sinc(π) not defined

[EthanAnderes]

The function sinc doesn't seem to be defined for π.

julia> sinc(3.1415926535897)
-0.04359862862916225

julia> sinc(π)
ERROR: `decompose` has no method matching decompose(::MathConst{:π})
 in sinpi at special/trig.jl:2
 in sinc at special/trig.jl:88

julia> sin(π)
1.2246467991473532e-16

[JeffBezanson]

See also #5561. It's not clear where to stop adding definitions for MathConsts.

[StefanKarpinski]

Yikes. Decompose should not really be called on MathConsts since they're typically not rational.

[tknopp]

There are of course simple workarounds for this by writing e.g. sinc(1π).

But still I do not understand why the decompose method is called here.

[simonbyrne]

I would never have guessed that this was the problem:

julia> isinf(pi)
ERROR: `decompose` has no method matching decompose(::MathConst{:π})
 in isinf at float.jl:217

@EthanAnderes Note that the sinc function is the normalised version that multiplies by pi internally, i.e. sinc(x) = sin(pi*x)/(pi*x).

[tknopp]

Maybe the concept behind MathConst is a little bit to clever? Lets have a look how we do with another important constant 1:

• Typing 1 gives an Int, typing 1.0 gives a Float64
• If one wants this to be parametric one has to use the one method.
  If I understand the MathConst concept right one wants to delegate the conversion to the next operation happening.

Maybe one could have pi beeing a Float64 and pi{T} beeing used if one wants a specific type (this is just brainstorm not a concrete proposal).

[EthanAnderes]

@simonbyrne That did initially trip me up. In fact, I was testing sinc(\pi) after seeing my code had a misspecified phase, ... then ran into it not being defined. Obviously, not a big deal but I figured someone would want to know about it. Hence the issue here. Thanks for looking into it. Cheers.

[stevengj]

Regardless, I feel like isfinite should work on a mathconst, maybe via isfinite(x::MathConst) = isfinite(convert(Float64,x)). That's the sort of basic numerical test that should be available for any real numeric type.

(Although sinc still won't work because of the oftype call in sinc. But sinpi will now work.)

[kshyatt]

So, on latest master...

julia> sinc(π)
ERROR: MethodError: Cannot `convert` an object of type Int64 to an object of type Irrational{:π}
This may have arisen from a call to the constructor Irrational{:π}(...),
since type constructors fall back to convert methods.
 in sinpi(::Irrational{:π}) at ./special/trig.jl:159
 in sinc(::Irrational{:π}) at ./special/trig.jl:296

julia> sinc(3.1415926535897)
-0.04359862862916225

[simonbyrne]

It appears to be due to this:

julia> one(typeof(pi))
ERROR: MethodError: Cannot `convert` an object of type Int64 to an object of type Irrational{:π}
This may have arisen from a call to the constructor Irrational{:π}(...),
since type constructors fall back to convert methods.
 in one(::Type{Irrational{:π}}) at ./number.jl:64

[stevengj]

It seems reasonable to define convert{T<:Irrational}(::Type{T}, x::Number) = x.

[simonbyrne]

I don't know: defining convert{T}(::Type{T}, x) to give something that isn't of type T seems dangerous.

[StefanKarpinski]

Hmm. This is a pretty tricky issue. We really want one(pi) to give a non-Irrational.

[martinholters]

According to ?one, one(π) should give "the multiplicative identity element for the type of" π. I don't think we have that at the moment (1*π == 1.0*π ≠ π). That would leave introducing Irrational{1} (or maybe a more appropriately named singleton type, say One) with correspondingly overloaded *. I'm not sure we want to go down that road, though.

[fredrikekre]

#21781

julia> sinc(π)
-0.04359862862918775