Another take on decimal data types

Sat Jan 13 22:05:02 UTC 2018

On Saturday, 13 January 2018 at 20:40:20 UTC, kdevel wrote:
> On Saturday, 13 January 2018 at 19:28:40 UTC, rumbu wrote:
>> On Saturday, 13 January 2018 at 18:37:10 UTC, kdevel wrote:
>>
>>> I get large numerical dicrepancies and an exception:
>>
>> That's because you are mixing floating point and decimal.
>>
>> Just to take one example: double 1.1 cannot be represented 
>> exactly as floating point and it's in fact 
>> 1.10000002384185791015625.
>
> Sure. double has 53 mantissa bits but float only 24. But that 
> is not my point.
> I am *not* talking about the 1e-18 but about these lines:
>
>      1.10     0.891207360061435339970703     
> 0.878166666666666700439167       -1e-02
>      1.20     0.932039085967226349689098     
> 0.932735999999999982229600        1e-04
>      1.30     0.963558185417192964729825     
> 0.964774416666666678037840
> 1e-03
>
> and
>
>      5.70    -0.550685542597637763537807   
> -25.165500000000002545915000          -
>
> At 5.7 the value is obviously out of range.
>

There was an error in 128/256 bit division. The exception might 
be caused also by the same division since in the output values 
are rounded also by division. I think now it's solved.

Now it prints:

      1.00    +0.841470984807896506690000 
+0.8414709848078965066525023216302990   +2.653e-18
      1.10    +0.891207360061435339970000 
+0.8912073600614353383642161528821827   +6.642e-19
      1.20    +0.932039085967226349660000 
+0.9320390859672263482207034175881317   +7.207e-19
      1.30    +0.963558185417192964750000 
+0.9635581854171929634976039012289115   +1.998e-18
      1.40    +0.985449729988460180680000 
+0.9854497299884601806594745788060975   +2.659e-18
      1.50    +0.997494986604054430920000 
+0.9974949866040544309417233711414873   +2.942e-18
      1.60    +0.999573603041505164340000 
+0.9995736030415051644881114370526778   +2.988e-18
      1.70    +0.991664810452468615300000 
+0.9916648104524686161192003644210237   +3.119e-18
      1.80    +0.973847630878195186490000 
+0.9738476308781951865323731788433576   +2.532e-18
      1.90    +0.946300087687414488450000 
+0.9463000876874144907527365796794817   +4.753e-18
      2.00    +0.909297426825681695360000 
+0.9092974268256816953960198659117448   +2.896e-18
      2.10    +0.863209366648873770580000 
+0.8632093666488737742146820454680267   +5.515e-18
      2.20    +0.808496403819590184280000 
+0.8084964038195901884235447312035390   +6.724e-18
      2.30    +0.745705212176720177430000 
+0.7457052121767201827156143818820931   +7.216e-18
      2.40    +0.675463180551150926640000 
+0.6754631805511509324649212496712473   +7.965e-18
      2.50    +0.598472144103956494230000 
+0.5984721441039565012621472421085657   +8.762e-18
      2.60    +0.515501371821464235500000 
+0.5155013718214642429697257155298933   +8.470e-18
      2.70    +0.427379880233829934900000 
+0.4273798802338299426927023640114310   +8.893e-18
      2.80    +0.334988150155904919980000 
+0.3349881501559049280238548187303455   +9.224e-18
      2.90    +0.239249329213982328710000 
+0.2392493292139823378938385702354806   +1.009e-17
      3.00    +0.141120008059867222730000 
+0.1411200080598672320006697688125648   +9.751e-18
      3.10    +0.041580662433290579925000 
+0.0415806624332905891860497743294677   +9.416e-18
      3.20    -0.058374143427579908319000 
-0.0583741434275798991542696566715643   +8.966e-18
      3.30    -0.157745694143248381120000 
-0.1577456941432483701618970386961038   +1.049e-17
      3.40    -0.255541102026831318290000 
-0.2555411020268313076483241184102069   +9.852e-18
      3.50    -0.350783227689619847110000 
-0.3507832276896198368828885525540795   +8.817e-18
      3.60    -0.442520443294852383210000 
-0.4425204432948523726088679351487828   +8.991e-18
      3.70    -0.529836140908493212180000 
-0.5298361409084932021854772134659022   +8.015e-18
      3.80    -0.611857890942719074680000 
-0.6118578909427190654510058312314653   +7.749e-18
      3.90    -0.687766159183973817050000 
-0.6877661591839738086537681707768678   +6.346e-18
      4.00    -0.756802495307928250370000 
-0.7568024953079282428752720232848741   +5.825e-18
      4.10    -0.818277111064410503450000 
-0.8182771110644104967923257194259585   +4.708e-18
      4.20    -0.871575772413588059290000 
-0.8715757724135880526646647777983275   +4.035e-18
      4.30    -0.916165936749454983420000 
-0.9161659367494549780197217790850059   +2.480e-18
      4.40    -0.951602073889515953550000 
-0.9516020738895159488107335437472529   +1.689e-18
      4.50    -0.977530117665097054990000 
-0.9775301176650970518056064241753746   -3.056e-19
      4.60    -0.993691003633464455930000 
-0.9936910036334644542315117020129026   -1.232e-18
      4.70    -0.999923257564100884190000 
-0.9999232575641008839565405992429380   -2.457e-18
      4.80    -0.996164608835840671960000 
-0.9961646088358406733565781684136726   -3.857e-18
      4.90    -0.982452612624332512720000 
-0.9824526126243325156335998995246860   -5.634e-18
      5.00    -0.958924274663138469490000 
-0.9589242746631384739990737444940666   -8.499e-18
      5.10    -0.925814682327732297800000 
-0.9258146823277323037497456163785133   -9.250e-18
      5.20    -0.883454655720153265820000 
-0.8834546557201532731063845238285883   -1.041e-17
      5.30    -0.832267442223901164880000 
-0.8322674422239011735432977190794839   -1.104e-17
      5.40    -0.772764487555987363960000 
-0.7727644875559873750523273015869194   -1.385e-17
      5.50    -0.705540325570391908070000 
-0.7055403255703919225313239842210499   -1.603e-17
      5.60    -0.631266637872321313520000 
-0.6312666378723213293016843594524164   -1.760e-17
      5.70    -0.550685542597637763540000 
-0.5506855425976377779216063046556619   -1.622e-17
      5.80    -0.464602179413757213930000 
-0.4646021794137572317851754163529263   -1.909e-17
      5.90    -0.373876664830236362540000 
-0.3738766648302363811468503760962045   -1.985e-17
      6.00    -0.279415498198925875720000 
-0.2794154981989258948954720395703132   -2.020e-17

>Chapter 9.2 of IEEE-754-2008 says the domain of sin(x) is (-inf, 
>inf). So if the argument >x is outside the radius of convergence 
>of the Taylor series x must be reduced modulo 2pi >such that it 
>fits.

That's exactly how it's done internally: 
https://github.com/rumbu13/decimal/blob/master/src/decimal/package.d#L13380

Your unity test also seems now to compute correctly. My maximum 
|δ| for decimal128 is now 1e-34

>There's more to come (sorry for the greek symbols, could not 
>resist to check this utf-8 feature)

I like them too: 
https://github.com/rumbu13/decimal/blob/master/src/decimal/package.d#L13558

Do you have something against including parts of your test 
published here as unittests? Thanks.