Supplemental support for numerical and mathematical functions

[kimikage]

In response to #179, I checked the support status and performance of some other functions. The (incomplete) list is shown below.

To be supported

• ^(::FixedPoint, ::Integer) for more accuracy
  • e.g. N0f8(0.8)^3 != N0f8(64/125)
• bitstring (PR Add bitstring for FixedPoint numbers #195)
• big (Issue Adding big(::FixedPoint) and rationalize(::FixedPoint) #184, PR Add big() and rationalize() for FixedPoint #186)
• clamp (Issue performance on clamp #179, PR Optimize clamp #194)
• copysign(x::Fixed, y) and flipsign(x::Fixed, y) for speed performance (PR Specialize sign-related functions #187)
• fma and muladd
• rationalize (Issue Adding big(::FixedPoint) and rationalize(::FixedPoint) #184, PR Add big() and rationalize() for FixedPoint #186)
• 3-arg rem and div (cld) (PR Add checked, wrapping and saturating arithmetic for div/cld/fld #226, PR Add checked, wrapping and saturating arithmetic for rem/mod #230)
• rem2pi and mod2pi
• signbit for speed performance (for Normed) (PR Specialize sign-related functions #187)

To be dropped

• abs(::Normed) specialization is not helpful. (PR Specialize sign-related functions #187)
  • The fallback implementation works fine.
• copysign(x::Normed, y) and flipsign(x::Normed, y) should be throw error. (PR Specialize sign-related functions #187)

TBD

• maxintfloat (maxintfixed and minintfixed?)

• parse and tryparse for fixed point numbers with suffix

• bit shift operators (Issue [Feature Request] shifting with << and >> #250)

  • I think they are usuful but somewhat dangerous.

• numerator and denominator

• widemul

[kimikage]

Ah, I forgot widemul.