[Development] Qt pi

[Lars Knoll]

Hi Eddy,

plan sounds good, just go ahead :)

Cheers,
Lars

> On 11 Jan 2017, at 15:35, Edward Welbourne <edward.welbourne at qt.io> wrote:
> 
> Hi all,
> 
> In the course of testing 5.8.0, I was puzzled by an example hard-coding
> a value for pi, rather than re-using one from some public header as I
> expected.  To my surprise, the standard library only provides M_PI as a
> POSIX extension.  It turns out we do have a qmath.h that, sensibly
> enough, does
> 
> #ifndef M_PI
> #define M_PI (3.14159265358979323846)
> #endif
> 
> Despite this, 302 other places in my Qt-dev source tree supply their own
> values for pi.  There is some diversity of values.  Let's start with the
> correctly-rounded ones:
> 
> 3.14159
> 3.14159265 (enough for float - see below)
> 3.14159265358979
> 3.141592653589793 (enough for double - see below)
> 3.1415926535897932
> 3.141592653589793238
> 3.14159265358979323846 (same as M_PI in qmath.h)
> 3.1415926535897932384626433832795
> 3.14159265358979323846264338327950288
> 3.14159265358979323846264338327950288419717
> 3.14159265359
> 3.1415927
> 
> Then the truncated ones that aren't correct roundings (in each case, the
> last digit needs +1):
> 3.1415
> 3.141592
> 3.1415926
> 3.1415926535
> 3.141592653589
> 
> Finally, the values that look suspiciously like they were meant to be
> pi, but aren't (inserting a space after the last matching digit):
> 
> 3.1415 2 (missing 9) In several parameters to sin(...)
> 3.14159 62 (last two digits swapped) In some JS benchmarks
> 3.14159265358979 23846 (missing 3) In an ECMA JS test
> 
> I am fairly sure the parameters to sin were meant to use pi; and I
> suspect changing the JS tests is out-of-scope as they look like imports
> (i.e. third-party).
> 
> Wikipedia gives the following first 49 digits (followed by a 0):
> 
> 3.1415926535897932384626433832795028841971693993751
> 
> Experiment with gcc on 64-bit Intel reveals that there is no point
> supplying more than the following digits, for each type:
> 
> long double: 3.1415926535897932385
>     double: 3.141592653589793
>      float: 3.1415927
> 
> So our M_PI is almost good.  It coincides with what Linux's <math.h>
> provides, except that we put parentheses round it - can anyone give me a
> good reason for that ?  I doubt it matters.  However, neither M_PI puts
> an L suffix on it, so its last four digits are effectively ignored
> (because a floating literal is double by default).
> 
> It looks like it would make sense to:
> 
> i) Change qmath.h's M_PI to (3.14159265358979323846L)
>   i.e. make it a long double, let context downgrade it as needed
> 
> ii) Change all other hand-crafted approximations to use M_PI.
> 
> Can anyone offer me a sane reason to not do this ?
> We have have little arithmetic irregularities creeping in from our
> inconsistencies ...
> 
> 	Eddy.
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