64CONST(4325643253124434363), UINT64CONST(74906821675075173)}, {UINT64CONST(10018740084832930858), UINT64CONST(93633527093843966)},
{UINT64CONST(3300053069186387764), UINT64CONST(117041908867304958)}, {UINT64CONST(15897591223523656064), UINT64CONST(73151193042065598)},
{UINT64CONST(10648616992549794273), UINT64CONST(91438991302581998)}, {UINT64CONST(4087399203832467033), UINT64CONST(114298739128227498)},
{UINT64CONST(14332621041645359599), UINT64CONST(142873423910284372)}, {UINT64CONST(18181260187883125557), UINT64CONST(89295889943927732)},
{UINT64CONST(4279831161144355331), UINT64CONST(111619862429909666)}, {UINT64CONST(14573160988285219972), UINT64CONST(139524828037387082)},
{UINT64CONST(13719911636105650386), UINT64CONST(87203017523366926)}, {UINT64CONST(7926517508277287175), UINT64CONST(109003771904208658)},
{UINT64CONST(684774848491833161), UINT64CONST(136254714880260823)}, {UINT64CONST(7345513307948477581), UINT64CONST(85159196800163014)},
{UINT64CONST(18405263671790372785), UINT64CONST(106448996000203767)}, {UINT64CONST(18394893571310578077), UINT64CONST(133061245000254709)},
{UINT64CONST(13802651491282805250), UINT64CONST(83163278125159193)}, {UINT64CONST(3418256308821342851), UINT64CONST(103954097656448992)},
{UINT64CONST(4272820386026678563), UINT64CONST(129942622070561240)}, {UINT64CONST(2670512741266674102), UINT64CONST(81214138794100775)},
{UINT64CONST(17173198981865506339), UINT64CONST(101517673492625968)}, {UINT64CONST(3019754653622331308), UINT64CONST(126897091865782461)},
{UINT64CONST(4193189667727651020), UINT64CONST(79310682416114038)}, {UINT64CONST(14464859121514339583), UINT64CONST(99138353020142547)},
{UINT64CONST(13469387883465536574), UINT64CONST(123922941275178184)}, {UINT64CONST(8418367427165960359), UINT64CONST(77451838296986365)},
{UINT64CONST(15134645302384838353), UINT64CONST(96814797871232956)}, {UINT64CONST(471562554271496325), UINT64CONST(121018497339041196)},
{UINT64CONST(9518098633274461011), UINT64CONST(75636560836900747)}, {UINT64CONST(7285937273165688360), UINT64CONST(94545701046125934)},
{UINT64CONST(18330793628311886258), UINT64CONST(118182126307657417)}, {UINT64CONST(4539216990053847055), UINT64CONST(73863828942285886)},
{UINT64CONST(14897393274422084627), UINT64CONST(92329786177857357)}, {UINT64CONST(4786683537745442072), UINT64CONST(115412232722321697)},
{UINT64CONST(14520892257159371055), UINT64CONST(72132645451451060)}, {UINT64CONST(18151115321449213818), UINT64CONST(90165806814313825)},
{UINT64CONST(8853836096529353561), UINT64CONST(112707258517892282)}, {UINT64CONST(1843923083806916143), UINT64CONST(140884073147365353)},
{UINT64CONST(12681666973447792349), UINT64CONST(88052545717103345)}, {UINT64CONST(2017025661527576725), UINT64CONST(110065682146379182)},
{UINT64CONST(11744654113764246714), UINT64CONST(137582102682973977)}, {UINT64CONST(422879793461572340), UINT64CONST(85988814176858736)},
{UINT64CONST(528599741826965425), UINT64CONST(107486017721073420)}, {UINT64CONST(660749677283706782), UINT64CONST(134357522151341775)},
{UINT64CONST(7330497575943398595), UINT64CONST(83973451344588609)}, {UINT64CONST(13774807988356636147), UINT64CONST(104966814180735761)},
{UINT64CONST(3383451930163631472), UINT64CONST(131208517725919702)}, {UINT64CONST(15949715511634433382), UINT64CONST(82005323578699813)},
{UINT64CONST(6102086334260878016), UINT64CONST(102506654473374767)}, {UINT64CONST(3015921899398709616), UINT64CONST(128133318091718459)},
{UINT64CONST(18025852251620051174), UINT64CONST(80083323807324036)}, {UINT64CONST(4085571240815512351), UINT64CONST(100104154759155046)},
{UINT64CONST(14330336087874166247), UINT64CONST(125130193448943807)}, {UINT64CONST(15873989082562435760), UINT64CONST(78206370905589879)},
{UINT64CONST(15230800334775656796), UINT64CONST(97757963631987349)}, {UINT64CONST(5203442363187407284), UINT64CONST(122197454539984187)},
{UINT64CONST(946308467778435600), UINT64CONST(76373409087490117)}, {UINT64CONST(5794571603150432404), UINT64CONST(95466761359362646)},
{UINT64CONST(16466586540792816313), UINT64CONST(119333451699203307)}, {UINT64CONST(7985773578781816244), UINT64CONST(74583407312002067)},
{UINT64CONST(5370530955049882401), UINT64CONST(93229259140002584)}, {UINT64CONST(6713163693812353001), UINT64CONST(116536573925003230)},
{UINT64CONST(18030785363914884337), UINT64CONST(72835358703127018)}, {UINT64CONST(13315109668038829614), UINT64CONST(91044198378908773)},
{UINT64CONST(2808829029766373305), UINT64CONST(113805247973635967)}, {UINT64CONST(17346094342490130344), UINT64CONST(142256559967044958)},
{UINT64CONST(6229622945628943561), UINT64CONST(88910349979403099)}, {UINT64CONST(3175342663608791547), UINT64CONST(111137937474253874)},
{UINT64CONST(13192550366365765242), UINT64CONST(138922421842817342)}, {UINT64CONST(3633657960551215372), UINT64CONST(86826513651760839)},
{UINT64CONST(18377130505971182927), UINT64CONST(108533142064701048)}, {UINT64CONST(4524669058754427043), UINT64CONST(135666427580876311)},
{UINT64CONST(9745447189362598758), UINT64CONST(84791517238047694)}, {UINT64CONST(2958436949848472639), UINT64CONST(105989396547559618)},
{UINT64CONST(12921418224165366607), UINT64CONST(132486745684449522)}, {UINT64CONST(12687572408530742033), UINT64CONST(82804216052780951)},
{UINT64CONST(11247779492236039638), UINT64CONST(103505270065976189)}, {UINT64CONST(224666310012885835), UINT64CONST(129381587582470237)},
{UINT64CONST(2446259452971747599), UINT64CONST(80863492239043898)}, {UINT64CONST(12281196353069460307), UINT64CONST(101079365298804872)},
{UINT64CONST(15351495441336825384), UINT64CONST(126349206623506090)}, {UINT64CONST(14206370669262903769), UINT64CONST(78968254139691306)},
{UINT64CONST(8534591299723853903), UINT64CONST(98710317674614133)}, {UINT64CONST(15279925143082205283), UINT64CONST(123387897093267666)},
{UINT64CONST(14161639232853766206), UINT64CONST(77117435683292291)}, {UINT64CONST(13090363022639819853), UINT64CONST(96396794604115364)},
{UINT64CONST(16362953778299774816), UINT64CONST(120495993255144205)}, {UINT64CONST(12532689120651053212), UINT64CONST(75309995784465128)},
{UINT64CONST(15665861400813816515), UINT64CONST(94137494730581410)}, {UINT64CONST(10358954714162494836), UINT64CONST(117671868413226763)},
{UINT64CONST(4168503687137865320), UINT64CONST(73544917758266727)}, {UINT64CONST(598943590494943747), UINT64CONST(91931147197833409)},
{UINT64CONST(5360365506546067587), UINT64CONST(114913933997291761)}, {UINT64CONST(11312142901609972388), UINT64CONST(143642417496614701)},
{UINT64CONST(9375932322719926695), UINT64CONST(89776510935384188)}, {UINT64CONST(11719915403399908368), UINT64CONST(112220638669230235)},
{UINT64CONST(10038208235822497557), UINT64CONST(140275798336537794)}, {UINT64CONST(10885566165816448877), UINT64CONST(87672373960336121)},
{UINT64CONST(18218643725697949000), UINT64CONST(109590467450420151)}, {UINT64CONST(18161618638695048346), UINT64CONST(136988084313025189)},
{UINT64CONST(13656854658398099168), UINT64CONST(85617552695640743)}, {UINT64CONST(12459382304570236056), UINT64CONST(107021940869550929)},
{UINT64CONST(1739169825430631358), UINT64CONST(133777426086938662)}, {UINT64CONST(14922039196176308311), UINT64CONST(83610891304336663)},
{UINT64CONST(14040862976792997485), UINT64CONST(104513614130420829)}, {UINT64CONST(3716020665709083144), UINT64CONST(130642017663026037)},
{UINT64CONST(4628355925281870917), UINT64CONST(81651261039391273)}, {UINT64CONST(10397130925029726550), UINT64CONST(102064076299239091)},
{UINT64CONST(8384727637859770284), UINT64CONST(127580095374048864)}, {UINT64CONST(5240454773662356427), UINT64CONST(79737559608780540)},
{UINT64CONST(6550568467077945534), UINT64CONST(99671949510975675)}, {UINT64CONST(3576524565420044014), UINT64CONST(124589936888719594)},
{UINT64CONST(6847013871814915412), UINT64CONST(77868710555449746)}, {UINT64CONST(17782139376623420074), UINT64CONST(97335888194312182)},
{UINT64CONST(13004302183924499284), UINT64CONST(121669860242890228)}, {UINT64CONST(17351060901807587860), UINT64CONST(76043662651806392)},
{UINT64CONST(3242082053549933210), UINT64CONST(95054578314757991)}, {UINT64CONST(17887660622219580224), UINT64CONST(118818222893447488)},
{UINT64CONST(11179787888887237640), UINT64CONST(74261389308404680)}, {UINT64CONST(13974734861109047050), UINT64CONST(92826736635505850)},
{UINT64CONST(8245046539531533005), UINT64CONST(116033420794382313)}, {UINT64CONST(16682369133275677888), UINT64CONST(72520887996488945)},
{UINT64CONST(7017903361312433648), UINT64CONST(90651109995611182)}, {UINT64CONST(17995751238495317868), UINT64CONST(113313887494513977)},
{UINT64CONST(8659630992836983623), UINT64CONST(141642359368142472)}, {UINT64CONST(5412269370523114764), UINT64CONST(88526474605089045)},
{UINT64CONST(11377022731581281359), UINT64CONST(110658093256361306)}, {UINT64CONST(4997906377621825891), UINT64CONST(138322616570451633)},
{UINT64CONST(14652906532082110942), UINT64CONST(86451635356532270)}, {UINT64CONST(9092761128247862869), UINT64CONST(108064544195665338)},
{UINT64CONST(2142579373455052779), UINT64CONST(135080680244581673)}, {UINT64CONST(12868327154477877747), UINT64CONST(84425425152863545)},
{UINT64CONST(2250350887815183471), UINT64CONST(105531781441079432)}, {UINT64CONST(2812938609768979339), UINT64CONST(131914726801349290)},
{UINT64CONST(6369772649532999991), UINT64CONST(82446704250843306)}, {UINT64CONST(17185587848771025797), UINT64CONST(103058380313554132)},
{UINT64CONST(3035240737254230630), UINT64CONST(128822975391942666)}, {UINT64CONST(6508711479211282048), UINT64CONST(80514359619964166)},
{UINT64CONST(17359261385868878368), UINT64CONST(100642949524955207)}, {UINT64CONST(17087390713908710056), UINT64CONST(125803686906194009)},
{UINT64CONST(3762090168551861929), UINT64CONST(78627304316371256)}, {UINT64CONST(4702612710689827411), UINT64CONST(98284130395464070)},
{UINT64CONST(15101637925217060072), UINT64CONST(122855162994330087)}, {UINT64CONST(16356052730901744401), UINT64CONST(76784476871456304)},
{UINT64CONST(1998321839917628885), UINT64CONST(95980596089320381)}, {UINT64CONST(7109588318324424010), UINT64CONST(119975745111650476)},
{UINT64CONST(13666864735807540814), UINT64CONST(74984840694781547)}, {UINT64CONST(12471894901332038114), UINT64CONST(93731050868476934)},
{UINT64CONST(6366496589810271835), UINT64CONST(117163813585596168)}, {UINT64CONST(3979060368631419896), UINT64CONST(73227383490997605)},
{UINT64CONST(9585511479216662775), UINT64CONST(91534229363747006)}, {UINT64CONST(2758517312166052660), UINT64CONST(114417786704683758)},
{UINT64CONST(12671518677062341634), UINT64CONST(143022233380854697)}, {UINT64CONST(1002170145522881665), UINT64CONST(89388895863034186)},
{UINT64CONST(10476084718758377889), UINT64CONST(111736119828792732)}, {UINT64CONST(13095105898447972362), UINT64CONST(139670149785990915)},
{UINT64CONST(5878598177316288774), UINT64CONST(87293843616244322)}, {UINT64CONST(16571619758500136775), UINT64CONST(109117304520305402)},
{UINT64CONST(11491152661270395161), UINT64CONST(136396630650381753)}, {UINT64CONST(264441385652915120), UINT64CONST(85247894156488596)},
{UINT64CONST(330551732066143900), UINT64CONST(106559867695610745)}, {UINT64CONST(5024875683510067779), UINT64CONST(133199834619513431)},
{UINT64CONST(10058076329834874218), UINT64CONST(83249896637195894)}, {UINT64CONST(3349223375438816964), UINT64CONST(104062370796494868)},
{UINT64CONST(4186529219298521205), UINT64CONST(130077963495618585)}, {UINT64CONST(14145795808130045513), UINT64CONST(81298727184761615)},
{UINT64CONST(13070558741735168987), UINT64CONST(101623408980952019)}, {UINT64CONST(11726512408741573330), UINT64CONST(127029261226190024)},
{UINT64CONST(7329070255463483331), UINT64CONST(79393288266368765)}, {UINT64CONST(13773023837756742068), UINT64CONST(99241610332960956)},
{UINT64CONST(17216279797195927585), UINT64CONST(124052012916201195)}, {UINT64CONST(8454331864033760789), UINT64CONST(77532508072625747)},
{UINT64CONST(5956228811614813082), UINT64CONST(96915635090782184)}, {UINT64CONST(7445286014518516353), UINT64CONST(121144543863477730)},
{UINT64CONST(9264989777501460624), UINT64CONST(75715339914673581)}, {UINT64CONST(16192923240304213684), UINT64CONST(94644174893341976)},
{UINT64CONST(1794409976670715490), UINT64CONST(118305218616677471)}, {UINT64CONST(8039035263060279037), UINT64CONST(73940761635423419)},
{UINT64CONST(5437108060397960892), UINT64CONST(92425952044279274)}, {UINT64CONST(16019757112352226923), UINT64CONST(115532440055349092)},
{UINT64CONST(788976158365366019), UINT64CONST(72207775034593183)}, {UINT64CONST(14821278253238871236), UINT64CONST(90259718793241478)},
{UINT64CONST(9303225779693813237), UINT64CONST(112824648491551848)}, {UINT64CONST(11629032224617266546), UINT64CONST(141030810614439810)},
{UINT64CONST(11879831158813179495), UINT64CONST(88144256634024881)}, {UINT64CONST(1014730893234310657), UINT64CONST(110180320792531102)},
{UINT64CONST(10491785653397664129), UINT64CONST(137725400990663877)}, {UINT64CONST(8863209042587234033), UINT64CONST(86078375619164923)},
{UINT64CONST(6467325284806654637), UINT64CONST(107597969523956154)}, {UINT64CONST(17307528642863094104), UINT64CONST(134497461904945192)},
{UINT64CONST(10817205401789433815), UINT64CONST(84060913690590745)}, {UINT64CONST(18133192770664180173), UINT64CONST(105076142113238431)},
{UINT64CONST(18054804944902837312), UINT64CONST(131345177641548039)}, {UINT64CONST(18201782118205355176), UINT64CONST(82090736025967524)},
{UINT64CONST(4305483574047142354), UINT64CONST(102613420032459406)}, {UINT64CONST(14605226504413703751), UINT64CONST(128266775040574257)},
{UINT64CONST(2210737537617482988), UINT64CONST(80166734400358911)}, {UINT64CONST(16598479977304017447), UINT64CONST(100208418000448638)},
{UINT64CONST(11524727934775246001), UINT64CONST(125260522500560798)}, {UINT64CONST(2591268940807140847), UINT64CONST(78287826562850499)},
{UINT64CONST(17074144231291089770), UINT64CONST(97859783203563123)}, {UINT64CONST(16730994270686474309), UINT64CONST(122324729004453904)},
{UINT64CONST(10456871419179046443), UINT64CONST(76452955627783690)}, {UINT64CONST(3847717237119032246), UINT64CONST(95566194534729613)},
{UINT64CONST(9421332564826178211), UINT64CONST(119457743168412016)}, {UINT64CONST(5888332853016361382), UINT64CONST(74661089480257510)},
{UINT64CONST(16583788103125227536), UINT64CONST(93326361850321887)}, {UINT64CONST(16118049110479146516), UINT64CONST(116657952312902359)},
{UINT64CONST(16991309721690548428), UINT64CONST(72911220195563974)}, {UINT64CONST(12015765115258409727), UINT64CONST(91139025244454968)},
{UINT64CONST(15019706394073012159), UINT64CONST(113923781555568710)}, {UINT64CONST(9551260955736489391), UINT64CONST(142404726944460888)},
{UINT64CONST(5969538097335305869), UINT64CONST(89002954340288055)}, {UINT64CONST(2850236603241744433), UINT64CONST(111253692925360069)}
};
#endif /* RYU_D2S_FULL_TABLE_H */

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src/common/d2s_intrinsics.h
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/*---------------------------------------------------------------------------
*
* Ryu floating-point output for double precision.
*
* Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
*
* IDENTIFICATION
* src/common/d2s_intrinsics.h
*
* This is a modification of code taken from github.com/ulfjack/ryu under the
* terms of the Boost license (not the Apache license). The original copyright
* notice follows:
*
* Copyright 2018 Ulf Adams
*
* The contents of this file may be used under the terms of the Apache
* License, Version 2.0.
*
* (See accompanying file LICENSE-Apache or copy at
* http://www.apache.org/licenses/LICENSE-2.0)
*
* Alternatively, the contents of this file may be used under the terms of the
* Boost Software License, Version 1.0.
*
* (See accompanying file LICENSE-Boost or copy at
* https://www.boost.org/LICENSE_1_0.txt)
*
* Unless required by applicable law or agreed to in writing, this software is
* distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied.
*
*---------------------------------------------------------------------------
*/
#ifndef RYU_D2S_INTRINSICS_H
#define RYU_D2S_INTRINSICS_H
#if defined(HAS_64_BIT_INTRINSICS)
#include <intrin.h>
static inline uint64
umul128(const uint64 a, const uint64 b, uint64 *const productHi)
{
return _umul128(a, b, productHi);
}
static inline uint64
shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
{
/*
* For the __shiftright128 intrinsic, the shift value is always modulo 64.
* In the current implementation of the double-precision version of Ryu,
* the shift value is always < 64. (In the case RYU_OPTIMIZE_SIZE == 0,
* the shift value is in the range [49, 58]. Otherwise in the range [2,
* 59].) Check this here in case a future change requires larger shift
* values. In this case this function needs to be adjusted.
*/
Assert(dist < 64);
return __shiftright128(lo, hi, (unsigned char) dist);
}
#else /* defined(HAS_64_BIT_INTRINSICS) */
static inline uint64
umul128(const uint64 a, const uint64 b, uint64 *const productHi)
{
/*
* The casts here help MSVC to avoid calls to the __allmul library
* function.
*/
const uint32 aLo = (uint32) a;
const uint32 aHi = (uint32) (a >> 32);
const uint32 bLo = (uint32) b;
const uint32 bHi = (uint32) (b >> 32);
const uint64 b00 = (uint64) aLo * bLo;
const uint64 b01 = (uint64) aLo * bHi;
const uint64 b10 = (uint64) aHi * bLo;
const uint64 b11 = (uint64) aHi * bHi;
const uint32 b00Lo = (uint32) b00;
const uint32 b00Hi = (uint32) (b00 >> 32);
const uint64 mid1 = b10 + b00Hi;
const uint32 mid1Lo = (uint32) (mid1);
const uint32 mid1Hi = (uint32) (mid1 >> 32);
const uint64 mid2 = b01 + mid1Lo;
const uint32 mid2Lo = (uint32) (mid2);
const uint32 mid2Hi = (uint32) (mid2 >> 32);
const uint64 pHi = b11 + mid1Hi + mid2Hi;
const uint64 pLo = ((uint64) mid2Lo << 32) + b00Lo;
*productHi = pHi;
return pLo;
}
static inline uint64
shiftright128(const uint64 lo, const uint64 hi, const uint32 dist)
{
/* We don't need to handle the case dist >= 64 here (see above). */
Assert(dist < 64);
#if !defined(RYU_32_BIT_PLATFORM)
Assert(dist > 0);
return (hi << (64 - dist)) | (lo >> dist);
#else
/* Avoid a 64-bit shift by taking advantage of the range of shift values. */
Assert(dist >= 32);
return (hi << (64 - dist)) | ((uint32) (lo >> 32) >> (dist - 32));
#endif
}
#endif /* // defined(HAS_64_BIT_INTRINSICS) */
#ifdef RYU_32_BIT_PLATFORM
/* Returns the high 64 bits of the 128-bit product of a and b. */
static inline uint64
umulh(const uint64 a, const uint64 b)
{
/*
* Reuse the umul128 implementation. Optimizers will likely eliminate the
* instructions used to compute the low part of the product.
*/
uint64 hi;
umul128(a, b, &hi);
return hi;
}
/*----
* On 32-bit platforms, compilers typically generate calls to library
* functions for 64-bit divisions, even if the divisor is a constant.
*
* E.g.:
* https://bugs.llvm.org/show_bug.cgi?id=37932
* https://gcc.gnu.org/bugzilla/show_bug.cgi?id=17958
* https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37443
*
* The functions here perform division-by-constant using multiplications
* in the same way as 64-bit compilers would do.
*
* NB:
* The multipliers and shift values are the ones generated by clang x64
* for expressions like x/5, x/10, etc.
*----
*/
static inline uint64
div5(const uint64 x)
{
return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 2;
}
static inline uint64
div10(const uint64 x)
{
return umulh(x, UINT64CONST(0xCCCCCCCCCCCCCCCD)) >> 3;
}
static inline uint64
div100(const uint64 x)
{
return umulh(x >> 2, UINT64CONST(0x28F5C28F5C28F5C3)) >> 2;
}
static inline uint64
div1e8(const uint64 x)
{
return umulh(x, UINT64CONST(0xABCC77118461CEFD)) >> 26;
}
#else /* RYU_32_BIT_PLATFORM */
static inline uint64
div5(const uint64 x)
{
return x / 5;
}
static inline uint64
div10(const uint64 x)
{
return x / 10;
}
static inline uint64
div100(const uint64 x)
{
return x / 100;
}
static inline uint64
div1e8(const uint64 x)
{
return x / 100000000;
}
#endif /* RYU_32_BIT_PLATFORM */
#endif /* RYU_D2S_INTRINSICS_H */

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src/common/digit_table.h
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#ifndef RYU_DIGIT_TABLE_H
#define RYU_DIGIT_TABLE_H
/*
* A table of all two-digit numbers. This is used to speed up decimal digit
* generation by copying pairs of digits into the final output.
*/
static const char DIGIT_TABLE[200] = {
'0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
'1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
'2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
'3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
'4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
'5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
'6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
'7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
'8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
'9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
};
#endif /* RYU_DIGIT_TABLE_H */

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src/common/f2s.c
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/*---------------------------------------------------------------------------
*
* Ryu floating-point output for single precision.
*
* Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
*
* IDENTIFICATION
* src/common/f2s.c
*
* This is a modification of code taken from github.com/ulfjack/ryu under the
* terms of the Boost license (not the Apache license). The original copyright
* notice follows:
*
* Copyright 2018 Ulf Adams
*
* The contents of this file may be used under the terms of the Apache
* License, Version 2.0.
*
* (See accompanying file LICENSE-Apache or copy at
* http://www.apache.org/licenses/LICENSE-2.0)
*
* Alternatively, the contents of this file may be used under the terms of the
* Boost Software License, Version 1.0.
*
* (See accompanying file LICENSE-Boost or copy at
* https://www.boost.org/LICENSE_1_0.txt)
*
* Unless required by applicable law or agreed to in writing, this software is
* distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied.
*
*---------------------------------------------------------------------------
*/
#ifndef FRONTEND
#include "postgres.h"
#else
#include "postgres_fe.h"
#endif
#include "common/shortest_dec.h"
#include "ryu_common.h"
#include "digit_table.h"
#define FLOAT_MANTISSA_BITS 23
#define FLOAT_EXPONENT_BITS 8
#define FLOAT_BIAS 127
/*
* This table is generated (by the upstream) by PrintFloatLookupTable,
* and modified (by us) to add UINT64CONST.
*/
#define FLOAT_POW5_INV_BITCOUNT 59
static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
};
#define FLOAT_POW5_BITCOUNT 61
static const uint64 FLOAT_POW5_SPLIT[47] = {
UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
};
static inline uint32
pow5Factor(uint32 value)
{
uint32 count = 0;
for (;;)
{
Assert(value != 0);
const uint32 q = value / 5;
const uint32 r = value % 5;
if (r != 0)
break;
value = q;
++count;
}
return count;
}
/* Returns true if value is divisible by 5^p. */
static inline bool
multipleOfPowerOf5(const uint32 value, const uint32 p)
{
return pow5Factor(value) >= p;
}
/* Returns true if value is divisible by 2^p. */
static inline bool
multipleOfPowerOf2(const uint32 value, const uint32 p)
{
/* return __builtin_ctz(value) >= p; */
return (value & ((1u << p) - 1)) == 0;
}
/*
* It seems to be slightly faster to avoid uint128_t here, although the
* generated code for uint128_t looks slightly nicer.
*/
static inline uint32
mulShift(const uint32 m, const uint64 factor, const int32 shift)
{
/*
* The casts here help MSVC to avoid calls to the __allmul library
* function.
*/
const uint32 factorLo = (uint32) (factor);
const uint32 factorHi = (uint32) (factor >> 32);
const uint64 bits0 = (uint64) m * factorLo;
const uint64 bits1 = (uint64) m * factorHi;
Assert(shift > 32);
#ifdef RYU_32_BIT_PLATFORM
/*
* On 32-bit platforms we can avoid a 64-bit shift-right since we only
* need the upper 32 bits of the result and the shift value is > 32.
*/
const uint32 bits0Hi = (uint32) (bits0 >> 32);
uint32 bits1Lo = (uint32) (bits1);
uint32 bits1Hi = (uint32) (bits1 >> 32);
bits1Lo += bits0Hi;
bits1Hi += (bits1Lo < bits0Hi);
const int32 s = shift - 32;
return (bits1Hi << (32 - s)) | (bits1Lo >> s);
#else /* RYU_32_BIT_PLATFORM */
const uint64 sum = (bits0 >> 32) + bits1;
const uint64 shiftedSum = sum >> (shift - 32);
Assert(shiftedSum <= UINT32_MAX);
return (uint32) shiftedSum;
#endif /* RYU_32_BIT_PLATFORM */
}
static inline uint32
mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
{
return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
}
static inline uint32
mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
{
return mulShift(m, FLOAT_POW5_SPLIT[i], j);
}
static inline uint32
decimalLength(const uint32 v)
{
/* Function precondition: v is not a 10-digit number. */
/* (9 digits are sufficient for round-tripping.) */
Assert(v < 1000000000);
if (v >= 100000000)
{
return 9;
}
if (v >= 10000000)
{
return 8;
}
if (v >= 1000000)
{
return 7;
}
if (v >= 100000)
{
return 6;
}
if (v >= 10000)
{
return 5;
}
if (v >= 1000)
{
return 4;
}
if (v >= 100)
{
return 3;
}
if (v >= 10)
{
return 2;
}
return 1;
}
/* A floating decimal representing m * 10^e. */
typedef struct floating_decimal_32
{
uint32 mantissa;
int32 exponent;
} floating_decimal_32;
static inline floating_decimal_32
f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
{
int32 e2;
uint32 m2;
if (ieeeExponent == 0)
{
/* We subtract 2 so that the bounds computation has 2 additional bits. */
e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
m2 = ieeeMantissa;
}
else
{
e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
}
#if STRICTLY_SHORTEST
const bool even = (m2 & 1) == 0;
const bool acceptBounds = even;
#else
const bool acceptBounds = false;
#endif
/* Step 2: Determine the interval of legal decimal representations. */
const uint32 mv = 4 * m2;
const uint32 mp = 4 * m2 + 2;
/* Implicit bool -> int conversion. True is 1, false is 0. */
const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
const uint32 mm = 4 * m2 - 1 - mmShift;
/* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
uint32 vr,
vp,
vm;
int32 e10;
bool vmIsTrailingZeros = false;
bool vrIsTrailingZeros = false;
uint8 lastRemovedDigit = 0;
if (e2 >= 0)
{
const uint32 q = log10Pow2(e2);
e10 = q;
const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
const int32 i = -e2 + q + k;
vr = mulPow5InvDivPow2(mv, q, i);
vp = mulPow5InvDivPow2(mp, q, i);
vm = mulPow5InvDivPow2(mm, q, i);
if (q != 0 && (vp - 1) / 10 <= vm / 10)
{
/*
* We need to know one removed digit even if we are not going to
* loop below. We could use q = X - 1 above, except that would
* require 33 bits for the result, and we've found that 32-bit
* arithmetic is faster even on 64-bit machines.
*/
const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
}
if (q <= 9)
{
/*
* The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
* seems to be safe as well.
*
* Only one of mp, mv, and mm can be a multiple of 5, if any.
*/
if (mv % 5 == 0)
{
vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
}
else if (acceptBounds)
{
vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
}
else
{
vp -= multipleOfPowerOf5(mp, q);
}
}
}
else
{
const uint32 q = log10Pow5(-e2);
e10 = q + e2;
const int32 i = -e2 - q;
const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
int32 j = q - k;
vr = mulPow5divPow2(mv, i, j);
vp = mulPow5divPow2(mp, i, j);
vm = mulPow5divPow2(mm, i, j);
if (q != 0 && (vp - 1) / 10 <= vm / 10)
{
j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
}
if (q <= 1)
{
/*
* {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
* trailing 0 bits.
*/
/* mv = 4 * m2, so it always has at least two trailing 0 bits. */
vrIsTrailingZeros = true;
if (acceptBounds)
{
/*
* mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
* mmShift == 1.
*/
vmIsTrailingZeros = mmShift == 1;
}
else
{
/*
* mp = mv + 2, so it always has at least one trailing 0 bit.
*/
--vp;
}
}
else if (q < 31)
{
/* TODO(ulfjack):Use a tighter bound here. */
vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
}
}
/*
* Step 4: Find the shortest decimal representation in the interval of
* legal representations.
*/
uint32 removed = 0;
uint32 output;
if (vmIsTrailingZeros || vrIsTrailingZeros)
{
/* General case, which happens rarely (~4.0%). */
while (vp / 10 > vm / 10)
{
vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8) (vr % 10);
vr /= 10;
vp /= 10;
vm /= 10;
++removed;
}
if (vmIsTrailingZeros)
{
while (vm % 10 == 0)
{
vrIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (uint8) (vr % 10);
vr /= 10;
vp /= 10;
vm /= 10;
++removed;
}
}
if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
{
/* Round even if the exact number is .....50..0. */
lastRemovedDigit = 4;
}
/*
* We need to take vr + 1 if vr is outside bounds or we need to round
* up.
*/
output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
}
else
{
/*
* Specialized for the common case (~96.0%). Percentages below are
* relative to this.
*
* Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
* 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
*/
while (vp / 10 > vm / 10)
{
lastRemovedDigit = (uint8) (vr % 10);
vr /= 10;
vp /= 10;
vm /= 10;
++removed;
}
/*
* We need to take vr + 1 if vr is outside bounds or we need to round
* up.
*/
output = vr + (vr == vm || lastRemovedDigit >= 5);
}
const int32 exp = e10 + removed;
floating_decimal_32 fd;
fd.exponent = exp;
fd.mantissa = output;
return fd;
}
static inline int
to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
{
/* Step 5: Print the decimal representation. */
int index = 0;
uint32 output = v.mantissa;
int32 exp = v.exponent;
/*----
* On entry, mantissa * 10^exp is the result to be output.
* Caller has already done the - sign if needed.
*
* We want to insert the point somewhere depending on the output length
* and exponent, which might mean adding zeros:
*
* exp | format
* 1+ | ddddddddd000000
* 0 | ddddddddd
* -1 .. -len+1 | dddddddd.d to d.ddddddddd
* -len ... | 0.ddddddddd to 0.000dddddd
*/
uint32 i = 0;
int32 nexp = exp + olength;
if (nexp <= 0)
{
/* -nexp is number of 0s to add after '.' */
Assert(nexp >= -3);
/* 0.000ddddd */
index = 2 - nexp;
/* copy 8 bytes rather than 5 to let compiler optimize */
memcpy(result, "0.000000", 8);
}
else if (exp < 0)
{
/*
* dddd.dddd; leave space at the start and move the '.' in after
*/
index = 1;
}
else
{
/*
* We can save some code later by pre-filling with zeros. We know
* that there can be no more than 6 output digits in this form,
* otherwise we would not choose fixed-point output. memset 8
* rather than 6 bytes to let the compiler optimize it.
*/
Assert(exp < 6 && exp + olength <= 6);
memset(result, '0', 8);
}
while (output >= 10000)
{
const uint32 c = output - 10000 * (output / 10000);
const uint32 c0 = (c % 100) << 1;
const uint32 c1 = (c / 100) << 1;
output /= 10000;
memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
i += 4;
}
if (output >= 100)
{
const uint32 c = (output % 100) << 1;
output /= 100;
memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
i += 2;
}
if (output >= 10)
{
const uint32 c = output << 1;
memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
}
else
{
result[index] = (char) ('0' + output);
}
if (index == 1)
{
/*
* nexp is 1..6 here, representing the number of digits before the
* point. A value of 7+ is not possible because we switch to
* scientific notation when the display exponent reaches 6.
*/
Assert(nexp < 7);
/* gcc only seems to want to optimize memmove for small 2^n */
if (nexp & 4)
{
memmove(result + index - 1, result + index, 4);
index += 4;
}
if (nexp & 2)
{
memmove(result + index - 1, result + index, 2);
index += 2;
}
if (nexp & 1)
{
result[index - 1] = result[index];
}
result[nexp] = '.';
index = olength + 1;
}
else if (exp >= 0)
{
/* we supplied the trailing zeros earlier, now just set the length. */
index = olength + exp;
}
else
{
index = olength + (2 - nexp);
}
return index;
}
static inline int
to_chars(const floating_decimal_32 v, const bool sign, char *const result)
{
/* Step 5: Print the decimal representation. */
int index = 0;
uint32 output = v.mantissa;
uint32 olength = decimalLength(output);
int32 exp = v.exponent + olength - 1;
if (sign)
result[index++] = '-';
/*
* The thresholds for fixed-point output are chosen to match printf
* defaults. Beware that both the code of to_chars_f and the value
* of FLOAT_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
*/
if (exp >= -4 && exp < 6)
return to_chars_f(v, olength, result + index) + sign;
/*
* If v.exponent is exactly 0, we might have reached here via the small
* integer fast path, in which case v.mantissa might contain trailing
* (decimal) zeros. For scientific notation we need to move these zeros
* into the exponent. (For fixed point this doesn't matter, which is why
* we do this here rather than above.)
*
* Since we already calculated the display exponent (exp) above based on
* the old decimal length, that value does not change here. Instead, we
* just reduce the display length for each digit removed.
*
* If we didn't get here via the fast path, the raw exponent will not
* usually be 0, and there will be no trailing zeros, so we pay no more
* than one div10/multiply extra cost. We claw back half of that by
* checking for divisibility by 2 before dividing by 10.
*/
if (v.exponent == 0)
{
while ((output & 1) == 0)
{
const uint32 q = output / 10;
const uint32 r = output - 10 * q;
if (r != 0)
break;
output = q;
--olength;
}
}
/*----
* Print the decimal digits.
* The following code is equivalent to:
*
* for (uint32 i = 0; i < olength - 1; ++i) {
* const uint32 c = output % 10; output /= 10;
* result[index + olength - i] = (char) ('0' + c);
* }
* result[index] = '0' + output % 10;
*/
uint32 i = 0;
while (output >= 10000)
{
const uint32 c = output - 10000 * (output / 10000);
const uint32 c0 = (c % 100) << 1;
const uint32 c1 = (c / 100) << 1;
output /= 10000;
memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
i += 4;
}
if (output >= 100)
{
const uint32 c = (output % 100) << 1;
output /= 100;
memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
i += 2;
}
if (output >= 10)
{
const uint32 c = output << 1;
/*
* We can't use memcpy here: the decimal dot goes between these two
* digits.
*/
result[index + olength - i] = DIGIT_TABLE[c + 1];
result[index] = DIGIT_TABLE[c];
}
else
{
result[index] = (char) ('0' + output);
}
/* Print decimal point if needed. */
if (olength > 1)
{
result[index + 1] = '.';
index += olength + 1;
}
else
{
++index;
}
/* Print the exponent. */
result[index++] = 'e';
if (exp < 0)
{
result[index++] = '-';
exp = -exp;
}
else
result[index++] = '+';
memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
index += 2;
return index;
}
static inline bool
f2d_small_int(const uint32 ieeeMantissa,
const uint32 ieeeExponent,
floating_decimal_32 *v)
{
const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS;
/*
* Avoid using multiple "return false;" here since it tends to provoke the
* compiler into inlining multiple copies of f2d, which is undesirable.
*/
if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0)
{
/*----
* Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23:
* 1 <= f = m2 / 2^-e2 < 2^24.
*
* Test if the lower -e2 bits of the significand are 0, i.e. whether
* the fraction is 0. We can use ieeeMantissa here, since the implied
* 1 bit can never be tested by this; the implied 1 can only be part
* of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already
* checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24)
*/
const uint32 mask = (1U << -e2) - 1;
const uint32 fraction = ieeeMantissa & mask;
if (fraction == 0)
{
/*----
* f is an integer in the range [1, 2^24).
* Note: mantissa might contain trailing (decimal) 0's.
* Note: since 2^24 < 10^9, there is no need to adjust
* decimalLength().
*/
const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
v->mantissa = m2 >> -e2;
v->exponent = 0;
return true;
}
}
return false;
}
/*
* Store the shortest decimal representation of the given float as an
* UNTERMINATED string in the caller's supplied buffer (which must be at least
* FLOAT_SHORTEST_DECIMAL_LEN-1 bytes long).
*
* Returns the number of bytes stored.
*/
int
float_to_shortest_decimal_bufn(float f, char *result)
{
/*
* Step 1: Decode the floating-point number, and unify normalized and
* subnormal cases.
*/
const uint32 bits = float_to_bits(f);
/* Decode bits into sign, mantissa, and exponent. */
const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
/* Case distinction; exit early for the easy cases. */
if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
{
return copy_special_str(result, ieeeSign, ieeeExponent, ieeeMantissa);
}
floating_decimal_32 v;
const bool isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v);
if (!isSmallInt)
{
v = f2d(ieeeMantissa, ieeeExponent);
}
return to_chars(v, ieeeSign, result);
}
/*
* Store the shortest decimal representation of the given float as a
* null-terminated string in the caller's supplied buffer (which must be at
* least FLOAT_SHORTEST_DECIMAL_LEN bytes long).
*
* Returns the string length.
*/
int
float_to_shortest_decimal_buf(float f, char *result)
{
const int index = float_to_shortest_decimal_bufn(f, result);
/* Terminate the string. */
Assert(index < FLOAT_SHORTEST_DECIMAL_LEN);
result[index] = '\0';
return index;
}
/*
* Return the shortest decimal representation as a null-terminated palloc'd
* string (outside the backend, uses malloc() instead).
*
* Caller is responsible for freeing the result.
*/
char *
float_to_shortest_decimal(float f)
{
char *const result = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN);
float_to_shortest_decimal_buf(f, result);
return result;
}

133
src/common/ryu_common.h
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/*---------------------------------------------------------------------------
*
* Common routines for Ryu floating-point output.
*
* Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
*
* IDENTIFICATION
* src/common/ryu_common.h
*
* This is a modification of code taken from github.com/ulfjack/ryu under the
* terms of the Boost license (not the Apache license). The original copyright
* notice follows:
*
* Copyright 2018 Ulf Adams
*
* The contents of this file may be used under the terms of the Apache
* License, Version 2.0.
*
* (See accompanying file LICENSE-Apache or copy at
* http://www.apache.org/licenses/LICENSE-2.0)
*
* Alternatively, the contents of this file may be used under the terms of the
* Boost Software License, Version 1.0.
*
* (See accompanying file LICENSE-Boost or copy at
* https://www.boost.org/LICENSE_1_0.txt)
*
* Unless required by applicable law or agreed to in writing, this software is
* distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied.
*
*---------------------------------------------------------------------------
*/
#ifndef RYU_COMMON_H
#define RYU_COMMON_H
/*
* Upstream Ryu's output is always the shortest possible. But we adjust that
* slightly to improve portability: we avoid outputting the exact midpoint
* value between two representable floats, since that relies on the reader
* getting the round-to-even rule correct, which seems to be the common
* failure mode.
*
* Defining this to 1 would restore the upstream behavior.
*/
#define STRICTLY_SHORTEST 0
#if SIZEOF_SIZE_T < 8
#define RYU_32_BIT_PLATFORM
#endif
/* Returns e == 0 ? 1 : ceil(log_2(5^e)). */
static inline uint32
pow5bits(const int32 e)
{
/*
* This approximation works up to the point that the multiplication
* overflows at e = 3529.
*
* If the multiplication were done in 64 bits, it would fail at 5^4004
* which is just greater than 2^9297.
*/
Assert(e >= 0);
Assert(e <= 3528);
return ((((uint32) e) * 1217359) >> 19) + 1;
}
/* Returns floor(log_10(2^e)). */
static inline int32
log10Pow2(const int32 e)
{
/*
* The first value this approximation fails for is 2^1651 which is just
* greater than 10^297.
*/
Assert(e >= 0);
Assert(e <= 1650);
return (int32) ((((uint32) e) * 78913) >> 18);
}
/* Returns floor(log_10(5^e)). */
static inline int32
log10Pow5(const int32 e)
{
/*
* The first value this approximation fails for is 5^2621 which is just
* greater than 10^1832.
*/
Assert(e >= 0);
Assert(e <= 2620);
return (int32) ((((uint32) e) * 732923) >> 20);
}
static inline int
copy_special_str(char *const result, const bool sign, const bool exponent, const bool mantissa)
{
if (mantissa)
{
memcpy(result, "NaN", 3);
return 3;
}
if (sign)
{
result[0] = '-';
}
if (exponent)
{
memcpy(result + sign, "Infinity", 8);
return sign + 8;
}
result[sign] = '0';
return sign + 1;
}
static inline uint32
float_to_bits(const float f)
{
uint32 bits = 0;
memcpy(&bits, &f, sizeof(float));
return bits;
}
static inline uint64
double_to_bits(const double d)
{
uint64 bits = 0;
memcpy(&bits, &d, sizeof(double));
return bits;
}
#endif /* RYU_COMMON_H */

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src/include/common/shortest_dec.h
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/*---------------------------------------------------------------------------
*
* Ryu floating-point output.
*
* Portions Copyright (c) 2018-2019, PostgreSQL Global Development Group
*
* IDENTIFICATION
* src/include/common/shortest_dec.h
*
* This is a modification of code taken from github.com/ulfjack/ryu under the
* terms of the Boost license (not the Apache license). The original copyright
* notice follows:
*
* Copyright 2018 Ulf Adams
*
* The contents of this file may be used under the terms of the Apache
* License, Version 2.0.
*
* (See accompanying file LICENSE-Apache or copy at
* http://www.apache.org/licenses/LICENSE-2.0)
*
* Alternatively, the contents of this file may be used under the terms of the
* Boost Software License, Version 1.0.
*
* (See accompanying file LICENSE-Boost or copy at
* https://www.boost.org/LICENSE_1_0.txt)
*
* Unless required by applicable law or agreed to in writing, this software is
* distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied.
*
*---------------------------------------------------------------------------
*/
#ifndef SHORTEST_DEC_H
#define SHORTEST_DEC_H
/*----
* The length of 25 comes from:
*
* Case 1: -9.9999999999999999e-299 = 24 bytes, plus 1 for null
*
* Case 2: -0.00099999999999999999 = 23 bytes, plus 1 for null
*/
#define DOUBLE_SHORTEST_DECIMAL_LEN 25
int double_to_shortest_decimal_bufn(double f, char *result);
int double_to_shortest_decimal_buf(double f, char *result);
char *double_to_shortest_decimal(double f);
/*
* The length of 16 comes from:
*
* Case 1: -9.99999999e+29 = 15 bytes, plus 1 for null
*
* Case 2: -0.000999999999 = 15 bytes, plus 1 for null
*/
#define FLOAT_SHORTEST_DECIMAL_LEN 16
int float_to_shortest_decimal_bufn(float f, char *result);
int float_to_shortest_decimal_buf(float f, char *result);
char *float_to_shortest_decimal(float f);
#endif /* SHORTEST_DEC_H */

2
src/test/regress/expected/aggregates.out
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@ -1,6 +1,8 @@
--
-- AGGREGATES
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
avg_1
--------------------

2
src/test/regress/expected/circle.out
Unescape View File

@ -1,6 +1,8 @@
--
-- CIRCLE
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');
INSERT INTO CIRCLE_TBL VALUES ('<(1,2),100>');

574
src/test/regress/expected/float4-misrounded-input.out
Unescape View File

@ -143,21 +143,21 @@ SELECT 'nan'::numeric::float4;
SELECT '' AS five, * FROM FLOAT4_TBL;
five | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e+20
| 1.23457e-20
| 1.2345679e+20
| 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
four | f1
------+-------------
------+---------------
| 0
| -34.84
| 1.23457e+20
| 1.23457e-20
| 1.2345679e+20
| 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@ -168,72 +168,72 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
three | f1
-------+-------------
-------+---------------
| 0
| -34.84
| 1.23457e-20
| 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
three | f1
-------+-------------
-------+---------------
| 0
| -34.84
| 1.23457e-20
| 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
four | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e-20
| 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
four | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e-20
| 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+--------------
-------+---------------+----------------
| 1004.3 | -10043
| 1.23457e+20 | -1.23457e+21
| 1.23457e-20 | -1.23457e-19
| 1.2345679e+20 | -1.2345678e+21
| 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+-------------
-------+---------------+---------------
| 1004.3 | 994.3
| 1.23457e+20 | 1.23457e+20
| 1.23457e-20 | -10
| 1.2345679e+20 | 1.2345679e+20
| 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+--------------
-------+---------------+----------------
| 1004.3 | -100.43
| 1.23457e+20 | -1.23457e+19
| 1.23457e-20 | -1.23457e-21
| 1.2345679e+20 | -1.2345679e+19
| 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+-------------
-------+---------------+---------------
| 1004.3 | 1014.3
| 1.23457e+20 | 1.23457e+20
| 1.23457e-20 | 10
| 1.2345679e+20 | 1.2345679e+20
| 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
@ -241,23 +241,23 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
five | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e+20
| 1.23457e-20
| 1.2345679e+20
| 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
five | f1 | abs_f1
------+-------------+-------------
------+---------------+---------------
| 0 | 0
| 1004.3 | 1004.3
| -34.84 | 34.84
| 1.23457e+20 | 1.23457e+20
| 1.23457e-20 | 1.23457e-20
| 1.2345679e+20 | 1.2345679e+20
| 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
@ -265,12 +265,12 @@ UPDATE FLOAT4_TBL
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
five | f1
------+--------------
------+----------------
| 0
| -34.84
| -1004.3
| -1.23457e+20
| -1.23457e-20
| -1.2345679e+20
| -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@ -434,3 +434,507 @@ SELECT float4send('1.1754944e-38'::float4);
\x00800000
(1 row)
-- test output (and round-trip safety) of various values.
-- To ensure we're testing what we think we're testing, start with
-- float values specified by bit patterns (as a useful side effect,
-- this means we'll fail on non-IEEE platforms).
create type xfloat4;
create function xfloat4in(cstring) returns xfloat4 immutable strict
language internal as 'int4in';
NOTICE: return type xfloat4 is only a shell
create function xfloat4out(xfloat4) returns cstring immutable strict
language internal as 'int4out';
NOTICE: argument type xfloat4 is only a shell
create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
create cast (xfloat4 as float4) without function;
create cast (float4 as xfloat4) without function;
create cast (xfloat4 as integer) without function;
create cast (integer as xfloat4) without function;
-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
-- we don't care to assume the platform's strtod() handles subnormals
-- correctly; those are "use at your own risk". However we do test
-- subnormal outputs, since those are under our control.
with testdata(bits) as (values
-- small subnormals
(x'00000001'),
(x'00000002'), (x'00000003'),
(x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
(x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
-- stress values
(x'0053c4f4'), -- 7693e-42
(x'006c85c4'), -- 996622e-44
(x'0041ca76'), -- 60419369e-46
(x'004b7678'), -- 6930161142e-48
-- taken from upstream testsuite
(x'00000007'),
(x'00424fe2'),
-- borderline between subnormal and normal
(x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
select float4send(flt) as ibits,
flt
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
ibits | flt
------------+---------------
\x00000001 | 1e-45
\x00000002 | 3e-45
\x00000003 | 4e-45
\x00000010 | 2.2e-44
\x00000011 | 2.4e-44
\x00000100 | 3.59e-43
\x00000101 | 3.6e-43
\x00004000 | 2.2959e-41
\x00004001 | 2.296e-41
\x00080000 | 7.34684e-40
\x00080001 | 7.34685e-40
\x0053c4f4 | 7.693e-39
\x006c85c4 | 9.96622e-39
\x0041ca76 | 6.041937e-39
\x004b7678 | 6.930161e-39
\x00000007 | 1e-44
\x00424fe2 | 6.0898e-39
\x007ffff0 | 1.1754921e-38
\x007ffff1 | 1.1754922e-38
\x007ffffe | 1.1754941e-38
\x007fffff | 1.1754942e-38
(21 rows)
with testdata(bits) as (values
(x'00000000'),
-- smallest normal values
(x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
(x'00800006'),
-- small normal values chosen for short vs. long output
(x'008002f1'), (x'008002f2'), (x'008002f3'),
(x'00800e17'), (x'00800e18'), (x'00800e19'),
-- assorted values (random mantissae)
(x'01000001'), (x'01102843'), (x'01a52c98'),
(x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
(x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
(x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
(x'1f850283'), (x'2874a9d6'),
-- values around 5e-08
(x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
-- around 1e-07
(x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
-- around 3e-07 .. 1e-04
(x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
(x'350637bc'), (x'350637bd'), (x'350637be'),
(x'35719786'), (x'35719787'), (x'35719788'),
(x'358637bc'), (x'358637bd'), (x'358637be'),
(x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
(x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
-- format crossover at 1e-04
(x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
(x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
(x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
(x'38d1b71d'),
--
(x'38dffffe'), (x'38dfffff'), (x'38e00000'),
(x'38efffff'), (x'38f00000'), (x'38f00001'),
(x'3a83126e'), (x'3a83126f'), (x'3a831270'),
(x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
(x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
-- chosen to need 9 digits for 3dcccd70
(x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
--
(x'3effffff'), (x'3f000000'), (x'3f000001'),
(x'3f333332'), (x'3f333333'), (x'3f333334'),
-- approach 1.0 with increasing numbers of 9s
(x'3f666665'), (x'3f666666'), (x'3f666667'),
(x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
(x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
(x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
(x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
(x'3f7fffee'), (x'3f7fffef'),
-- values very close to 1
(x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
(x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
(x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
(x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
(x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
(x'3f7fffff'),
(x'3f800000'),
(x'3f800001'), (x'3f800002'), (x'3f800003'),
(x'3f800004'), (x'3f800005'), (x'3f800006'),
(x'3f800007'), (x'3f800008'), (x'3f800009'),
-- values 1 to 1.1
(x'3f80000f'), (x'3f800010'), (x'3f800011'),
(x'3f800012'), (x'3f800013'), (x'3f800014'),
(x'3f800017'), (x'3f800018'), (x'3f800019'),
(x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
(x'3f800029'), (x'3f80002a'), (x'3f80002b'),
(x'3f800053'), (x'3f800054'), (x'3f800055'),
(x'3f800346'), (x'3f800347'), (x'3f800348'),
(x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
(x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
(x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
--
(x'3fc90fdb'), -- pi/2
(x'402df854'), -- e
(x'40490fdb'), -- pi
--
(x'409fffff'), (x'40a00000'), (x'40a00001'),
(x'40afffff'), (x'40b00000'), (x'40b00001'),
(x'411fffff'), (x'41200000'), (x'41200001'),
(x'42c7ffff'), (x'42c80000'), (x'42c80001'),
(x'4479ffff'), (x'447a0000'), (x'447a0001'),
(x'461c3fff'), (x'461c4000'), (x'461c4001'),
(x'47c34fff'), (x'47c35000'), (x'47c35001'),
(x'497423ff'), (x'49742400'), (x'49742401'),
(x'4b18967f'), (x'4b189680'), (x'4b189681'),
(x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
(x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
(x'501502f8'), (x'501502f9'), (x'501502fa'),
(x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
-- stress values
(x'1f6c1e4a'), -- 5e-20
(x'59be6cea'), -- 67e14
(x'5d5ab6c4'), -- 985e15
(x'2cc4a9bd'), -- 55895e-16
(x'15ae43fd'), -- 7038531e-32
(x'2cf757ca'), -- 702990899e-20
(x'665ba998'), -- 25933168707e13
(x'743c3324'), -- 596428896559e20
-- exercise fixed-point memmoves
(x'47f1205a'),
(x'4640e6ae'),
(x'449a5225'),
(x'42f6e9d5'),
(x'414587dd'),
(x'3f9e064b'),
-- these cases come from the upstream's testsuite
-- BoundaryRoundEven
(x'4c000004'),
(x'50061c46'),
(x'510006a8'),
-- ExactValueRoundEven
(x'48951f84'),
(x'45fd1840'),
-- LotsOfTrailingZeros
(x'39800000'),
(x'3b200000'),
(x'3b900000'),
(x'3bd00000'),
-- Regression
(x'63800000'),
(x'4b000000'),
(x'4b800000'),
(x'4c000001'),
(x'4c800b0d'),
(x'00d24584'),
(x'800000b0'),
(x'00d90b88'),
(x'45803f34'),
(x'4f9f24f7'),
(x'3a8722c3'),
(x'5c800041'),
(x'15ae43fd'),
(x'5d4cccfb'),
(x'4c800001'),
(x'57800ed8'),
(x'5f000000'),
(x'700000f0'),
(x'5f23e9ac'),
(x'5e9502f9'),
(x'5e8012b1'),
(x'3c000028'),
(x'60cde861'),
(x'03aa2a50'),
(x'43480000'),
(x'4c000000'),
-- LooksLikePow5
(x'5D1502F9'),
(x'5D9502F9'),
(x'5E1502F9'),
-- OutputLength
(x'3f99999a'),
(x'3f9d70a4'),
(x'3f9df3b6'),
(x'3f9e0419'),
(x'3f9e0610'),
(x'3f9e064b'),
(x'3f9e0651'),
(x'03d20cfe')
)
select float4send(flt) as ibits,
flt,
flt::text::float4 as r_flt,
float4send(flt::text::float4) as obits,
float4send(flt::text::float4) = float4send(flt) as correct
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
ibits | flt | r_flt | obits | correct
------------+----------------+----------------+------------+---------
\x00000000 | 0 | 0 | \x00000000 | t
\x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
\x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
\x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
\x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
\x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
\x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
\x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
\x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
\x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
\x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
\x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
\x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
\x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
\x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
\x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
\x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
\x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
\x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
\x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
\x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
\x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
\x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
\x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
\x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
\x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
\x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
\x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
\x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
\x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
\x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
\x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
\x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
\x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
\x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
\x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
\x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
\x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
\x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
\x350637bd | 5e-07 | 5e-07 | \x350637bd | t
\x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
\x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
\x35719787 | 9e-07 | 9e-07 | \x35719787 | t
\x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
\x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
\x358637bd | 1e-06 | 1e-06 | \x358637bd | t
\x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
\x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
\x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
\x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
\x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
\x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
\x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
\x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
\x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
\x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
\x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
\x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
\x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
\x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
\x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
\x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
\x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
\x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
\x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
\x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
\x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
\x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
\x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
\x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
\x3a83126f | 0.001 | 0.001 | \x3a83126f | t
\x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
\x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
\x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
\x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
\x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
\x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
\x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
\x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
\x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
\x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
\x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
\x3f000000 | 0.5 | 0.5 | \x3f000000 | t
\x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
\x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
\x3f333333 | 0.7 | 0.7 | \x3f333333 | t
\x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
\x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
\x3f666666 | 0.9 | 0.9 | \x3f666666 | t
\x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
\x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
\x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
\x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
\x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
\x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
\x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
\x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
\x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
\x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
\x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
\x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
\x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
\x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
\x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
\x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
\x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
\x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
\x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
\x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
\x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
\x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
\x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
\x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
\x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
\x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
\x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
\x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
\x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
\x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
\x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
\x3f800000 | 1 | 1 | \x3f800000 | t
\x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
\x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
\x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
\x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
\x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
\x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
\x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
\x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
\x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
\x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
\x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
\x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
\x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
\x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
\x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
\x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
\x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
\x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
\x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
\x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
\x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
\x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
\x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
\x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
\x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
\x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
\x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
\x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
\x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
\x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
\x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
\x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
\x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
\x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
\x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
\x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
\x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
\x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
\x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
\x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
\x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
\x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
\x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
\x40a00000 | 5 | 5 | \x40a00000 | t
\x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
\x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
\x40b00000 | 5.5 | 5.5 | \x40b00000 | t
\x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
\x411fffff | 9.999999 | 9.999999 | \x411fffff | t
\x41200000 | 10 | 10 | \x41200000 | t
\x41200001 | 10.000001 | 10.000001 | \x41200001 | t
\x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
\x42c80000 | 100 | 100 | \x42c80000 | t
\x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
\x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
\x447a0000 | 1000 | 1000 | \x447a0000 | t
\x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
\x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
\x461c4000 | 10000 | 10000 | \x461c4000 | t
\x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
\x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
\x47c35000 | 100000 | 100000 | \x47c35000 | t
\x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
\x497423ff | 999999.94 | 999999.94 | \x497423ff | t
\x49742400 | 1e+06 | 1e+06 | \x49742400 | t
\x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
\x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
\x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
\x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
\x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
\x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
\x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
\x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
\x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
\x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
\x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
\x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
\x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
\x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
\x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
\x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
\x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
\x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
\x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
\x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
\x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
\x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
\x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
\x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
\x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
\x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
\x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
\x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
\x414587dd | 12.34567 | 12.34567 | \x414587dd | t
\x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
\x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
\x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
\x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
\x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
\x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
\x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
\x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
\x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
\x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
\x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
\x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
\x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
\x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
\x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
\x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
\x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
\x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
\x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
\x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
\x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
\x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
\x15ae43fd | 7.038531e-26 | 7.0385313e-26 | \x15ae43fe | f
\x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
\x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
\x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
\x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
\x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
\x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
\x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
\x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
\x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
\x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
\x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
\x43480000 | 200 | 200 | \x43480000 | t
\x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
\x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
\x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
\x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
\x3f99999a | 1.2 | 1.2 | \x3f99999a | t
\x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
\x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
\x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
\x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
\x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
\x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
\x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
(262 rows)
-- clean up, lest opr_sanity complain
\set VERBOSITY terse
drop type xfloat4 cascade;
NOTICE: drop cascades to 6 other objects
\set VERBOSITY default
--

574
src/test/regress/expected/float4.out
Unescape View File

@ -143,21 +143,21 @@ SELECT 'nan'::numeric::float4;
SELECT '' AS five, * FROM FLOAT4_TBL;
five | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e+20
| 1.23457e-20
| 1.2345679e+20
| 1.2345679e-20
(5 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <> '1004.3';
four | f1
------+-------------
------+---------------
| 0
| -34.84
| 1.23457e+20
| 1.23457e-20
| 1.2345679e+20
| 1.2345679e-20
(4 rows)
SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
@ -168,72 +168,72 @@ SELECT '' AS one, f.* FROM FLOAT4_TBL f WHERE f.f1 = '1004.3';
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE '1004.3' > f.f1;
three | f1
-------+-------------
-------+---------------
| 0
| -34.84
| 1.23457e-20
| 1.2345679e-20
(3 rows)
SELECT '' AS three, f.* FROM FLOAT4_TBL f WHERE f.f1 < '1004.3';
three | f1
-------+-------------
-------+---------------
| 0
| -34.84
| 1.23457e-20
| 1.2345679e-20
(3 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE '1004.3' >= f.f1;
four | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e-20
| 1.2345679e-20
(4 rows)
SELECT '' AS four, f.* FROM FLOAT4_TBL f WHERE f.f1 <= '1004.3';
four | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e-20
| 1.2345679e-20
(4 rows)
SELECT '' AS three, f.f1, f.f1 * '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+--------------
-------+---------------+----------------
| 1004.3 | -10043
| 1.23457e+20 | -1.23457e+21
| 1.23457e-20 | -1.23457e-19
| 1.2345679e+20 | -1.2345678e+21
| 1.2345679e-20 | -1.2345678e-19
(3 rows)
SELECT '' AS three, f.f1, f.f1 + '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+-------------
-------+---------------+---------------
| 1004.3 | 994.3
| 1.23457e+20 | 1.23457e+20
| 1.23457e-20 | -10
| 1.2345679e+20 | 1.2345679e+20
| 1.2345679e-20 | -10
(3 rows)
SELECT '' AS three, f.f1, f.f1 / '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+--------------
-------+---------------+----------------
| 1004.3 | -100.43
| 1.23457e+20 | -1.23457e+19
| 1.23457e-20 | -1.23457e-21
| 1.2345679e+20 | -1.2345679e+19
| 1.2345679e-20 | -1.2345679e-21
(3 rows)
SELECT '' AS three, f.f1, f.f1 - '-10' AS x FROM FLOAT4_TBL f
WHERE f.f1 > '0.0';
three | f1 | x
-------+-------------+-------------
-------+---------------+---------------
| 1004.3 | 1014.3
| 1.23457e+20 | 1.23457e+20
| 1.23457e-20 | 10
| 1.2345679e+20 | 1.2345679e+20
| 1.2345679e-20 | 10
(3 rows)
-- test divide by zero
@ -241,23 +241,23 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT4_TBL f;
ERROR: division by zero
SELECT '' AS five, * FROM FLOAT4_TBL;
five | f1
------+-------------
------+---------------
| 0
| 1004.3
| -34.84
| 1.23457e+20
| 1.23457e-20
| 1.2345679e+20
| 1.2345679e-20
(5 rows)
-- test the unary float4abs operator
SELECT '' AS five, f.f1, @f.f1 AS abs_f1 FROM FLOAT4_TBL f;
five | f1 | abs_f1
------+-------------+-------------
------+---------------+---------------
| 0 | 0
| 1004.3 | 1004.3
| -34.84 | 34.84
| 1.23457e+20 | 1.23457e+20
| 1.23457e-20 | 1.23457e-20
| 1.2345679e+20 | 1.2345679e+20
| 1.2345679e-20 | 1.2345679e-20
(5 rows)
UPDATE FLOAT4_TBL
@ -265,12 +265,12 @@ UPDATE FLOAT4_TBL
WHERE FLOAT4_TBL.f1 > '0.0';
SELECT '' AS five, * FROM FLOAT4_TBL;
five | f1
------+--------------
------+----------------
| 0
| -34.84
| -1004.3
| -1.23457e+20
| -1.23457e-20
| -1.2345679e+20
| -1.2345679e-20
(5 rows)
-- test edge-case coercions to integer
@ -434,3 +434,507 @@ SELECT float4send('1.1754944e-38'::float4);
\x00800000
(1 row)
-- test output (and round-trip safety) of various values.
-- To ensure we're testing what we think we're testing, start with
-- float values specified by bit patterns (as a useful side effect,
-- this means we'll fail on non-IEEE platforms).
create type xfloat4;
create function xfloat4in(cstring) returns xfloat4 immutable strict
language internal as 'int4in';
NOTICE: return type xfloat4 is only a shell
create function xfloat4out(xfloat4) returns cstring immutable strict
language internal as 'int4out';
NOTICE: argument type xfloat4 is only a shell
create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
create cast (xfloat4 as float4) without function;
create cast (float4 as xfloat4) without function;
create cast (xfloat4 as integer) without function;
create cast (integer as xfloat4) without function;
-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
-- we don't care to assume the platform's strtod() handles subnormals
-- correctly; those are "use at your own risk". However we do test
-- subnormal outputs, since those are under our control.
with testdata(bits) as (values
-- small subnormals
(x'00000001'),
(x'00000002'), (x'00000003'),
(x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
(x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
-- stress values
(x'0053c4f4'), -- 7693e-42
(x'006c85c4'), -- 996622e-44
(x'0041ca76'), -- 60419369e-46
(x'004b7678'), -- 6930161142e-48
-- taken from upstream testsuite
(x'00000007'),
(x'00424fe2'),
-- borderline between subnormal and normal
(x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
select float4send(flt) as ibits,
flt
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
ibits | flt
------------+---------------
\x00000001 | 1e-45
\x00000002 | 3e-45
\x00000003 | 4e-45
\x00000010 | 2.2e-44
\x00000011 | 2.4e-44
\x00000100 | 3.59e-43
\x00000101 | 3.6e-43
\x00004000 | 2.2959e-41
\x00004001 | 2.296e-41
\x00080000 | 7.34684e-40
\x00080001 | 7.34685e-40
\x0053c4f4 | 7.693e-39
\x006c85c4 | 9.96622e-39
\x0041ca76 | 6.041937e-39
\x004b7678 | 6.930161e-39
\x00000007 | 1e-44
\x00424fe2 | 6.0898e-39
\x007ffff0 | 1.1754921e-38
\x007ffff1 | 1.1754922e-38
\x007ffffe | 1.1754941e-38
\x007fffff | 1.1754942e-38
(21 rows)
with testdata(bits) as (values
(x'00000000'),
-- smallest normal values
(x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
(x'00800006'),
-- small normal values chosen for short vs. long output
(x'008002f1'), (x'008002f2'), (x'008002f3'),
(x'00800e17'), (x'00800e18'), (x'00800e19'),
-- assorted values (random mantissae)
(x'01000001'), (x'01102843'), (x'01a52c98'),
(x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
(x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
(x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
(x'1f850283'), (x'2874a9d6'),
-- values around 5e-08
(x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
-- around 1e-07
(x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
-- around 3e-07 .. 1e-04
(x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
(x'350637bc'), (x'350637bd'), (x'350637be'),
(x'35719786'), (x'35719787'), (x'35719788'),
(x'358637bc'), (x'358637bd'), (x'358637be'),
(x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
(x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
-- format crossover at 1e-04
(x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
(x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
(x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
(x'38d1b71d'),
--
(x'38dffffe'), (x'38dfffff'), (x'38e00000'),
(x'38efffff'), (x'38f00000'), (x'38f00001'),
(x'3a83126e'), (x'3a83126f'), (x'3a831270'),
(x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
(x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
-- chosen to need 9 digits for 3dcccd70
(x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
--
(x'3effffff'), (x'3f000000'), (x'3f000001'),
(x'3f333332'), (x'3f333333'), (x'3f333334'),
-- approach 1.0 with increasing numbers of 9s
(x'3f666665'), (x'3f666666'), (x'3f666667'),
(x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
(x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
(x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
(x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
(x'3f7fffee'), (x'3f7fffef'),
-- values very close to 1
(x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
(x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
(x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
(x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
(x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
(x'3f7fffff'),
(x'3f800000'),
(x'3f800001'), (x'3f800002'), (x'3f800003'),
(x'3f800004'), (x'3f800005'), (x'3f800006'),
(x'3f800007'), (x'3f800008'), (x'3f800009'),
-- values 1 to 1.1
(x'3f80000f'), (x'3f800010'), (x'3f800011'),
(x'3f800012'), (x'3f800013'), (x'3f800014'),
(x'3f800017'), (x'3f800018'), (x'3f800019'),
(x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
(x'3f800029'), (x'3f80002a'), (x'3f80002b'),
(x'3f800053'), (x'3f800054'), (x'3f800055'),
(x'3f800346'), (x'3f800347'), (x'3f800348'),
(x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
(x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
(x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
--
(x'3fc90fdb'), -- pi/2
(x'402df854'), -- e
(x'40490fdb'), -- pi
--
(x'409fffff'), (x'40a00000'), (x'40a00001'),
(x'40afffff'), (x'40b00000'), (x'40b00001'),
(x'411fffff'), (x'41200000'), (x'41200001'),
(x'42c7ffff'), (x'42c80000'), (x'42c80001'),
(x'4479ffff'), (x'447a0000'), (x'447a0001'),
(x'461c3fff'), (x'461c4000'), (x'461c4001'),
(x'47c34fff'), (x'47c35000'), (x'47c35001'),
(x'497423ff'), (x'49742400'), (x'49742401'),
(x'4b18967f'), (x'4b189680'), (x'4b189681'),
(x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
(x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
(x'501502f8'), (x'501502f9'), (x'501502fa'),
(x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
-- stress values
(x'1f6c1e4a'), -- 5e-20
(x'59be6cea'), -- 67e14
(x'5d5ab6c4'), -- 985e15
(x'2cc4a9bd'), -- 55895e-16
(x'15ae43fd'), -- 7038531e-32
(x'2cf757ca'), -- 702990899e-20
(x'665ba998'), -- 25933168707e13
(x'743c3324'), -- 596428896559e20
-- exercise fixed-point memmoves
(x'47f1205a'),
(x'4640e6ae'),
(x'449a5225'),
(x'42f6e9d5'),
(x'414587dd'),
(x'3f9e064b'),
-- these cases come from the upstream's testsuite
-- BoundaryRoundEven
(x'4c000004'),
(x'50061c46'),
(x'510006a8'),
-- ExactValueRoundEven
(x'48951f84'),
(x'45fd1840'),
-- LotsOfTrailingZeros
(x'39800000'),
(x'3b200000'),
(x'3b900000'),
(x'3bd00000'),
-- Regression
(x'63800000'),
(x'4b000000'),
(x'4b800000'),
(x'4c000001'),
(x'4c800b0d'),
(x'00d24584'),
(x'800000b0'),
(x'00d90b88'),
(x'45803f34'),
(x'4f9f24f7'),
(x'3a8722c3'),
(x'5c800041'),
(x'15ae43fd'),
(x'5d4cccfb'),
(x'4c800001'),
(x'57800ed8'),
(x'5f000000'),
(x'700000f0'),
(x'5f23e9ac'),
(x'5e9502f9'),
(x'5e8012b1'),
(x'3c000028'),
(x'60cde861'),
(x'03aa2a50'),
(x'43480000'),
(x'4c000000'),
-- LooksLikePow5
(x'5D1502F9'),
(x'5D9502F9'),
(x'5E1502F9'),
-- OutputLength
(x'3f99999a'),
(x'3f9d70a4'),
(x'3f9df3b6'),
(x'3f9e0419'),
(x'3f9e0610'),
(x'3f9e064b'),
(x'3f9e0651'),
(x'03d20cfe')
)
select float4send(flt) as ibits,
flt,
flt::text::float4 as r_flt,
float4send(flt::text::float4) as obits,
float4send(flt::text::float4) = float4send(flt) as correct
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
ibits | flt | r_flt | obits | correct
------------+----------------+----------------+------------+---------
\x00000000 | 0 | 0 | \x00000000 | t
\x00800000 | 1.1754944e-38 | 1.1754944e-38 | \x00800000 | t
\x00800001 | 1.1754945e-38 | 1.1754945e-38 | \x00800001 | t
\x00800004 | 1.1754949e-38 | 1.1754949e-38 | \x00800004 | t
\x00800005 | 1.175495e-38 | 1.175495e-38 | \x00800005 | t
\x00800006 | 1.1754952e-38 | 1.1754952e-38 | \x00800006 | t
\x008002f1 | 1.1755999e-38 | 1.1755999e-38 | \x008002f1 | t
\x008002f2 | 1.1756e-38 | 1.1756e-38 | \x008002f2 | t
\x008002f3 | 1.1756001e-38 | 1.1756001e-38 | \x008002f3 | t
\x00800e17 | 1.1759998e-38 | 1.1759998e-38 | \x00800e17 | t
\x00800e18 | 1.176e-38 | 1.176e-38 | \x00800e18 | t
\x00800e19 | 1.1760001e-38 | 1.1760001e-38 | \x00800e19 | t
\x01000001 | 2.350989e-38 | 2.350989e-38 | \x01000001 | t
\x01102843 | 2.647751e-38 | 2.647751e-38 | \x01102843 | t
\x01a52c98 | 6.0675416e-38 | 6.0675416e-38 | \x01a52c98 | t
\x0219c229 | 1.1296386e-37 | 1.1296386e-37 | \x0219c229 | t
\x02e4464d | 3.354194e-37 | 3.354194e-37 | \x02e4464d | t
\x037343c1 | 7.148906e-37 | 7.148906e-37 | \x037343c1 | t
\x03a91b36 | 9.939175e-37 | 9.939175e-37 | \x03a91b36 | t
\x047ada65 | 2.948764e-36 | 2.948764e-36 | \x047ada65 | t
\x0496fe87 | 3.5498577e-36 | 3.5498577e-36 | \x0496fe87 | t
\x0550844f | 9.804414e-36 | 9.804414e-36 | \x0550844f | t
\x05999da3 | 1.4445957e-35 | 1.4445957e-35 | \x05999da3 | t
\x060ea5e2 | 2.6829103e-35 | 2.6829103e-35 | \x060ea5e2 | t
\x06e63c45 | 8.660494e-35 | 8.660494e-35 | \x06e63c45 | t
\x07f1e548 | 3.639641e-34 | 3.639641e-34 | \x07f1e548 | t
\x0fc5282b | 1.9441172e-29 | 1.9441172e-29 | \x0fc5282b | t
\x1f850283 | 5.6331846e-20 | 5.6331846e-20 | \x1f850283 | t
\x2874a9d6 | 1.3581548e-14 | 1.3581548e-14 | \x2874a9d6 | t
\x3356bf94 | 4.9999997e-08 | 4.9999997e-08 | \x3356bf94 | t
\x3356bf95 | 5e-08 | 5e-08 | \x3356bf95 | t
\x3356bf96 | 5.0000004e-08 | 5.0000004e-08 | \x3356bf96 | t
\x33d6bf94 | 9.9999994e-08 | 9.9999994e-08 | \x33d6bf94 | t
\x33d6bf95 | 1e-07 | 1e-07 | \x33d6bf95 | t
\x33d6bf96 | 1.0000001e-07 | 1.0000001e-07 | \x33d6bf96 | t
\x34a10faf | 2.9999998e-07 | 2.9999998e-07 | \x34a10faf | t
\x34a10fb0 | 3e-07 | 3e-07 | \x34a10fb0 | t
\x34a10fb1 | 3.0000004e-07 | 3.0000004e-07 | \x34a10fb1 | t
\x350637bc | 4.9999994e-07 | 4.9999994e-07 | \x350637bc | t
\x350637bd | 5e-07 | 5e-07 | \x350637bd | t
\x350637be | 5.0000006e-07 | 5.0000006e-07 | \x350637be | t
\x35719786 | 8.999999e-07 | 8.999999e-07 | \x35719786 | t
\x35719787 | 9e-07 | 9e-07 | \x35719787 | t
\x35719788 | 9.0000003e-07 | 9.0000003e-07 | \x35719788 | t
\x358637bc | 9.999999e-07 | 9.999999e-07 | \x358637bc | t
\x358637bd | 1e-06 | 1e-06 | \x358637bd | t
\x358637be | 1.0000001e-06 | 1.0000001e-06 | \x358637be | t
\x36a7c5ab | 4.9999994e-06 | 4.9999994e-06 | \x36a7c5ab | t
\x36a7c5ac | 5e-06 | 5e-06 | \x36a7c5ac | t
\x36a7c5ad | 5.0000003e-06 | 5.0000003e-06 | \x36a7c5ad | t
\x3727c5ab | 9.999999e-06 | 9.999999e-06 | \x3727c5ab | t
\x3727c5ac | 1e-05 | 1e-05 | \x3727c5ac | t
\x3727c5ad | 1.0000001e-05 | 1.0000001e-05 | \x3727c5ad | t
\x38d1b714 | 9.9999976e-05 | 9.9999976e-05 | \x38d1b714 | t
\x38d1b715 | 9.999998e-05 | 9.999998e-05 | \x38d1b715 | t
\x38d1b716 | 9.999999e-05 | 9.999999e-05 | \x38d1b716 | t
\x38d1b717 | 0.0001 | 0.0001 | \x38d1b717 | t
\x38d1b718 | 0.000100000005 | 0.000100000005 | \x38d1b718 | t
\x38d1b719 | 0.00010000001 | 0.00010000001 | \x38d1b719 | t
\x38d1b71a | 0.00010000002 | 0.00010000002 | \x38d1b71a | t
\x38d1b71b | 0.00010000003 | 0.00010000003 | \x38d1b71b | t
\x38d1b71c | 0.000100000034 | 0.000100000034 | \x38d1b71c | t
\x38d1b71d | 0.00010000004 | 0.00010000004 | \x38d1b71d | t
\x38dffffe | 0.00010681151 | 0.00010681151 | \x38dffffe | t
\x38dfffff | 0.000106811516 | 0.000106811516 | \x38dfffff | t
\x38e00000 | 0.00010681152 | 0.00010681152 | \x38e00000 | t
\x38efffff | 0.00011444091 | 0.00011444091 | \x38efffff | t
\x38f00000 | 0.00011444092 | 0.00011444092 | \x38f00000 | t
\x38f00001 | 0.000114440925 | 0.000114440925 | \x38f00001 | t
\x3a83126e | 0.0009999999 | 0.0009999999 | \x3a83126e | t
\x3a83126f | 0.001 | 0.001 | \x3a83126f | t
\x3a831270 | 0.0010000002 | 0.0010000002 | \x3a831270 | t
\x3c23d709 | 0.009999999 | 0.009999999 | \x3c23d709 | t
\x3c23d70a | 0.01 | 0.01 | \x3c23d70a | t
\x3c23d70b | 0.010000001 | 0.010000001 | \x3c23d70b | t
\x3dcccccc | 0.099999994 | 0.099999994 | \x3dcccccc | t
\x3dcccccd | 0.1 | 0.1 | \x3dcccccd | t
\x3dccccce | 0.10000001 | 0.10000001 | \x3dccccce | t
\x3dcccd6f | 0.10000121 | 0.10000121 | \x3dcccd6f | t
\x3dcccd70 | 0.100001216 | 0.100001216 | \x3dcccd70 | t
\x3dcccd71 | 0.10000122 | 0.10000122 | \x3dcccd71 | t
\x3effffff | 0.49999997 | 0.49999997 | \x3effffff | t
\x3f000000 | 0.5 | 0.5 | \x3f000000 | t
\x3f000001 | 0.50000006 | 0.50000006 | \x3f000001 | t
\x3f333332 | 0.6999999 | 0.6999999 | \x3f333332 | t
\x3f333333 | 0.7 | 0.7 | \x3f333333 | t
\x3f333334 | 0.70000005 | 0.70000005 | \x3f333334 | t
\x3f666665 | 0.8999999 | 0.8999999 | \x3f666665 | t
\x3f666666 | 0.9 | 0.9 | \x3f666666 | t
\x3f666667 | 0.90000004 | 0.90000004 | \x3f666667 | t
\x3f7d70a3 | 0.98999995 | 0.98999995 | \x3f7d70a3 | t
\x3f7d70a4 | 0.99 | 0.99 | \x3f7d70a4 | t
\x3f7d70a5 | 0.99000007 | 0.99000007 | \x3f7d70a5 | t
\x3f7fbe76 | 0.99899995 | 0.99899995 | \x3f7fbe76 | t
\x3f7fbe77 | 0.999 | 0.999 | \x3f7fbe77 | t
\x3f7fbe78 | 0.9990001 | 0.9990001 | \x3f7fbe78 | t
\x3f7ff971 | 0.9998999 | 0.9998999 | \x3f7ff971 | t
\x3f7ff972 | 0.9999 | 0.9999 | \x3f7ff972 | t
\x3f7ff973 | 0.99990004 | 0.99990004 | \x3f7ff973 | t
\x3f7fff57 | 0.9999899 | 0.9999899 | \x3f7fff57 | t
\x3f7fff58 | 0.99999 | 0.99999 | \x3f7fff58 | t
\x3f7fff59 | 0.99999005 | 0.99999005 | \x3f7fff59 | t
\x3f7fffee | 0.9999989 | 0.9999989 | \x3f7fffee | t
\x3f7fffef | 0.999999 | 0.999999 | \x3f7fffef | t
\x3f7ffff0 | 0.99999905 | 0.99999905 | \x3f7ffff0 | t
\x3f7ffff1 | 0.9999991 | 0.9999991 | \x3f7ffff1 | t
\x3f7ffff2 | 0.99999917 | 0.99999917 | \x3f7ffff2 | t
\x3f7ffff3 | 0.9999992 | 0.9999992 | \x3f7ffff3 | t
\x3f7ffff4 | 0.9999993 | 0.9999993 | \x3f7ffff4 | t
\x3f7ffff5 | 0.99999934 | 0.99999934 | \x3f7ffff5 | t
\x3f7ffff6 | 0.9999994 | 0.9999994 | \x3f7ffff6 | t
\x3f7ffff7 | 0.99999946 | 0.99999946 | \x3f7ffff7 | t
\x3f7ffff8 | 0.9999995 | 0.9999995 | \x3f7ffff8 | t
\x3f7ffff9 | 0.9999996 | 0.9999996 | \x3f7ffff9 | t
\x3f7ffffa | 0.99999964 | 0.99999964 | \x3f7ffffa | t
\x3f7ffffb | 0.9999997 | 0.9999997 | \x3f7ffffb | t
\x3f7ffffc | 0.99999976 | 0.99999976 | \x3f7ffffc | t
\x3f7ffffd | 0.9999998 | 0.9999998 | \x3f7ffffd | t
\x3f7ffffe | 0.9999999 | 0.9999999 | \x3f7ffffe | t
\x3f7fffff | 0.99999994 | 0.99999994 | \x3f7fffff | t
\x3f800000 | 1 | 1 | \x3f800000 | t
\x3f800001 | 1.0000001 | 1.0000001 | \x3f800001 | t
\x3f800002 | 1.0000002 | 1.0000002 | \x3f800002 | t
\x3f800003 | 1.0000004 | 1.0000004 | \x3f800003 | t
\x3f800004 | 1.0000005 | 1.0000005 | \x3f800004 | t
\x3f800005 | 1.0000006 | 1.0000006 | \x3f800005 | t
\x3f800006 | 1.0000007 | 1.0000007 | \x3f800006 | t
\x3f800007 | 1.0000008 | 1.0000008 | \x3f800007 | t
\x3f800008 | 1.000001 | 1.000001 | \x3f800008 | t
\x3f800009 | 1.0000011 | 1.0000011 | \x3f800009 | t
\x3f80000f | 1.0000018 | 1.0000018 | \x3f80000f | t
\x3f800010 | 1.0000019 | 1.0000019 | \x3f800010 | t
\x3f800011 | 1.000002 | 1.000002 | \x3f800011 | t
\x3f800012 | 1.0000021 | 1.0000021 | \x3f800012 | t
\x3f800013 | 1.0000023 | 1.0000023 | \x3f800013 | t
\x3f800014 | 1.0000024 | 1.0000024 | \x3f800014 | t
\x3f800017 | 1.0000027 | 1.0000027 | \x3f800017 | t
\x3f800018 | 1.0000029 | 1.0000029 | \x3f800018 | t
\x3f800019 | 1.000003 | 1.000003 | \x3f800019 | t
\x3f80001a | 1.0000031 | 1.0000031 | \x3f80001a | t
\x3f80001b | 1.0000032 | 1.0000032 | \x3f80001b | t
\x3f80001c | 1.0000033 | 1.0000033 | \x3f80001c | t
\x3f800029 | 1.0000049 | 1.0000049 | \x3f800029 | t
\x3f80002a | 1.000005 | 1.000005 | \x3f80002a | t
\x3f80002b | 1.0000051 | 1.0000051 | \x3f80002b | t
\x3f800053 | 1.0000099 | 1.0000099 | \x3f800053 | t
\x3f800054 | 1.00001 | 1.00001 | \x3f800054 | t
\x3f800055 | 1.0000101 | 1.0000101 | \x3f800055 | t
\x3f800346 | 1.0000999 | 1.0000999 | \x3f800346 | t
\x3f800347 | 1.0001 | 1.0001 | \x3f800347 | t
\x3f800348 | 1.0001001 | 1.0001001 | \x3f800348 | t
\x3f8020c4 | 1.0009999 | 1.0009999 | \x3f8020c4 | t
\x3f8020c5 | 1.001 | 1.001 | \x3f8020c5 | t
\x3f8020c6 | 1.0010002 | 1.0010002 | \x3f8020c6 | t
\x3f8147ad | 1.0099999 | 1.0099999 | \x3f8147ad | t
\x3f8147ae | 1.01 | 1.01 | \x3f8147ae | t
\x3f8147af | 1.0100001 | 1.0100001 | \x3f8147af | t
\x3f8ccccc | 1.0999999 | 1.0999999 | \x3f8ccccc | t
\x3f8ccccd | 1.1 | 1.1 | \x3f8ccccd | t
\x3f8cccce | 1.1000001 | 1.1000001 | \x3f8cccce | t
\x3fc90fdb | 1.5707964 | 1.5707964 | \x3fc90fdb | t
\x402df854 | 2.7182817 | 2.7182817 | \x402df854 | t
\x40490fdb | 3.1415927 | 3.1415927 | \x40490fdb | t
\x409fffff | 4.9999995 | 4.9999995 | \x409fffff | t
\x40a00000 | 5 | 5 | \x40a00000 | t
\x40a00001 | 5.0000005 | 5.0000005 | \x40a00001 | t
\x40afffff | 5.4999995 | 5.4999995 | \x40afffff | t
\x40b00000 | 5.5 | 5.5 | \x40b00000 | t
\x40b00001 | 5.5000005 | 5.5000005 | \x40b00001 | t
\x411fffff | 9.999999 | 9.999999 | \x411fffff | t
\x41200000 | 10 | 10 | \x41200000 | t
\x41200001 | 10.000001 | 10.000001 | \x41200001 | t
\x42c7ffff | 99.99999 | 99.99999 | \x42c7ffff | t
\x42c80000 | 100 | 100 | \x42c80000 | t
\x42c80001 | 100.00001 | 100.00001 | \x42c80001 | t
\x4479ffff | 999.99994 | 999.99994 | \x4479ffff | t
\x447a0000 | 1000 | 1000 | \x447a0000 | t
\x447a0001 | 1000.00006 | 1000.00006 | \x447a0001 | t
\x461c3fff | 9999.999 | 9999.999 | \x461c3fff | t
\x461c4000 | 10000 | 10000 | \x461c4000 | t
\x461c4001 | 10000.001 | 10000.001 | \x461c4001 | t
\x47c34fff | 99999.99 | 99999.99 | \x47c34fff | t
\x47c35000 | 100000 | 100000 | \x47c35000 | t
\x47c35001 | 100000.01 | 100000.01 | \x47c35001 | t
\x497423ff | 999999.94 | 999999.94 | \x497423ff | t
\x49742400 | 1e+06 | 1e+06 | \x49742400 | t
\x49742401 | 1.00000006e+06 | 1.00000006e+06 | \x49742401 | t
\x4b18967f | 9.999999e+06 | 9.999999e+06 | \x4b18967f | t
\x4b189680 | 1e+07 | 1e+07 | \x4b189680 | t
\x4b189681 | 1.0000001e+07 | 1.0000001e+07 | \x4b189681 | t
\x4cbebc1f | 9.999999e+07 | 9.999999e+07 | \x4cbebc1f | t
\x4cbebc20 | 1e+08 | 1e+08 | \x4cbebc20 | t
\x4cbebc21 | 1.0000001e+08 | 1.0000001e+08 | \x4cbebc21 | t
\x4e6e6b27 | 9.9999994e+08 | 9.9999994e+08 | \x4e6e6b27 | t
\x4e6e6b28 | 1e+09 | 1e+09 | \x4e6e6b28 | t
\x4e6e6b29 | 1.00000006e+09 | 1.00000006e+09 | \x4e6e6b29 | t
\x501502f8 | 9.999999e+09 | 9.999999e+09 | \x501502f8 | t
\x501502f9 | 1e+10 | 1e+10 | \x501502f9 | t
\x501502fa | 1.0000001e+10 | 1.0000001e+10 | \x501502fa | t
\x51ba43b6 | 9.999999e+10 | 9.999999e+10 | \x51ba43b6 | t
\x51ba43b7 | 1e+11 | 1e+11 | \x51ba43b7 | t
\x51ba43b8 | 1.0000001e+11 | 1.0000001e+11 | \x51ba43b8 | t
\x1f6c1e4a | 5e-20 | 5e-20 | \x1f6c1e4a | t
\x59be6cea | 6.7e+15 | 6.7e+15 | \x59be6cea | t
\x5d5ab6c4 | 9.85e+17 | 9.85e+17 | \x5d5ab6c4 | t
\x2cc4a9bd | 5.5895e-12 | 5.5895e-12 | \x2cc4a9bd | t
\x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
\x2cf757ca | 7.0299088e-12 | 7.0299088e-12 | \x2cf757ca | t
\x665ba998 | 2.5933168e+23 | 2.5933168e+23 | \x665ba998 | t
\x743c3324 | 5.9642887e+31 | 5.9642887e+31 | \x743c3324 | t
\x47f1205a | 123456.7 | 123456.7 | \x47f1205a | t
\x4640e6ae | 12345.67 | 12345.67 | \x4640e6ae | t
\x449a5225 | 1234.567 | 1234.567 | \x449a5225 | t
\x42f6e9d5 | 123.4567 | 123.4567 | \x42f6e9d5 | t
\x414587dd | 12.34567 | 12.34567 | \x414587dd | t
\x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
\x4c000004 | 3.3554448e+07 | 3.3554448e+07 | \x4c000004 | t
\x50061c46 | 8.999999e+09 | 8.999999e+09 | \x50061c46 | t
\x510006a8 | 3.4366718e+10 | 3.4366718e+10 | \x510006a8 | t
\x48951f84 | 305404.12 | 305404.12 | \x48951f84 | t
\x45fd1840 | 8099.0312 | 8099.0312 | \x45fd1840 | t
\x39800000 | 0.00024414062 | 0.00024414062 | \x39800000 | t
\x3b200000 | 0.0024414062 | 0.0024414062 | \x3b200000 | t
\x3b900000 | 0.0043945312 | 0.0043945312 | \x3b900000 | t
\x3bd00000 | 0.0063476562 | 0.0063476562 | \x3bd00000 | t
\x63800000 | 4.7223665e+21 | 4.7223665e+21 | \x63800000 | t
\x4b000000 | 8.388608e+06 | 8.388608e+06 | \x4b000000 | t
\x4b800000 | 1.6777216e+07 | 1.6777216e+07 | \x4b800000 | t
\x4c000001 | 3.3554436e+07 | 3.3554436e+07 | \x4c000001 | t
\x4c800b0d | 6.7131496e+07 | 6.7131496e+07 | \x4c800b0d | t
\x00d24584 | 1.9310392e-38 | 1.9310392e-38 | \x00d24584 | t
\x800000b0 | -2.47e-43 | -2.47e-43 | \x800000b0 | t
\x00d90b88 | 1.993244e-38 | 1.993244e-38 | \x00d90b88 | t
\x45803f34 | 4103.9004 | 4103.9004 | \x45803f34 | t
\x4f9f24f7 | 5.3399997e+09 | 5.3399997e+09 | \x4f9f24f7 | t
\x3a8722c3 | 0.0010310042 | 0.0010310042 | \x3a8722c3 | t
\x5c800041 | 2.882326e+17 | 2.882326e+17 | \x5c800041 | t
\x15ae43fd | 7.038531e-26 | 7.038531e-26 | \x15ae43fd | t
\x5d4cccfb | 9.223404e+17 | 9.223404e+17 | \x5d4cccfb | t
\x4c800001 | 6.710887e+07 | 6.710887e+07 | \x4c800001 | t
\x57800ed8 | 2.816025e+14 | 2.816025e+14 | \x57800ed8 | t
\x5f000000 | 9.223372e+18 | 9.223372e+18 | \x5f000000 | t
\x700000f0 | 1.5846086e+29 | 1.5846086e+29 | \x700000f0 | t
\x5f23e9ac | 1.1811161e+19 | 1.1811161e+19 | \x5f23e9ac | t
\x5e9502f9 | 5.368709e+18 | 5.368709e+18 | \x5e9502f9 | t
\x5e8012b1 | 4.6143166e+18 | 4.6143166e+18 | \x5e8012b1 | t
\x3c000028 | 0.007812537 | 0.007812537 | \x3c000028 | t
\x60cde861 | 1.18697725e+20 | 1.18697725e+20 | \x60cde861 | t
\x03aa2a50 | 1.00014165e-36 | 1.00014165e-36 | \x03aa2a50 | t
\x43480000 | 200 | 200 | \x43480000 | t
\x4c000000 | 3.3554432e+07 | 3.3554432e+07 | \x4c000000 | t
\x5d1502f9 | 6.7108864e+17 | 6.7108864e+17 | \x5d1502f9 | t
\x5d9502f9 | 1.3421773e+18 | 1.3421773e+18 | \x5d9502f9 | t
\x5e1502f9 | 2.6843546e+18 | 2.6843546e+18 | \x5e1502f9 | t
\x3f99999a | 1.2 | 1.2 | \x3f99999a | t
\x3f9d70a4 | 1.23 | 1.23 | \x3f9d70a4 | t
\x3f9df3b6 | 1.234 | 1.234 | \x3f9df3b6 | t
\x3f9e0419 | 1.2345 | 1.2345 | \x3f9e0419 | t
\x3f9e0610 | 1.23456 | 1.23456 | \x3f9e0610 | t
\x3f9e064b | 1.234567 | 1.234567 | \x3f9e064b | t
\x3f9e0651 | 1.2345678 | 1.2345678 | \x3f9e0651 | t
\x03d20cfe | 1.23456735e-36 | 1.23456735e-36 | \x03d20cfe | t
(262 rows)
-- clean up, lest opr_sanity complain
\set VERBOSITY terse
drop type xfloat4 cascade;
NOTICE: drop cascades to 6 other objects
\set VERBOSITY default
--

447
src/test/regress/expected/float8-small-is-zero.out
Unescape View File

@ -28,6 +28,13 @@ SELECT '-10e-400'::float8;
-0
(1 row)
-- test smallest normalized input
SELECT float8send('2.2250738585072014E-308'::float8);
float8send
--------------------
\x0010000000000000
(1 row)
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@ -213,7 +220,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
| 1004.3 | -100.43
| 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@ -231,8 +238,8 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
one | square_f1
-----+------------
| 1008618.49
-----+--------------------
| 1008618.4899999999
(1 row)
-- absolute value
@ -314,6 +321,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@ -449,6 +458,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@ -528,7 +538,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@ -630,4 +639,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
RESET extra_float_digits;
--
-- test output (and round-trip safety) of various values.
-- To ensure we're testing what we think we're testing, start with
-- float values specified by bit patterns (as a useful side effect,
-- this means we'll fail on non-IEEE platforms).
create type xfloat8;
create function xfloat8in(cstring) returns xfloat8 immutable strict
language internal as 'int8in';
NOTICE: return type xfloat8 is only a shell
create function xfloat8out(xfloat8) returns cstring immutable strict
language internal as 'int8out';
NOTICE: argument type xfloat8 is only a shell
create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
create cast (xfloat8 as float8) without function;
create cast (float8 as xfloat8) without function;
create cast (xfloat8 as bigint) without function;
create cast (bigint as xfloat8) without function;
-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
-- we don't care to assume the platform's strtod() handles subnormals
-- correctly; those are "use at your own risk". However we do test
-- subnormal outputs, since those are under our control.
with testdata(bits) as (values
-- small subnormals
(x'0000000000000001'),
(x'0000000000000002'), (x'0000000000000003'),
(x'0000000000001000'), (x'0000000100000000'),
(x'0000010000000000'), (x'0000010100000000'),
(x'0000400000000000'), (x'0000400100000000'),
(x'0000800000000000'), (x'0000800000000001'),
-- these values taken from upstream testsuite
(x'00000000000f4240'),
(x'00000000016e3600'),
(x'0000008cdcdea440'),
-- borderline between subnormal and normal
(x'000ffffffffffff0'), (x'000ffffffffffff1'),
(x'000ffffffffffffe'), (x'000fffffffffffff'))
select float8send(flt) as ibits,
flt
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
ibits | flt
--------------------+-------------------------
\x0000000000000001 | 5e-324
\x0000000000000002 | 1e-323
\x0000000000000003 | 1.5e-323
\x0000000000001000 | 2.0237e-320
\x0000000100000000 | 2.121995791e-314
\x0000010000000000 | 5.43230922487e-312
\x0000010100000000 | 5.45352918278e-312
\x0000400000000000 | 3.4766779039175e-310
\x0000400100000000 | 3.4768901034966e-310
\x0000800000000000 | 6.953355807835e-310
\x0000800000000001 | 6.95335580783505e-310
\x00000000000f4240 | 4.940656e-318
\x00000000016e3600 | 1.18575755e-316
\x0000008cdcdea440 | 2.989102097996e-312
\x000ffffffffffff0 | 2.2250738585071935e-308
\x000ffffffffffff1 | 2.225073858507194e-308
\x000ffffffffffffe | 2.2250738585072004e-308
\x000fffffffffffff | 2.225073858507201e-308
(18 rows)
-- round-trip tests
with testdata(bits) as (values
(x'0000000000000000'),
-- smallest normal values
(x'0010000000000000'), (x'0010000000000001'),
(x'0010000000000002'), (x'0018000000000000'),
--
(x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
(x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
(x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
(x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
(x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
(x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
(x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
(x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
(x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
(x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
-- values very close to 1
(x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
(x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
(x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
(x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
(x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
(x'3fefffffffffffff'),
(x'3ff0000000000000'),
(x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
(x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
(x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
--
(x'3ff921fb54442d18'),
(x'4005bf0a8b14576a'),
(x'400921fb54442d18'),
--
(x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
(x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
(x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
(x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
(x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
(x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
(x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
(x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
(x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
(x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
(x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
(x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
(x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
(x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
(x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
(x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
(x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
(x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
(x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
(x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
(x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
(x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
(x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
(x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
(x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
--
(x'7feffffffffffffe'), (x'7fefffffffffffff'),
-- round to even tests (+ve)
(x'4350000000000002'),
(x'4350000000002e06'),
(x'4352000000000003'),
(x'4352000000000004'),
(x'4358000000000003'),
(x'4358000000000004'),
(x'435f000000000020'),
-- round to even tests (-ve)
(x'c350000000000002'),
(x'c350000000002e06'),
(x'c352000000000003'),
(x'c352000000000004'),
(x'c358000000000003'),
(x'c358000000000004'),
(x'c35f000000000020'),
-- exercise fixed-point memmoves
(x'42dc12218377de66'),
(x'42a674e79c5fe51f'),
(x'4271f71fb04cb74c'),
(x'423cbe991a145879'),
(x'4206fee0e1a9e061'),
(x'41d26580b487e6b4'),
(x'419d6f34540ca453'),
(x'41678c29dcd6e9dc'),
(x'4132d687e3df217d'),
(x'40fe240c9fcb68c8'),
(x'40c81cd6e63c53d3'),
(x'40934a4584fd0fdc'),
(x'405edd3c07fb4c93'),
(x'4028b0fcd32f7076'),
(x'3ff3c0ca428c59f8'),
-- these cases come from the upstream's testsuite
-- LotsOfTrailingZeros)
(x'3e60000000000000'),
-- Regression
(x'c352bd2668e077c4'),
(x'434018601510c000'),
(x'43d055dc36f24000'),
(x'43e052961c6f8000'),
(x'3ff3c0ca2a5b1d5d'),
-- LooksLikePow5
(x'4830f0cf064dd592'),
(x'4840f0cf064dd592'),
(x'4850f0cf064dd592'),
-- OutputLength
(x'3ff3333333333333'),
(x'3ff3ae147ae147ae'),
(x'3ff3be76c8b43958'),
(x'3ff3c083126e978d'),
(x'3ff3c0c1fc8f3238'),
(x'3ff3c0c9539b8887'),
(x'3ff3c0ca2a5b1d5d'),
(x'3ff3c0ca4283de1b'),
(x'3ff3c0ca43db770a'),
(x'3ff3c0ca428abd53'),
(x'3ff3c0ca428c1d2b'),
(x'3ff3c0ca428c51f2'),
(x'3ff3c0ca428c58fc'),
(x'3ff3c0ca428c59dd'),
(x'3ff3c0ca428c59f8'),
(x'3ff3c0ca428c59fb'),
-- 32-bit chunking
(x'40112e0be8047a7d'),
(x'40112e0be815a889'),
(x'40112e0be826d695'),
(x'40112e0be83804a1'),
(x'40112e0be84932ad'),
-- MinMaxShift
(x'0040000000000000'),
(x'007fffffffffffff'),
(x'0290000000000000'),
(x'029fffffffffffff'),
(x'4350000000000000'),
(x'435fffffffffffff'),
(x'1330000000000000'),
(x'133fffffffffffff'),
(x'3a6fa7161a4d6e0c')
)
select float8send(flt) as ibits,
flt,
flt::text::float8 as r_flt,
float8send(flt::text::float8) as obits,
float8send(flt::text::float8) = float8send(flt) as correct
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
ibits | flt | r_flt | obits | correct
--------------------+-------------------------+-------------------------+--------------------+---------
\x0000000000000000 | 0 | 0 | \x0000000000000000 | t
\x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
\x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
\x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
\x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
\x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
\x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
\x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
\x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
\x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
\x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
\x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
\x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
\x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
\x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
\x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
\x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
\x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
\x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
\x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
\x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
\x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
\x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
\x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
\x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
\x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
\x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
\x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
\x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
\x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
\x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
\x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
\x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
\x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
\x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
\x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
\x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
\x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
\x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
\x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
\x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
\x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
\x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
\x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
\x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
\x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
\x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
\x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
\x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
\x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
\x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
\x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
\x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
\x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
\x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
\x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
\x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
\x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
\x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
\x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
\x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
\x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
\x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
\x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
\x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
\x4024000000000000 | 10 | 10 | \x4024000000000000 | t
\x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
\x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
\x4059000000000000 | 100 | 100 | \x4059000000000000 | t
\x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
\x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
\x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
\x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
\x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
\x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
\x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
\x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
\x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
\x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
\x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
\x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
\x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
\x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
\x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
\x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
\x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
\x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
\x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
\x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
\x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
\x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
\x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
\x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
\x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
\x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
\x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
\x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
\x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
\x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
\x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
\x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
\x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
\x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
\x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
\x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
\x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
\x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
\x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
\x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
\x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
\x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
\x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
\x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
\x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
\x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
\x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
\x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
\x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
\x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
\x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
\x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
\x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
\x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
\x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
\x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
\x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
\x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
\x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
\x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
\x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
\x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
\x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
\x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
\x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
\x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
\x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
\x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
\x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
\x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
\x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
\x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
\x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
\x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
\x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
\x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
\x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
\x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
\x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
\xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
\xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
\xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
\xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
\xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
\xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
\xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
\x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
\x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
\x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
\x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
\x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
\x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
\x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
\x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
\x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
\x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
\x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
\x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
\x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
\x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
\x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
\x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
\xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
\x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
\x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
\x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
\x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
\x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
\x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
\x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
\x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
\x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
\x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
\x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
\x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
\x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
\x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
\x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
\x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
\x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
\x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
\x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
\x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
\x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
\x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
\x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
\x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
\x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
\x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
\x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
\x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
\x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
\x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
\x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
\x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
\x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
\x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
\x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
\x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
\x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
(209 rows)
-- clean up, lest opr_sanity complain
\set VERBOSITY terse
drop type xfloat8 cascade;
NOTICE: drop cascades to 6 other objects
\set VERBOSITY default
--

447
src/test/regress/expected/float8.out
Unescape View File

@ -24,6 +24,13 @@ SELECT '-10e-400'::float8;
ERROR: "-10e-400" is out of range for type double precision
LINE 1: SELECT '-10e-400'::float8;
^
-- test smallest normalized input
SELECT float8send('2.2250738585072014E-308'::float8);
float8send
--------------------
\x0010000000000000
(1 row)
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
ERROR: invalid input syntax for type double precision: ""
@ -209,7 +216,7 @@ SELECT '' AS three, f.f1, f.f1 / '-10' AS x
WHERE f.f1 > '0.0';
three | f1 | x
-------+----------------------+-----------------------
| 1004.3 | -100.43
| 1004.3 | -100.42999999999999
| 1.2345678901234e+200 | -1.2345678901234e+199
| 1.2345678901234e-200 | -1.2345678901234e-201
(3 rows)
@ -227,8 +234,8 @@ SELECT '' AS three, f.f1, f.f1 - '-10' AS x
SELECT '' AS one, f.f1 ^ '2.0' AS square_f1
FROM FLOAT8_TBL f where f.f1 = '1004.3';
one | square_f1
-----+------------
| 1008618.49
-----+--------------------
| 1008618.4899999999
(1 row)
-- absolute value
@ -310,6 +317,8 @@ select sign(f1) as sign_f1 from float8_tbl f;
1
(5 rows)
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
eight
@ -445,6 +454,7 @@ SELECT '' AS five, * FROM FLOAT8_TBL;
| -1.2345678901234e-200
(5 rows)
RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
ERROR: "10e400" is out of range for type double precision
@ -530,7 +540,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
ERROR: bigint out of range
-- test exact cases for trigonometric functions in degrees
SET extra_float_digits = 3;
SELECT x,
sind(x),
sind(x) IN (-1,-0.5,0,0.5,1) AS sind_exact
@ -632,4 +641,432 @@ FROM (SELECT 10*cosd(a), 10*sind(a)
10 | 0 | 0 | t
(5 rows)
RESET extra_float_digits;
--
-- test output (and round-trip safety) of various values.
-- To ensure we're testing what we think we're testing, start with
-- float values specified by bit patterns (as a useful side effect,
-- this means we'll fail on non-IEEE platforms).
create type xfloat8;
create function xfloat8in(cstring) returns xfloat8 immutable strict
language internal as 'int8in';
NOTICE: return type xfloat8 is only a shell
create function xfloat8out(xfloat8) returns cstring immutable strict
language internal as 'int8out';
NOTICE: argument type xfloat8 is only a shell
create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
create cast (xfloat8 as float8) without function;
create cast (float8 as xfloat8) without function;
create cast (xfloat8 as bigint) without function;
create cast (bigint as xfloat8) without function;
-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
-- we don't care to assume the platform's strtod() handles subnormals
-- correctly; those are "use at your own risk". However we do test
-- subnormal outputs, since those are under our control.
with testdata(bits) as (values
-- small subnormals
(x'0000000000000001'),
(x'0000000000000002'), (x'0000000000000003'),
(x'0000000000001000'), (x'0000000100000000'),
(x'0000010000000000'), (x'0000010100000000'),
(x'0000400000000000'), (x'0000400100000000'),
(x'0000800000000000'), (x'0000800000000001'),
-- these values taken from upstream testsuite
(x'00000000000f4240'),
(x'00000000016e3600'),
(x'0000008cdcdea440'),
-- borderline between subnormal and normal
(x'000ffffffffffff0'), (x'000ffffffffffff1'),
(x'000ffffffffffffe'), (x'000fffffffffffff'))
select float8send(flt) as ibits,
flt
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
ibits | flt
--------------------+-------------------------
\x0000000000000001 | 5e-324
\x0000000000000002 | 1e-323
\x0000000000000003 | 1.5e-323
\x0000000000001000 | 2.0237e-320
\x0000000100000000 | 2.121995791e-314
\x0000010000000000 | 5.43230922487e-312
\x0000010100000000 | 5.45352918278e-312
\x0000400000000000 | 3.4766779039175e-310
\x0000400100000000 | 3.4768901034966e-310
\x0000800000000000 | 6.953355807835e-310
\x0000800000000001 | 6.95335580783505e-310
\x00000000000f4240 | 4.940656e-318
\x00000000016e3600 | 1.18575755e-316
\x0000008cdcdea440 | 2.989102097996e-312
\x000ffffffffffff0 | 2.2250738585071935e-308
\x000ffffffffffff1 | 2.225073858507194e-308
\x000ffffffffffffe | 2.2250738585072004e-308
\x000fffffffffffff | 2.225073858507201e-308
(18 rows)
-- round-trip tests
with testdata(bits) as (values
(x'0000000000000000'),
-- smallest normal values
(x'0010000000000000'), (x'0010000000000001'),
(x'0010000000000002'), (x'0018000000000000'),
--
(x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
(x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
(x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
(x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
(x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
(x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
(x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
(x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
(x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
(x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
-- values very close to 1
(x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
(x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
(x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
(x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
(x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
(x'3fefffffffffffff'),
(x'3ff0000000000000'),
(x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
(x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
(x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
--
(x'3ff921fb54442d18'),
(x'4005bf0a8b14576a'),
(x'400921fb54442d18'),
--
(x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
(x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
(x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
(x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
(x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
(x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
(x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
(x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
(x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
(x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
(x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
(x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
(x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
(x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
(x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
(x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
(x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
(x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
(x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
(x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
(x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
(x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
(x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
(x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
(x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
--
(x'7feffffffffffffe'), (x'7fefffffffffffff'),
-- round to even tests (+ve)
(x'4350000000000002'),
(x'4350000000002e06'),
(x'4352000000000003'),
(x'4352000000000004'),
(x'4358000000000003'),
(x'4358000000000004'),
(x'435f000000000020'),
-- round to even tests (-ve)
(x'c350000000000002'),
(x'c350000000002e06'),
(x'c352000000000003'),
(x'c352000000000004'),
(x'c358000000000003'),
(x'c358000000000004'),
(x'c35f000000000020'),
-- exercise fixed-point memmoves
(x'42dc12218377de66'),
(x'42a674e79c5fe51f'),
(x'4271f71fb04cb74c'),
(x'423cbe991a145879'),
(x'4206fee0e1a9e061'),
(x'41d26580b487e6b4'),
(x'419d6f34540ca453'),
(x'41678c29dcd6e9dc'),
(x'4132d687e3df217d'),
(x'40fe240c9fcb68c8'),
(x'40c81cd6e63c53d3'),
(x'40934a4584fd0fdc'),
(x'405edd3c07fb4c93'),
(x'4028b0fcd32f7076'),
(x'3ff3c0ca428c59f8'),
-- these cases come from the upstream's testsuite
-- LotsOfTrailingZeros)
(x'3e60000000000000'),
-- Regression
(x'c352bd2668e077c4'),
(x'434018601510c000'),
(x'43d055dc36f24000'),
(x'43e052961c6f8000'),
(x'3ff3c0ca2a5b1d5d'),
-- LooksLikePow5
(x'4830f0cf064dd592'),
(x'4840f0cf064dd592'),
(x'4850f0cf064dd592'),
-- OutputLength
(x'3ff3333333333333'),
(x'3ff3ae147ae147ae'),
(x'3ff3be76c8b43958'),
(x'3ff3c083126e978d'),
(x'3ff3c0c1fc8f3238'),
(x'3ff3c0c9539b8887'),
(x'3ff3c0ca2a5b1d5d'),
(x'3ff3c0ca4283de1b'),
(x'3ff3c0ca43db770a'),
(x'3ff3c0ca428abd53'),
(x'3ff3c0ca428c1d2b'),
(x'3ff3c0ca428c51f2'),
(x'3ff3c0ca428c58fc'),
(x'3ff3c0ca428c59dd'),
(x'3ff3c0ca428c59f8'),
(x'3ff3c0ca428c59fb'),
-- 32-bit chunking
(x'40112e0be8047a7d'),
(x'40112e0be815a889'),
(x'40112e0be826d695'),
(x'40112e0be83804a1'),
(x'40112e0be84932ad'),
-- MinMaxShift
(x'0040000000000000'),
(x'007fffffffffffff'),
(x'0290000000000000'),
(x'029fffffffffffff'),
(x'4350000000000000'),
(x'435fffffffffffff'),
(x'1330000000000000'),
(x'133fffffffffffff'),
(x'3a6fa7161a4d6e0c')
)
select float8send(flt) as ibits,
flt,
flt::text::float8 as r_flt,
float8send(flt::text::float8) as obits,
float8send(flt::text::float8) = float8send(flt) as correct
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
ibits | flt | r_flt | obits | correct
--------------------+-------------------------+-------------------------+--------------------+---------
\x0000000000000000 | 0 | 0 | \x0000000000000000 | t
\x0010000000000000 | 2.2250738585072014e-308 | 2.2250738585072014e-308 | \x0010000000000000 | t
\x0010000000000001 | 2.225073858507202e-308 | 2.225073858507202e-308 | \x0010000000000001 | t
\x0010000000000002 | 2.2250738585072024e-308 | 2.2250738585072024e-308 | \x0010000000000002 | t
\x0018000000000000 | 3.337610787760802e-308 | 3.337610787760802e-308 | \x0018000000000000 | t
\x3ddb7cdfd9d7bdba | 9.999999999999999e-11 | 9.999999999999999e-11 | \x3ddb7cdfd9d7bdba | t
\x3ddb7cdfd9d7bdbb | 1e-10 | 1e-10 | \x3ddb7cdfd9d7bdbb | t
\x3ddb7cdfd9d7bdbc | 1.0000000000000002e-10 | 1.0000000000000002e-10 | \x3ddb7cdfd9d7bdbc | t
\x3e112e0be826d694 | 9.999999999999999e-10 | 9.999999999999999e-10 | \x3e112e0be826d694 | t
\x3e112e0be826d695 | 1e-09 | 1e-09 | \x3e112e0be826d695 | t
\x3e112e0be826d696 | 1.0000000000000003e-09 | 1.0000000000000003e-09 | \x3e112e0be826d696 | t
\x3e45798ee2308c39 | 9.999999999999999e-09 | 9.999999999999999e-09 | \x3e45798ee2308c39 | t
\x3e45798ee2308c3a | 1e-08 | 1e-08 | \x3e45798ee2308c3a | t
\x3e45798ee2308c3b | 1.0000000000000002e-08 | 1.0000000000000002e-08 | \x3e45798ee2308c3b | t
\x3e7ad7f29abcaf47 | 9.999999999999998e-08 | 9.999999999999998e-08 | \x3e7ad7f29abcaf47 | t
\x3e7ad7f29abcaf48 | 1e-07 | 1e-07 | \x3e7ad7f29abcaf48 | t
\x3e7ad7f29abcaf49 | 1.0000000000000001e-07 | 1.0000000000000001e-07 | \x3e7ad7f29abcaf49 | t
\x3eb0c6f7a0b5ed8c | 9.999999999999997e-07 | 9.999999999999997e-07 | \x3eb0c6f7a0b5ed8c | t
\x3eb0c6f7a0b5ed8d | 1e-06 | 1e-06 | \x3eb0c6f7a0b5ed8d | t
\x3eb0c6f7a0b5ed8e | 1.0000000000000002e-06 | 1.0000000000000002e-06 | \x3eb0c6f7a0b5ed8e | t
\x3ee4f8b588e368ef | 9.999999999999997e-06 | 9.999999999999997e-06 | \x3ee4f8b588e368ef | t
\x3ee4f8b588e368f0 | 9.999999999999999e-06 | 9.999999999999999e-06 | \x3ee4f8b588e368f0 | t
\x3ee4f8b588e368f1 | 1e-05 | 1e-05 | \x3ee4f8b588e368f1 | t
\x3f1a36e2eb1c432c | 9.999999999999999e-05 | 9.999999999999999e-05 | \x3f1a36e2eb1c432c | t
\x3f1a36e2eb1c432d | 0.0001 | 0.0001 | \x3f1a36e2eb1c432d | t
\x3f1a36e2eb1c432e | 0.00010000000000000002 | 0.00010000000000000002 | \x3f1a36e2eb1c432e | t
\x3f50624dd2f1a9fb | 0.0009999999999999998 | 0.0009999999999999998 | \x3f50624dd2f1a9fb | t
\x3f50624dd2f1a9fc | 0.001 | 0.001 | \x3f50624dd2f1a9fc | t
\x3f50624dd2f1a9fd | 0.0010000000000000002 | 0.0010000000000000002 | \x3f50624dd2f1a9fd | t
\x3f847ae147ae147a | 0.009999999999999998 | 0.009999999999999998 | \x3f847ae147ae147a | t
\x3f847ae147ae147b | 0.01 | 0.01 | \x3f847ae147ae147b | t
\x3f847ae147ae147c | 0.010000000000000002 | 0.010000000000000002 | \x3f847ae147ae147c | t
\x3fb9999999999999 | 0.09999999999999999 | 0.09999999999999999 | \x3fb9999999999999 | t
\x3fb999999999999a | 0.1 | 0.1 | \x3fb999999999999a | t
\x3fb999999999999b | 0.10000000000000002 | 0.10000000000000002 | \x3fb999999999999b | t
\x3feffffffffffff0 | 0.9999999999999982 | 0.9999999999999982 | \x3feffffffffffff0 | t
\x3feffffffffffff1 | 0.9999999999999983 | 0.9999999999999983 | \x3feffffffffffff1 | t
\x3feffffffffffff2 | 0.9999999999999984 | 0.9999999999999984 | \x3feffffffffffff2 | t
\x3feffffffffffff3 | 0.9999999999999986 | 0.9999999999999986 | \x3feffffffffffff3 | t
\x3feffffffffffff4 | 0.9999999999999987 | 0.9999999999999987 | \x3feffffffffffff4 | t
\x3feffffffffffff5 | 0.9999999999999988 | 0.9999999999999988 | \x3feffffffffffff5 | t
\x3feffffffffffff6 | 0.9999999999999989 | 0.9999999999999989 | \x3feffffffffffff6 | t
\x3feffffffffffff7 | 0.999999999999999 | 0.999999999999999 | \x3feffffffffffff7 | t
\x3feffffffffffff8 | 0.9999999999999991 | 0.9999999999999991 | \x3feffffffffffff8 | t
\x3feffffffffffff9 | 0.9999999999999992 | 0.9999999999999992 | \x3feffffffffffff9 | t
\x3feffffffffffffa | 0.9999999999999993 | 0.9999999999999993 | \x3feffffffffffffa | t
\x3feffffffffffffb | 0.9999999999999994 | 0.9999999999999994 | \x3feffffffffffffb | t
\x3feffffffffffffc | 0.9999999999999996 | 0.9999999999999996 | \x3feffffffffffffc | t
\x3feffffffffffffd | 0.9999999999999997 | 0.9999999999999997 | \x3feffffffffffffd | t
\x3feffffffffffffe | 0.9999999999999998 | 0.9999999999999998 | \x3feffffffffffffe | t
\x3fefffffffffffff | 0.9999999999999999 | 0.9999999999999999 | \x3fefffffffffffff | t
\x3ff0000000000000 | 1 | 1 | \x3ff0000000000000 | t
\x3ff0000000000001 | 1.0000000000000002 | 1.0000000000000002 | \x3ff0000000000001 | t
\x3ff0000000000002 | 1.0000000000000004 | 1.0000000000000004 | \x3ff0000000000002 | t
\x3ff0000000000003 | 1.0000000000000007 | 1.0000000000000007 | \x3ff0000000000003 | t
\x3ff0000000000004 | 1.0000000000000009 | 1.0000000000000009 | \x3ff0000000000004 | t
\x3ff0000000000005 | 1.000000000000001 | 1.000000000000001 | \x3ff0000000000005 | t
\x3ff0000000000006 | 1.0000000000000013 | 1.0000000000000013 | \x3ff0000000000006 | t
\x3ff0000000000007 | 1.0000000000000016 | 1.0000000000000016 | \x3ff0000000000007 | t
\x3ff0000000000008 | 1.0000000000000018 | 1.0000000000000018 | \x3ff0000000000008 | t
\x3ff0000000000009 | 1.000000000000002 | 1.000000000000002 | \x3ff0000000000009 | t
\x3ff921fb54442d18 | 1.5707963267948966 | 1.5707963267948966 | \x3ff921fb54442d18 | t
\x4005bf0a8b14576a | 2.7182818284590455 | 2.7182818284590455 | \x4005bf0a8b14576a | t
\x400921fb54442d18 | 3.141592653589793 | 3.141592653589793 | \x400921fb54442d18 | t
\x4023ffffffffffff | 9.999999999999998 | 9.999999999999998 | \x4023ffffffffffff | t
\x4024000000000000 | 10 | 10 | \x4024000000000000 | t
\x4024000000000001 | 10.000000000000002 | 10.000000000000002 | \x4024000000000001 | t
\x4058ffffffffffff | 99.99999999999999 | 99.99999999999999 | \x4058ffffffffffff | t
\x4059000000000000 | 100 | 100 | \x4059000000000000 | t
\x4059000000000001 | 100.00000000000001 | 100.00000000000001 | \x4059000000000001 | t
\x408f3fffffffffff | 999.9999999999999 | 999.9999999999999 | \x408f3fffffffffff | t
\x408f400000000000 | 1000 | 1000 | \x408f400000000000 | t
\x408f400000000001 | 1000.0000000000001 | 1000.0000000000001 | \x408f400000000001 | t
\x40c387ffffffffff | 9999.999999999998 | 9999.999999999998 | \x40c387ffffffffff | t
\x40c3880000000000 | 10000 | 10000 | \x40c3880000000000 | t
\x40c3880000000001 | 10000.000000000002 | 10000.000000000002 | \x40c3880000000001 | t
\x40f869ffffffffff | 99999.99999999999 | 99999.99999999999 | \x40f869ffffffffff | t
\x40f86a0000000000 | 100000 | 100000 | \x40f86a0000000000 | t
\x40f86a0000000001 | 100000.00000000001 | 100000.00000000001 | \x40f86a0000000001 | t
\x412e847fffffffff | 999999.9999999999 | 999999.9999999999 | \x412e847fffffffff | t
\x412e848000000000 | 1000000 | 1000000 | \x412e848000000000 | t
\x412e848000000001 | 1000000.0000000001 | 1000000.0000000001 | \x412e848000000001 | t
\x416312cfffffffff | 9999999.999999998 | 9999999.999999998 | \x416312cfffffffff | t
\x416312d000000000 | 10000000 | 10000000 | \x416312d000000000 | t
\x416312d000000001 | 10000000.000000002 | 10000000.000000002 | \x416312d000000001 | t
\x4197d783ffffffff | 99999999.99999999 | 99999999.99999999 | \x4197d783ffffffff | t
\x4197d78400000000 | 100000000 | 100000000 | \x4197d78400000000 | t
\x4197d78400000001 | 100000000.00000001 | 100000000.00000001 | \x4197d78400000001 | t
\x41cdcd64ffffffff | 999999999.9999999 | 999999999.9999999 | \x41cdcd64ffffffff | t
\x41cdcd6500000000 | 1000000000 | 1000000000 | \x41cdcd6500000000 | t
\x41cdcd6500000001 | 1000000000.0000001 | 1000000000.0000001 | \x41cdcd6500000001 | t
\x4202a05f1fffffff | 9999999999.999998 | 9999999999.999998 | \x4202a05f1fffffff | t
\x4202a05f20000000 | 10000000000 | 10000000000 | \x4202a05f20000000 | t
\x4202a05f20000001 | 10000000000.000002 | 10000000000.000002 | \x4202a05f20000001 | t
\x42374876e7ffffff | 99999999999.99998 | 99999999999.99998 | \x42374876e7ffffff | t
\x42374876e8000000 | 100000000000 | 100000000000 | \x42374876e8000000 | t
\x42374876e8000001 | 100000000000.00002 | 100000000000.00002 | \x42374876e8000001 | t
\x426d1a94a1ffffff | 999999999999.9999 | 999999999999.9999 | \x426d1a94a1ffffff | t
\x426d1a94a2000000 | 1000000000000 | 1000000000000 | \x426d1a94a2000000 | t
\x426d1a94a2000001 | 1000000000000.0001 | 1000000000000.0001 | \x426d1a94a2000001 | t
\x42a2309ce53fffff | 9999999999999.998 | 9999999999999.998 | \x42a2309ce53fffff | t
\x42a2309ce5400000 | 10000000000000 | 10000000000000 | \x42a2309ce5400000 | t
\x42a2309ce5400001 | 10000000000000.002 | 10000000000000.002 | \x42a2309ce5400001 | t
\x42d6bcc41e8fffff | 99999999999999.98 | 99999999999999.98 | \x42d6bcc41e8fffff | t
\x42d6bcc41e900000 | 100000000000000 | 100000000000000 | \x42d6bcc41e900000 | t
\x42d6bcc41e900001 | 100000000000000.02 | 100000000000000.02 | \x42d6bcc41e900001 | t
\x430c6bf52633ffff | 999999999999999.9 | 999999999999999.9 | \x430c6bf52633ffff | t
\x430c6bf526340000 | 1e+15 | 1e+15 | \x430c6bf526340000 | t
\x430c6bf526340001 | 1.0000000000000001e+15 | 1.0000000000000001e+15 | \x430c6bf526340001 | t
\x4341c37937e07fff | 9.999999999999998e+15 | 9.999999999999998e+15 | \x4341c37937e07fff | t
\x4341c37937e08000 | 1e+16 | 1e+16 | \x4341c37937e08000 | t
\x4341c37937e08001 | 1.0000000000000002e+16 | 1.0000000000000002e+16 | \x4341c37937e08001 | t
\x4376345785d89fff | 9.999999999999998e+16 | 9.999999999999998e+16 | \x4376345785d89fff | t
\x4376345785d8a000 | 1e+17 | 1e+17 | \x4376345785d8a000 | t
\x4376345785d8a001 | 1.0000000000000002e+17 | 1.0000000000000002e+17 | \x4376345785d8a001 | t
\x43abc16d674ec7ff | 9.999999999999999e+17 | 9.999999999999999e+17 | \x43abc16d674ec7ff | t
\x43abc16d674ec800 | 1e+18 | 1e+18 | \x43abc16d674ec800 | t
\x43abc16d674ec801 | 1.0000000000000001e+18 | 1.0000000000000001e+18 | \x43abc16d674ec801 | t
\x43e158e460913cff | 9.999999999999998e+18 | 9.999999999999998e+18 | \x43e158e460913cff | t
\x43e158e460913d00 | 1e+19 | 1e+19 | \x43e158e460913d00 | t
\x43e158e460913d01 | 1.0000000000000002e+19 | 1.0000000000000002e+19 | \x43e158e460913d01 | t
\x4415af1d78b58c3f | 9.999999999999998e+19 | 9.999999999999998e+19 | \x4415af1d78b58c3f | t
\x4415af1d78b58c40 | 1e+20 | 1e+20 | \x4415af1d78b58c40 | t
\x4415af1d78b58c41 | 1.0000000000000002e+20 | 1.0000000000000002e+20 | \x4415af1d78b58c41 | t
\x444b1ae4d6e2ef4f | 9.999999999999999e+20 | 9.999999999999999e+20 | \x444b1ae4d6e2ef4f | t
\x444b1ae4d6e2ef50 | 1e+21 | 1e+21 | \x444b1ae4d6e2ef50 | t
\x444b1ae4d6e2ef51 | 1.0000000000000001e+21 | 1.0000000000000001e+21 | \x444b1ae4d6e2ef51 | t
\x4480f0cf064dd591 | 9.999999999999998e+21 | 9.999999999999998e+21 | \x4480f0cf064dd591 | t
\x4480f0cf064dd592 | 1e+22 | 1e+22 | \x4480f0cf064dd592 | t
\x4480f0cf064dd593 | 1.0000000000000002e+22 | 1.0000000000000002e+22 | \x4480f0cf064dd593 | t
\x44b52d02c7e14af5 | 9.999999999999997e+22 | 9.999999999999997e+22 | \x44b52d02c7e14af5 | t
\x44b52d02c7e14af6 | 9.999999999999999e+22 | 9.999999999999999e+22 | \x44b52d02c7e14af6 | t
\x44b52d02c7e14af7 | 1.0000000000000001e+23 | 1.0000000000000001e+23 | \x44b52d02c7e14af7 | t
\x44ea784379d99db3 | 9.999999999999998e+23 | 9.999999999999998e+23 | \x44ea784379d99db3 | t
\x44ea784379d99db4 | 1e+24 | 1e+24 | \x44ea784379d99db4 | t
\x44ea784379d99db5 | 1.0000000000000001e+24 | 1.0000000000000001e+24 | \x44ea784379d99db5 | t
\x45208b2a2c280290 | 9.999999999999999e+24 | 9.999999999999999e+24 | \x45208b2a2c280290 | t
\x45208b2a2c280291 | 1e+25 | 1e+25 | \x45208b2a2c280291 | t
\x45208b2a2c280292 | 1.0000000000000003e+25 | 1.0000000000000003e+25 | \x45208b2a2c280292 | t
\x7feffffffffffffe | 1.7976931348623155e+308 | 1.7976931348623155e+308 | \x7feffffffffffffe | t
\x7fefffffffffffff | 1.7976931348623157e+308 | 1.7976931348623157e+308 | \x7fefffffffffffff | t
\x4350000000000002 | 1.8014398509481992e+16 | 1.8014398509481992e+16 | \x4350000000000002 | t
\x4350000000002e06 | 1.8014398509529112e+16 | 1.8014398509529112e+16 | \x4350000000002e06 | t
\x4352000000000003 | 2.0266198323167244e+16 | 2.0266198323167244e+16 | \x4352000000000003 | t
\x4352000000000004 | 2.0266198323167248e+16 | 2.0266198323167248e+16 | \x4352000000000004 | t
\x4358000000000003 | 2.7021597764222988e+16 | 2.7021597764222988e+16 | \x4358000000000003 | t
\x4358000000000004 | 2.7021597764222992e+16 | 2.7021597764222992e+16 | \x4358000000000004 | t
\x435f000000000020 | 3.4902897112121472e+16 | 3.4902897112121472e+16 | \x435f000000000020 | t
\xc350000000000002 | -1.8014398509481992e+16 | -1.8014398509481992e+16 | \xc350000000000002 | t
\xc350000000002e06 | -1.8014398509529112e+16 | -1.8014398509529112e+16 | \xc350000000002e06 | t
\xc352000000000003 | -2.0266198323167244e+16 | -2.0266198323167244e+16 | \xc352000000000003 | t
\xc352000000000004 | -2.0266198323167248e+16 | -2.0266198323167248e+16 | \xc352000000000004 | t
\xc358000000000003 | -2.7021597764222988e+16 | -2.7021597764222988e+16 | \xc358000000000003 | t
\xc358000000000004 | -2.7021597764222992e+16 | -2.7021597764222992e+16 | \xc358000000000004 | t
\xc35f000000000020 | -3.4902897112121472e+16 | -3.4902897112121472e+16 | \xc35f000000000020 | t
\x42dc12218377de66 | 123456789012345.6 | 123456789012345.6 | \x42dc12218377de66 | t
\x42a674e79c5fe51f | 12345678901234.56 | 12345678901234.56 | \x42a674e79c5fe51f | t
\x4271f71fb04cb74c | 1234567890123.456 | 1234567890123.456 | \x4271f71fb04cb74c | t
\x423cbe991a145879 | 123456789012.3456 | 123456789012.3456 | \x423cbe991a145879 | t
\x4206fee0e1a9e061 | 12345678901.23456 | 12345678901.23456 | \x4206fee0e1a9e061 | t
\x41d26580b487e6b4 | 1234567890.123456 | 1234567890.123456 | \x41d26580b487e6b4 | t
\x419d6f34540ca453 | 123456789.0123456 | 123456789.0123456 | \x419d6f34540ca453 | t
\x41678c29dcd6e9dc | 12345678.90123456 | 12345678.90123456 | \x41678c29dcd6e9dc | t
\x4132d687e3df217d | 1234567.890123456 | 1234567.890123456 | \x4132d687e3df217d | t
\x40fe240c9fcb68c8 | 123456.7890123456 | 123456.7890123456 | \x40fe240c9fcb68c8 | t
\x40c81cd6e63c53d3 | 12345.67890123456 | 12345.67890123456 | \x40c81cd6e63c53d3 | t
\x40934a4584fd0fdc | 1234.567890123456 | 1234.567890123456 | \x40934a4584fd0fdc | t
\x405edd3c07fb4c93 | 123.4567890123456 | 123.4567890123456 | \x405edd3c07fb4c93 | t
\x4028b0fcd32f7076 | 12.34567890123456 | 12.34567890123456 | \x4028b0fcd32f7076 | t
\x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
\x3e60000000000000 | 2.9802322387695312e-08 | 2.9802322387695312e-08 | \x3e60000000000000 | t
\xc352bd2668e077c4 | -2.1098088986959632e+16 | -2.1098088986959632e+16 | \xc352bd2668e077c4 | t
\x434018601510c000 | 9.0608011534336e+15 | 9.0608011534336e+15 | \x434018601510c000 | t
\x43d055dc36f24000 | 4.708356024711512e+18 | 4.708356024711512e+18 | \x43d055dc36f24000 | t
\x43e052961c6f8000 | 9.409340012568248e+18 | 9.409340012568248e+18 | \x43e052961c6f8000 | t
\x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
\x4830f0cf064dd592 | 5.764607523034235e+39 | 5.764607523034235e+39 | \x4830f0cf064dd592 | t
\x4840f0cf064dd592 | 1.152921504606847e+40 | 1.152921504606847e+40 | \x4840f0cf064dd592 | t
\x4850f0cf064dd592 | 2.305843009213694e+40 | 2.305843009213694e+40 | \x4850f0cf064dd592 | t
\x3ff3333333333333 | 1.2 | 1.2 | \x3ff3333333333333 | t
\x3ff3ae147ae147ae | 1.23 | 1.23 | \x3ff3ae147ae147ae | t
\x3ff3be76c8b43958 | 1.234 | 1.234 | \x3ff3be76c8b43958 | t
\x3ff3c083126e978d | 1.2345 | 1.2345 | \x3ff3c083126e978d | t
\x3ff3c0c1fc8f3238 | 1.23456 | 1.23456 | \x3ff3c0c1fc8f3238 | t
\x3ff3c0c9539b8887 | 1.234567 | 1.234567 | \x3ff3c0c9539b8887 | t
\x3ff3c0ca2a5b1d5d | 1.2345678 | 1.2345678 | \x3ff3c0ca2a5b1d5d | t
\x3ff3c0ca4283de1b | 1.23456789 | 1.23456789 | \x3ff3c0ca4283de1b | t
\x3ff3c0ca43db770a | 1.234567895 | 1.234567895 | \x3ff3c0ca43db770a | t
\x3ff3c0ca428abd53 | 1.2345678901 | 1.2345678901 | \x3ff3c0ca428abd53 | t
\x3ff3c0ca428c1d2b | 1.23456789012 | 1.23456789012 | \x3ff3c0ca428c1d2b | t
\x3ff3c0ca428c51f2 | 1.234567890123 | 1.234567890123 | \x3ff3c0ca428c51f2 | t
\x3ff3c0ca428c58fc | 1.2345678901234 | 1.2345678901234 | \x3ff3c0ca428c58fc | t
\x3ff3c0ca428c59dd | 1.23456789012345 | 1.23456789012345 | \x3ff3c0ca428c59dd | t
\x3ff3c0ca428c59f8 | 1.234567890123456 | 1.234567890123456 | \x3ff3c0ca428c59f8 | t
\x3ff3c0ca428c59fb | 1.2345678901234567 | 1.2345678901234567 | \x3ff3c0ca428c59fb | t
\x40112e0be8047a7d | 4.294967294 | 4.294967294 | \x40112e0be8047a7d | t
\x40112e0be815a889 | 4.294967295 | 4.294967295 | \x40112e0be815a889 | t
\x40112e0be826d695 | 4.294967296 | 4.294967296 | \x40112e0be826d695 | t
\x40112e0be83804a1 | 4.294967297 | 4.294967297 | \x40112e0be83804a1 | t
\x40112e0be84932ad | 4.294967298 | 4.294967298 | \x40112e0be84932ad | t
\x0040000000000000 | 1.7800590868057611e-307 | 1.7800590868057611e-307 | \x0040000000000000 | t
\x007fffffffffffff | 2.8480945388892175e-306 | 2.8480945388892175e-306 | \x007fffffffffffff | t
\x0290000000000000 | 2.446494580089078e-296 | 2.446494580089078e-296 | \x0290000000000000 | t
\x029fffffffffffff | 4.8929891601781557e-296 | 4.8929891601781557e-296 | \x029fffffffffffff | t
\x4350000000000000 | 1.8014398509481984e+16 | 1.8014398509481984e+16 | \x4350000000000000 | t
\x435fffffffffffff | 3.6028797018963964e+16 | 3.6028797018963964e+16 | \x435fffffffffffff | t
\x1330000000000000 | 2.900835519859558e-216 | 2.900835519859558e-216 | \x1330000000000000 | t
\x133fffffffffffff | 5.801671039719115e-216 | 5.801671039719115e-216 | \x133fffffffffffff | t
\x3a6fa7161a4d6e0c | 3.196104012172126e-27 | 3.196104012172126e-27 | \x3a6fa7161a4d6e0c | t
(209 rows)
-- clean up, lest opr_sanity complain
\set VERBOSITY terse
drop type xfloat8 cascade;
NOTICE: drop cascades to 6 other objects
\set VERBOSITY default
--

24
src/test/regress/expected/int8.out
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@ -330,22 +330,22 @@ SELECT '' AS five, q1, q2, q1 / q2 AS divide, q1 % q2 AS mod FROM INT8_TBL;
SELECT '' AS five, q1, float8(q1) FROM INT8_TBL;
five | q1 | float8
------+------------------+----------------------
------+------------------+-----------------------
| 123 | 123
| 123 | 123
| 4567890123456789 | 4.56789012345679e+15
| 4567890123456789 | 4.56789012345679e+15
| 4567890123456789 | 4.56789012345679e+15
| 4567890123456789 | 4.567890123456789e+15
| 4567890123456789 | 4.567890123456789e+15
| 4567890123456789 | 4.567890123456789e+15
(5 rows)
SELECT '' AS five, q2, float8(q2) FROM INT8_TBL;
five | q2 | float8
------+-------------------+-----------------------
------+-------------------+------------------------
| 456 | 456
| 4567890123456789 | 4.56789012345679e+15
| 4567890123456789 | 4.567890123456789e+15
| 123 | 123
| 4567890123456789 | 4.56789012345679e+15
| -4567890123456789 | -4.56789012345679e+15
| 4567890123456789 | 4.567890123456789e+15
| -4567890123456789 | -4.567890123456789e+15
(5 rows)
SELECT 37 + q1 AS plus4 FROM INT8_TBL;
@ -727,12 +727,12 @@ SELECT CAST('42'::int2 AS int8), CAST('-37'::int2 AS int8);
SELECT CAST(q1 AS float4), CAST(q2 AS float8) FROM INT8_TBL;
q1 | q2
-------------+-----------------------
-------------+------------------------
123 | 456
123 | 4.56789012345679e+15
123 | 4.567890123456789e+15
4.56789e+15 | 123
4.56789e+15 | 4.56789012345679e+15
4.56789e+15 | -4.56789012345679e+15
4.56789e+15 | 4.567890123456789e+15
4.56789e+15 | -4.567890123456789e+15
(5 rows)
SELECT CAST('36854775807.0'::float4 AS int8);

4
src/test/regress/expected/jsonb.out
Unescape View File

@ -4377,8 +4377,8 @@ select '12345.05'::jsonb::numeric;
select '12345.05'::jsonb::float4;
float4
--------
12345
----------
12345.05
(1 row)
select '12345.05'::jsonb::float8;

4
src/test/regress/expected/line.out
Unescape View File

@ -65,13 +65,13 @@ INSERT INTO LINE_TBL VALUES (line(point '(1,0)', point '(1,0)'));
ERROR: invalid line specification: must be two distinct points
select * from LINE_TBL;
s
---------------------------------------------
------------------------------------------------
{0,-1,5}
{1,0,5}
{0,3,0}
{1,-1,0}
{-0.4,-1,-6}
{-0.000184615384615385,-1,15.3846153846154}
{-0.0001846153846153846,-1,15.384615384615387}
{3,NaN,5}
{NaN,NaN,NaN}
{0,-1,3}

2
src/test/regress/expected/point.out
Unescape View File

@ -1,6 +1,8 @@
--
-- POINT
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');
INSERT INTO POINT_TBL(f1) VALUES ('(-10.0,0.0)');

8
src/test/regress/expected/rules.out
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@ -911,23 +911,23 @@ insert into rtest_comp values ('p5', 'inch', 7.0);
insert into rtest_comp values ('p6', 'inch', 4.4);
select * from rtest_vcomp order by part;
part | size_in_cm
------+------------
------+--------------------
p1 | 500
p2 | 300
p3 | 5
p4 | 15
p5 | 17.78
p6 | 11.176
p6 | 11.176000000000002
(6 rows)
select * from rtest_vcomp where size_in_cm > 10.0 order by size_in_cm using >;
part | size_in_cm
------+------------
------+--------------------
p1 | 500
p2 | 300
p5 | 17.78
p4 | 15
p6 | 11.176
p6 | 11.176000000000002
(5 rows)
--

4
src/test/regress/expected/tsearch.out
Unescape View File

@ -971,8 +971,8 @@ Water, water, every where,
S. T. Coleridge (1772-1834)
'), to_tsquery('english', 'breath&motion&water'));
ts_rank_cd
------------
0.00833333
-------------
0.008333334
(1 row)
SELECT ts_rank_cd(to_tsvector('english', '

46
src/test/regress/expected/tstypes.out
Unescape View File

@ -788,56 +788,56 @@ select to_tsvector('simple', '') @@ '!foo' AS "true";
--ranking
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a | s');
ts_rank
-----------
0.0911891
-------------
0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s');
ts_rank
-----------
0.0303964
-------------
0.030396355
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | s:*');
ts_rank
-----------
0.0911891
-------------
0.091189064
(1 row)
SELECT ts_rank(' a:1 sa:2C d g'::tsvector, 'a | sa:*');
ts_rank
-----------
0.0911891
-------------
0.091189064
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a | s');
ts_rank
----------
0.151982
------------
0.15198177
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a | s');
ts_rank
-----------
0.0607927
------------
0.06079271
(1 row)
SELECT ts_rank(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank
----------
0.140153
------------
0.14015312
(1 row)
SELECT ts_rank(' a:1 s:2B d g'::tsvector, 'a & s');
ts_rank
----------
0.198206
------------
0.19820644
(1 row)
SELECT ts_rank(' a:1 s:2 d g'::tsvector, 'a & s');
ts_rank
-----------
0.0991032
------------
0.09910322
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a | s');
@ -885,7 +885,7 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a | s');
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a & s');
ts_rank_cd
------------
0.133333
0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2B d g'::tsvector, 'a & s');
@ -903,13 +903,13 @@ SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a & s');
SELECT ts_rank_cd(' a:1 s:2A d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
0.181818
0.18181819
(1 row)
SELECT ts_rank_cd(' a:1 s:2C d g'::tsvector, 'a <-> s');
ts_rank_cd
------------
0.133333
0.13333334
(1 row)
SELECT ts_rank_cd(' a:1 s:2 d g'::tsvector, 'a <-> s');
@ -927,13 +927,13 @@ SELECT ts_rank_cd(' a:1 s:2 d:2A g'::tsvector, 'a <-> s');
SELECT ts_rank_cd(' a:1 s:2,3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
0.0909091
0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 b:2 s:3A d:2A g'::tsvector, 'a <2> s:A');
ts_rank_cd
------------
0.0909091
0.09090909
(1 row)
SELECT ts_rank_cd(' a:1 sa:2D sb:2A g'::tsvector, 'a <-> s:*');

2
src/test/regress/expected/updatable_views.out
Unescape View File

@ -1,6 +1,8 @@
--
-- UPDATABLE VIEWS
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages
CREATE TABLE base_tbl (a int PRIMARY KEY, b text DEFAULT 'Unspecified');

10
src/test/regress/expected/window.out
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@ -205,13 +205,13 @@ SELECT dense_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1
SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
percent_rank | ten | four
-------------------+-----+------
--------------------+-----+------
0 | 0 | 0
0 | 0 | 0
1 | 4 | 0
0 | 1 | 1
0 | 1 | 1
0.666666666666667 | 7 | 1
0.6666666666666666 | 7 | 1
1 | 9 | 1
0 | 0 | 2
0 | 1 | 3
@ -220,9 +220,9 @@ SELECT percent_rank() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk
SELECT cume_dist() OVER (PARTITION BY four ORDER BY ten), ten, four FROM tenk1 WHERE unique2 < 10;
cume_dist | ten | four
-------------------+-----+------
0.666666666666667 | 0 | 0
0.666666666666667 | 0 | 0
--------------------+-----+------
0.6666666666666666 | 0 | 0
0.6666666666666666 | 0 | 0
1 | 4 | 0
0.5 | 1 | 1
0.5 | 1 | 1

3
src/test/regress/sql/aggregates.sql
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@ -2,6 +2,9 @@
-- AGGREGATES
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
SELECT avg(four) AS avg_1 FROM onek;
SELECT avg(a) AS avg_32 FROM aggtest WHERE a < 100;

3
src/test/regress/sql/circle.sql
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@ -2,6 +2,9 @@
-- CIRCLE
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
CREATE TABLE CIRCLE_TBL (f1 circle);
INSERT INTO CIRCLE_TBL VALUES ('<(5,1),3>');

219
src/test/regress/sql/float4.sql
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@ -132,3 +132,222 @@ SELECT float4send('750486563e-38'::float4);
SELECT float4send('1.17549435e-38'::float4);
SELECT float4send('1.1754944e-38'::float4);
-- test output (and round-trip safety) of various values.
-- To ensure we're testing what we think we're testing, start with
-- float values specified by bit patterns (as a useful side effect,
-- this means we'll fail on non-IEEE platforms).
create type xfloat4;
create function xfloat4in(cstring) returns xfloat4 immutable strict
language internal as 'int4in';
create function xfloat4out(xfloat4) returns cstring immutable strict
language internal as 'int4out';
create type xfloat4 (input = xfloat4in, output = xfloat4out, like = float4);
create cast (xfloat4 as float4) without function;
create cast (float4 as xfloat4) without function;
create cast (xfloat4 as integer) without function;
create cast (integer as xfloat4) without function;
-- float4: seeeeeee emmmmmmm mmmmmmmm mmmmmmmm
-- we don't care to assume the platform's strtod() handles subnormals
-- correctly; those are "use at your own risk". However we do test
-- subnormal outputs, since those are under our control.
with testdata(bits) as (values
-- small subnormals
(x'00000001'),
(x'00000002'), (x'00000003'),
(x'00000010'), (x'00000011'), (x'00000100'), (x'00000101'),
(x'00004000'), (x'00004001'), (x'00080000'), (x'00080001'),
-- stress values
(x'0053c4f4'), -- 7693e-42
(x'006c85c4'), -- 996622e-44
(x'0041ca76'), -- 60419369e-46
(x'004b7678'), -- 6930161142e-48
-- taken from upstream testsuite
(x'00000007'),
(x'00424fe2'),
-- borderline between subnormal and normal
(x'007ffff0'), (x'007ffff1'), (x'007ffffe'), (x'007fffff'))
select float4send(flt) as ibits,
flt
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
with testdata(bits) as (values
(x'00000000'),
-- smallest normal values
(x'00800000'), (x'00800001'), (x'00800004'), (x'00800005'),
(x'00800006'),
-- small normal values chosen for short vs. long output
(x'008002f1'), (x'008002f2'), (x'008002f3'),
(x'00800e17'), (x'00800e18'), (x'00800e19'),
-- assorted values (random mantissae)
(x'01000001'), (x'01102843'), (x'01a52c98'),
(x'0219c229'), (x'02e4464d'), (x'037343c1'), (x'03a91b36'),
(x'047ada65'), (x'0496fe87'), (x'0550844f'), (x'05999da3'),
(x'060ea5e2'), (x'06e63c45'), (x'07f1e548'), (x'0fc5282b'),
(x'1f850283'), (x'2874a9d6'),
-- values around 5e-08
(x'3356bf94'), (x'3356bf95'), (x'3356bf96'),
-- around 1e-07
(x'33d6bf94'), (x'33d6bf95'), (x'33d6bf96'),
-- around 3e-07 .. 1e-04
(x'34a10faf'), (x'34a10fb0'), (x'34a10fb1'),
(x'350637bc'), (x'350637bd'), (x'350637be'),
(x'35719786'), (x'35719787'), (x'35719788'),
(x'358637bc'), (x'358637bd'), (x'358637be'),
(x'36a7c5ab'), (x'36a7c5ac'), (x'36a7c5ad'),
(x'3727c5ab'), (x'3727c5ac'), (x'3727c5ad'),
-- format crossover at 1e-04
(x'38d1b714'), (x'38d1b715'), (x'38d1b716'),
(x'38d1b717'), (x'38d1b718'), (x'38d1b719'),
(x'38d1b71a'), (x'38d1b71b'), (x'38d1b71c'),
(x'38d1b71d'),
--
(x'38dffffe'), (x'38dfffff'), (x'38e00000'),
(x'38efffff'), (x'38f00000'), (x'38f00001'),
(x'3a83126e'), (x'3a83126f'), (x'3a831270'),
(x'3c23d709'), (x'3c23d70a'), (x'3c23d70b'),
(x'3dcccccc'), (x'3dcccccd'), (x'3dccccce'),
-- chosen to need 9 digits for 3dcccd70
(x'3dcccd6f'), (x'3dcccd70'), (x'3dcccd71'),
--
(x'3effffff'), (x'3f000000'), (x'3f000001'),
(x'3f333332'), (x'3f333333'), (x'3f333334'),
-- approach 1.0 with increasing numbers of 9s
(x'3f666665'), (x'3f666666'), (x'3f666667'),
(x'3f7d70a3'), (x'3f7d70a4'), (x'3f7d70a5'),
(x'3f7fbe76'), (x'3f7fbe77'), (x'3f7fbe78'),
(x'3f7ff971'), (x'3f7ff972'), (x'3f7ff973'),
(x'3f7fff57'), (x'3f7fff58'), (x'3f7fff59'),
(x'3f7fffee'), (x'3f7fffef'),
-- values very close to 1
(x'3f7ffff0'), (x'3f7ffff1'), (x'3f7ffff2'),
(x'3f7ffff3'), (x'3f7ffff4'), (x'3f7ffff5'),
(x'3f7ffff6'), (x'3f7ffff7'), (x'3f7ffff8'),
(x'3f7ffff9'), (x'3f7ffffa'), (x'3f7ffffb'),
(x'3f7ffffc'), (x'3f7ffffd'), (x'3f7ffffe'),
(x'3f7fffff'),
(x'3f800000'),
(x'3f800001'), (x'3f800002'), (x'3f800003'),
(x'3f800004'), (x'3f800005'), (x'3f800006'),
(x'3f800007'), (x'3f800008'), (x'3f800009'),
-- values 1 to 1.1
(x'3f80000f'), (x'3f800010'), (x'3f800011'),
(x'3f800012'), (x'3f800013'), (x'3f800014'),
(x'3f800017'), (x'3f800018'), (x'3f800019'),
(x'3f80001a'), (x'3f80001b'), (x'3f80001c'),
(x'3f800029'), (x'3f80002a'), (x'3f80002b'),
(x'3f800053'), (x'3f800054'), (x'3f800055'),
(x'3f800346'), (x'3f800347'), (x'3f800348'),
(x'3f8020c4'), (x'3f8020c5'), (x'3f8020c6'),
(x'3f8147ad'), (x'3f8147ae'), (x'3f8147af'),
(x'3f8ccccc'), (x'3f8ccccd'), (x'3f8cccce'),
--
(x'3fc90fdb'), -- pi/2
(x'402df854'), -- e
(x'40490fdb'), -- pi
--
(x'409fffff'), (x'40a00000'), (x'40a00001'),
(x'40afffff'), (x'40b00000'), (x'40b00001'),
(x'411fffff'), (x'41200000'), (x'41200001'),
(x'42c7ffff'), (x'42c80000'), (x'42c80001'),
(x'4479ffff'), (x'447a0000'), (x'447a0001'),
(x'461c3fff'), (x'461c4000'), (x'461c4001'),
(x'47c34fff'), (x'47c35000'), (x'47c35001'),
(x'497423ff'), (x'49742400'), (x'49742401'),
(x'4b18967f'), (x'4b189680'), (x'4b189681'),
(x'4cbebc1f'), (x'4cbebc20'), (x'4cbebc21'),
(x'4e6e6b27'), (x'4e6e6b28'), (x'4e6e6b29'),
(x'501502f8'), (x'501502f9'), (x'501502fa'),
(x'51ba43b6'), (x'51ba43b7'), (x'51ba43b8'),
-- stress values
(x'1f6c1e4a'), -- 5e-20
(x'59be6cea'), -- 67e14
(x'5d5ab6c4'), -- 985e15
(x'2cc4a9bd'), -- 55895e-16
(x'15ae43fd'), -- 7038531e-32
(x'2cf757ca'), -- 702990899e-20
(x'665ba998'), -- 25933168707e13
(x'743c3324'), -- 596428896559e20
-- exercise fixed-point memmoves
(x'47f1205a'),
(x'4640e6ae'),
(x'449a5225'),
(x'42f6e9d5'),
(x'414587dd'),
(x'3f9e064b'),
-- these cases come from the upstream's testsuite
-- BoundaryRoundEven
(x'4c000004'),
(x'50061c46'),
(x'510006a8'),
-- ExactValueRoundEven
(x'48951f84'),
(x'45fd1840'),
-- LotsOfTrailingZeros
(x'39800000'),
(x'3b200000'),
(x'3b900000'),
(x'3bd00000'),
-- Regression
(x'63800000'),
(x'4b000000'),
(x'4b800000'),
(x'4c000001'),
(x'4c800b0d'),
(x'00d24584'),
(x'800000b0'),
(x'00d90b88'),
(x'45803f34'),
(x'4f9f24f7'),
(x'3a8722c3'),
(x'5c800041'),
(x'15ae43fd'),
(x'5d4cccfb'),
(x'4c800001'),
(x'57800ed8'),
(x'5f000000'),
(x'700000f0'),
(x'5f23e9ac'),
(x'5e9502f9'),
(x'5e8012b1'),
(x'3c000028'),
(x'60cde861'),
(x'03aa2a50'),
(x'43480000'),
(x'4c000000'),
-- LooksLikePow5
(x'5D1502F9'),
(x'5D9502F9'),
(x'5E1502F9'),
-- OutputLength
(x'3f99999a'),
(x'3f9d70a4'),
(x'3f9df3b6'),
(x'3f9e0419'),
(x'3f9e0610'),
(x'3f9e064b'),
(x'3f9e0651'),
(x'03d20cfe')
)
select float4send(flt) as ibits,
flt,
flt::text::float4 as r_flt,
float4send(flt::text::float4) as obits,
float4send(flt::text::float4) = float4send(flt) as correct
from (select bits::integer::xfloat4::float4 as flt
from testdata
offset 0) s;
-- clean up, lest opr_sanity complain
\set VERBOSITY terse
drop type xfloat4 cascade;
\set VERBOSITY default
--

210
src/test/regress/sql/float8.sql
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@ -16,6 +16,9 @@ SELECT '-10e400'::float8;
SELECT '10e-400'::float8;
SELECT '-10e-400'::float8;
-- test smallest normalized input
SELECT float8send('2.2250738585072014E-308'::float8);
-- bad input
INSERT INTO FLOAT8_TBL(f1) VALUES ('');
INSERT INTO FLOAT8_TBL(f1) VALUES (' ');
@ -97,6 +100,9 @@ select floor(f1) as floor_f1 from float8_tbl f;
-- sign
select sign(f1) as sign_f1 from float8_tbl f;
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
-- square root
SELECT sqrt(float8 '64') AS eight;
@ -148,6 +154,8 @@ SELECT '' AS bad, f.f1 / '0.0' from FLOAT8_TBL f;
SELECT '' AS five, * FROM FLOAT8_TBL;
RESET extra_float_digits;
-- test for over- and underflow
INSERT INTO FLOAT8_TBL(f1) VALUES ('10e400');
@ -189,7 +197,6 @@ SELECT '-9223372036854775808.5'::float8::int8;
SELECT '-9223372036854780000'::float8::int8;
-- test exact cases for trigonometric functions in degrees
SET extra_float_digits = 3;
SELECT x,
sind(x),
@ -232,4 +239,203 @@ SELECT x, y,
FROM (SELECT 10*cosd(a), 10*sind(a)
FROM generate_series(0, 360, 90) AS t(a)) AS t(x,y);
RESET extra_float_digits;
--
-- test output (and round-trip safety) of various values.
-- To ensure we're testing what we think we're testing, start with
-- float values specified by bit patterns (as a useful side effect,
-- this means we'll fail on non-IEEE platforms).
create type xfloat8;
create function xfloat8in(cstring) returns xfloat8 immutable strict
language internal as 'int8in';
create function xfloat8out(xfloat8) returns cstring immutable strict
language internal as 'int8out';
create type xfloat8 (input = xfloat8in, output = xfloat8out, like = float8);
create cast (xfloat8 as float8) without function;
create cast (float8 as xfloat8) without function;
create cast (xfloat8 as bigint) without function;
create cast (bigint as xfloat8) without function;
-- float8: seeeeeee eeeeeeee eeeeeeee mmmmmmmm mmmmmmmm(x4)
-- we don't care to assume the platform's strtod() handles subnormals
-- correctly; those are "use at your own risk". However we do test
-- subnormal outputs, since those are under our control.
with testdata(bits) as (values
-- small subnormals
(x'0000000000000001'),
(x'0000000000000002'), (x'0000000000000003'),
(x'0000000000001000'), (x'0000000100000000'),
(x'0000010000000000'), (x'0000010100000000'),
(x'0000400000000000'), (x'0000400100000000'),
(x'0000800000000000'), (x'0000800000000001'),
-- these values taken from upstream testsuite
(x'00000000000f4240'),
(x'00000000016e3600'),
(x'0000008cdcdea440'),
-- borderline between subnormal and normal
(x'000ffffffffffff0'), (x'000ffffffffffff1'),
(x'000ffffffffffffe'), (x'000fffffffffffff'))
select float8send(flt) as ibits,
flt
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
-- round-trip tests
with testdata(bits) as (values
(x'0000000000000000'),
-- smallest normal values
(x'0010000000000000'), (x'0010000000000001'),
(x'0010000000000002'), (x'0018000000000000'),
--
(x'3ddb7cdfd9d7bdba'), (x'3ddb7cdfd9d7bdbb'), (x'3ddb7cdfd9d7bdbc'),
(x'3e112e0be826d694'), (x'3e112e0be826d695'), (x'3e112e0be826d696'),
(x'3e45798ee2308c39'), (x'3e45798ee2308c3a'), (x'3e45798ee2308c3b'),
(x'3e7ad7f29abcaf47'), (x'3e7ad7f29abcaf48'), (x'3e7ad7f29abcaf49'),
(x'3eb0c6f7a0b5ed8c'), (x'3eb0c6f7a0b5ed8d'), (x'3eb0c6f7a0b5ed8e'),
(x'3ee4f8b588e368ef'), (x'3ee4f8b588e368f0'), (x'3ee4f8b588e368f1'),
(x'3f1a36e2eb1c432c'), (x'3f1a36e2eb1c432d'), (x'3f1a36e2eb1c432e'),
(x'3f50624dd2f1a9fb'), (x'3f50624dd2f1a9fc'), (x'3f50624dd2f1a9fd'),
(x'3f847ae147ae147a'), (x'3f847ae147ae147b'), (x'3f847ae147ae147c'),
(x'3fb9999999999999'), (x'3fb999999999999a'), (x'3fb999999999999b'),
-- values very close to 1
(x'3feffffffffffff0'), (x'3feffffffffffff1'), (x'3feffffffffffff2'),
(x'3feffffffffffff3'), (x'3feffffffffffff4'), (x'3feffffffffffff5'),
(x'3feffffffffffff6'), (x'3feffffffffffff7'), (x'3feffffffffffff8'),
(x'3feffffffffffff9'), (x'3feffffffffffffa'), (x'3feffffffffffffb'),
(x'3feffffffffffffc'), (x'3feffffffffffffd'), (x'3feffffffffffffe'),
(x'3fefffffffffffff'),
(x'3ff0000000000000'),
(x'3ff0000000000001'), (x'3ff0000000000002'), (x'3ff0000000000003'),
(x'3ff0000000000004'), (x'3ff0000000000005'), (x'3ff0000000000006'),
(x'3ff0000000000007'), (x'3ff0000000000008'), (x'3ff0000000000009'),
--
(x'3ff921fb54442d18'),
(x'4005bf0a8b14576a'),
(x'400921fb54442d18'),
--
(x'4023ffffffffffff'), (x'4024000000000000'), (x'4024000000000001'),
(x'4058ffffffffffff'), (x'4059000000000000'), (x'4059000000000001'),
(x'408f3fffffffffff'), (x'408f400000000000'), (x'408f400000000001'),
(x'40c387ffffffffff'), (x'40c3880000000000'), (x'40c3880000000001'),
(x'40f869ffffffffff'), (x'40f86a0000000000'), (x'40f86a0000000001'),
(x'412e847fffffffff'), (x'412e848000000000'), (x'412e848000000001'),
(x'416312cfffffffff'), (x'416312d000000000'), (x'416312d000000001'),
(x'4197d783ffffffff'), (x'4197d78400000000'), (x'4197d78400000001'),
(x'41cdcd64ffffffff'), (x'41cdcd6500000000'), (x'41cdcd6500000001'),
(x'4202a05f1fffffff'), (x'4202a05f20000000'), (x'4202a05f20000001'),
(x'42374876e7ffffff'), (x'42374876e8000000'), (x'42374876e8000001'),
(x'426d1a94a1ffffff'), (x'426d1a94a2000000'), (x'426d1a94a2000001'),
(x'42a2309ce53fffff'), (x'42a2309ce5400000'), (x'42a2309ce5400001'),
(x'42d6bcc41e8fffff'), (x'42d6bcc41e900000'), (x'42d6bcc41e900001'),
(x'430c6bf52633ffff'), (x'430c6bf526340000'), (x'430c6bf526340001'),
(x'4341c37937e07fff'), (x'4341c37937e08000'), (x'4341c37937e08001'),
(x'4376345785d89fff'), (x'4376345785d8a000'), (x'4376345785d8a001'),
(x'43abc16d674ec7ff'), (x'43abc16d674ec800'), (x'43abc16d674ec801'),
(x'43e158e460913cff'), (x'43e158e460913d00'), (x'43e158e460913d01'),
(x'4415af1d78b58c3f'), (x'4415af1d78b58c40'), (x'4415af1d78b58c41'),
(x'444b1ae4d6e2ef4f'), (x'444b1ae4d6e2ef50'), (x'444b1ae4d6e2ef51'),
(x'4480f0cf064dd591'), (x'4480f0cf064dd592'), (x'4480f0cf064dd593'),
(x'44b52d02c7e14af5'), (x'44b52d02c7e14af6'), (x'44b52d02c7e14af7'),
(x'44ea784379d99db3'), (x'44ea784379d99db4'), (x'44ea784379d99db5'),
(x'45208b2a2c280290'), (x'45208b2a2c280291'), (x'45208b2a2c280292'),
--
(x'7feffffffffffffe'), (x'7fefffffffffffff'),
-- round to even tests (+ve)
(x'4350000000000002'),
(x'4350000000002e06'),
(x'4352000000000003'),
(x'4352000000000004'),
(x'4358000000000003'),
(x'4358000000000004'),
(x'435f000000000020'),
-- round to even tests (-ve)
(x'c350000000000002'),
(x'c350000000002e06'),
(x'c352000000000003'),
(x'c352000000000004'),
(x'c358000000000003'),
(x'c358000000000004'),
(x'c35f000000000020'),
-- exercise fixed-point memmoves
(x'42dc12218377de66'),
(x'42a674e79c5fe51f'),
(x'4271f71fb04cb74c'),
(x'423cbe991a145879'),
(x'4206fee0e1a9e061'),
(x'41d26580b487e6b4'),
(x'419d6f34540ca453'),
(x'41678c29dcd6e9dc'),
(x'4132d687e3df217d'),
(x'40fe240c9fcb68c8'),
(x'40c81cd6e63c53d3'),
(x'40934a4584fd0fdc'),
(x'405edd3c07fb4c93'),
(x'4028b0fcd32f7076'),
(x'3ff3c0ca428c59f8'),
-- these cases come from the upstream's testsuite
-- LotsOfTrailingZeros)
(x'3e60000000000000'),
-- Regression
(x'c352bd2668e077c4'),
(x'434018601510c000'),
(x'43d055dc36f24000'),
(x'43e052961c6f8000'),
(x'3ff3c0ca2a5b1d5d'),
-- LooksLikePow5
(x'4830f0cf064dd592'),
(x'4840f0cf064dd592'),
(x'4850f0cf064dd592'),
-- OutputLength
(x'3ff3333333333333'),
(x'3ff3ae147ae147ae'),
(x'3ff3be76c8b43958'),
(x'3ff3c083126e978d'),
(x'3ff3c0c1fc8f3238'),
(x'3ff3c0c9539b8887'),
(x'3ff3c0ca2a5b1d5d'),
(x'3ff3c0ca4283de1b'),
(x'3ff3c0ca43db770a'),
(x'3ff3c0ca428abd53'),
(x'3ff3c0ca428c1d2b'),
(x'3ff3c0ca428c51f2'),
(x'3ff3c0ca428c58fc'),
(x'3ff3c0ca428c59dd'),
(x'3ff3c0ca428c59f8'),
(x'3ff3c0ca428c59fb'),
-- 32-bit chunking
(x'40112e0be8047a7d'),
(x'40112e0be815a889'),
(x'40112e0be826d695'),
(x'40112e0be83804a1'),
(x'40112e0be84932ad'),
-- MinMaxShift
(x'0040000000000000'),
(x'007fffffffffffff'),
(x'0290000000000000'),
(x'029fffffffffffff'),
(x'4350000000000000'),
(x'435fffffffffffff'),
(x'1330000000000000'),
(x'133fffffffffffff'),
(x'3a6fa7161a4d6e0c')
)
select float8send(flt) as ibits,
flt,
flt::text::float8 as r_flt,
float8send(flt::text::float8) as obits,
float8send(flt::text::float8) = float8send(flt) as correct
from (select bits::bigint::xfloat8::float8 as flt
from testdata
offset 0) s;
-- clean up, lest opr_sanity complain
\set VERBOSITY terse
drop type xfloat8 cascade;
\set VERBOSITY default
--

3
src/test/regress/sql/point.sql
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@ -2,6 +2,9 @@
-- POINT
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
CREATE TABLE POINT_TBL(f1 point);
INSERT INTO POINT_TBL(f1) VALUES ('(0.0,0.0)');

3
src/test/regress/sql/updatable_views.sql
Unescape View File

@ -2,6 +2,9 @@
-- UPDATABLE VIEWS
--
-- avoid bit-exact output here because operations may not be bit-exact.
SET extra_float_digits = 0;
-- check that non-updatable views and columns are rejected with useful error
-- messages

2
src/tools/msvc/Mkvcbuild.pm
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@ -119,7 +119,7 @@ sub mkvcbuild
}
our @pgcommonallfiles = qw(
base64.c config_info.c controldata_utils.c exec.c file_perm.c ip.c
base64.c config_info.c controldata_utils.c d2s.c exec.c f2s.c file_perm.c ip.c
keywords.c kwlookup.c link-canary.c md5.c
pg_lzcompress.c pgfnames.c psprintf.c relpath.c rmtree.c
saslprep.c scram-common.c string.c unicode_norm.c username.c

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