Aw: Re: Re: no tests for trigonometric functions? need help / hints how to adapt tests for gnumeric 'long' version,

[newbie nullzwei via gnumeric-list]

  
>> - how to deal with / construct tests for functions / ranges where 'long' and 
>> 'double' version have justified different results?  
    ( how to build tests which allow / demand improved results, but accept 
'double accuracy results' when using double datatype? )  
  
let me give it an example ( pros will find better ones ):  
  
t1013-crlibm, crlibm.gnumeric, row 18278:  
  
formula:                     '=exp(239.043590469953)'  
reference:                   6.536003490281019E+103,  
'double' result:             6.536003490281019E+103    - 'quality': ' ' or '99' 
or 100% or best ...  
'long' result:               6.536003490281029007E+103 - 'quality' only 
14.819377377076821122 digits, thus bad?  
my 'srt-deco-round' version: 6.536003490281095E+103,   - 'quality' only 
13.934498683160548 digits, thus worse? but!!!  
correct acc. 'ttmath.org':   
6.5360034902810943723150710853138994266057660109196409934141980800730... E103,  
and acc. 'wolframalpha.com': 
6.5360034902810943723150710853138994266057660109196409934141... × 10^103  
  
thus ttmath and wolframalpha seem correct ( equal ), 6.536003490281094E+103 
would be the best approximation with doubles,  
my improved version second, 'long' third and double 'acceptable' ?  
  
idea ... use the correct result as reference, protect against messing it up by 
saves from low capa versions by storing as text ( '=value(".... ")' ), prepare 
for future improved versions by storing more digits (50?), calculate the 
'quality' ( correct digits? ) with the log formula as of now, and require a 
threshold of e.g 13.9 digits for double and 16.9 digits for long results to 
pass the test ... ???  one would immediately see that the long version has far 
less accuracy ( ~13.99 digits ) than it pretends by it's precision, and could 
try to dig for the reason ...  
  
disclaimer: 'no!', I don't really need this level of accuracy, I'm seeking for 
modes to calculate which don't undermine math logic, and in this area - tests - 
I am looking for something that is oriented to normal mathematics, rewards good 
results and marks deviations ... for this I also have to play through extreme 
considerations ...
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