Slightly improve accuracy of stod in to_floats

[davidwendt]

Reference #10599

Provides a slight improvement in accuracy for the internal stod device function used by the cudf::strings::to_floats() API.

Reduces the number of floating-point operations by 1 and also applies the exponent by conditionally multiplying or dividing depending on it being positive or negative. This slightly improves accuracy of the result since multiplying decimal fractions in floating point can compound errors.

>>> s = cudf.Series(['1.0','2.0','0.1','0.2','0.3'])
>>> x = cudf.to_numeric(s)
>>> x[0]
1.0        previously 0.9999999999999999
>>> x[1]
2.0        previously 1.9999999999999998
>>> x[2]
0.1        previously 0.09999999999999999
>>> x[3]
0.2        previously 0.19999999999999998
>>> x[4]
0.3        same

The 1.0 floating-point value in bits was 3FEFFFFFFFFFFFFF and now computes to 3FF0000000000000 which is 1.0.
The 0.1 floating-point value in bits was 3FB9999999999999 and now computes to 3FB999999999999A which is now 0.10000000000000001 so the error is the same as 0.09999999999999999 but both are within expected epsilon.

Since the overall error is within std::numerics<T>::epsilon() error threshold, no tests had to be modified.

[codecov]

Codecov Report

Merging #10622 (18a565b) into branch-22.06 (956c7b5) will increase coverage by 0.03%.
The diff coverage is 88.97%.

@@               Coverage Diff                @@
##           branch-22.06   #10622      +/-   ##
================================================
+ Coverage         86.30%   86.34%   +0.03%     
================================================
  Files               140      140              
  Lines             22255    22280      +25     
================================================
+ Hits              19207    19237      +30     
+ Misses             3048     3043       -5     

Impacted Files	Coverage Δ
python/cudf/cudf/core/frame.py	94.75% <ø> (+1.02%)	⬆️
python/dask_cudf/dask_cudf/tests/test_accessor.py	98.41% <ø> (ø)
python/cudf/cudf/core/indexed_frame.py	91.77% <87.93%> (-0.87%)	⬇️
python/cudf/cudf/core/column/lists.py	90.62% <100.00%> (+0.57%)	⬆️
python/cudf/cudf/core/dataframe.py	93.59% <100.00%> (ø)
python/cudf/cudf/core/series.py	95.28% <100.00%> (-0.01%)	⬇️
python/cudf/cudf/core/column/column.py	89.45% <0.00%> (+0.10%)	⬆️
python/cudf/cudf/core/column/string.py	89.10% <0.00%> (+0.12%)	⬆️
python/cudf/cudf/core/groupby/groupby.py	91.72% <0.00%> (+0.22%)	⬆️
python/cudf/cudf/core/tools/datetimes.py	84.49% <0.00%> (+0.30%)	⬆️
... and 1 more

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[vyasr]

Nice find, LGTM. I assume unifying the different methods in #10599 is pending a longer discussion, perhaps about porting to libcu++ eventually?

[davidwendt]

Nice find, LGTM. I assume unifying the different methods in #10599 is pending a longer discussion, perhaps about porting to libcu++ eventually?

Yes. The current discussion is about having cuIO try to reuse this stod function. The original complaint was the results were different and so Spark changed their code from using to_floats() back to using cuIO instead. I thought this change would possibly allow them to move back to using to_floats() until #10599 is resolved. @andygrove

[karthikeyann]

LGTM 👍

[davidwendt]

@gpucibot merge