The Show instances for RealFloat types provided in base are very elegant,
as they produce the shortest string which 'read' converts back to the
original number. That, however, involves a check after each digit has been
determined and arithmetic of usually fairly large Integers, which makes these
Show instances rather slow.
For cases where having the conversion fast is more important than having it
produce elegant output, this package provides alternative conversions, which
avoid the checks and reduce the occurrences of large Integers by just producing
a sufficiently long output string.
The speed gain can be substantial if the numbers have exponents of large
absolute modulus, but for the more common case of numbers whose exponents
have small absolute modulus, the difference is (although still significant
for Double) too small in my opinion to seriously consider replacing the
Show instances.
Some benchmarks produced with criterion (http://hackage.haskell.org/package/criterion)
show a considerable speedup, or example, converting 10,000 numbers to String
and calculating the length produced:
------------------------------------------------------------------
benchmarking show @ Double
collecting 100 samples, 1 iterations each, in estimated 46.89312 s
mean: 358.0839 ms, lb 356.3200 ms, ub 364.6815 ms, ci 0.950
std dev: 15.48404 ms, lb 3.952743 ms, ub 35.75519 ms, ci 0.950
benchmarking fshow @ Double
collecting 100 samples, 1 iterations each, in estimated 4.252911 s
mean: 42.75838 ms, lb 42.62119 ms, ub 43.06433 ms, ci 0.950
std dev: 996.1030 us, lb 550.6931 us, ub 1.925554 ms, ci 0.950
benchmarking show @ Double7
collecting 100 samples, 1 iterations each, in estimated 3.706884 s
mean: 37.06166 ms, lb 36.94387 ms, ub 37.32157 ms, ci 0.950
std dev: 861.9554 us, lb 445.2281 us, ub 1.401369 ms, ci 0.950
benchmarking show @ Float
collecting 100 samples, 1 iterations each, in estimated 11.79528 s
mean: 133.0406 ms, lb 127.1293 ms, ub 141.4778 ms, ci 0.950
std dev: 35.72864 ms, lb 27.26726 ms, ub 45.51660 ms, ci 0.950
benchmarking fshow @ Float
collecting 100 samples, 1 iterations each, in estimated 2.885604 s
mean: 28.91291 ms, lb 28.77308 ms, ub 29.28824 ms, ci 0.950
std dev: 1.091232 ms, lb 489.6288 us, ub 2.287669 ms, ci 0.950
benchmarking show @ Float7
collecting 100 samples, 1 iterations each, in estimated 2.264500 s
mean: 22.70168 ms, lb 22.59001 ms, ub 22.97338 ms, ci 0.950
std dev: 827.6377 us, lb 248.5136 us, ub 1.466120 ms, ci 0.950
------------------------------------------------------------------
The difference is far smaller however if we consider only numbers
with exponents of small absolute modulus (numbers between 1e-8 and
1e8 here):
------------------------------------------------------------------
benchmarking show @ Double
collecting 100 samples, 1 iterations each, in estimated 18.12048 s
mean: 183.0913 ms, lb 182.7177 ms, ub 183.6225 ms, ci 0.950
std dev: 2.261846 ms, lb 1.735274 ms, ub 2.905363 ms, ci 0.950
benchmarking fshow @ Double
collecting 100 samples, 1 iterations each, in estimated 3.522301 s
mean: 35.31092 ms, lb 35.19515 ms, ub 35.49955 ms, ci 0.950
std dev: 745.9619 us, lb 519.2986 us, ub 1.078124 ms, ci 0.950
benchmarking show @ Double7
collecting 100 samples, 1 iterations each, in estimated 3.172088 s
mean: 30.59535 ms, lb 29.79293 ms, ub 31.93459 ms, ci 0.950
std dev: 5.227548 ms, lb 3.553355 ms, ub 7.501725 ms, ci 0.950
benchmarking show @ Float
collecting 100 samples, 1 iterations each, in estimated 2.982783 s
mean: 32.53753 ms, lb 31.31817 ms, ub 34.15244 ms, ci 0.950
std dev: 7.154208 ms, lb 5.749231 ms, ub 8.477582 ms, ci 0.950
benchmarking fshow @ Float
collecting 100 samples, 1 iterations each, in estimated 2.393794 s
mean: 24.16462 ms, lb 24.06772 ms, ub 24.41152 ms, ci 0.950
std dev: 735.0625 us, lb 348.1389 us, ub 1.499519 ms, ci 0.950
benchmarking show @ Float7
collecting 100 samples, 1 iterations each, in estimated 2.562690 s
mean: 25.74102 ms, lb 25.67765 ms, ub 25.93221 ms, ci 0.950
std dev: 509.0308 us, lb 199.9313 us, ub 1.099169 ms, ci 0.950
------------------------------------------------------------------
Another benchmark, calculating d*sin(d^2) for d = 1, ..., 200000
and writing their string representations to a file, timed 'show'
at 4.26s, 'fshow' at 1.08s and 'show' for the newtype wrapper
Double7 (rounds to seven significant digits) around Double at 0.55s.
A corresponding C programme ran in 0.26s with the default precision
and in 0.32s with a precision of 17 digits.
