====== 2021-03-20 - still too much engineering ======

i started this year with a description [[:blog:2021:01:01:2021-01-01 - too much engineering|how i started RE on device, only to learn that it's power cable was loose]]. and here we are -- a quarter year later i did exactly the same. this time i've decided to memorize [[wp>e (mathematical constant)|e]] (that i remember up to 2 decimal places) and [[wp>pi]] (i remember 4 decimal places) up to 10 decimal places. what can i do with it? well -- play with calc, of course. ;)

with ''e'' it was simple -- ''ln(e)=1''. so i started calc app on my phone: ''ln(2.7182818285)=1.00000000001506641592''. sweet.

problem started with ''pi'' -- ''sin(pi)=0''. so i started calc app on my phone:
  * ''sin(3)=0.1411...''
  * ''sin(3.14)=0.0015926...''
  * ''sin(3.1415)=0.054802050...''
  * ''sin(3.1415926535)=0.05480366...''

crap! not only value is not equal to ''0'' on 2nd decimal place already, but it is RAISING with improved precision! problem seemed consistent on 3 different calculator apps -- looks like hardware/API thing. what can i do? i've checked if CPU type -- if it is 64-bit. turned out to be Cortex-A53, so 64-bit (i.e. not an issue of 32-bit and small floating-point precision). maybe some weirdo ''float'' vs. ''double'' in software? let's see on my PC:

<code cpp>
#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

int main()
{
  cout << "float:  sin(3.14000000) = " << std::fixed << std::setprecision(20) << sinf(3.14f) << endl;
  cout << "float:  sin(3.14159265) = " << std::fixed << std::setprecision(20) << sinf(3.14159265f) << endl;
  cout << endl;

  cout << "double: sin(3.14000000) = " << std::fixed << std::setprecision(20) << sin(3.14) << endl;
  cout << "double: sin(3.14159265) = " << std::fixed << std::setprecision(20) << sin(3.14159265) << endl;
}
</code>

and we have:
  float:  sin(3.14000000) = 0.00159254798199981451
  float:  sin(3.14159265) = -0.00000008742277657348
  
  double: sin(3.14000000) = 0.00159265291648682823
  double: sin(3.14159265) = 0.00000000358979302984

hmmm... ''sin(3.14)'' is very close to ''float''/''double'' results, but other results are more accurate. can't be that...

so i took another look at the calc app... and voila! trigonometric functions there use by default degrees -- i.e. ''sin(180)=0''. after switching to radians, ''sin(3.1415926535)=0.00000000008979323846''. works. engineer -- engineer never changes... ;)