Extract math from Float trait

text/0000-extract-math-from-float.md

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+- Feature Name: extract_math_from_float
+- Start Date: 2015-03-03
+- RFC PR: (leave this empty)
+- Rust Issue: (leave this empty)
+
+# Summary
+
+Extract mathematical functions from `Float` trait to `Math` trait.
+
+# Motivation
+
+Currently `Float` trait is kind of God-trait that manage everything that floats
+can do. [This also cause some problems for newcomers about usage of basic mathematical
+functions like `sin`][sin-problem].
+
+# Detailed design
+
+Move most of `Float` methods to additional trait that will be defined as follows:
+
+```rust
+trait Math + Copy + NumCast {
+    fn ln(self) -> Self;
+    fn log(self, base: Self) -> Self;
+    fn log2(self) -> Self;
+    fn log10(self) -> Self;
+
+    fn hypot(self, other: Self) -> Self;
+
+    fn sin(self) -> Self;
+    fn cos(self) -> Self;
+    fn tan(self) -> Self;
+    fn sin_cos(self) -> (Self, Self);
+
+    fn asin(self) -> Self;
+    fn acos(self) -> Self;
+    fn atan(self) -> Self;
+    fn atan2(self, other: Self) -> Self;
+
+    fn exp_m1(self) -> Self;
+    fn ln_1p(self) -> Self;
+
+    fn sinh(self) -> Self;
+    fn cosh(self) -> Self;
+    fn tanh(self) -> Self;
+
+    fn asinh(self) -> Self;
+    fn acosh(self) -> Self;
+    fn atanh(self) -> Self;
+}
+```
+
+Which would be implemented for `f64` and `f32` as is. This will be more idiomatic
+to use `std::num::Math` when we need trigonometric function and will allow calls
+like `Math::sin(3.14)` which will be more familiar to newcomers from other languages
+than `Float::sin(3.14)`.
+
+Also this will allow more generic code, i.e. we do not need to create additional
+trait to add this functions, i.e. to `Complex` numbers or interval arithmetic.
+
+It kind of reverse [RFC #0369][rfc-0369], but in my opinion it has been too radical
+which can be seen as [`num` crate][num] bring most of these traits back. This makes
+`num` crate kind of _must have_ for any code related to math.
+
+## Examples of reintroducing RFC #0369 traits
+
+- [`num`][num]
+- [`image`](https://github.com/PistonDevelopers/image/blob/master/src/traits.rs)
+- [`onezero.rs`](https://github.com/japaric/onezero.rs)
+- [`rust-geom`](https://github.com/servo/rust-geom/blob/master/src/num.rs)
+- [`scirust`](https://github.com/indigits/scirust/tree/master/src/number)
+- [`cgmath`](https://github.com/bjz/cgmath-rs)
+
+# Drawbacks
+
+It seems that it add another layer of complexity to codebase, but in long term
+I think that this would improve newcomers experience.
+
+# Alternatives
+
+- Leave this as is.
+- Move all math from `libstd` to `num` crate (IMHO too radical).
+
+# Unresolved questions
+
+- List of methods in `Math` trait. Should it be less/more?
+- Leave with one trait or split it into even more?
+
+[sin-problem]: http://stackoverflow.com/questions/28010779/where-is-the-sine-function
+[rfc-0369]: https://github.com/rust-lang/rfcs/blob/master/text/0369-num-reform.md
+[num]: https://github.com/rust-lang/num