Remove num-rational

This removes `num-rational` as a dependency. As it turns out,
`num-rational`, based on which features are active, can very easily end
up on the critical path during compilation, meaning that it is the crate
that determines how long it takes to compile the `image` crate. This is
because `cargo` can parallelize compilation of many crates, but crates
with a long dependency chains (rather than wide), are the ones that in
the end determine the compilation speed. This is one of the learnings of
the `serde` drama, where it has been noticed that allowing `serde` and
`serde_derive` to compile in parallel reduces its long dependency chain,
resulting in faster compile times. This introduces the same kind of
optimization here, where for all the following features, `num-rational`
turns out to be the longest dependency chain:

`png,jpeg,gif,bmp,ico,pnm,tga,tiff,webp,hdr,dxt,dds,farbfeld,qoi`

The critical path is the following:

`autocfg` → `num-traits` compile build.rs → `num-traits` run build.rs →
`num-traits` → `num-integer` → `num-rational` → `image`

As it turns out, the only thing really used in `num-rational` is
`Ratio`, which can be easily replicated.

This cuts out both `num-integer` and `num-rational` cutting compile
times by around 0.5 seconds on a debug build.

Cargo.toml

@@ -32,7 +32,6 @@ path = "./src/lib.rs"
 [dependencies]
 bytemuck = { version = "1.7.0", features = ["extern_crate_alloc"] } # includes cast_vec
 byteorder = "1.3.2"
-num-rational = { version = "0.4", default-features = false }
 num-traits = "0.2.0"
 gif = { version = "0.12", optional = true }
 jpeg = { package = "jpeg-decoder", version = "0.3.0", default-features = false, optional = true }

src/animation.rs

@@ -1,8 +1,7 @@
+use std::cmp::Ordering;
 use std::iter::Iterator;
 use std::time::Duration;
 
-use num_rational::Ratio;
-
 use crate::error::ImageResult;
 use crate::RgbaImage;
 
@@ -49,14 +48,14 @@ pub struct Frame {
 /// The delay of a frame relative to the previous one.
 #[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd)]
 pub struct Delay {
-    ratio: Ratio<u32>,
+    ratio: Ratio,
 }
 
 impl Frame {
     /// Constructs a new frame without any delay.
     pub fn new(buffer: RgbaImage) -> Frame {
         Frame {
-            delay: Delay::from_ratio(Ratio::from_integer(0)),
+            delay: Delay::from_ratio(Ratio { numer: 0, denom: 1 }),
             left: 0,
             top: 0,
             buffer,
@@ -115,7 +114,7 @@ impl Delay {
     /// ```
     pub fn from_numer_denom_ms(numerator: u32, denominator: u32) -> Self {
         Delay {
-            ratio: Ratio::new_raw(numerator, denominator),
+            ratio: Ratio::new(numerator, denominator),
         }
     }
 
@@ -163,14 +162,14 @@ impl Delay {
     /// This is guaranteed to be an exact conversion if the `Delay` was previously created with the
     /// `from_numer_denom_ms` constructor.
     pub fn numer_denom_ms(self) -> (u32, u32) {
-        (*self.ratio.numer(), *self.ratio.denom())
+        (self.ratio.numer, self.ratio.denom)
     }
 
-    pub(crate) fn from_ratio(ratio: Ratio<u32>) -> Self {
+    pub(crate) fn from_ratio(ratio: Ratio) -> Self {
         Delay { ratio }
     }
 
-    pub(crate) fn into_ratio(self) -> Ratio<u32> {
+    pub(crate) fn into_ratio(self) -> Ratio {
         self.ratio
     }
 
@@ -179,7 +178,7 @@ impl Delay {
     /// Note that `denom_bound` bounds nominator and denominator of all intermediate
     /// approximations and the end result.
     fn closest_bounded_fraction(denom_bound: u32, nom: u32, denom: u32) -> (u32, u32) {
-        use std::cmp::Ordering::{self, *};
+        use std::cmp::Ordering::*;
         assert!(0 < denom);
         assert!(0 < denom_bound);
         assert!(nom < denom);
@@ -271,12 +270,69 @@ impl From<Delay> for Duration {
     fn from(delay: Delay) -> Self {
         let ratio = delay.into_ratio();
         let ms = ratio.to_integer();
-        let rest = ratio.numer() % ratio.denom();
-        let nanos = (u64::from(rest) * 1_000_000) / u64::from(*ratio.denom());
+        let rest = ratio.numer % ratio.denom;
+        let nanos = (u64::from(rest) * 1_000_000) / u64::from(ratio.denom);
         Duration::from_millis(ms.into()) + Duration::from_nanos(nanos)
     }
 }
 
+#[derive(Copy, Clone, Debug)]
+pub(crate) struct Ratio {
+    numer: u32,
+    denom: u32,
+}
+
+impl Ratio {
+    #[inline]
+    pub(crate) fn new(numerator: u32, denominator: u32) -> Self {
+        assert_ne!(denominator, 0);
+        Self {
+            numer: numerator,
+            denom: denominator,
+        }
+    }
+
+    #[inline]
+    pub(crate) fn to_integer(&self) -> u32 {
+        self.numer / self.denom
+    }
+}
+
+impl PartialEq for Ratio {
+    fn eq(&self, other: &Self) -> bool {
+        self.cmp(other) == Ordering::Equal
+    }
+}
+
+impl Eq for Ratio {}
+
+impl PartialOrd for Ratio {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for Ratio {
+    fn cmp(&self, other: &Self) -> Ordering {
+        // The following comparison can be simplified:
+        // a / b <cmp> c / d
+        // We multiply both sides by `b`:
+        // a <cmp> c * b / d
+        // We multiply both sides by `d`:
+        // a * d <cmp> c * b
+
+        let a: u32 = self.numer;
+        let b: u32 = self.denom;
+        let c: u32 = other.numer;
+        let d: u32 = other.denom;
+
+        // We cast the types from `u32` to `u64` in order
+        // to not overflow the multiplications.
+
+        (a as u64 * d as u64).cmp(&(c as u64 * b as u64))
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::{Delay, Duration, Ratio};

src/codecs/gif.rs

@@ -34,9 +34,8 @@ use std::mem;
 
 use gif::ColorOutput;
 use gif::{DisposalMethod, Frame};
-use num_rational::Ratio;
 
-use crate::animation;
+use crate::animation::{self, Ratio};
 use crate::color::{ColorType, Rgba};
 use crate::error::{
     DecodingError, EncodingError, ImageError, ImageResult, ParameterError, ParameterErrorKind,

src/codecs/png.rs

@@ -10,10 +10,9 @@ use std::convert::TryFrom;
 use std::fmt;
 use std::io::{self, Read, Write};
 
-use num_rational::Ratio;
 use png::{BlendOp, DisposeOp};
 
-use crate::animation::{Delay, Frame, Frames};
+use crate::animation::{Delay, Frame, Frames, Ratio};
 use crate::color::{Blend, ColorType, ExtendedColorType};
 use crate::error::{
     DecodingError, EncodingError, ImageError, ImageResult, LimitError, LimitErrorKind,