Rollup merge of #96129 - mattheww:2022-04_float_rounding, r=Dylan-DPC

Document rounding for floating-point primitive operations and string parsing

The docs for floating point don't have much to say at present about either the precision of their results or rounding behaviour.

As I understand it[^1][^2], Rust doesn't support operating with non-default rounding directions, so we need only describe roundTiesToEven.

[^1]: https://github.com/rust-lang/rust/issues/41753#issuecomment-299322887
[^2]: https://github.com/llvm/llvm-project/issues/8472#issuecomment-980888781

This PR makes a start by documenting that for primitive operations and `from_str()`.

library/core/src/num/dec2flt/mod.rs

@@ -143,8 +143,10 @@ macro_rules! from_str_float_impl {
             /// # Return value
             ///
             /// `Err(ParseFloatError)` if the string did not represent a valid
-            /// number. Otherwise, `Ok(n)` where `n` is the floating-point
-            /// number represented by `src`.
+            /// number. Otherwise, `Ok(n)` where `n` is the closest
+            /// representable floating-point number to the number represented
+            /// by `src` (following the same rules for rounding as for the
+            /// results of primitive operations).
             #[inline]
             fn from_str(src: &str) -> Result<Self, ParseFloatError> {
                 dec2flt(src)

library/core/src/primitive_docs.rs

@@ -994,6 +994,19 @@ mod prim_tuple {}
 ///     surprising results upon inspecting the bit patterns,
 ///     as the same calculations might produce NaNs with different bit patterns.
 ///
+/// When the number resulting from a primitive operation (addition,
+/// subtraction, multiplication, or division) on this type is not exactly
+/// representable as `f32`, it is rounded according to the roundTiesToEven
+/// direction defined in IEEE 754-2008. That means:
+///
+/// - The result is the representable value closest to the true value, if there
+///   is a unique closest representable value.
+/// - If the true value is exactly half-way between two representable values,
+///   the result is the one with an even least-significant binary digit.
+/// - If the true value's magnitude is ≥ `f32::MAX` + 2<sup>(`f32::MAX_EXP` −
+///   `f32::MANTISSA_DIGITS` − 1)</sup>, the result is ∞ or −∞ (preserving the
+///   true value's sign).
+///
 /// For more information on floating point numbers, see [Wikipedia][wikipedia].
 ///
 /// *[See also the `std::f32::consts` module](crate::f32::consts).*

library/std/src/primitive_docs.rs

@@ -994,6 +994,19 @@ mod prim_tuple {}
 ///     surprising results upon inspecting the bit patterns,
 ///     as the same calculations might produce NaNs with different bit patterns.
 ///
+/// When the number resulting from a primitive operation (addition,
+/// subtraction, multiplication, or division) on this type is not exactly
+/// representable as `f32`, it is rounded according to the roundTiesToEven
+/// direction defined in IEEE 754-2008. That means:
+///
+/// - The result is the representable value closest to the true value, if there
+///   is a unique closest representable value.
+/// - If the true value is exactly half-way between two representable values,
+///   the result is the one with an even least-significant binary digit.
+/// - If the true value's magnitude is ≥ `f32::MAX` + 2<sup>(`f32::MAX_EXP` −
+///   `f32::MANTISSA_DIGITS` − 1)</sup>, the result is ∞ or −∞ (preserving the
+///   true value's sign).
+///
 /// For more information on floating point numbers, see [Wikipedia][wikipedia].
 ///
 /// *[See also the `std::f32::consts` module](crate::f32::consts).*