>99.7% speedup to lookup tables

benches/bench.rs

@@ -10,19 +10,13 @@ fn pow2_benchmarks(group: &mut BenchmarkGroup<WallTime>, x_f64: &[f64], x_f32: &
         b.iter(|| x_f64.iter().map(|&x| black_box(x).fast_pow2()).collect::<Vec<f64>>())
     });
     group.bench_function("f64_builtin_fn", |b| {
-        b.iter(|| x_f64.iter().map(|&x| black_box(x).powi(2)).collect::<Vec<f64>>())
+        b.iter(|| x_f64.iter().map(|&x| 2.0f64.powf(black_box(x))).collect::<Vec<f64>>())
-    });
-    group.bench_function("f64_builtin_mul", |b| {
-        b.iter(|| x_f64.iter().map(|&x| black_box(x) * x).collect::<Vec<f64>>())
     });
     group.bench_function("f32_fast", |b| {
         b.iter(|| x_f32.iter().map(|&x| black_box(x).fast_pow2()).collect::<Vec<f32>>())
     });
     group.bench_function("f32_builtin_fn", |b| {
-        b.iter(|| x_f32.iter().map(|&x| black_box(x).powi(2)).collect::<Vec<f32>>())
+        b.iter(|| x_f32.iter().map(|&x| 2.0f32.powf(black_box(x))).collect::<Vec<f32>>())
-    });
-    group.bench_function("f32_builtin_mul", |b| {
-        b.iter(|| x_f32.iter().map(|&x| black_box(x) * x).collect::<Vec<f32>>())
     });
 }
 

build.rs

@@ -1,42 +1,137 @@
 // build.rs
 
 mod precalculate_lookup_tables {
+    use std::f32::consts as f32_consts;
+    use std::f64::consts as f64_consts;
     use std::fs::{create_dir_all, File};
     use std::io::Write;
-    include!("src/lookup/lookup_table.rs");
+    include!("src/lookup/config.rs");
-    use bincode::serialize;
+    // use bincode::serialize;
 
-    const PRECISION: usize = 1000;
+    // fn precalculate_sin_tables() -> Result<(), Box<dyn std::error::Error>> {
+    //     let data = serialize(&EndoSinLookupTable::<f32>::new(PRECISION))?;
+    //     let mut file = File::create("src/lookup/data/sin_f32.bin")?;
+    //     file.write_all(&data)?;
 
-    fn precalculate_sin_tables() -> Result<(), Box<dyn std::error::Error>> {
+    //     let data = serialize(&EndoSinLookupTable::<f64>::new(PRECISION))?;
-        let data = serialize(&EndoSinLookupTable::<f32>::new(PRECISION))?;
+    //     let mut file = File::create("src/lookup/data/sin_f64.bin")?;
-        let mut file = File::create("src/lookup/data/sin_f32.bin")?;
+    //     file.write_all(&data)?;
-        file.write_all(&data)?;
 
-        let data = serialize(&EndoSinLookupTable::<f64>::new(PRECISION))?;
+    //     Ok(())
-        let mut file = File::create("src/lookup/data/sin_f64.bin")?;
+    // }
-        file.write_all(&data)?;
 
-        Ok(())
+    // fn precalculate_cos_tables() -> Result<(), Box<dyn std::error::Error>> {
+    //     let data = serialize(&EndoCosLookupTable::<f32>::new(PRECISION))?;
+    //     let mut file = File::create("src/lookup/data/cos_f32.bin")?;
+    //     file.write_all(&data)?;
+
+    //     let data = serialize(&EndoCosLookupTable::<f64>::new(PRECISION))?;
+    //     let mut file = File::create("src/lookup/data/cos_f64.bin")?;
+    //     file.write_all(&data)?;
+
+    //     Ok(())
+    // }
+
+    // fn precalculate_sin_tables() -> Result<(), Box<dyn std::error::Error>> {
+    //     let step: f32 = f32_consts::FRAC_PI_2 / TABLE_SIZE as f32;
+    //     let half_step: f32 = step / 2.0;
+
+    //     let keys: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+    //         (step * (i as f32)) - half_step
+    //     }).collect::<Vec<f32>>().try_into().unwrap_or([0.0f32; TABLE_SIZE]);
+    //     let values: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+    //         (step * (i as f32)).sin()
+    //     }).collect::<Vec<f32>>().try_into().unwrap_or([0.0f32; TABLE_SIZE]);
+    //     let data = format!("pub const KEYS: [f32; {}] = {:?};\npub const VALUES: [f32; {}] = {:?};\n", TABLE_SIZE, keys, TABLE_SIZE, values);
+
+    //     let mut file = File::create("src/lookup/data/sin_f32.rs")?;
+    //     file.write_all(data.as_bytes())?;
+
+    //     let step: f64 = f64_consts::FRAC_PI_2 / TABLE_SIZE as f64;
+    //     let half_step: f64 = step / 2.0;
+
+    //     let keys: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+    //         (step * (i as f64)) - half_step
+    //     }).collect::<Vec<f64>>().try_into().unwrap_or([0.0f64; TABLE_SIZE]);
+    //     let values: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+    //         (step * (i as f64)).sin()
+    //     }).collect::<Vec<f64>>().try_into().unwrap_or([0.0f64; TABLE_SIZE]);
+    //     let data = format!("pub const KEYS: [f64; {}] = {:?};\npub const VALUES: [f64; {}] = {:?};\n", TABLE_SIZE, keys, TABLE_SIZE, values);
+
+    //     let mut file = File::create("src/lookup/data/sin_f64.rs")?;
+    //     file.write_all(data.as_bytes())?;
+
+    //     Ok(())
+    // }
+
+    macro_rules! precalculate_sin_tables {
+        () => {{
+            let step: f32 = f32_consts::FRAC_PI_2 / TABLE_SIZE as f32;
+            let half_step: f32 = step / 2.0;
+
+            let keys: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+                (step * (i as f32)) - half_step
+            }).collect::<Vec<f32>>().try_into().unwrap_or([0.0f32; TABLE_SIZE]);
+            let values: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+                (step * (i as f32)).sin()
+            }).collect::<Vec<f32>>().try_into().unwrap_or([0.0f32; TABLE_SIZE]);
+            let data = format!("pub const SIN_F32_KEYS: [f32; {}] = {:?};\npub const SIN_F32_VALUES: [f32; {}] = {:?};\n", TABLE_SIZE, keys, TABLE_SIZE, values);
+
+            let mut file = File::create("src/lookup/data/sin_f32.rs").expect("Failed to create sin_f32.rs");
+            file.write_all(data.as_bytes()).expect("Failed to write sin_f32.rs");
+
+            let step: f64 = f64_consts::FRAC_PI_2 / TABLE_SIZE as f64;
+            let half_step: f64 = step / 2.0;
+
+            let keys: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+                (step * (i as f64)) - half_step
+            }).collect::<Vec<f64>>().try_into().unwrap_or([0.0f64; TABLE_SIZE]);
+            let values: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+                (step * (i as f64)).sin()
+            }).collect::<Vec<f64>>().try_into().unwrap_or([0.0f64; TABLE_SIZE]);
+            let data = format!("pub const SIN_F64_KEYS: [f64; {}] = {:?};\npub const SIN_F64_VALUES: [f64; {}] = {:?};\n", TABLE_SIZE, keys, TABLE_SIZE, values);
+
+            let mut file = File::create("src/lookup/data/sin_f64.rs").expect("Failed to create sin_f64.rs");
+            file.write_all(data.as_bytes()).expect("Failed to write sin_f64.rs");
+        }};
     }
+    // fn precalculate_sin_tables() -> Result<(), Box<dyn std::error::Error>> {
+    //     let step: f32 = f32_consts::FRAC_PI_2 / TABLE_SIZE as f32;
+    //     let half_step: f32 = step / 2.0;
 
-    fn precalculate_cos_tables() -> Result<(), Box<dyn std::error::Error>> {
+    //     let keys: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
-        let data = serialize(&EndoCosLookupTable::<f32>::new(PRECISION))?;
+    //         (step * (i as f32)) - half_step
-        let mut file = File::create("src/lookup/data/cos_f32.bin")?;
+    //     }).collect::<Vec<f32>>().try_into().unwrap_or([0.0f32; TABLE_SIZE]);
-        file.write_all(&data)?;
+    //     let values: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+    //         (step * (i as f32)).sin()
+    //     }).collect::<Vec<f32>>().try_into().unwrap_or([0.0f32; TABLE_SIZE]);
+    //     let data = format!("pub const KEYS: [f32; {}] = {:?};\npub const VALUES: [f32; {}] = {:?};\n", TABLE_SIZE, keys, TABLE_SIZE, values);
 
-        let data = serialize(&EndoCosLookupTable::<f64>::new(PRECISION))?;
+    //     let mut file = File::create("src/lookup/data/sin_f32.rs")?;
-        let mut file = File::create("src/lookup/data/cos_f64.bin")?;
+    //     file.write_all(data.as_bytes())?;
-        file.write_all(&data)?;
 
-        Ok(())
+    //     let step: f64 = f64_consts::FRAC_PI_2 / TABLE_SIZE as f64;
-    }
+    //     let half_step: f64 = step / 2.0;
+
+    //     let keys: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+    //         (step * (i as f64)) - half_step
+    //     }).collect::<Vec<f64>>().try_into().unwrap_or([0.0f64; TABLE_SIZE]);
+    //     let values: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| {
+    //         (step * (i as f64)).sin()
+    //     }).collect::<Vec<f64>>().try_into().unwrap_or([0.0f64; TABLE_SIZE]);
+    //     let data = format!("pub const KEYS: [f64; {}] = {:?};\npub const VALUES: [f64; {}] = {:?};\n", TABLE_SIZE, keys, TABLE_SIZE, values);
+
+    //     let mut file = File::create("src/lookup/data/sin_f64.rs")?;
+    //     file.write_all(data.as_bytes())?;
+
+    //     Ok(())
+    // }
 
     pub fn generate() -> Result<(), Box<dyn std::error::Error>> {
         create_dir_all("src/lookup/data")?;
     
-        precalculate_sin_tables()?;
+        precalculate_sin_tables!();
-        precalculate_cos_tables()?;
+        // precalculate_cos_tables()?;
         
         Ok(())
     }

src/fastmath.rs

@@ -4,12 +4,19 @@
 
 use std::f32::consts as f32_consts;
 use std::f64::consts as f64_consts;
-use crate::lookup::*;
+// use crate::lookup::*;
+use crate::lookup::lookup_table::EndoCosLookupTable;
 
-pub trait FastMath: FastCos + FastPow2 + FastExp + FastSigmoid {}
+const COS_LOOKUP_F32: EndoCosLookupTable<f32> = EndoCosLookupTable::<f32>::new();
+const COS_LOOKUP_F64: EndoCosLookupTable<f64> = EndoCosLookupTable::<f64>::new();
+
+pub trait FastMath: FastCos + FastExp + FastSigmoid {}
 impl FastMath for f32 {}
 impl FastMath for f64 {}
 
+const V_SCALE_F32: f32 = 8388608.0; // the largest possible mantissa of an f32
+const V_SCALE_F64: f64 = 4503599627370496.0; // the largest possible mantissa of an f64
+
 
 pub trait LookupCos {
     fn lookup_cos(self: Self) -> Self;
@@ -35,93 +42,66 @@ pub trait FastCos {
 impl FastCos for f32 {
     #[inline]
     fn fast_cos(self: Self) -> f32 {
-        const BITAND: u32 = u32::MAX / 2;
         const ONE: f32 = 1.0;
-        let mod_x = (((self + f32_consts::PI).abs()) % f32_consts::TAU) - f32_consts::PI;
+        let v = ((((self + f32_consts::PI).abs()) % f32_consts::TAU) - f32_consts::PI).abs();
-        let v = mod_x.to_bits() & BITAND;
+        let qpprox = ONE - f32_consts::FRAC_2_PI * v;
-        let qpprox = ONE - f32_consts::FRAC_2_PI * f32::from_bits(v);
         qpprox + f32_consts::FRAC_PI_6 * qpprox * (ONE - qpprox * qpprox)
     }
 }
 impl FastCos for f64 {
     #[inline]
     fn fast_cos(self: Self) -> f64 {
-        const BITAND: u64 = u64::MAX / 2;
         const ONE: f64 = 1.0;
-        let mod_x = (((self + f64_consts::PI).abs()) % f64_consts::TAU) - f64_consts::PI;
+        let v = ((((self + f64_consts::PI).abs()) % f64_consts::TAU) - f64_consts::PI).abs();
-        let v = mod_x.to_bits() & BITAND;
+        let qpprox = ONE - f64_consts::FRAC_2_PI * v;
-        let qpprox = ONE - f64_consts::FRAC_2_PI * f64::from_bits(v);
         qpprox + f64_consts::FRAC_PI_6 * qpprox * (ONE - qpprox * qpprox)
     }
 }
 
-pub trait FastPow2 {
-    fn fast_pow2(self: Self) -> Self;
-}
-impl FastPow2 for f32 {
-    #[inline]
-    fn fast_pow2(self: Self) -> f32 {
-        // Khinchins constant over 3. IDK why it gives the best fit, but it does
-        const KHINCHIN_3: f32 = 2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515 / 3.0;
-        const CLIPP_THRESH: f32 = 0.12847338;
-        const V_SCALE: f32 = 8388608.0; // (1_i32 << 23) as f32
-        const CLIPP_SHIFT: f32 = 126.67740855;
-        let abs_p = self.abs();
-        let clipp = abs_p.max(CLIPP_THRESH); // if abs_p < CLIPP_THRESH { CLIPP_THRESH } else { abs_p };
-        let v = (V_SCALE * (clipp + CLIPP_SHIFT)) as u32;
-        f32::from_bits(v) - KHINCHIN_3
-    }
-}
-impl FastPow2 for f64 {
-    #[inline]
-    fn fast_pow2(self: Self) -> f64 {
-        const KHINCHIN_3: f64 = 2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515 / 3.0;
-        const CLIPP_THRESH: f64 = -45774.9247660416;
-        const V_SCALE: f64 = 4503599627370496.0; // (1i64 << 52) as f64
-        const CLIPP_SHIFT: f64 = 1022.6769200000002;
-        const ZERO: f64 = 0.;
-        let abs_p = self.abs();
-        let clipp = abs_p.max(CLIPP_THRESH); // if abs_p < CLIPP_THRESH { CLIPP_THRESH } else { abs_p };
-        let v = (V_SCALE * (clipp + CLIPP_SHIFT)) as u64;
-        let y = f64::from_bits(v) - KHINCHIN_3;
-        if y.is_sign_positive() {
-            y
-        } else {
-            ZERO
-        }
-    }
-}
-
 pub trait FastExp {
     fn fast_exp(self: Self) -> Self;
 }
 impl FastExp for f32 {
     #[inline]
     fn fast_exp(self: Self) -> f32 {
-        const CLIPP_THRESH: f32 = -126.0; // 0.12847338;
+        const CLIPP_THRESH: f32 = -126.0; // exponent of smallest possible f32 to prevent underflow
-        const V_SCALE: f32 = 8388608.0; // (1_i32 << 23) as f32
+        const CLIPP_SHIFT: f32 = 126.94269504; // shift to align curve, found by regression
-        const CLIPP_SHIFT: f32 = 126.94269504; // 126.67740855;
 
         let scaled_p = f32_consts::LOG2_E * self;
-        let clipp = scaled_p.max(CLIPP_THRESH); // if scaled_p < CLIPP_THRESH { CLIPP_THRESH } else { scaled_p };
+        let clipp = scaled_p.max(CLIPP_THRESH);
-        let v = (V_SCALE * (clipp + CLIPP_SHIFT)) as u32;
+        let v = (V_SCALE_F32 * (clipp + CLIPP_SHIFT)) as u32;
         f32::from_bits(v)
     }
 }
 impl FastExp for f64 {
     #[inline]
     fn fast_exp(self: Self) -> f64 {
-        const CLIPP_THRESH: f64 = -180335.51911105003;
+        const CLIPP_THRESH: f64 = -1022.0; // exponent of smallest possible f64 to prevent underflow
-        const V_SCALE: f64 = 4524653012949098.0;
+        const CLIPP_SHIFT: f64 = 1022.9349439517318; // shift to align curve, found by regression
-        const CLIPP_SHIFT: f64 = 1018.1563534409383;
 
         let scaled_p = f64_consts::LOG2_E * self;
-        let clipp = scaled_p.max(CLIPP_THRESH); // let clipp = if scaled_p < CLIPP_THRESH { CLIPP_THRESH } else { scaled_p };
+        let clipp = scaled_p.max(CLIPP_THRESH);
-        let v = (V_SCALE * (clipp + CLIPP_SHIFT)) as u64;
+        let v = (V_SCALE_F64 * (clipp + CLIPP_SHIFT)) as u64;
         f64::from_bits(v)
     }
 }
 
+pub trait FastPow2 {
+    fn fast_pow2(self: Self) -> Self;
+}
+impl FastPow2 for f32 {
+    #[inline]
+    fn fast_pow2(self: Self) -> f32 {
+        (f32_consts::LN_2 * self).fast_exp()
+    }
+}
+impl FastPow2 for f64 {
+    #[inline]
+    fn fast_pow2(self: Self) -> f64 {
+        (f64_consts::LN_2 * self).fast_exp()
+    }
+}
+
 pub trait FastSigmoid {
     fn fast_sigmoid(self: Self) -> Self;
 }
@@ -140,63 +120,7 @@ impl FastSigmoid for f64 {
     }
 }
 
-// A trait for testing and improving implementations of fast functions
+// functions for testing the accuracy of fast functions against builtin functions
-pub trait Test {
-    fn test(self: Self) -> Self;
-}
-impl Test for f32 {
-    #[inline]
-    fn test(self: Self) -> f32 {
-        // Khinchins constant over 3. IDK why it gives the best fit, but it does
-        // const KHINCHIN_3: f32 = 2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515 / 3.0;
-        const CLIPP_THRESH: f32 = -126.0; // 0.12847338;
-        const V_SCALE: f32 = 8388608.0; // (1_i32 << 23) as f32
-        const CLIPP_SHIFT: f32 = 126.94269504; // 126.67740855;
-
-        let scaled_p = f32_consts::LOG2_E * self;
-        let clipp = if scaled_p < CLIPP_THRESH {
-            CLIPP_THRESH
-        } else {
-            scaled_p
-        };
-        let v = (V_SCALE * (clipp + CLIPP_SHIFT)) as u32;
-        f32::from_bits(v) // - KHINCHIN_3
-    }
-}
-impl Test for f64 {
-    #[inline]
-    fn test(self: Self) -> f64 {
-        const CLIPP_THRESH: f64 = -180335.51911105003;
-        const V_SCALE: f64 = 4524653012949098.0;
-        const CLIPP_SHIFT: f64 = 1018.1563534409383;
-
-        let scaled_p = f64_consts::LOG2_E * self;
-        let clipp = if scaled_p < CLIPP_THRESH {
-            CLIPP_THRESH
-        } else {
-            scaled_p
-        };
-        let v = (V_SCALE * (clipp + CLIPP_SHIFT)) as u64;
-        f64::from_bits(v)
-    }
-}
-
-#[allow(non_snake_case, dead_code)]
-pub fn optimizing(p: f64, CLIPP_THRESH: f64, V_SCALE: f64, CLIPP_SHIFT: f64) -> f64 {
-    // const CLIPP_THRESH: f64 = -45774.9247660416;
-    // const V_SCALE: f64 = 4503599627370496.0;
-    // const CLIPP_SHIFT: f64 = 1022.6769200000002;
-
-    let scaled_p = f64_consts::LOG2_E * p;
-    let clipp = if scaled_p < CLIPP_THRESH {
-        CLIPP_THRESH
-    } else {
-        scaled_p
-    };
-    let v = (V_SCALE * (clipp + CLIPP_SHIFT)) as u64;
-    f64::from_bits(v)
-}
-
 #[inline]
 pub fn sigmoid_builtin_f32(p: f32) -> f32 {
     (1. + (-p).exp()).recip()

src/lookup/config.rs

@@ -0,0 +1,3 @@
+// lookup/config.rs
+
+const TABLE_SIZE: usize = 1000;

src/lookup/const_tables.rs

@@ -1,30 +1,4 @@
 // lookup/const_tables.rs
 
-use once_cell::sync::Lazy;
+include!("data/sin_f32.rs");
-use std::fs::read;
+include!("data/sin_f64.rs");
-use bincode::deserialize;
-use super::lookup_table::*;
-
-pub const SIN_LOOKUP_F32: Lazy<EndoSinLookupTable<f32>> = Lazy::new(|| {
-    deserialize(
-        &read("src/lookup/data/sin_f32.bin").expect("Failed to read sin_f64.bin")
-    ).expect("Failed to load SIN_LOOKUP_F32")
-});
-
-pub const SIN_LOOKUP_F64: Lazy<EndoSinLookupTable<f64>> = Lazy::new(|| {
-    deserialize(
-        &read("src/lookup/data/sin_f64.bin").expect("Failed to read sin_f32.bin")
-    ).expect("Failed to load SIN_LOOKUP_F64")
-});
-
-pub const COS_LOOKUP_F32: Lazy<EndoCosLookupTable<f32>> = Lazy::new(|| {
-    deserialize(
-        &read("src/lookup/data/cos_f32.bin").expect("Failed to read cos_f64.bin")
-    ).expect("Failed to load COS_LOOKUP_F32")
-});
-
-pub const COS_LOOKUP_F64: Lazy<EndoCosLookupTable<f64>> = Lazy::new(|| {
-    deserialize(
-        &read("src/lookup/data/cos_f64.bin").expect("Failed to read cos_f32.bin")
-    ).expect("Failed to load COS_LOOKUP_F64")
-});

src/lookup/lookup_table.rs

@@ -1,89 +1,153 @@
-use num_traits::sign::Signed;
+use std::f32::consts as f32_consts;
+use std::f64::consts as f64_consts;
 use num_traits::float::{Float, FloatConst};
-use num_traits::NumCast;
+use crate::lookup::TABLE_SIZE;
-use std::ops::{Sub, Rem};
+use crate::lookup::const_tables::*;
-use serde::{Serialize, Deserialize};
-// use packed_simd::f64x4;
 
-#[derive(Default, Debug, Serialize, Deserialize, Clone)]
+// This function should never be used in a non-const context.
+// It only exists as a workaround for the fact that const fn's cannot use iterators.
+const fn make_ordinal<T: Float>(
+    input: [T; TABLE_SIZE],
+    mut map_target: [FloatOrd<T>; TABLE_SIZE],
+) -> () {
+    // let mut map_target = [FloatOrd::<T>::new(); TABLE_SIZE];
+    let mut index = 0;
+    while index < TABLE_SIZE {
+        map_target[index] = FloatOrd(input[index]);
+        index += 1;
+    }
+}
+
+
+// The following macros are to minimise the amount of boilerplate for static types on the lookup tables.
+macro_rules! impl_fbitfbit_lookup_table {
+    ($key_type:ty, $value_type:ty) => {
+        impl FloatLookupTable<$key_type, $value_type> {
+            pub const fn new_const(keys: [$key_type; TABLE_SIZE], values: [$value_type; TABLE_SIZE]) -> Self {
+                let ord_keys: [FloatOrd<$key_type>; TABLE_SIZE] = [FloatOrd(0.0 as $key_type); TABLE_SIZE];
+                make_ordinal(keys, ord_keys);
+                FloatLookupTable {
+                    keys: ord_keys,
+                    values,
+                }
+            }
+        }
+    };
+}
+
+macro_rules! impl_cycling_fbitfbit_lookup_table {
+    ($key_type:ty, $value_type:ty) => {
+        impl CyclingFloatLookupTable<$key_type, $value_type> {
+            pub const fn new_const(keys: [$key_type; TABLE_SIZE], values: [$value_type; TABLE_SIZE], lower_bound: $key_type, upper_bound: $key_type) -> Self {
+                CyclingFloatLookupTable {
+                    lookup_table: FloatLookupTable::<$key_type, $value_type>::new_const(keys, values),
+                    lower_bound,
+                    upper_bound,
+                }
+            }
+        }
+    };
+}
+
+
+#[derive(Default, Debug,Clone, Copy, PartialEq,  PartialOrd)]
+pub struct FloatOrd<T: Float>(pub T);
+impl<T: Float> FloatOrd<T> {
+    pub fn new() -> Self {
+        FloatOrd(T::zero())
+    }
+}
+impl<T: Float> Eq for FloatOrd<T> {}
+impl<T: Float> Ord for FloatOrd<T> {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        self.partial_cmp(other).unwrap_or(std::cmp::Ordering::Equal)
+    }
+}
+
+
+#[derive(Debug, Clone)]
 pub struct FloatLookupTable<T1, T2>
-where T1: Float,
+where 
+    T1: Float,
     T2: Float,
 {
-    keys: Vec<T1>,
+    keys: [FloatOrd<T1>; TABLE_SIZE],
-    values: Vec<T2>,
+    values: [T2; TABLE_SIZE],
 }
 impl<T1, T2> FloatLookupTable<T1, T2>
-where T1: Float,
+where 
+    T1: Float,
     T2: Float,
 {
-    pub fn new(mut keys: Vec<T1>, mut values: Vec<T2>) -> Self {
+    pub fn new(keys: [T1; TABLE_SIZE], values: [T2; TABLE_SIZE]) -> Self {
-        let mut indices: Vec<_> = (0..keys.len()).collect();
+        FloatLookupTable {
-        indices.sort_by(|&i, &j| keys[i].partial_cmp(&keys[j]).unwrap());
+            keys: keys.map(|key| FloatOrd(key)),
-        for i in 0..keys.len() {
+            values,
-            while i != indices[i] {
-                let swap_index = indices[i];
-                keys.swap(i, swap_index);
-                values.swap(i, swap_index);
-                indices.swap(i, swap_index);
         }
     }
-        FloatLookupTable { keys, values }
-    }
 
-    #[allow(dead_code)]
+    pub fn get_next(&self, key: T1) -> T2 {
+        let ord_key = FloatOrd(key);
+        let mut lower_bound = 0;
+        let mut upper_bound = self.keys.len() - 1;
+        let mut mid = (lower_bound + upper_bound) / 2;
+        while upper_bound - lower_bound > 1 {
+            if self.keys[mid] < ord_key {
+                lower_bound = mid;
+            } else {
+                upper_bound = mid;
+            }
+            mid = (lower_bound + upper_bound) / 2;
+        }
+        self.values[mid]
+    }
+
     pub fn lookup(&self, key: T1) -> T2 {
-        match self.keys.binary_search_by(|probe| probe.partial_cmp(&key).unwrap()) {
+        self.get_next(key)
-            Ok(index) => self.values[index],
-            Err(index) => {
-                let upper_key = &self.keys[index];
-                let upper_val = &self.values[index];
-                let low_index = index - 1;
-                let lower_key = &self.keys[low_index];
-                let lower_val = &self.values[low_index];
-                // select nearest neighbour
-                let diff_upper = (key - *upper_key).abs();
-                let diff_lower = (key - *lower_key).abs();
-                let mask = diff_lower <= diff_upper;
-                (*lower_val * T2::from(mask as u8).expect("Failed to unwrap mask")) +
-                (*upper_val * T2::from(!mask as u8).expect("Failed to unwrap !mask"))
-            }
-        }
     }
 }
+impl_fbitfbit_lookup_table!(f32, f32);
+impl_fbitfbit_lookup_table!(f64, f64);
+impl_fbitfbit_lookup_table!(f32, f64);
+impl_fbitfbit_lookup_table!(f64, f32);
 
 
-#[derive(Default, Debug, Serialize, Deserialize, Clone)]
+#[derive(Debug, Clone)]
 pub struct CyclingFloatLookupTable<T1, T2>
-where T1: Float,
+where 
+    T1: Float,
     T2: Float,
 {
     lookup_table: FloatLookupTable<T1, T2>,
     lower_bound: T1,
     upper_bound: T1,
-    bound_range: T1,
 }
 impl<T1, T2> CyclingFloatLookupTable<T1, T2>
-where T1: Float,
+where
+    T1: Float,
     T2: Float,
 {
-    pub fn new(keys: Vec<T1>, values: Vec<T2>, lower_bound: T1, upper_bound: T1) -> Self {
+    pub fn new(keys: [T1; TABLE_SIZE], values: [T2; TABLE_SIZE], lower_bound: T1, upper_bound: T1) -> Self {
         CyclingFloatLookupTable {
             lookup_table: FloatLookupTable::new(keys, values),
-            lower_bound: lower_bound,
+            lower_bound,
-            upper_bound: upper_bound,
+            upper_bound,
-            bound_range: upper_bound - lower_bound,
         }
     }
 
     pub fn lookup(&self, key: T1) -> T2 {
-        let key = (key % self.bound_range) + self.lower_bound;
+        let key = (key % (self.upper_bound - self.lower_bound)) + self.lower_bound;
         self.lookup_table.lookup(key)
     }
 }
+impl_cycling_fbitfbit_lookup_table!(f32, f32);
+impl_cycling_fbitfbit_lookup_table!(f64, f64);
+impl_cycling_fbitfbit_lookup_table!(f32, f64);
+impl_cycling_fbitfbit_lookup_table!(f64, f32);
 
 
-#[derive(Default, Debug, Serialize, Deserialize, Clone)]
+
+#[derive(Debug, Clone)]
 pub struct EndoSinLookupTable<T>
 where
     T: Float + FloatConst,
@@ -94,22 +158,6 @@ impl<T> EndoSinLookupTable<T>
 where
     T: Float + FloatConst,
 {
-    pub fn new(precision: usize) -> Self {
-        let mut keys = Vec::with_capacity(precision);
-        let mut values = Vec::with_capacity(precision);
-        let upper_bound = T::PI();
-        let step = T::FRAC_PI_2() / <T as NumCast>::from(precision).unwrap();
-        for i in 0..precision+1 {
-            let key = step * <T as NumCast>::from(i).unwrap();
-            let value = key.sin();
-            keys.push(key);
-            values.push(value);
-        }
-        EndoSinLookupTable {
-            lookup_table: CyclingFloatLookupTable::new(keys, values, T::zero(), upper_bound),
-        }
-    }
-
     #[allow(dead_code)]
     pub fn lookup(&self, key: T) -> T {
         if key < T::zero() {
@@ -123,27 +171,57 @@ where
         }
     }
 }
+impl EndoSinLookupTable<f32>
+{
+    pub const fn new() -> Self {
+        const UPPER_BOUND: f32 = f32_consts::PI;
+
+        EndoSinLookupTable {
+            lookup_table: CyclingFloatLookupTable::<f32, f32>::new_const(SIN_F32_KEYS, SIN_F32_VALUES, 0.0f32, UPPER_BOUND),
+        }
+    }
+}
+impl EndoSinLookupTable<f64>
+{
+    pub const fn new() -> Self {
+        let upper_bound = f64_consts::PI;
+        
+        EndoSinLookupTable {
+            lookup_table: CyclingFloatLookupTable::<f64, f64>::new_const(SIN_F64_KEYS, SIN_F64_VALUES, 0.0f64, upper_bound),
+        }
+    }
+}
 
 
-#[derive(Default, Debug, Serialize, Deserialize, Clone)]
+#[derive(Debug, Clone)]
 pub struct EndoCosLookupTable<T>
 where
-    T: Float + FloatConst + Signed + Sub<Output = T> + Rem<Output = T> + NumCast + From<u8>,
+    T: Float + FloatConst,
 {
     lookup_table: EndoSinLookupTable<T>,
 }
 impl<T> EndoCosLookupTable<T>
 where
-    T: Float + FloatConst + Signed + Sub<Output = T> + Rem<Output = T> + NumCast + From<u8>,
+    T: Float + FloatConst + std::fmt::Debug,
 {
-    pub fn new(precision: usize) -> Self {
-        EndoCosLookupTable {
-            lookup_table: EndoSinLookupTable::new(precision),
-        }
-    }
-
     #[allow(dead_code)]
     pub fn lookup(&self, key: T) -> T {
         self.lookup_table.lookup(key + T::FRAC_PI_2())
     }
 }
+impl EndoCosLookupTable<f32>
+{
+    pub const fn new() -> Self {
+        EndoCosLookupTable {
+            lookup_table: EndoSinLookupTable::<f32>::new(),
+        }
+    }
+}
+impl EndoCosLookupTable<f64>
+{
+    pub const fn new() -> Self {
+        EndoCosLookupTable {
+            lookup_table: EndoSinLookupTable::<f64>::new(),
+        }
+    }
+}

src/lookup/mod.rs

@@ -2,3 +2,5 @@ mod const_tables;
 pub mod lookup_table;
 
 pub use const_tables::*;
+
+include!("config.rs");

src/main.rs

@@ -0,0 +1,12 @@
+use fastmath::LookupCos;
+
+fn main() {
+    let x = (-10000..10000)
+        .map(|a| (a as f64) / 1000.)
+        .collect::<Vec<f64>>();
+
+    let y = x.iter().map(|&x| x.lookup_cos()).collect::<Vec<f64>>();
+    
+    // to ensure the compiler doesn't optimize away the function call, we print the result
+    println!("{:?}", y);
+}

src/tests.rs

@@ -39,7 +39,7 @@ mod tests {
         fn pow2() -> Result<(), Box<dyn std::error::Error>> {
             let percentage_error = calculate_percentage_error(
                 &X.iter().map(|&x| x.fast_pow2()).collect::<Vec<f64>>(),
-                &X.iter().map(|&x| x.powi(2)).collect::<Vec<f64>>()
+                &X.iter().map(|&x| 2.0f64.powf(x)).collect::<Vec<f64>>()
             );
             assert!(!percentage_error.is_nan(), "fast_pow2<f64> percentage error is NaN");
             assert!(
@@ -77,6 +77,17 @@ mod tests {
                 "fast_cos<f64> percentage error: {0}",
                 percentage_error
             );
+            // lookup
+            let percentage_error = calculate_percentage_error(
+                &X.iter().map(|&x| x.lookup_cos()).collect::<Vec<f64>>(),
+                &X.iter().map(|&x| x.cos()).collect::<Vec<f64>>()
+            );
+            assert!(!percentage_error.is_nan(), "lookup_cos<f64> percentage error is NaN");
+            assert!(
+                percentage_error < TOLERANCE,
+                "lookup_cos<f64> percentage error: {0}",
+                percentage_error
+            );
             Ok(())
         }
 
@@ -114,7 +125,7 @@ mod tests {
             assert!(
                 calculate_percentage_error(
                     &X.iter().map(|&x| x.fast_pow2()).collect::<Vec<f32>>(),
-                    &X.iter().map(|&x| x.powi(2)).collect::<Vec<f32>>()
+                    &X.iter().map(|&x| 2.0f32.powf(x)).collect::<Vec<f32>>()
                 ) < TOLERANCE
             );
             Ok(())
@@ -139,6 +150,13 @@ mod tests {
                     &X.iter().map(|&x| x.cos()).collect::<Vec<f32>>()
                 ) < TOLERANCE
             );
+            // lookup
+            assert!(
+                calculate_percentage_error(
+                    &X.iter().map(|&x| x.lookup_cos()).collect::<Vec<f32>>(),
+                    &X.iter().map(|&x| x.cos()).collect::<Vec<f32>>()
+                ) < TOLERANCE
+            );
             Ok(())
         }