Issue #1580: use short float repr where possible.

 - incorporate and adapt David Gay's dtoa and strtod
   into the Python core
 - on platforms where we can use Gay's code (almost
   all!), repr(float) is based on the shortest
   sequence of decimal digits that rounds correctly.
 - add sys.float_repr_style attribute to indicate
   whether we're using Gay's code or not
 - add autoconf magic to detect and enable SSE2
   instructions on x86/gcc
 - slight change to repr and str:  repr switches
   to exponential notation at 1e16 instead of
   1e17, str switches at 1e11 instead of 1e12

1 files changed, 354 insertions, 0 deletions

diff --git a/Lib/test/formatfloat_testcases.txt b/Lib/test/formatfloat_testcases.txt
new file mode 100644
index 0000000..3abe938
--- /dev/null
+++ b/Lib/test/formatfloat_testcases.txt
@@ -0,0 +1,354 @@
+-- 'f' code formatting, with explicit precision (>= 0).  Output always
+-- has the given number of places after the point;  zeros are added if
+-- necessary to make this true.
+
+-- zeros
+%.0f 0 -> 0
+%.1f 0 -> 0.0
+%.2f 0 -> 0.00
+%.3f 0 -> 0.000
+%.50f 0 -> 0.00000000000000000000000000000000000000000000000000
+
+-- precision 0;  result should never include a .
+%.0f 1.5 -> 2
+%.0f 2.5 -> 2
+%.0f 3.5 -> 4
+%.0f 0.0 -> 0
+%.0f 0.1 -> 0
+%.0f 0.001 -> 0
+%.0f 10.0 -> 10
+%.0f 10.1 -> 10
+%.0f 10.01 -> 10
+%.0f 123.456 -> 123
+%.0f 1234.56 -> 1235
+%.0f 1e49 -> 9999999999999999464902769475481793196872414789632
+-- %.0f 1e50 -> 100000000000000007629769841091887003294964970946560
+%.0f 9.9999999999999987e+49 -> 99999999999999986860582406952576489172979654066176
+
+-- precision 1
+%.1f 0.0001 -> 0.0
+%.1f 0.001 -> 0.0
+%.1f 0.01 -> 0.0
+%.1f 0.04 -> 0.0
+%.1f 0.06 -> 0.1
+%.1f 0.25 -> 0.2
+%.1f 0.75 -> 0.8
+%.1f 1.4 -> 1.4
+%.1f 1.5 -> 1.5
+%.1f 10.0 -> 10.0
+%.1f 1000.03 -> 1000.0
+%.1f 1234.5678 -> 1234.6
+%.1f 1234.7499 -> 1234.7
+%.1f 1234.75 -> 1234.8
+
+-- precision 2
+%.2f 0.0001 -> 0.00
+%.2f 0.001 -> 0.00
+%.2f 0.004999 -> 0.00
+%.2f 0.005001 -> 0.01
+%.2f 0.01 -> 0.01
+%.2f 0.125 -> 0.12
+%.2f 0.375 -> 0.38
+%.2f 1234500 -> 1234500.00
+%.2f 1234560 -> 1234560.00
+%.2f 1234567 -> 1234567.00
+%.2f 1234567.8 -> 1234567.80
+%.2f 1234567.89 -> 1234567.89
+%.2f 1234567.891 -> 1234567.89
+%.2f 1234567.8912 -> 1234567.89
+
+-- alternate form always includes a decimal point.  This only
+-- makes a difference when the precision is 0.
+%#.0f 0 -> 0.
+%#.1f 0 -> 0.0
+%#.0f 1.5 -> 2.
+%#.0f 2.5 -> 2.
+%#.0f 10.1 -> 10.
+%#.0f 1234.56 -> 1235.
+%#.1f 1.4 -> 1.4
+%#.2f 0.375 -> 0.38
+
+-- if precision is omitted it defaults to 6
+%f 0 -> 0.000000
+%f 1230000 -> 1230000.000000
+%f 1234567 -> 1234567.000000
+%f 123.4567 -> 123.456700
+%f 1.23456789 -> 1.234568
+%f 0.00012 -> 0.000120
+%f 0.000123 -> 0.000123
+%f 0.00012345 -> 0.000123
+%f 0.000001 -> 0.000001
+%f 0.0000005001 -> 0.000001
+%f 0.0000004999 -> 0.000000
+
+-- 'e' code formatting with explicit precision (>= 0). Output should
+-- always have exactly the number of places after the point that were
+-- requested.
+
+-- zeros
+%.0e 0 -> 0e+00
+%.1e 0 -> 0.0e+00
+%.2e 0 -> 0.00e+00
+%.10e 0 -> 0.0000000000e+00
+%.50e 0 -> 0.00000000000000000000000000000000000000000000000000e+00
+
+-- precision 0.  no decimal point in the output
+%.0e 0.01 -> 1e-02
+%.0e 0.1 -> 1e-01
+%.0e 1 -> 1e+00
+%.0e 10 -> 1e+01
+%.0e 100 -> 1e+02
+%.0e 0.012 -> 1e-02
+%.0e 0.12 -> 1e-01
+%.0e 1.2 -> 1e+00
+%.0e 12 -> 1e+01
+%.0e 120 -> 1e+02
+%.0e 123.456 -> 1e+02
+%.0e 0.000123456 -> 1e-04
+%.0e 123456000 -> 1e+08
+%.0e 0.5 -> 5e-01
+%.0e 1.4 -> 1e+00
+%.0e 1.5 -> 2e+00
+%.0e 1.6 -> 2e+00
+%.0e 2.4999999 -> 2e+00
+%.0e 2.5 -> 2e+00
+%.0e 2.5000001 -> 3e+00
+%.0e 3.499999999999 -> 3e+00
+%.0e 3.5 -> 4e+00
+%.0e 4.5 -> 4e+00
+%.0e 5.5 -> 6e+00
+%.0e 6.5 -> 6e+00
+%.0e 7.5 -> 8e+00
+%.0e 8.5 -> 8e+00
+%.0e 9.4999 -> 9e+00
+%.0e 9.5 -> 1e+01
+%.0e 10.5 -> 1e+01
+%.0e 14.999 -> 1e+01
+%.0e 15 -> 2e+01
+
+-- precision 1
+%.1e 0.0001 -> 1.0e-04
+%.1e 0.001 -> 1.0e-03
+%.1e 0.01 -> 1.0e-02
+%.1e 0.1 -> 1.0e-01
+%.1e 1 -> 1.0e+00
+%.1e 10 -> 1.0e+01
+%.1e 100 -> 1.0e+02
+%.1e 120 -> 1.2e+02
+%.1e 123 -> 1.2e+02
+%.1e 123.4 -> 1.2e+02
+
+-- precision 2
+%.2e 0.00013 -> 1.30e-04
+%.2e 0.000135 -> 1.35e-04
+%.2e 0.0001357 -> 1.36e-04
+%.2e 0.0001 -> 1.00e-04
+%.2e 0.001 -> 1.00e-03
+%.2e 0.01 -> 1.00e-02
+%.2e 0.1 -> 1.00e-01
+%.2e 1 -> 1.00e+00
+%.2e 10 -> 1.00e+01
+%.2e 100 -> 1.00e+02
+%.2e 1000 -> 1.00e+03
+%.2e 1500 -> 1.50e+03
+%.2e 1590 -> 1.59e+03
+%.2e 1598 -> 1.60e+03
+%.2e 1598.7 -> 1.60e+03
+%.2e 1598.76 -> 1.60e+03
+%.2e 9999 -> 1.00e+04
+
+-- omitted precision defaults to 6
+%e 0 -> 0.000000e+00
+%e 165 -> 1.650000e+02
+%e 1234567 -> 1.234567e+06
+%e 12345678 -> 1.234568e+07
+%e 1.1 -> 1.100000e+00
+
+-- alternate form always contains a decimal point.  This only makes
+-- a difference when precision is 0.
+
+%#.0e 0.01 -> 1.e-02
+%#.0e 0.1 -> 1.e-01
+%#.0e 1 -> 1.e+00
+%#.0e 10 -> 1.e+01
+%#.0e 100 -> 1.e+02
+%#.0e 0.012 -> 1.e-02
+%#.0e 0.12 -> 1.e-01
+%#.0e 1.2 -> 1.e+00
+%#.0e 12 -> 1.e+01
+%#.0e 120 -> 1.e+02
+%#.0e 123.456 -> 1.e+02
+%#.0e 0.000123456 -> 1.e-04
+%#.0e 123456000 -> 1.e+08
+%#.0e 0.5 -> 5.e-01
+%#.0e 1.4 -> 1.e+00
+%#.0e 1.5 -> 2.e+00
+%#.0e 1.6 -> 2.e+00
+%#.0e 2.4999999 -> 2.e+00
+%#.0e 2.5 -> 2.e+00
+%#.0e 2.5000001 -> 3.e+00
+%#.0e 3.499999999999 -> 3.e+00
+%#.0e 3.5 -> 4.e+00
+%#.0e 4.5 -> 4.e+00
+%#.0e 5.5 -> 6.e+00
+%#.0e 6.5 -> 6.e+00
+%#.0e 7.5 -> 8.e+00
+%#.0e 8.5 -> 8.e+00
+%#.0e 9.4999 -> 9.e+00
+%#.0e 9.5 -> 1.e+01
+%#.0e 10.5 -> 1.e+01
+%#.0e 14.999 -> 1.e+01
+%#.0e 15 -> 2.e+01
+%#.1e 123.4 -> 1.2e+02
+%#.2e 0.0001357 -> 1.36e-04
+
+-- 'g' code formatting.
+
+-- zeros
+%.0g 0 -> 0
+%.1g 0 -> 0
+%.2g 0 -> 0
+%.3g 0 -> 0
+%.4g 0 -> 0
+%.10g 0 -> 0
+%.50g 0 -> 0
+%.100g 0 -> 0
+
+-- precision 0 doesn't make a lot of sense for the 'g' code (what does
+-- it mean to have no significant digits?); in practice, it's interpreted
+-- as identical to precision 1
+%.0g 1000 -> 1e+03
+%.0g 100 -> 1e+02
+%.0g 10 -> 1e+01
+%.0g 1 -> 1
+%.0g 0.1 -> 0.1
+%.0g 0.01 -> 0.01
+%.0g 1e-3 -> 0.001
+%.0g 1e-4 -> 0.0001
+%.0g 1e-5 -> 1e-05
+%.0g 1e-6 -> 1e-06
+%.0g 12 -> 1e+01
+%.0g 120 -> 1e+02
+%.0g 1.2 -> 1
+%.0g 0.12 -> 0.1
+%.0g 0.012 -> 0.01
+%.0g 0.0012 -> 0.001
+%.0g 0.00012 -> 0.0001
+%.0g 0.000012 -> 1e-05
+%.0g 0.0000012 -> 1e-06
+
+-- precision 1 identical to precision 0
+%.1g 1000 -> 1e+03
+%.1g 100 -> 1e+02
+%.1g 10 -> 1e+01
+%.1g 1 -> 1
+%.1g 0.1 -> 0.1
+%.1g 0.01 -> 0.01
+%.1g 1e-3 -> 0.001
+%.1g 1e-4 -> 0.0001
+%.1g 1e-5 -> 1e-05
+%.1g 1e-6 -> 1e-06
+%.1g 12 -> 1e+01
+%.1g 120 -> 1e+02
+%.1g 1.2 -> 1
+%.1g 0.12 -> 0.1
+%.1g 0.012 -> 0.01
+%.1g 0.0012 -> 0.001
+%.1g 0.00012 -> 0.0001
+%.1g 0.000012 -> 1e-05
+%.1g 0.0000012 -> 1e-06
+
+-- precision 2
+%.2g 1000 -> 1e+03
+%.2g 100 -> 1e+02
+%.2g 10 -> 10
+%.2g 1 -> 1
+%.2g 0.1 -> 0.1
+%.2g 0.01 -> 0.01
+%.2g 0.001 -> 0.001
+%.2g 1e-4 -> 0.0001
+%.2g 1e-5 -> 1e-05
+%.2g 1e-6 -> 1e-06
+%.2g 1234 -> 1.2e+03
+%.2g 123 -> 1.2e+02
+%.2g 12.3 -> 12
+%.2g 1.23 -> 1.2
+%.2g 0.123 -> 0.12
+%.2g 0.0123 -> 0.012
+%.2g 0.00123 -> 0.0012
+%.2g 0.000123 -> 0.00012
+%.2g 0.0000123 -> 1.2e-05
+
+-- alternate g formatting:  always include decimal point and
+-- exactly <precision> significant digits.
+%#.0g 0 -> 0.
+%#.1g 0 -> 0.
+%#.2g 0 -> 0.0
+%#.3g 0 -> 0.00
+%#.4g 0 -> 0.000
+
+%#.0g 0.2 -> 0.2
+%#.1g 0.2 -> 0.2
+%#.2g 0.2 -> 0.20
+%#.3g 0.2 -> 0.200
+%#.4g 0.2 -> 0.2000
+%#.10g 0.2 -> 0.2000000000
+
+%#.0g 2 -> 2.
+%#.1g 2 -> 2.
+%#.2g 2 -> 2.0
+%#.3g 2 -> 2.00
+%#.4g 2 -> 2.000
+
+%#.0g 20 -> 2.e+01
+%#.1g 20 -> 2.e+01
+%#.2g 20 -> 20.
+%#.3g 20 -> 20.0
+%#.4g 20 -> 20.00
+
+%#.0g 234.56 -> 2.e+02
+%#.1g 234.56 -> 2.e+02
+%#.2g 234.56 -> 2.3e+02
+%#.3g 234.56 -> 235.
+%#.4g 234.56 -> 234.6
+%#.5g 234.56 -> 234.56
+%#.6g 234.56 -> 234.560
+
+-- for repr formatting see the separate test_short_repr test in
+-- test_float.py.  Not all platforms use short repr for floats.
+
+-- str formatting.  Result always includes decimal point and at
+-- least one digit after the point, or an exponent.
+%s 0 -> 0.0
+%s 1 -> 1.0
+
+%s 0.01 -> 0.01
+%s 0.02 -> 0.02
+%s 0.03 -> 0.03
+%s 0.04 -> 0.04
+%s 0.05 -> 0.05
+
+-- str truncates to 12 significant digits
+%s 1.234123412341 -> 1.23412341234
+%s 1.23412341234 -> 1.23412341234
+%s 1.2341234123 -> 1.2341234123
+
+-- values >= 1e11 get an exponent
+%s 10 -> 10.0
+%s 100 -> 100.0
+%s 1e10 -> 10000000000.0
+%s 9.999e10 -> 99990000000.0
+%s 99999999999 -> 99999999999.0
+%s 1e11 -> 1e+11
+%s 1e12 -> 1e+12
+
+-- as do values < 1e-4
+%s 1e-3 -> 0.001
+%s 1.001e-4 -> 0.0001001
+%s 1.000000000001e-4 -> 0.0001
+%s 1.00000000001e-4 -> 0.000100000000001
+%s 1.0000000001e-4 -> 0.00010000000001
+%s 1e-4 -> 0.0001
+%s 0.999999999999e-4 -> 9.99999999999e-05
+%s 0.999e-4 -> 9.99e-05
+%s 1e-5 -> 1e-05