Implements a simply polynomial root finder function
polynomialRoot, intended to be used for benchmarking
against mathjs.
For this purpose, adds numerous other functions (e.g.
cbrt, arg, cis), refactors sqrt (so that you can
definitely get the complex square root when you want
it), and makes numerous enhancements to the core so
that a template can match after conversions.
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #57
Provides the infrastructure to allow annotating the return types of functions, and does so for essentially every operation in the system (the only known exceptions being add, multiply, etc., on arbitrarily many arguments).
One main infrastructure enhancements are bounded template types, e.g. `T:number` being a template parameter where T can take on the type `number` or any subtype thereof.
A main internal enhancement is that base template types are no longer added to the typed universe; rather, there is a secondary, "meta" typed universe where they live. The primary point/purpose of this change is then the necessary search order for implementations can be much better modeled by typed-function's search order, using the `onMismatch` facility to redirect the search from fully instantiated implementations to the generic catchall implementations for each template (these catchalls live in the meta universe).
Numerous other small improvements and bugfixes were encountered along the way.
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #53
Even in the setup just prior to this commit, a quaternion with entries
of type `number` is simply a `Complex<Complex<number>>`
So if we provide a convenience wrapper to create sucha thing, we
instantly have a quaternion data type. All of the operations come for
"free" if they were properly defined for the `Complex` template.
Multiplication already was, `abs` needed a little tweak, but there is
absolutely no "extra" code to support quaternions. (This commit
does not go through and check all arithmetic functions for proper operation
and tweak those that still need some generalization.)
Note that with the recursive template instantiation, a limit had to be placed
on template instantiation depth. The limit moves deeper as actual arguments
that are deeper nested instantiations are seen, so as long as one doesn't
immediately invoke a triply-nested template, for example, the limit will
never prevent an actual computation. It just prevents a runaway in the types
that Pocomath thinks it needs to know about. (Basically before, using the
quaternion creator would produce `Complex<Complex<number>>`. Then when you
called it again, Pocomath would think "Maybe I will need
`Complex<Complex<Complex<number>>>`?!" and create that, even though it had
never seen that, and then another level next time, and so on. The limit
just stops this progression one level beyond any nesting depth that's
actually been observed.
This means that the real and imaginary parts of a Complex must now be
the same type. This seems like a real benefit: a Complex with a number real
part and a bigint imaginary part does not seem sensible.
Note that this is now straining typed-function in (at least) the following
ways:
(1) In this change, it was necessary to remove the logic that the square root
of a negative number calls complex square root, which then calls back
to the number square root in its algorithm. (This was creating a circular
reference in the typed-function which the old implementation of Complex
was somehow sidestepping.)
(2) typed-function could not follow conversions that would be allowed by
uninstantiated templates (e.g. number => Complex<number> if the latter
template has not been instantiated) and so the facility for
instantiating a template was surfaced (and for example is called explicitly
in the demo loader `extendToComplex`. Similarly, this necessitated
making the unary signature of the `complex` conversion function explicit,
rather than just via implicit conversion to Complex.
(3) I find the order of implementations is mattering more in typed-function
definitions, implying that typed-function's sorting algorithm is having
trouble distinguishing alternatives.
But otherwise, the conversion went quite smoothly and I think is a good demo
of the power of this approach. And I expect that it will work even more
smoothly if some of the underlying facilities (subtypes, template types) are
integrated into typed-function.
Relational functions are added using templates, and existing generic functions are made more strict with them. Also a new built-in typeOf function is added, that automatically updates itself.
Resolves#34.
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #41
This should eventually be moved into typed-function itself, but for
now it can be implemented on top of the existing typed-function.
Uses subtypes to define (and error-check) gcd and lcm, which are only
defined for integer arguments.
Resolves#36.
This allows types to be collected; prior to this commit they
were conflicting from different modules.
Uses this fix to extend sqrt to bigint, with the convention
that it is undefined for non-perfect squares when 'predictable'
is false and is the "best" approximation to the square root when
'predictable' is true. Furthermore, for negative bigints, you might
get a Gaussian integer when predictable is false; or you will just get
your argument back when 'predictable' is true because what other
bigint could you give back for a negative bigint?
Also had to modify tests on the sign in sqrt(Complex) and add functions
'zero' and 'one' to get types to match, as expected in #27.
Adds numerous tests.
Resolves#26.
Resolves#27.
Also implements a config object that upon change, lazily invalidates
all operations that access it.
Also allows references to signatures with nonexistent types (which
typed-function does not); they come back as undefined.
Uses these features to implement sqrt for number and complex.
Resolves#7.
Glen Whitney