Change floating-point output format for improved performance.

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

Author: RhodiumToad

configure

@@ -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

configure.in

@@ -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++

contrib/btree_gist/expected/float4.out

@@ -33,11 +33,11 @@ SELECT count(*) FROM float4tmp WHERE a >  -179.0;
 (1 row)
 
 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
+     a      | ?column?  
+------------+-----------
+       -179 |         0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
 (3 rows)
 
 CREATE INDEX float4idx ON float4tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-179.0' FROM float4tmp ORDER BY a <-> '-179.0' LIMIT 3;
 (3 rows)
 
 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
+     a      | ?column?  
+------------+-----------
+       -179 |         0
+ -189.02386 | 10.023865
+ -158.17741 | 20.822586
 (3 rows)
 

contrib/btree_gist/expected/float8.out

@@ -33,11 +33,11 @@ SELECT count(*) FROM float8tmp WHERE a >  -1890.0;
 (1 row)
 
 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
+      a       |      ?column?      
+--------------+--------------------
+        -1890 |                  0
+ -2003.634512 | 113.63451200000009
+  -1769.73634 | 120.26366000000007
 (3 rows)
 
 CREATE INDEX float8idx ON float8tmp USING gist ( a );
@@ -82,10 +82,10 @@ SELECT a, a <-> '-1890.0' FROM float8tmp ORDER BY a <-> '-1890.0' LIMIT 3;
 (3 rows)
 
 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
+      a       |      ?column?      
+--------------+--------------------
+        -1890 |                  0
+ -2003.634512 | 113.63451200000009
+  -1769.73634 | 120.26366000000007
 (3 rows)
 

contrib/cube/expected/cube.out

@@ -81,21 +81,21 @@ SELECT 'NaN'::cube AS cube;
 (1 row)
 
 SELECT '.1234567890123456'::cube AS cube;
-        cube         
----------------------
- (0.123456789012346)
+         cube         
+----------------------
+ (0.1234567890123456)
 (1 row)
 
 SELECT '+.1234567890123456'::cube AS cube;
-        cube         
----------------------
- (0.123456789012346)
+         cube         
+----------------------
+ (0.1234567890123456)
 (1 row)
 
 SELECT '-.1234567890123456'::cube AS cube;
-         cube         
-----------------------
- (-0.123456789012346)
+         cube          
+-----------------------
+ (-0.1234567890123456)
 (1 row)
 
 -- simple lists (points)
@@ -943,9 +943,9 @@ SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
 (1 row)
 
 SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
-  cube_distance   
-------------------
- 140.762210837994
+   cube_distance    
+--------------------
+ 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 
 -------------------------+------

contrib/cube/expected/cube_sci.out

@@ -87,20 +87,20 @@ SELECT '-1e-300'::cube AS cube;
 (1 row)
 
 SELECT '1234567890123456'::cube AS cube;
-          cube          
-------------------------
- (1.23456789012346e+15)
+          cube           
+-------------------------
+ (1.234567890123456e+15)
 (1 row)
 
 SELECT '+1234567890123456'::cube AS cube;
-          cube          
-------------------------
- (1.23456789012346e+15)
+          cube           
+-------------------------
+ (1.234567890123456e+15)
 (1 row)
 
 SELECT '-1234567890123456'::cube AS cube;
-          cube           
--------------------------
- (-1.23456789012346e+15)
+           cube           
+--------------------------
+ (-1.234567890123456e+15)
 (1 row)
 

contrib/cube/sql/cube.sql

@@ -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

contrib/pg_trgm/expected/pg_strict_word_trgm.out

@@ -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    
 -------------------------------------+----------

contrib/pg_trgm/expected/pg_trgm.out

@@ -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 
 -----------

contrib/pg_trgm/expected/pg_word_trgm.out

@@ -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    
 -------------------------------------+----------

contrib/pg_trgm/sql/pg_strict_word_trgm.sql

@@ -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;

contrib/pg_trgm/sql/pg_trgm.sql

@@ -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');

contrib/pg_trgm/sql/pg_word_trgm.sql

@@ -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;

contrib/seg/expected/seg.out

@@ -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