misc math

[timotheecour]

• ^ (int pow) should also accept y<0, in which case it uses 1/x ^ (-y)

[timotheecour]

• should we rename Inf to inf so that doAssert $inf == "inf" ($Inf is already "inf", and "inf" is commonly used in other languages, not "Inf")

[timotheecour]

• abs(-0.0) returns -0.0 instead of 0.0
  (can be seen with signbit for eg)

EDIT: => nim-lang#16494

[timotheecour]

• check at least all importc math procs (ideally all importc procs) for correctness wrt cfloat vs float32, cdouble vs float (these aren't necessarily same types); eg:
  proc c_copysign(x, y: float64): float64 {.importc: "copysign", header: "<math.h>".}
  should be:
  proc c_copysign(x, y: cdouble): cdouble {.importc: "copysign", header: "<math.h>".}

refs https://github.com/nim-lang/Nim/pull/16406/files#r549490523

[timotheecour]

• check all importc procs to use header angle brackets for stdlib headers, eg:

proc c_copysign(x, y: cdouble): cdouble {.importc: "copysign", header: "math.h".}
should be:
proc c_copysign(x, y: cdouble): cdouble {.importc: "copysign", header: "<math.h>".}

[timotheecour]

• check whether we can impement abs(SomeNumber) more efficiently (at least on some platforms) using bit manipulation (seems like simply amounts to setting a bit)
  maybe fabs is as efficient? refs https://en.cppreference.com/w/c/numeric/math/fabs
  (but using fabs wouldn't allow inlining unless using --passc:-flto ?)

eg: something along those lines (but adapted for the simpler case of abs)

## D20201228T203049
float copysignf(float x, float y)
{
  union {float f; uint32_t i;} ux={x}, uy={y};
  ux.i &= 0x7fffffff;
  ux.i |= uy.i & 0x80000000;
  return ux.f;
}

[timotheecour]

• math.nim should use runnableExamples

[timotheecour]

• classify doesn't work with --passc:-ffast-math => Make std/math classify work without --passc:-fast-math. nim-lang/Nim#23211

[timotheecour]

• tmath.nim should wrap all code inside template main so it tests in VM + RT, and also test in js,c,cpp, using the usual disableVM (etc) as needed

[timotheecour]

• add signbit => add math.signbit nim-lang/Nim#16592

[timotheecour]

• add nextAfter (it's neither in math nor in fenv right now)

there are other related functions, eg nexttoward, nextup, nextdown + their variants but nextafter seems like the most useful / versatile

refs https://www.gnu.org/software/libc/manual/html_node/FP-Bit-Twiddling.html

[timotheecour]

• doAssert copySign(-1.0, -NaN) == 1.0 gives different results in VM vs RT
  refs: [do not merge] add math.copySign #496 (comment)
  refs: cast[uint](NaN) differs at CT vs RT; `-NaN and NaN have same bit representation #499

[timotheecour]

• js: use Object.is for math.copySign and $float (for -0.0),
  refs: fix printing negative zero in JS backend nim-lang/Nim#16505 (comment)
  refs: Add math.copySign nim-lang/Nim#16406 (comment)

[timotheecour]

• add math.isFinite

refs: nim-lang#16179 (comment)
refs: #501 (comment)

[timotheecour]

• update this wording for isNaN to reflect reality:

Returns whether x is a NaN, more efficiently than via classify(x) == fcNan. Works even with: --passc:-ffast-math.

=> (preferably) make this actually true, or specify where this holds true or say simply this depends on compilers/arthitectures

[timotheecour]

• toBits/fromBits or equivalent
  refs add toBits and fromBits to math by xflywind · Pull Request #16403 · nim-lang/Nim

[timotheecour]

• fix this to add () outer parens /cc @xflywind (ok, i agree)

func mod(x, y: float32): float32 {.importcpp: "# % #".}
func mod(x, y: float64): float64 {.importcpp: "# % #".}

[timotheecour]

• add to math: uabs or absUnsigned:

proc absUnsigned*(a: SomeSigned): auto =
  type T = toUnsigned(type(a))
  if a >= 0: cast[T](a)
  else: cast[T](not(a)) + 1

refs https://github.com/nim-lang/Nim/pull/17106/files#diff-41e0f628f50989d7cd4eecdf69497f294772f292348ebd996c342ec294fe816bR342

avoids overflow errors