diff --git a/.gitignore b/.gitignore index b169044..cc3aa71 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,8 @@ -/target -/.vscode -/tmp +Cargo.lock +debug/ +target/ +**/*.rs.bk +*.pdb +.vscode/ +tmp/ *.ipynb \ No newline at end of file diff --git a/Cargo.lock b/Cargo.lock index f2e7446..cd1cf0c 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -120,6 +120,17 @@ version = "0.5.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "2da6da31387c7e4ef160ffab6d5e7f00c42626fe39aea70a7b0f1773f7dd6c1b" +[[package]] +name = "colored" +version = "2.0.4" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "2674ec482fbc38012cf31e6c42ba0177b431a0cb6f15fe40efa5aab1bda516f6" +dependencies = [ + "is-terminal", + "lazy_static", + "windows-sys 0.48.0", +] + [[package]] name = "criterion" version = "0.5.1" @@ -213,7 +224,7 @@ checksum = "4bcfec3a70f97c962c307b2d2c56e358cf1d00b558d74262b5f929ee8cc7e73a" dependencies = [ "errno-dragonfly", "libc", - "windows-sys", + "windows-sys 0.48.0", ] [[package]] @@ -232,9 +243,12 @@ version = "0.1.0" dependencies = [ "bincode", "criterion", + "log", "num-traits", "once_cell", "serde", + "serde_json", + "simple_logger", ] [[package]] @@ -257,7 +271,7 @@ checksum = "cb0889898416213fab133e1d33a0e5858a48177452750691bde3666d0fdbaf8b" dependencies = [ "hermit-abi", "rustix", - "windows-sys", + "windows-sys 0.48.0", ] [[package]] @@ -284,6 +298,12 @@ dependencies = [ "wasm-bindgen", ] +[[package]] +name = "lazy_static" +version = "1.4.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "e2abad23fbc42b3700f2f279844dc832adb2b2eb069b2df918f455c4e18cc646" + [[package]] name = "libc" version = "0.2.147" @@ -336,6 +356,15 @@ dependencies = [ "libc", ] +[[package]] +name = "num_threads" +version = "0.1.6" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "2819ce041d2ee131036f4fc9d6ae7ae125a3a40e97ba64d04fe799ad9dabbb44" +dependencies = [ + "libc", +] + [[package]] name = "once_cell" version = "1.18.0" @@ -455,7 +484,7 @@ dependencies = [ "errno", "libc", "linux-raw-sys", - "windows-sys", + "windows-sys 0.48.0", ] [[package]] @@ -501,15 +530,27 @@ dependencies = [ [[package]] name = "serde_json" -version = "1.0.103" +version = "1.0.106" source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "d03b412469450d4404fe8499a268edd7f8b79fecb074b0d812ad64ca21f4031b" +checksum = "2cc66a619ed80bf7a0f6b17dd063a84b88f6dea1813737cf469aef1d081142c2" dependencies = [ "itoa", "ryu", "serde", ] +[[package]] +name = "simple_logger" +version = "4.2.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "2230cd5c29b815c9b699fb610b49a5ed65588f3509d9f0108be3a885da629333" +dependencies = [ + "colored", + "log", + "time", + "windows-sys 0.42.0", +] + [[package]] name = "syn" version = "2.0.26" @@ -521,6 +562,35 @@ dependencies = [ "unicode-ident", ] +[[package]] +name = "time" +version = "0.3.23" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "59e399c068f43a5d116fedaf73b203fa4f9c519f17e2b34f63221d3792f81446" +dependencies = [ + "itoa", + "libc", + "num_threads", + "serde", + "time-core", + "time-macros", +] + +[[package]] +name = "time-core" +version = "0.1.1" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "7300fbefb4dadc1af235a9cef3737cea692a9d97e1b9cbcd4ebdae6f8868e6fb" + +[[package]] +name = "time-macros" +version = "0.2.10" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "96ba15a897f3c86766b757e5ac7221554c6750054d74d5b28844fce5fb36a6c4" +dependencies = [ + "time-core", +] + [[package]] name = "tinytemplate" version = "1.2.1" @@ -642,6 +712,21 @@ version = "0.4.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f" +[[package]] +name = "windows-sys" +version = "0.42.0" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "5a3e1820f08b8513f676f7ab6c1f99ff312fb97b553d30ff4dd86f9f15728aa7" +dependencies = [ + "windows_aarch64_gnullvm 0.42.2", + "windows_aarch64_msvc 0.42.2", + "windows_i686_gnu 0.42.2", + "windows_i686_msvc 0.42.2", + "windows_x86_64_gnu 0.42.2", + "windows_x86_64_gnullvm 0.42.2", + "windows_x86_64_msvc 0.42.2", +] + [[package]] name = "windows-sys" version = "0.48.0" @@ -657,51 +742,93 @@ version = "0.48.1" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "05d4b17490f70499f20b9e791dcf6a299785ce8af4d709018206dc5b4953e95f" dependencies = [ - "windows_aarch64_gnullvm", - "windows_aarch64_msvc", - "windows_i686_gnu", - "windows_i686_msvc", - "windows_x86_64_gnu", - "windows_x86_64_gnullvm", - "windows_x86_64_msvc", + "windows_aarch64_gnullvm 0.48.0", + "windows_aarch64_msvc 0.48.0", + "windows_i686_gnu 0.48.0", + "windows_i686_msvc 0.48.0", + "windows_x86_64_gnu 0.48.0", + "windows_x86_64_gnullvm 0.48.0", + "windows_x86_64_msvc 0.48.0", ] +[[package]] +name = "windows_aarch64_gnullvm" +version = "0.42.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "597a5118570b68bc08d8d59125332c54f1ba9d9adeedeef5b99b02ba2b0698f8" + [[package]] name = "windows_aarch64_gnullvm" version = "0.48.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "91ae572e1b79dba883e0d315474df7305d12f569b400fcf90581b06062f7e1bc" +[[package]] +name = "windows_aarch64_msvc" +version = "0.42.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "e08e8864a60f06ef0d0ff4ba04124db8b0fb3be5776a5cd47641e942e58c4d43" + [[package]] name = "windows_aarch64_msvc" version = "0.48.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "b2ef27e0d7bdfcfc7b868b317c1d32c641a6fe4629c171b8928c7b08d98d7cf3" +[[package]] +name = "windows_i686_gnu" +version = "0.42.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "c61d927d8da41da96a81f029489353e68739737d3beca43145c8afec9a31a84f" + [[package]] name = "windows_i686_gnu" version = "0.48.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "622a1962a7db830d6fd0a69683c80a18fda201879f0f447f065a3b7467daa241" +[[package]] +name = "windows_i686_msvc" +version = "0.42.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "44d840b6ec649f480a41c8d80f9c65108b92d89345dd94027bfe06ac444d1060" + [[package]] name = "windows_i686_msvc" version = "0.48.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "4542c6e364ce21bf45d69fdd2a8e455fa38d316158cfd43b3ac1c5b1b19f8e00" +[[package]] +name = "windows_x86_64_gnu" +version = "0.42.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "8de912b8b8feb55c064867cf047dda097f92d51efad5b491dfb98f6bbb70cb36" + [[package]] name = "windows_x86_64_gnu" version = "0.48.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "ca2b8a661f7628cbd23440e50b05d705db3686f894fc9580820623656af974b1" +[[package]] +name = "windows_x86_64_gnullvm" +version = "0.42.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "26d41b46a36d453748aedef1486d5c7a85db22e56aff34643984ea85514e94a3" + [[package]] name = "windows_x86_64_gnullvm" version = "0.48.0" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "7896dbc1f41e08872e9d5e8f8baa8fdd2677f29468c4e156210174edc7f7b953" +[[package]] +name = "windows_x86_64_msvc" +version = "0.42.2" +source = "registry+https://github.com/rust-lang/crates.io-index" +checksum = "9aec5da331524158c6d1a4ac0ab1541149c0b9505fde06423b02f5ef0106b9f0" + [[package]] name = "windows_x86_64_msvc" version = "0.48.0" diff --git a/Cargo.toml b/Cargo.toml index 53b4b0f..b4e2354 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -7,9 +7,11 @@ edition = "2021" [dependencies] bincode = "1.3.3" +log = "0.4.19" num-traits = "0.2.15" once_cell = "1.18.0" serde = {version = "1.0.171", features = ["derive"] } +simple_logger = "4.2.0" [build-dependencies] bincode = "1.3.3" @@ -26,5 +28,11 @@ bench = true name = "bench" harness = false +[[bench]] +name = "devbench" +harness = false + [dev-dependencies] criterion = "0.5.1" +serde = "1.0.171" +serde_json = "1.0.106" diff --git a/benches/bench.rs b/benches/bench.rs index afd7e1c..a9a3cab 100644 --- a/benches/bench.rs +++ b/benches/bench.rs @@ -5,18 +5,23 @@ use fastmath::*; use criterion::{Criterion, BenchmarkGroup, measurement::WallTime}; use criterion::{black_box, criterion_group, criterion_main}; +pub mod exact { + include!("../src/tests/accuracy/exact.rs"); +} +include!("../src/tests/accuracy/x.rs"); + fn pow2_benchmarks(group: &mut BenchmarkGroup, x_f64: &[f64], x_f32: &[f32]) { group.bench_function("f64_fast", |b| { b.iter(|| x_f64.iter().map(|&x| black_box(x).fast_pow2()).collect::>()) }); group.bench_function("f64_builtin_fn", |b| { - b.iter(|| x_f64.iter().map(|&x| 2.0f64.powf(black_box(x))).collect::>()) + b.iter(|| x_f64.iter().map(|&x| exact::f64::pow2(black_box(x))).collect::>()) }); group.bench_function("f32_fast", |b| { b.iter(|| x_f32.iter().map(|&x| black_box(x).fast_pow2()).collect::>()) }); group.bench_function("f32_builtin_fn", |b| { - b.iter(|| x_f32.iter().map(|&x| 2.0f32.powf(black_box(x))).collect::>()) + b.iter(|| x_f32.iter().map(|&x| exact::f32::pow2(black_box(x))).collect::>()) }); } @@ -25,13 +30,13 @@ fn exp_benchmarks(group: &mut BenchmarkGroup, x_f64: &[f64], x_f32: &[ b.iter(|| x_f64.iter().map(|&x| black_box(x).fast_exp()).collect::>()) }); group.bench_function("f64_builtin", |b| { - b.iter(|| x_f64.iter().map(|&x| black_box(x).exp()).collect::>()) + b.iter(|| x_f64.iter().map(|&x| exact::f64::exp(black_box(x))).collect::>()) }); group.bench_function("f32_fast", |b| { b.iter(|| x_f32.iter().map(|&x| black_box(x).fast_exp()).collect::>()) }); group.bench_function("f32_builtin", |b| { - b.iter(|| x_f32.iter().map(|&x| black_box(x).exp()).collect::>()) + b.iter(|| x_f32.iter().map(|&x| exact::f32::exp(black_box(x))).collect::>()) }); } @@ -43,7 +48,7 @@ fn cos_benchmarks(group: &mut BenchmarkGroup, x_f64: &[f64], x_f32: &[ b.iter(|| x_f64.iter().map(|&x| black_box(x).lookup_cos()).collect::>()) }); group.bench_function("f64_builtin", |b| { - b.iter(|| x_f64.iter().map(|&x| black_box(x).cos()).collect::>()) + b.iter(|| x_f64.iter().map(|&x| exact::f64::cos(black_box(x))).collect::>()) }); group.bench_function("f32_fast", |b| { b.iter(|| x_f32.iter().map(|&x| black_box(x).fast_cos()).collect::>()) @@ -52,7 +57,7 @@ fn cos_benchmarks(group: &mut BenchmarkGroup, x_f64: &[f64], x_f32: &[ b.iter(|| x_f32.iter().map(|&x| black_box(x).lookup_cos()).collect::>()) }); group.bench_function("f32_builtin", |b| { - b.iter(|| x_f32.iter().map(|&x| black_box(x).cos()).collect::>()) + b.iter(|| x_f32.iter().map(|&x| exact::f32::cos(black_box(x))).collect::>()) }); } @@ -61,42 +66,35 @@ fn sigmoid_benchmarks(group: &mut BenchmarkGroup, x_f64: &[f64], x_f32 b.iter(|| x_f64.iter().map(|&x| black_box(x).fast_sigmoid()).collect::>()) }); group.bench_function("f64_builtin", |b| { - b.iter(|| x_f64.iter().map(|&x| sigmoid_builtin_f64(black_box(x))).collect::>()) + b.iter(|| x_f64.iter().map(|&x| exact::f64::sigmoid(black_box(x))).collect::>()) }); group.bench_function("f32_fast", |b| { b.iter(|| x_f32.iter().map(|&x| black_box(x).fast_sigmoid()).collect::>()) }); group.bench_function("f32_builtin", |b| { - b.iter(|| x_f32.iter().map(|&x| sigmoid_builtin_f32(black_box(x))).collect::>()) + b.iter(|| x_f32.iter().map(|&x| exact::f32::sigmoid(black_box(x))).collect::>()) }); } fn criterion_benchmark(c: &mut Criterion) { - // Prepare x values for testing functions - let x_f64 = (-10000..10000) - .map(|a| (a as f64) / 1000.) - .collect::>(); - let x_f32 = (-10000..10000) - .map(|a| (a as f32) / 1000.) - .collect::>(); // to ensure tests are fair, we need to instantiate the lookup tables 1.0f64.lookup_cos(); 1.0f32.lookup_cos(); // Then, tests can begin let mut group = c.benchmark_group("pow2"); - pow2_benchmarks(&mut group, &x_f64, &x_f32); + pow2_benchmarks(&mut group, &X_F64, &X_F32); group.finish(); let mut group = c.benchmark_group("exp"); - exp_benchmarks(&mut group, &x_f64, &x_f32); + exp_benchmarks(&mut group, &X_F64, &X_F32); group.finish(); let mut group = c.benchmark_group("cos"); - cos_benchmarks(&mut group, &x_f64, &x_f32); + cos_benchmarks(&mut group, &X_F64, &X_F32); group.finish(); let mut group = c.benchmark_group("sigmoid"); - sigmoid_benchmarks(&mut group, &x_f64, &x_f32); + sigmoid_benchmarks(&mut group, &X_F64, &X_F32); group.finish(); } diff --git a/benches/devbench.rs b/benches/devbench.rs new file mode 100644 index 0000000..867170a --- /dev/null +++ b/benches/devbench.rs @@ -0,0 +1,46 @@ +#![allow(dead_code, unused_imports)] + +extern crate fastmath; + +use fastmath::*; +use criterion::{Criterion, BenchmarkGroup, measurement::WallTime}; +use criterion::{black_box, criterion_group, criterion_main}; +use std::f32::consts as f32_consts; +use std::f64::consts as f64_consts; + +pub mod exact { + include!("../src/tests/accuracy/exact.rs"); +} +include!("../src/tests/accuracy/x.rs"); + +fn dev_cos(x: f64) -> f64 { + const ONE: f64 = 1.0; + let v = ((((x + f64_consts::PI).abs()) % f64_consts::TAU) - f64_consts::PI).abs(); + let qpprox = ONE - f64_consts::FRAC_2_PI * v; + qpprox + f64_consts::FRAC_PI_6 * qpprox * (ONE - qpprox * qpprox) +} + +fn devbench(group: &mut BenchmarkGroup) { + group.bench_function("dev_cos", |b| { + b.iter(|| X_F64.iter().map(|&x| dev_cos(black_box(x))).collect::>()) + }); + group.bench_function("fast_cos", |b| { + b.iter(|| X_F64.iter().map(|&x| black_box(x).fast_cos()).collect::>()) + }); + group.bench_function("lookup_cos", |b| { + b.iter(|| X_F64.iter().map(|&x| black_box(x).lookup_cos()).collect::>()) + }); + group.bench_function("builtin_cos", |b| { + b.iter(|| X_F64.iter().map(|&x| exact::f64::cos(black_box(x))).collect::>()) + }); +} + +fn criterion_benchmark(c: &mut Criterion) { + // Then, tests can begin + let mut group = c.benchmark_group("devbench"); + devbench(&mut group); + group.finish(); +} + +criterion_group!(devbenches, criterion_benchmark); +criterion_main!(devbenches); \ No newline at end of file diff --git a/build.rs b/build.rs index 5c9a350..5527aec 100644 --- a/build.rs +++ b/build.rs @@ -6,126 +6,39 @@ mod precalculate_lookup_tables { use std::fs::{create_dir_all, File}; use std::io::Write; include!("src/lookup/config.rs"); - // use bincode::serialize; - - // fn precalculate_sin_tables() -> Result<(), Box> { - // let data = serialize(&EndoSinLookupTable::::new(PRECISION))?; - // let mut file = File::create("src/lookup/data/sin_f32.bin")?; - // file.write_all(&data)?; - - // let data = serialize(&EndoSinLookupTable::::new(PRECISION))?; - // let mut file = File::create("src/lookup/data/sin_f64.bin")?; - // file.write_all(&data)?; - - // Ok(()) - // } - - // fn precalculate_cos_tables() -> Result<(), Box> { - // let data = serialize(&EndoCosLookupTable::::new(PRECISION))?; - // let mut file = File::create("src/lookup/data/cos_f32.bin")?; - // file.write_all(&data)?; - - // let data = serialize(&EndoCosLookupTable::::new(PRECISION))?; - // let mut file = File::create("src/lookup/data/cos_f64.bin")?; - // file.write_all(&data)?; - - // Ok(()) - // } - - // fn precalculate_sin_tables() -> Result<(), Box> { - // 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::>().try_into().unwrap_or([0.0f32; TABLE_SIZE]); - // let values: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { - // (step * (i as f32)).sin() - // }).collect::>().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::>().try_into().unwrap_or([0.0f64; TABLE_SIZE]); - // let values: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { - // (step * (i as f64)).sin() - // }).collect::>().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(()) - // } + include!("src/lookup/ordinal_float.rs"); 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::>().try_into().unwrap_or([0.0f32; TABLE_SIZE]); + let keys: [FloatOrd; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { + FloatOrd( (step * (i as f32)) - half_step ) + }).collect::>>().try_into().unwrap_or([FloatOrd::new(); TABLE_SIZE]); let values: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { (step * (i as f32)).sin() }).collect::>().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 data = format!("pub(crate) const SIN_F32_KEYS: [FloatOrd; {}] = {:?};\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 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::>().try_into().unwrap_or([0.0f64; TABLE_SIZE]); + let keys: [FloatOrd; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { + FloatOrd( (step * (i as f64)) - half_step ) + }).collect::>>().try_into().unwrap_or([FloatOrd::new(); TABLE_SIZE]); let values: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { (step * (i as f64)).sin() }).collect::>().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 data = format!("pub const SIN_F64_KEYS: [FloatOrd; {}] = {:?};\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"); + let mut file = File::create("src/lookup/data/sin_f64.rs")?; + file.write_all(data.as_bytes())?; }}; } - // fn precalculate_sin_tables() -> Result<(), Box> { - // 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::>().try_into().unwrap_or([0.0f32; TABLE_SIZE]); - // let values: [f32; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { - // (step * (i as f32)).sin() - // }).collect::>().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::>().try_into().unwrap_or([0.0f64; TABLE_SIZE]); - // let values: [f64; TABLE_SIZE] = (0..TABLE_SIZE).map(|i| { - // (step * (i as f64)).sin() - // }).collect::>().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> { create_dir_all("src/lookup/data")?; @@ -137,8 +50,49 @@ mod precalculate_lookup_tables { } } +mod precalculate_test_tables { + use std::fs::{create_dir_all, File}; + use std::io::Write; + include!("src/tests/accuracy/config.rs"); + + macro_rules! precalculate_test_tables { + () => {{ + let scaling: f32 = X_SIZE as f32 / (X_MAX as f32 - X_MIN as f32); + let x_f32: [f32; X_SIZE] = + (0..X_SIZE) + .map(|a| ((a as f32) / scaling) + X_MIN as f32) + .collect::>() + .try_into().map_err(|_| "Failed to convert Vec to [f32; X_SIZE]")?; + + let scaling: f64 = X_SIZE as f64 / (X_MAX as f64 - X_MIN as f64); + let x_f64: [f64; X_SIZE] = + (0..X_SIZE) + .map(|a| ((a as f64) / scaling) + X_MIN as f64) + .collect::>() + .try_into().map_err(|_| "Failed to convert Vec to [f64; X_SIZE]")?; + + let data = format!( + "#[cfg(test)]\n#[allow(dead_code)]\npub const X_F32: [f32; {}] = {:?};\n#[cfg(test)]\n#[allow(dead_code)]\npub const X_F64: [f64; {}] = {:?};", + X_SIZE, x_f32, X_SIZE, x_f64 + ); + + let mut file = File::create("src/tests/accuracy/x.rs")?; + file.write_all(data.as_bytes())?; + }}; + } + + pub fn generate() -> Result<(), Box> { + create_dir_all("src/tests/accuracy")?; + + precalculate_test_tables!(); + + Ok(()) + } +} + fn main() -> Result<(), Box> { precalculate_lookup_tables::generate()?; + precalculate_test_tables::generate()?; Ok(()) } \ No newline at end of file diff --git a/src/bit_magic.rs b/src/bit_magic.rs new file mode 100644 index 0000000..1b3f3b2 --- /dev/null +++ b/src/bit_magic.rs @@ -0,0 +1,73 @@ +fn bool_to_full_byte(b: bool) -> T +where + T: WrappingSub + One + From + std::ops::Not, + +{ + !( + ( T::from( unsafe { std::mem::transmute::(b) } ) ) + .wrapping_sub(&T::one()) + ) +} + +pub trait AndBool { + fn and(self: Self, b: bool) -> Self; +} +impl AndBool for f32 { + fn and(self: f32, b: bool) -> f32 { + let b_byte: u32 = bool_to_full_byte(b); + unsafe { + std::mem::transmute( + std::mem::transmute::(self) & b_byte + ) + } + } +} +impl AndBool for f64 { + fn and(self: f64, b: bool) -> f64 { + let b_byte: u64 = bool_to_full_byte(b); + unsafe { + std::mem::transmute( + std::mem::transmute::(self) & b_byte + ) + } + } +} + + +pub trait GetSign { + fn sign(self: Self) -> Self; +} +impl GetSign for f32 { + fn sign(self: f32) -> f32 { + let x_bytes: [u8; 4] = unsafe { std::mem::transmute(self) }; + unsafe { + std::mem::transmute( + [ + 0u8, + 0u8, + 128u8, + (x_bytes[3] & 128u8) | 63u8, + ] + ) + } + } +} +impl GetSign for f64 { + fn sign(self: f64) -> f64 { + let x_bytes: [u8; 8] = unsafe { std::mem::transmute(self) }; + unsafe { + std::mem::transmute( + [ + 0u8, + 0u8, + 0u8, + 0u8, + 0u8, + 0u8, + 240u8, + (x_bytes[7] & 128u8) | 63u8, + ] + ) + } + } +} \ No newline at end of file diff --git a/src/fastmath.rs b/src/fastmath.rs index 2c7e14d..00e7087 100644 --- a/src/fastmath.rs +++ b/src/fastmath.rs @@ -1,12 +1,13 @@ //! A collection of fast (often approximate) mathematical functions for accelerating mathematical functions -// Optimisation note: lookup tables become faster when calculation takes > ~1ms +// Optimisation note: lookup tables become faster when calculation takes > ~400us use std::f32::consts as f32_consts; use std::f64::consts as f64_consts; -// use crate::lookup::*; -use crate::lookup::lookup_table::EndoCosLookupTable; +use crate::lookup::{EndoCosLookupTable, EndoSinLookupTable}; +const SIN_LOOKUP_F32: EndoSinLookupTable = EndoSinLookupTable::::new(); +const SIN_LOOKUP_F64: EndoSinLookupTable = EndoSinLookupTable::::new(); const COS_LOOKUP_F32: EndoCosLookupTable = EndoCosLookupTable::::new(); const COS_LOOKUP_F64: EndoCosLookupTable = EndoCosLookupTable::::new(); @@ -18,6 +19,25 @@ 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 LookupSin { + fn lookup_sin(self: Self) -> Self; +} +impl LookupSin for f64 { + #[inline] + fn lookup_sin(self: Self) -> f64 { + // Look up the value in the table + SIN_LOOKUP_F64.lookup(self) + } +} +impl LookupSin for f32 { + #[inline] + fn lookup_sin(self: Self) -> f32 { + // Look up the value in the table + SIN_LOOKUP_F32.lookup(self) + } +} + + pub trait LookupCos { fn lookup_cos(self: Self) -> Self; } @@ -118,15 +138,4 @@ impl FastSigmoid for f64 { const ONE: f64 = 1.0; (ONE + (-self).fast_exp()).recip() } -} - -// functions for testing the accuracy of fast functions against builtin functions -#[inline] -pub fn sigmoid_builtin_f32(p: f32) -> f32 { - (1. + (-p).exp()).recip() -} - -#[inline] -pub fn sigmoid_builtin_f64(p: f64) -> f64 { - (1. + (-p).exp()).recip() -} +} \ No newline at end of file diff --git a/src/lib.rs b/src/lib.rs index 7427728..bfa4506 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -2,9 +2,10 @@ #![allow(unused_imports)] pub mod lookup; -mod fastmath; +pub mod macros; +mod fastmath; pub use fastmath::*; #[cfg(test)] -mod tests; \ No newline at end of file +pub(crate) mod tests; \ No newline at end of file diff --git a/src/lookup/const_tables.rs b/src/lookup/const_tables.rs index 7369580..d6ff4a8 100644 --- a/src/lookup/const_tables.rs +++ b/src/lookup/const_tables.rs @@ -1,4 +1,5 @@ // lookup/const_tables.rs +use crate::lookup::ordinal_float::FloatOrd; include!("data/sin_f32.rs"); include!("data/sin_f64.rs"); \ No newline at end of file diff --git a/src/lookup/data/sin_f32.rs b/src/lookup/data/sin_f32.rs index 237a898..a39b429 100644 --- a/src/lookup/data/sin_f32.rs +++ b/src/lookup/data/sin_f32.rs @@ -1,2 +1,2 @@ -pub const SIN_F32_KEYS: [f32; 1000] = [-0.0007853982, 0.0007853982, 0.0023561944, 0.0039269906, 0.005497787, 0.0070685837, 0.008639379, 0.010210176, 0.011780973, 0.013351769, 0.014922566, 0.016493363, 0.018064158, 0.019634955, 0.021205751, 0.022776548, 0.024347344, 0.025918141, 0.027488938, 0.029059734, 0.03063053, 0.032201324, 0.033772122, 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1.4129313, 1.4145021, 1.416073, 1.4176438, 1.4192146, 1.4207853, 1.4223561, 1.423927, 1.4254978, 1.4270686, 1.4286393, 1.4302101, 1.4317809, 1.4333518, 1.4349226, 1.4364933, 1.4380641, 1.4396349, 1.4412057, 1.4427766, 1.4443473, 1.4459181, 1.4474889, 1.4490597, 1.4506305, 1.4522012, 1.4537721, 1.4553429, 1.4569137, 1.4584844, 1.4600552, 1.461626, 1.4631969, 1.4647677, 1.4663384, 1.4679092, 1.46948, 1.4710509, 1.4726217, 1.4741924, 1.4757632, 1.477334, 1.4789048, 1.4804757, 1.4820464, 1.4836172, 1.485188, 1.4867588, 1.4883296, 1.4899004, 1.4914712, 1.493042, 1.4946128, 1.4961836, 1.4977543, 1.4993252, 1.500896, 1.5024668, 1.5040376, 1.5056083, 1.5071791, 1.50875, 1.5103208, 1.5118916, 1.5134623, 1.5150331, 1.516604, 1.5181748, 1.5197455, 1.5213163, 1.5228871, 1.5244579, 1.5260288, 1.5275995, 1.5291703, 1.5307411, 1.5323119, 1.5338827, 1.5354534, 1.5370243, 1.5385951, 1.5401659, 1.5417367, 1.5433074, 1.5448782, 1.5464491, 1.5480199, 1.5495907, 1.5511614, 1.5527322, 1.554303, 1.5558739, 1.5574447, 1.5590154, 1.5605862, 1.562157, 1.5637279, 1.5652987, 1.5668694, 1.5684402]; +pub(crate) const SIN_F32_KEYS: [FloatOrd; 1000] = [FloatOrd(-0.0007853982), FloatOrd(0.0007853982), FloatOrd(0.0023561944), FloatOrd(0.0039269906), FloatOrd(0.005497787), FloatOrd(0.0070685837), FloatOrd(0.008639379), FloatOrd(0.010210176), FloatOrd(0.011780973), FloatOrd(0.013351769), FloatOrd(0.014922566), FloatOrd(0.016493363), FloatOrd(0.018064158), FloatOrd(0.019634955), FloatOrd(0.021205751), FloatOrd(0.022776548), FloatOrd(0.024347344), FloatOrd(0.025918141), FloatOrd(0.027488938), FloatOrd(0.029059734), FloatOrd(0.03063053), FloatOrd(0.032201324), FloatOrd(0.033772122), FloatOrd(0.035342917), FloatOrd(0.03691371), FloatOrd(0.03848451), FloatOrd(0.040055305), FloatOrd(0.041626103), FloatOrd(0.043196898), FloatOrd(0.044767696), FloatOrd(0.04633849), FloatOrd(0.04790929), FloatOrd(0.049480084), FloatOrd(0.05105088), FloatOrd(0.052621678), FloatOrd(0.054192472), FloatOrd(0.05576327), FloatOrd(0.057334065), FloatOrd(0.058904864), FloatOrd(0.06047566), FloatOrd(0.062046457), FloatOrd(0.06361725), FloatOrd(0.06518805), FloatOrd(0.06675885), FloatOrd(0.06832965), FloatOrd(0.06990044), FloatOrd(0.07147124), FloatOrd(0.073042035), FloatOrd(0.074612826), FloatOrd(0.076183625), FloatOrd(0.07775442), FloatOrd(0.07932522), FloatOrd(0.08089601), FloatOrd(0.08246681), FloatOrd(0.08403761), FloatOrd(0.08560841), FloatOrd(0.0871792), FloatOrd(0.08875), FloatOrd(0.090320796), FloatOrd(0.09189159), FloatOrd(0.093462385), FloatOrd(0.09503318), FloatOrd(0.09660398), FloatOrd(0.09817477), FloatOrd(0.09974557), FloatOrd(0.10131637), FloatOrd(0.10288716), FloatOrd(0.10445796), FloatOrd(0.10602876), FloatOrd(0.10759956), FloatOrd(0.10917035), FloatOrd(0.110741146), FloatOrd(0.112311944), FloatOrd(0.113882735), FloatOrd(0.115453534), FloatOrd(0.11702433), FloatOrd(0.11859513), FloatOrd(0.12016592), FloatOrd(0.12173672), FloatOrd(0.12330752), FloatOrd(0.12487832), FloatOrd(0.12644911), FloatOrd(0.1280199), FloatOrd(0.1295907), FloatOrd(0.1311615), FloatOrd(0.1327323), FloatOrd(0.1343031), FloatOrd(0.13587388), FloatOrd(0.13744469), FloatOrd(0.13901548), FloatOrd(0.14058627), FloatOrd(0.14215708), FloatOrd(0.14372787), FloatOrd(0.14529866), FloatOrd(0.14686947), FloatOrd(0.14844026), FloatOrd(0.15001105), FloatOrd(0.15158185), FloatOrd(0.15315264), FloatOrd(0.15472345), FloatOrd(0.15629424), FloatOrd(0.15786503), FloatOrd(0.15943584), FloatOrd(0.16100663), FloatOrd(0.16257742), FloatOrd(0.16414823), FloatOrd(0.16571902), FloatOrd(0.16728981), FloatOrd(0.16886061), FloatOrd(0.1704314), FloatOrd(0.17200221), FloatOrd(0.173573), FloatOrd(0.1751438), FloatOrd(0.1767146), FloatOrd(0.17828539), FloatOrd(0.17985618), FloatOrd(0.18142699), FloatOrd(0.18299778), FloatOrd(0.18456857), FloatOrd(0.18613937), FloatOrd(0.18771017), FloatOrd(0.18928096), FloatOrd(0.19085176), FloatOrd(0.19242255), FloatOrd(0.19399336), FloatOrd(0.19556415), FloatOrd(0.19713494), FloatOrd(0.19870575), FloatOrd(0.20027654), FloatOrd(0.20184733), FloatOrd(0.20341814), FloatOrd(0.20498893), FloatOrd(0.20655972), FloatOrd(0.20813052), FloatOrd(0.20970131), FloatOrd(0.21127212), FloatOrd(0.21284291), FloatOrd(0.2144137), FloatOrd(0.21598451), FloatOrd(0.2175553), FloatOrd(0.21912609), FloatOrd(0.2206969), FloatOrd(0.22226769), FloatOrd(0.22383848), FloatOrd(0.22540928), FloatOrd(0.22698008), FloatOrd(0.22855087), FloatOrd(0.23012167), FloatOrd(0.23169246), FloatOrd(0.23326327), FloatOrd(0.23483406), FloatOrd(0.23640485), FloatOrd(0.23797566), FloatOrd(0.23954645), FloatOrd(0.24111724), FloatOrd(0.24268804), FloatOrd(0.24425884), FloatOrd(0.24582963), FloatOrd(0.24740043), FloatOrd(0.24897122), FloatOrd(0.250542), FloatOrd(0.2521128), FloatOrd(0.2536836), FloatOrd(0.2552544), FloatOrd(0.25682518), FloatOrd(0.258396), FloatOrd(0.2599668), FloatOrd(0.26153758), FloatOrd(0.26310837), FloatOrd(0.26467916), FloatOrd(0.26624998), FloatOrd(0.26782078), FloatOrd(0.26939157), FloatOrd(0.27096236), FloatOrd(0.27253315), FloatOrd(0.27410394), FloatOrd(0.27567476), FloatOrd(0.27724555), FloatOrd(0.27881634), FloatOrd(0.28038713), FloatOrd(0.28195792), FloatOrd(0.28352875), FloatOrd(0.28509954), FloatOrd(0.28667033), FloatOrd(0.28824112), FloatOrd(0.2898119), FloatOrd(0.2913827), FloatOrd(0.29295352), FloatOrd(0.2945243), FloatOrd(0.2960951), FloatOrd(0.2976659), FloatOrd(0.29923669), FloatOrd(0.30080748), FloatOrd(0.3023783), FloatOrd(0.3039491), FloatOrd(0.30551988), FloatOrd(0.30709067), FloatOrd(0.30866146), FloatOrd(0.31023228), FloatOrd(0.31180307), FloatOrd(0.31337386), FloatOrd(0.31494465), FloatOrd(0.31651545), FloatOrd(0.31808624), FloatOrd(0.31965706), FloatOrd(0.32122785), FloatOrd(0.32279864), FloatOrd(0.32436943), FloatOrd(0.32594022), FloatOrd(0.32751104), FloatOrd(0.32908183), FloatOrd(0.33065262), FloatOrd(0.33222342), FloatOrd(0.3337942), FloatOrd(0.335365), FloatOrd(0.33693582), FloatOrd(0.3385066), FloatOrd(0.3400774), FloatOrd(0.3416482), FloatOrd(0.34321898), FloatOrd(0.3447898), FloatOrd(0.3463606), FloatOrd(0.34793139), FloatOrd(0.34950218), FloatOrd(0.35107297), FloatOrd(0.35264376), FloatOrd(0.35421458), FloatOrd(0.35578537), FloatOrd(0.35735616), FloatOrd(0.35892695), FloatOrd(0.36049774), FloatOrd(0.36206856), FloatOrd(0.36363935), FloatOrd(0.36521015), FloatOrd(0.36678094), FloatOrd(0.36835173), FloatOrd(0.36992252), FloatOrd(0.37149334), FloatOrd(0.37306413), FloatOrd(0.37463492), FloatOrd(0.3762057), FloatOrd(0.3777765), FloatOrd(0.3793473), FloatOrd(0.38091812), FloatOrd(0.3824889), FloatOrd(0.3840597), FloatOrd(0.3856305), FloatOrd(0.38720128), FloatOrd(0.3887721), FloatOrd(0.3903429), FloatOrd(0.39191368), FloatOrd(0.39348447), FloatOrd(0.39505526), FloatOrd(0.39662606), FloatOrd(0.39819688), FloatOrd(0.39976767), FloatOrd(0.40133846), FloatOrd(0.40290925), FloatOrd(0.40448004), FloatOrd(0.40605086), FloatOrd(0.40762165), FloatOrd(0.40919244), FloatOrd(0.41076323), FloatOrd(0.41233402), FloatOrd(0.41390482), FloatOrd(0.41547564), FloatOrd(0.41704643), FloatOrd(0.41861722), FloatOrd(0.420188), FloatOrd(0.4217588), FloatOrd(0.42332962), FloatOrd(0.4249004), FloatOrd(0.4264712), FloatOrd(0.428042), FloatOrd(0.4296128), FloatOrd(0.43118358), FloatOrd(0.4327544), FloatOrd(0.4343252), FloatOrd(0.43589598), FloatOrd(0.43746677), FloatOrd(0.43903756), FloatOrd(0.44060835), FloatOrd(0.44217917), FloatOrd(0.44374996), FloatOrd(0.44532076), FloatOrd(0.44689155), FloatOrd(0.44846234), FloatOrd(0.45003316), FloatOrd(0.45160395), FloatOrd(0.45317474), FloatOrd(0.45474553), FloatOrd(0.45631632), FloatOrd(0.4578871), FloatOrd(0.45945793), FloatOrd(0.46102872), FloatOrd(0.46259952), FloatOrd(0.4641703), FloatOrd(0.4657411), FloatOrd(0.46731192), FloatOrd(0.4688827), FloatOrd(0.4704535), FloatOrd(0.4720243), FloatOrd(0.47359508), FloatOrd(0.47516587), FloatOrd(0.4767367), FloatOrd(0.4783075), FloatOrd(0.47987828), FloatOrd(0.48144907), FloatOrd(0.48301986), FloatOrd(0.48459068), FloatOrd(0.48616147), FloatOrd(0.48773226), FloatOrd(0.48930305), FloatOrd(0.49087384), FloatOrd(0.49244463), FloatOrd(0.49401546), FloatOrd(0.49558625), FloatOrd(0.49715704), FloatOrd(0.49872783), FloatOrd(0.5002986), FloatOrd(0.50186944), FloatOrd(0.5034402), FloatOrd(0.505011), FloatOrd(0.50658184), FloatOrd(0.5081526), FloatOrd(0.5097234), FloatOrd(0.5112942), FloatOrd(0.512865), FloatOrd(0.51443577), FloatOrd(0.5160066), FloatOrd(0.5175774), FloatOrd(0.5191482), FloatOrd(0.520719), FloatOrd(0.52228975), FloatOrd(0.5238606), FloatOrd(0.5254314), FloatOrd(0.52700216), FloatOrd(0.528573), FloatOrd(0.53014374), FloatOrd(0.53171456), FloatOrd(0.5332854), FloatOrd(0.53485614), FloatOrd(0.53642696), FloatOrd(0.5379977), FloatOrd(0.53956854), FloatOrd(0.5411393), FloatOrd(0.5427101), FloatOrd(0.54428095), FloatOrd(0.5458517), FloatOrd(0.5474225), FloatOrd(0.5489933), FloatOrd(0.5505641), FloatOrd(0.55213493), FloatOrd(0.5537057), FloatOrd(0.5552765), FloatOrd(0.5568473), FloatOrd(0.5584181), FloatOrd(0.5599889), FloatOrd(0.5615597), FloatOrd(0.5631305), FloatOrd(0.56470126), FloatOrd(0.5662721), FloatOrd(0.5678429), FloatOrd(0.56941366), FloatOrd(0.5709845), FloatOrd(0.57255524), FloatOrd(0.57412606), FloatOrd(0.5756968), FloatOrd(0.57726765), FloatOrd(0.57883847), FloatOrd(0.5804092), FloatOrd(0.58198005), FloatOrd(0.5835508), FloatOrd(0.58512163), FloatOrd(0.58669245), FloatOrd(0.5882632), FloatOrd(0.58983403), FloatOrd(0.5914048), FloatOrd(0.5929756), FloatOrd(0.59454644), FloatOrd(0.5961172), FloatOrd(0.597688), FloatOrd(0.5992588), FloatOrd(0.6008296), FloatOrd(0.60240036), FloatOrd(0.6039712), FloatOrd(0.605542), FloatOrd(0.60711277), FloatOrd(0.6086836), FloatOrd(0.61025435), FloatOrd(0.61182517), FloatOrd(0.613396), FloatOrd(0.61496675), FloatOrd(0.6165376), FloatOrd(0.61810833), FloatOrd(0.61967915), FloatOrd(0.62125), FloatOrd(0.62282073), FloatOrd(0.62439156), FloatOrd(0.6259623), FloatOrd(0.62753314), FloatOrd(0.62910396), FloatOrd(0.6306747), FloatOrd(0.63224554), FloatOrd(0.6338163), FloatOrd(0.6353871), FloatOrd(0.6369579), FloatOrd(0.6385287), FloatOrd(0.6400995), FloatOrd(0.6416703), FloatOrd(0.6432411), FloatOrd(0.64481187), FloatOrd(0.6463827), FloatOrd(0.6479535), FloatOrd(0.6495243), FloatOrd(0.6510951), FloatOrd(0.65266585), FloatOrd(0.6542367), FloatOrd(0.6558075), FloatOrd(0.65737826), FloatOrd(0.6589491), FloatOrd(0.66051984), FloatOrd(0.66209066), FloatOrd(0.6636615), FloatOrd(0.66523224), FloatOrd(0.66680306), FloatOrd(0.6683738), FloatOrd(0.66994464), FloatOrd(0.6715154), FloatOrd(0.6730862), FloatOrd(0.67465705), FloatOrd(0.6762278), FloatOrd(0.6777986), FloatOrd(0.6793694), FloatOrd(0.6809402), FloatOrd(0.68251103), FloatOrd(0.6840818), FloatOrd(0.6856526), FloatOrd(0.6872234), FloatOrd(0.6887942), FloatOrd(0.690365), FloatOrd(0.6919358), FloatOrd(0.6935066), FloatOrd(0.69507736), FloatOrd(0.6966482), FloatOrd(0.69821894), FloatOrd(0.69978976), FloatOrd(0.7013606), FloatOrd(0.70293134), FloatOrd(0.70450217), FloatOrd(0.7060729), FloatOrd(0.70764375), FloatOrd(0.70921457), FloatOrd(0.7107853), FloatOrd(0.71235615), FloatOrd(0.7139269), FloatOrd(0.71549773), FloatOrd(0.71706855), FloatOrd(0.7186393), FloatOrd(0.72021013), FloatOrd(0.7217809), FloatOrd(0.7233517), FloatOrd(0.72492254), FloatOrd(0.7264933), FloatOrd(0.7280641), FloatOrd(0.7296349), FloatOrd(0.7312057), FloatOrd(0.73277646), FloatOrd(0.7343473), FloatOrd(0.7359181), FloatOrd(0.73748887), FloatOrd(0.7390597), FloatOrd(0.74063045), FloatOrd(0.74220127), FloatOrd(0.7437721), FloatOrd(0.74534285), FloatOrd(0.7469137), FloatOrd(0.74848443), FloatOrd(0.75005525), FloatOrd(0.7516261), FloatOrd(0.75319684), FloatOrd(0.75476766), FloatOrd(0.7563384), FloatOrd(0.75790924), FloatOrd(0.75948), FloatOrd(0.7610508), FloatOrd(0.76262164), FloatOrd(0.7641924), FloatOrd(0.7657632), FloatOrd(0.767334), FloatOrd(0.7689048), FloatOrd(0.7704756), FloatOrd(0.7720464), FloatOrd(0.7736172), FloatOrd(0.77518797), FloatOrd(0.7767588), FloatOrd(0.7783296), FloatOrd(0.7799004), FloatOrd(0.7814712), FloatOrd(0.78304195), FloatOrd(0.7846128), FloatOrd(0.7861836), FloatOrd(0.78775436), FloatOrd(0.7893252), FloatOrd(0.79089594), FloatOrd(0.79246676), FloatOrd(0.7940375), FloatOrd(0.79560834), FloatOrd(0.79717916), FloatOrd(0.7987499), FloatOrd(0.80032074), FloatOrd(0.8018915), FloatOrd(0.8034623), FloatOrd(0.80503315), FloatOrd(0.8066039), FloatOrd(0.8081747), FloatOrd(0.8097455), FloatOrd(0.8113163), FloatOrd(0.81288713), FloatOrd(0.8144579), FloatOrd(0.8160287), FloatOrd(0.8175995), FloatOrd(0.8191703), FloatOrd(0.82074106), FloatOrd(0.8223119), FloatOrd(0.8238827), FloatOrd(0.82545346), FloatOrd(0.8270243), FloatOrd(0.82859504), FloatOrd(0.83016586), FloatOrd(0.8317367), FloatOrd(0.83330745), FloatOrd(0.83487827), FloatOrd(0.836449), FloatOrd(0.83801985), FloatOrd(0.83959067), FloatOrd(0.84116143), FloatOrd(0.84273225), FloatOrd(0.844303), FloatOrd(0.84587383), FloatOrd(0.84744465), FloatOrd(0.8490154), FloatOrd(0.85058624), FloatOrd(0.852157), FloatOrd(0.8537278), FloatOrd(0.8552986), FloatOrd(0.8568694), FloatOrd(0.8584402), FloatOrd(0.860011), FloatOrd(0.8615818), FloatOrd(0.86315256), FloatOrd(0.8647234), FloatOrd(0.8662942), FloatOrd(0.86786497), FloatOrd(0.8694358), FloatOrd(0.87100655), FloatOrd(0.87257737), FloatOrd(0.8741482), FloatOrd(0.87571895), FloatOrd(0.8772898), FloatOrd(0.87886053), FloatOrd(0.88043135), FloatOrd(0.8820021), FloatOrd(0.88357294), FloatOrd(0.88514376), FloatOrd(0.8867145), FloatOrd(0.88828534), FloatOrd(0.8898561), FloatOrd(0.8914269), FloatOrd(0.89299774), FloatOrd(0.8945685), FloatOrd(0.8961393), FloatOrd(0.8977101), FloatOrd(0.8992809), FloatOrd(0.9008517), FloatOrd(0.9024225), FloatOrd(0.9039933), FloatOrd(0.90556407), FloatOrd(0.9071349), FloatOrd(0.9087057), FloatOrd(0.9102765), FloatOrd(0.9118473), FloatOrd(0.91341805), FloatOrd(0.9149889), FloatOrd(0.91655964), FloatOrd(0.91813046), FloatOrd(0.9197013), FloatOrd(0.92127204), FloatOrd(0.92284286), FloatOrd(0.9244136), FloatOrd(0.92598444), FloatOrd(0.92755526), FloatOrd(0.929126), FloatOrd(0.93069685), FloatOrd(0.9322676), FloatOrd(0.9338384), FloatOrd(0.93540925), FloatOrd(0.93698), FloatOrd(0.93855083), FloatOrd(0.9401216), FloatOrd(0.9416924), FloatOrd(0.9432632), FloatOrd(0.944834), FloatOrd(0.9464048), FloatOrd(0.9479756), FloatOrd(0.9495464), FloatOrd(0.95111716), FloatOrd(0.952688), FloatOrd(0.9542588), FloatOrd(0.95582956), FloatOrd(0.9574004), FloatOrd(0.95897114), FloatOrd(0.96054196), FloatOrd(0.9621128), FloatOrd(0.96368355), FloatOrd(0.96525437), FloatOrd(0.9668251), FloatOrd(0.96839595), FloatOrd(0.96996677), FloatOrd(0.97153753), FloatOrd(0.97310835), FloatOrd(0.9746791), FloatOrd(0.97624993), FloatOrd(0.9778207), FloatOrd(0.9793915), FloatOrd(0.98096234), FloatOrd(0.9825331), FloatOrd(0.9841039), FloatOrd(0.9856747), FloatOrd(0.9872455), FloatOrd(0.9888163), FloatOrd(0.9903871), FloatOrd(0.9919579), FloatOrd(0.99352866), FloatOrd(0.9950995), FloatOrd(0.9966703), FloatOrd(0.99824107), FloatOrd(0.9998118), FloatOrd(1.0013827), FloatOrd(1.0029535), FloatOrd(1.0045244), FloatOrd(1.0060952), FloatOrd(1.0076659), FloatOrd(1.0092367), FloatOrd(1.0108075), FloatOrd(1.0123783), FloatOrd(1.0139492), FloatOrd(1.0155199), FloatOrd(1.0170907), FloatOrd(1.0186615), FloatOrd(1.0202323), FloatOrd(1.021803), FloatOrd(1.0233738), FloatOrd(1.0249447), FloatOrd(1.0265155), FloatOrd(1.0280863), FloatOrd(1.029657), FloatOrd(1.0312278), FloatOrd(1.0327986), FloatOrd(1.0343695), FloatOrd(1.0359403), FloatOrd(1.037511), FloatOrd(1.0390818), FloatOrd(1.0406526), FloatOrd(1.0422235), FloatOrd(1.0437943), FloatOrd(1.045365), FloatOrd(1.0469358), FloatOrd(1.0485066), FloatOrd(1.0500774), FloatOrd(1.0516483), FloatOrd(1.053219), FloatOrd(1.0547898), FloatOrd(1.0563606), FloatOrd(1.0579314), FloatOrd(1.0595022), FloatOrd(1.061073), FloatOrd(1.0626438), FloatOrd(1.0642146), FloatOrd(1.0657854), FloatOrd(1.0673562), FloatOrd(1.0689269), FloatOrd(1.0704978), FloatOrd(1.0720686), FloatOrd(1.0736394), FloatOrd(1.0752102), FloatOrd(1.0767809), FloatOrd(1.0783517), FloatOrd(1.0799226), FloatOrd(1.0814934), FloatOrd(1.0830641), FloatOrd(1.0846349), FloatOrd(1.0862057), FloatOrd(1.0877765), FloatOrd(1.0893474), FloatOrd(1.0909181), FloatOrd(1.0924889), FloatOrd(1.0940597), FloatOrd(1.0956305), FloatOrd(1.0972013), FloatOrd(1.098772), FloatOrd(1.1003429), FloatOrd(1.1019137), FloatOrd(1.1034845), FloatOrd(1.1050553), FloatOrd(1.106626), FloatOrd(1.1081969), FloatOrd(1.1097677), FloatOrd(1.1113385), FloatOrd(1.1129093), FloatOrd(1.11448), FloatOrd(1.1160508), FloatOrd(1.1176217), FloatOrd(1.1191925), FloatOrd(1.1207633), FloatOrd(1.122334), FloatOrd(1.1239048), FloatOrd(1.1254756), FloatOrd(1.1270465), FloatOrd(1.1286173), FloatOrd(1.130188), FloatOrd(1.1317588), FloatOrd(1.1333296), FloatOrd(1.1349005), FloatOrd(1.1364713), FloatOrd(1.138042), FloatOrd(1.1396128), FloatOrd(1.1411836), FloatOrd(1.1427544), FloatOrd(1.1443251), FloatOrd(1.145896), FloatOrd(1.1474668), FloatOrd(1.1490376), FloatOrd(1.1506084), FloatOrd(1.1521791), FloatOrd(1.15375), FloatOrd(1.1553208), FloatOrd(1.1568916), FloatOrd(1.1584624), FloatOrd(1.1600331), FloatOrd(1.1616039), FloatOrd(1.1631747), FloatOrd(1.1647456), FloatOrd(1.1663164), FloatOrd(1.1678871), FloatOrd(1.1694579), FloatOrd(1.1710287), FloatOrd(1.1725996), FloatOrd(1.1741704), FloatOrd(1.1757411), FloatOrd(1.1773119), FloatOrd(1.1788827), FloatOrd(1.1804535), FloatOrd(1.1820244), FloatOrd(1.1835951), FloatOrd(1.1851659), FloatOrd(1.1867367), FloatOrd(1.1883075), FloatOrd(1.1898783), FloatOrd(1.191449), FloatOrd(1.1930199), FloatOrd(1.1945907), FloatOrd(1.1961615), FloatOrd(1.1977323), FloatOrd(1.199303), FloatOrd(1.2008739), FloatOrd(1.2024447), FloatOrd(1.2040155), FloatOrd(1.2055862), FloatOrd(1.207157), FloatOrd(1.2087278), FloatOrd(1.2102987), FloatOrd(1.2118695), FloatOrd(1.2134402), FloatOrd(1.215011), FloatOrd(1.2165818), FloatOrd(1.2181526), FloatOrd(1.2197235), FloatOrd(1.2212942), FloatOrd(1.222865), FloatOrd(1.2244358), FloatOrd(1.2260066), FloatOrd(1.2275774), FloatOrd(1.2291481), FloatOrd(1.230719), FloatOrd(1.2322898), FloatOrd(1.2338606), FloatOrd(1.2354314), FloatOrd(1.2370021), FloatOrd(1.238573), FloatOrd(1.2401438), FloatOrd(1.2417146), FloatOrd(1.2432854), FloatOrd(1.2448561), FloatOrd(1.2464269), FloatOrd(1.2479978), FloatOrd(1.2495686), FloatOrd(1.2511394), FloatOrd(1.2527101), FloatOrd(1.2542809), FloatOrd(1.2558517), FloatOrd(1.2574226), FloatOrd(1.2589934), FloatOrd(1.2605641), FloatOrd(1.2621349), FloatOrd(1.2637057), FloatOrd(1.2652766), FloatOrd(1.2668474), FloatOrd(1.2684181), FloatOrd(1.2699889), FloatOrd(1.2715597), FloatOrd(1.2731305), FloatOrd(1.2747012), FloatOrd(1.276272), FloatOrd(1.2778429), FloatOrd(1.2794137), FloatOrd(1.2809845), FloatOrd(1.2825552), FloatOrd(1.284126), FloatOrd(1.2856969), FloatOrd(1.2872677), FloatOrd(1.2888385), FloatOrd(1.2904092), FloatOrd(1.29198), FloatOrd(1.2935508), FloatOrd(1.2951217), FloatOrd(1.2966925), FloatOrd(1.2982632), FloatOrd(1.299834), FloatOrd(1.3014048), FloatOrd(1.3029757), FloatOrd(1.3045465), FloatOrd(1.3061172), FloatOrd(1.307688), FloatOrd(1.3092588), FloatOrd(1.3108296), FloatOrd(1.3124005), FloatOrd(1.3139712), FloatOrd(1.315542), FloatOrd(1.3171128), FloatOrd(1.3186836), FloatOrd(1.3202544), FloatOrd(1.3218251), FloatOrd(1.323396), FloatOrd(1.3249668), FloatOrd(1.3265376), FloatOrd(1.3281084), FloatOrd(1.3296791), FloatOrd(1.33125), FloatOrd(1.3328208), FloatOrd(1.3343916), FloatOrd(1.3359623), FloatOrd(1.3375331), FloatOrd(1.3391039), FloatOrd(1.3406748), FloatOrd(1.3422456), FloatOrd(1.3438163), FloatOrd(1.3453871), FloatOrd(1.3469579), FloatOrd(1.3485287), FloatOrd(1.3500996), FloatOrd(1.3516703), FloatOrd(1.3532411), FloatOrd(1.3548119), FloatOrd(1.3563827), FloatOrd(1.3579535), FloatOrd(1.3595243), FloatOrd(1.3610951), FloatOrd(1.3626659), FloatOrd(1.3642367), FloatOrd(1.3658075), FloatOrd(1.3673782), FloatOrd(1.368949), FloatOrd(1.3705199), FloatOrd(1.3720907), FloatOrd(1.3736615), FloatOrd(1.3752322), FloatOrd(1.376803), FloatOrd(1.3783739), FloatOrd(1.3799447), FloatOrd(1.3815155), FloatOrd(1.3830862), FloatOrd(1.384657), FloatOrd(1.3862278), FloatOrd(1.3877987), FloatOrd(1.3893695), FloatOrd(1.3909402), FloatOrd(1.392511), FloatOrd(1.3940818), FloatOrd(1.3956527), FloatOrd(1.3972234), FloatOrd(1.3987942), FloatOrd(1.400365), FloatOrd(1.4019358), FloatOrd(1.4035066), FloatOrd(1.4050773), FloatOrd(1.4066482), FloatOrd(1.408219), FloatOrd(1.4097898), FloatOrd(1.4113606), FloatOrd(1.4129313), FloatOrd(1.4145021), FloatOrd(1.416073), FloatOrd(1.4176438), FloatOrd(1.4192146), FloatOrd(1.4207853), FloatOrd(1.4223561), FloatOrd(1.423927), FloatOrd(1.4254978), FloatOrd(1.4270686), FloatOrd(1.4286393), FloatOrd(1.4302101), FloatOrd(1.4317809), FloatOrd(1.4333518), FloatOrd(1.4349226), FloatOrd(1.4364933), FloatOrd(1.4380641), FloatOrd(1.4396349), FloatOrd(1.4412057), FloatOrd(1.4427766), FloatOrd(1.4443473), FloatOrd(1.4459181), FloatOrd(1.4474889), FloatOrd(1.4490597), FloatOrd(1.4506305), FloatOrd(1.4522012), FloatOrd(1.4537721), FloatOrd(1.4553429), FloatOrd(1.4569137), FloatOrd(1.4584844), FloatOrd(1.4600552), FloatOrd(1.461626), FloatOrd(1.4631969), FloatOrd(1.4647677), FloatOrd(1.4663384), FloatOrd(1.4679092), FloatOrd(1.46948), FloatOrd(1.4710509), FloatOrd(1.4726217), FloatOrd(1.4741924), FloatOrd(1.4757632), FloatOrd(1.477334), FloatOrd(1.4789048), FloatOrd(1.4804757), FloatOrd(1.4820464), FloatOrd(1.4836172), FloatOrd(1.485188), FloatOrd(1.4867588), FloatOrd(1.4883296), FloatOrd(1.4899004), FloatOrd(1.4914712), FloatOrd(1.493042), FloatOrd(1.4946128), FloatOrd(1.4961836), FloatOrd(1.4977543), FloatOrd(1.4993252), FloatOrd(1.500896), FloatOrd(1.5024668), FloatOrd(1.5040376), FloatOrd(1.5056083), FloatOrd(1.5071791), FloatOrd(1.50875), FloatOrd(1.5103208), FloatOrd(1.5118916), FloatOrd(1.5134623), FloatOrd(1.5150331), FloatOrd(1.516604), FloatOrd(1.5181748), FloatOrd(1.5197455), FloatOrd(1.5213163), FloatOrd(1.5228871), FloatOrd(1.5244579), FloatOrd(1.5260288), FloatOrd(1.5275995), FloatOrd(1.5291703), FloatOrd(1.5307411), FloatOrd(1.5323119), FloatOrd(1.5338827), FloatOrd(1.5354534), FloatOrd(1.5370243), FloatOrd(1.5385951), FloatOrd(1.5401659), FloatOrd(1.5417367), FloatOrd(1.5433074), FloatOrd(1.5448782), FloatOrd(1.5464491), FloatOrd(1.5480199), FloatOrd(1.5495907), FloatOrd(1.5511614), FloatOrd(1.5527322), FloatOrd(1.554303), FloatOrd(1.5558739), FloatOrd(1.5574447), FloatOrd(1.5590154), FloatOrd(1.5605862), FloatOrd(1.562157), FloatOrd(1.5637279), FloatOrd(1.5652987), FloatOrd(1.5668694), FloatOrd(1.5684402)]; pub const SIN_F32_VALUES: [f32; 1000] = [0.0, 0.0015707957, 0.0031415876, 0.0047123716, 0.006283144, 0.007853901, 0.009424638, 0.010995353, 0.01256604, 0.014136696, 0.015707318, 0.0172779, 0.01884844, 0.020418933, 0.021989375, 0.023559766, 0.025130097, 0.026700364, 0.028270569, 0.0298407, 0.03141076, 0.03298074, 0.034550644, 0.036120456, 0.03769018, 0.039259817, 0.040829353, 0.042398788, 0.04396812, 0.04553734, 0.047106452, 0.048675448, 0.05024432, 0.051813066, 0.053381693, 0.05495018, 0.056518536, 0.05808675, 0.059654824, 0.061222747, 0.06279052, 0.06435814, 0.0659256, 0.067492895, 0.06906003, 0.07062698, 0.07219377, 0.07376038, 0.0753268, 0.07689305, 0.0784591, 0.08002496, 0.08159061, 0.08315607, 0.08472133, 0.08628637, 0.0878512, 0.08941581, 0.09098021, 0.09254437, 0.09410831, 0.09567203, 0.0972355, 0.09879873, 0.10036172, 0.10192446, 0.10348695, 0.10504918, 0.106611155, 0.10817287, 0.10973431, 0.111295484, 0.11285639, 0.114417, 0.11597735, 0.1175374, 0.119097166, 0.12065663, 0.1222158, 0.12377468, 0.12533323, 0.1268915, 0.12844943, 0.13000706, 0.13156436, 0.13312134, 0.13467799, 0.13623431, 0.13779029, 0.13934594, 0.14090122, 0.14245619, 0.14401078, 0.14556502, 0.14711891, 0.14867243, 0.15022558, 0.15177839, 0.15333079, 0.15488282, 0.15643448, 0.15798573, 0.15953662, 0.16108708, 0.16263716, 0.16418685, 0.16573612, 0.16728498, 0.16883345, 0.17038149, 0.1719291, 0.1734763, 0.17502306, 0.1765694, 0.1781153, 0.17966075, 0.18120578, 0.18275033, 0.18429445, 0.18583812, 0.18738131, 0.18892406, 0.19046634, 0.19200814, 0.19354948, 0.19509032, 0.1966307, 0.19817059, 0.19970998, 0.20124888, 0.20278731, 0.20432521, 0.20586261, 0.20739952, 0.20893589, 0.21047178, 0.21200712, 0.21354194, 0.21507625, 0.21661001, 0.21814324, 0.21967594, 0.2212081, 0.2227397, 0.22427078, 0.22580127, 0.22733122, 0.22886062, 0.23038943, 0.2319177, 0.23344538, 0.23497248, 0.23649901, 0.23802495, 0.23955029, 0.24107507, 0.24259923, 0.2441228, 0.24564578, 0.24716814, 0.2486899, 0.25021103, 0.25173154, 0.25325143, 0.25477073, 0.2562894, 0.2578074, 0.25932476, 0.26084152, 0.2623576, 0.26387307, 0.26538786, 0.266902, 0.26841548, 0.2699283, 0.27144045, 0.27295196, 0.27446276, 0.2759729, 0.27748233, 0.2789911, 0.28049922, 0.2820066, 0.28351328, 0.28501928, 0.28652456, 0.28802913, 0.28953302, 0.2910362, 0.2925386, 0.29404032, 0.29554132, 0.29704157, 0.29854113, 0.30003992, 0.30153796, 0.30303526, 0.30453184, 0.30602765, 0.3075227, 0.309017, 0.31051055, 0.31200328, 0.31349528, 0.31498653, 0.31647697, 0.31796664, 0.3194555, 0.3209436, 0.32243094, 0.32391742, 0.32540312, 0.32688802, 0.32837212, 0.3298554, 0.3313379, 0.33281955, 0.3343004, 0.33578038, 0.33725956, 0.33873793, 0.34021544, 0.34169212, 0.34316793, 0.34464294, 0.34611705, 0.34759036, 0.34906277, 0.35053432, 0.35200503, 0.35347486, 0.3549438, 0.3564119, 0.3578791, 0.3593454, 0.36081082, 0.36227536, 0.36373904, 0.36520177, 0.3666636, 0.36812454, 0.3695846, 0.3710437, 0.37250194, 0.3739592, 0.3754156, 0.37687102, 0.37832552, 0.37977913, 0.38123176, 0.38268346, 0.3841342, 0.385584, 0.38703284, 0.38848075, 0.38992772, 0.39137366, 0.3928187, 0.39426273, 0.39570582, 0.3971479, 0.39858902, 0.40002915, 0.40146828, 0.40290642, 0.4043436, 0.40577978, 0.40721494, 0.4086491, 0.41008222, 0.41151437, 0.4129455, 0.4143756, 0.41580465, 0.41723272, 0.41865975, 0.42008576, 0.4215107, 0.4229346, 0.42435747, 0.42577928, 0.42720005, 0.4286198, 0.43003845, 0.43145606, 0.4328726, 0.43428805, 0.43570247, 0.4371158, 0.43852803, 0.43993917, 0.44134924, 0.44275823, 0.44416615, 0.44557294, 0.44697863, 0.4483832, 0.4497867, 0.4511891, 0.45259038, 0.45399052, 0.45538953, 0.45678744, 0.4581842, 0.45957989, 0.4609744, 0.46236777, 0.46376, 0.46515107, 0.46654105, 0.46792984, 0.46931747, 0.47070393, 0.47208926, 0.4734734, 0.4748564, 0.47623822, 0.47761884, 0.4789983, 0.48037657, 0.4817537, 0.48312956, 0.4845043, 0.48587784, 0.48725012, 0.48862126, 0.48999116, 0.49135986, 0.49272734, 0.49409363, 0.4954587, 0.4968225, 0.49818513, 0.49954647, 0.50090665, 0.5022656, 0.5036232, 0.50497967, 0.5063348, 0.50768876, 0.5090414, 0.51039284, 0.511743, 0.51309186, 0.5144395, 0.5157859, 0.517131, 0.5184748, 0.51981735, 0.52115864, 0.52249855, 0.52383727, 0.5251747, 0.5265107, 0.5278455, 0.529179, 0.5305112, 0.5318421, 0.5331716, 0.5344999, 0.5358268, 0.5371524, 0.5384767, 0.53979963, 0.5411213, 0.54244155, 0.5437605, 0.5450781, 0.54639435, 0.5477093, 0.5490228, 0.55033505, 0.5516459, 0.5529554, 0.55426353, 0.55557024, 0.55687565, 0.5581796, 0.5594823, 0.56078357, 0.56208336, 0.5633819, 0.56467897, 0.56597465, 0.5672689, 0.56856185, 0.56985337, 0.57114345, 0.57243216, 0.5737194, 0.57500523, 0.5762897, 0.5775727, 0.5788543, 0.58013445, 0.5814132, 0.58269054, 0.5839663, 0.5852408, 0.5865137, 0.58778524, 0.58905536, 0.5903239, 0.5915911, 0.5928568, 0.5941211, 0.5953838, 0.5966452, 0.59790504, 0.59916335, 0.60042024, 0.6016756, 0.60292953, 0.604182, 0.6054329, 0.60668236, 0.6079303, 0.60917675, 0.6104217, 0.6116651, 0.61290705, 0.6141475, 0.61538637, 0.61662376, 0.6178596, 0.61909395, 0.62032676, 0.62155807, 0.6227878, 0.624016, 0.6252427, 0.62646776, 0.6276914, 0.6289134, 0.63013387, 0.63135284, 0.63257015, 0.63378596, 0.6350002, 0.6362129, 0.63742405, 0.63863355, 0.6398415, 0.64104784, 0.6422527, 0.64345586, 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0.82796246, 0.82884234, 0.82972014, 0.8305959, 0.83146966, 0.83234125, 0.8332109, 0.83407843, 0.83494395, 0.8358074, 0.8366687, 0.83752805, 0.8383853, 0.8392405, 0.84009355, 0.8409446, 0.84179354, 0.8426404, 0.84348524, 0.8443279, 0.8451686, 0.8460071, 0.84684354, 0.84767795, 0.84851027, 0.84934044, 0.85016847, 0.85099447, 0.8518184, 0.8526402, 0.85345984, 0.85427743, 0.8550929, 0.8559063, 0.8567175, 0.85752666, 0.85833365, 0.8591386, 0.85994136, 0.86074203, 0.86154056, 0.862337, 0.8631313, 0.86392343, 0.8647135, 0.86550134, 0.8662871, 0.86707073, 0.8678522, 0.86863154, 0.86940867, 0.87018377, 0.87095666, 0.8717274, 0.87249607, 0.87326247, 0.8740268, 0.8747889, 0.8755489, 0.8763067, 0.8770623, 0.87781584, 0.87856716, 0.87931633, 0.88006335, 0.8808081, 0.8815508, 0.88229126, 0.8830295, 0.88376564, 0.88449955, 0.8852313, 0.8859609, 0.8866883, 0.88741344, 0.88813645, 0.88885725, 0.8895759, 0.89029235, 0.8910065, 0.89171857, 0.8924284, 0.893136, 0.89384145, 0.8945446, 0.8952457, 0.8959445, 0.8966411, 0.89733547, 0.89802754, 0.8987175, 0.89940524, 0.90009075, 0.90077406, 0.9014551, 0.90213394, 0.9028106, 0.903485, 0.90415716, 0.90482706, 0.90549475, 0.90616024, 0.90682346, 0.9074845, 0.90814316, 0.9087997, 0.909454, 0.910106, 0.91075575, 0.9114033, 0.9120486, 0.9126916, 0.9133324, 0.9139709, 0.91460717, 0.9152412, 0.91587293, 0.9165025, 0.91712964, 0.91775465, 0.91837734, 0.91899776, 0.919616, 0.9202318, 0.9208455, 0.9214569, 0.922066, 0.92267275, 0.92327726, 0.9238795, 0.92447954, 0.9250772, 0.92567265, 0.9262657, 0.9268566, 0.9274452, 0.92803144, 0.92861545, 0.9291971, 0.9297765, 0.9303536, 0.9309284, 0.9315009, 0.9320711, 0.932639, 0.93320465, 0.933768, 0.9343289, 0.93488765, 0.93544406, 0.93599814, 0.9365499, 0.93709934, 0.9376465, 0.93819135, 0.9387339, 0.9392741, 0.93981194, 0.9403475, 0.9408808, 0.94141173, 0.9419403, 0.94246656, 0.94299054, 0.9435122, 0.9440315, 0.9445485, 0.94506305, 0.94557536, 0.9460854, 0.94659305, 0.9470983, 0.94760126, 0.9481019, 0.94860023, 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0.99896264, 0.9990329, 0.99910074, 0.99916613, 0.999229, 0.99928945, 0.99934745, 0.99940294, 0.999456, 0.99950653, 0.9995547, 0.9996003, 0.9996435, 0.9996842, 0.9997224, 0.9997582, 0.9997915, 0.9998224, 0.99985075, 0.9998766, 0.99990004, 0.999921, 0.99993956, 0.9999556, 0.9999692, 0.9999803, 0.9999889, 0.99999505, 0.99999875]; diff --git a/src/lookup/data/sin_f64.rs b/src/lookup/data/sin_f64.rs index 186706b..74e841a 100644 --- a/src/lookup/data/sin_f64.rs +++ b/src/lookup/data/sin_f64.rs @@ -1,2 +1,2 @@ -pub const SIN_F64_KEYS: [f64; 1000] = [-0.0007853981633974483, 0.0007853981633974483, 0.002356194490192345, 0.003926990816987242, 0.005497787143782139, 0.0070685834705770355, 0.008639379797371931, 0.01021017612416683, 0.011780972450961725, 0.013351768777756621, 0.014922565104551519, 0.016493361431346415, 0.01806415775814131, 0.019634954084936207, 0.021205750411731106, 0.022776546738526002, 0.0243473430653209, 0.025918139392115794, 0.02748893571891069, 0.02905973204570559, 0.030630528372500486, 0.03220132469929538, 0.03377212102609028, 0.035342917352885174, 0.03691371367968007, 0.038484510006474966, 0.04005530633326986, 0.041626102660064765, 0.04319689898685966, 0.04476769531365456, 0.04633849164044945, 0.04790928796724435, 0.049480084294039245, 0.05105088062083414, 0.05262167694762904, 0.05419247327442393, 0.05576326960121883, 0.057334065928013725, 0.05890486225480863, 0.060475658581603524, 0.06204645490839842, 0.06361725123519331, 0.0651880475619882, 0.0667588438887831, 0.068329640215578, 0.06990043654237289, 0.07147123286916779, 0.07304202919596268, 0.07461282552275758, 0.07618362184955248, 0.07775441817634737, 0.07932521450314227, 0.08089601082993716, 0.08246680715673206, 0.08403760348352697, 0.08560839981032187, 0.08717919613711676, 0.08874999246391166, 0.09032078879070655, 0.09189158511750145, 0.09346238144429635, 0.09503317777109124, 0.09660397409788614, 0.09817477042468103, 0.09974556675147593, 0.10131636307827083, 0.10288715940506572, 0.10445795573186062, 0.10602875205865551, 0.10759954838545041, 0.1091703447122453, 0.1107411410390402, 0.1123119373658351, 0.11388273369263, 0.11545353001942489, 0.1170243263462198, 0.1185951226730147, 0.12016591899980959, 0.12173671532660449, 0.12330751165339938, 0.12487830798019428, 0.12644910430698916, 0.12801990063378407, 0.12959069696057895, 0.13116149328737386, 0.13273228961416875, 0.13430308594096366, 0.13587388226775857, 0.13744467859455345, 0.13901547492134836, 0.14058627124814324, 0.14215706757493815, 0.14372786390173303, 0.14529866022852794, 0.14686945655532282, 0.14844025288211773, 0.15001104920891262, 0.15158184553570753, 0.1531526418625024, 0.15472343818929732, 0.1562942345160922, 0.1578650308428871, 0.159435827169682, 0.1610066234964769, 0.16257741982327178, 0.1641482161500667, 0.16571901247686158, 0.1672898088036565, 0.1688606051304514, 0.17043140145724628, 0.1720021977840412, 0.17357299411083607, 0.17514379043763098, 0.17671458676442586, 0.17828538309122077, 0.17985617941801565, 0.18142697574481056, 0.18299777207160545, 0.18456856839840036, 0.18613936472519524, 0.18771016105199015, 0.18928095737878503, 0.19085175370557994, 0.19242255003237482, 0.19399334635916973, 0.19556414268596461, 0.19713493901275952, 0.1987057353395544, 0.20027653166634932, 0.20184732799314423, 0.2034181243199391, 0.20498892064673402, 0.2065597169735289, 0.2081305133003238, 0.2097013096271187, 0.2112721059539136, 0.21284290228070848, 0.2144136986075034, 0.21598449493429828, 0.2175552912610932, 0.21912608758788807, 0.22069688391468298, 0.22226768024147786, 0.22383847656827277, 0.22540927289506765, 0.22698006922186256, 0.22855086554865744, 0.23012166187545235, 0.23169245820224724, 0.23326325452904215, 0.23483405085583706, 0.23640484718263194, 0.23797564350942685, 0.23954643983622173, 0.24111723616301664, 0.24268803248981152, 0.24425882881660643, 0.24582962514340131, 0.24740042147019622, 0.2489712177969911, 0.250542014123786, 0.2521128104505809, 0.2536836067773758, 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1.5056082792329084, 1.5071790755597034, 1.5087498718864982, 1.5103206682132932, 1.511891464540088, 1.513462260866883, 1.5150330571936779, 1.5166038535204727, 1.5181746498472677, 1.5197454461740625, 1.5213162425008575, 1.5228870388276523, 1.5244578351544473, 1.5260286314812421, 1.5275994278080371, 1.529170224134832, 1.5307410204616267, 1.5323118167884218, 1.5338826131152166, 1.5354534094420116, 1.5370242057688064, 1.5385950020956014, 1.5401657984223962, 1.5417365947491912, 1.543307391075986, 1.5448781874027808, 1.5464489837295758, 1.5480197800563706, 1.5495905763831657, 1.5511613727099605, 1.5527321690367555, 1.5543029653635503, 1.555873761690345, 1.55744455801714, 1.559015354343935, 1.56058615067073, 1.5621569469975247, 1.5637277433243197, 1.5652985396511145, 1.5668693359779096, 1.5684401323047044]; +pub const SIN_F64_KEYS: [FloatOrd; 1000] = [FloatOrd(-0.0007853981633974483), FloatOrd(0.0007853981633974483), FloatOrd(0.002356194490192345), FloatOrd(0.003926990816987242), 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FloatOrd(0.9259844346455917), FloatOrd(0.9275552309723866), FloatOrd(0.9291260272991814), FloatOrd(0.9306968236259763), FloatOrd(0.9322676199527712), FloatOrd(0.9338384162795661), FloatOrd(0.935409212606361), FloatOrd(0.9369800089331559), FloatOrd(0.9385508052599508), FloatOrd(0.9401216015867457), FloatOrd(0.9416923979135406), FloatOrd(0.9432631942403354), FloatOrd(0.9448339905671304), FloatOrd(0.9464047868939253), FloatOrd(0.9479755832207202), FloatOrd(0.9495463795475151), FloatOrd(0.95111717587431), FloatOrd(0.9526879722011049), FloatOrd(0.9542587685278998), FloatOrd(0.9558295648546946), FloatOrd(0.9574003611814895), FloatOrd(0.9589711575082844), FloatOrd(0.9605419538350793), FloatOrd(0.9621127501618743), FloatOrd(0.9636835464886692), FloatOrd(0.9652543428154641), FloatOrd(0.966825139142259), FloatOrd(0.9683959354690538), FloatOrd(0.9699667317958487), FloatOrd(0.9715375281226436), FloatOrd(0.9731083244494385), FloatOrd(0.9746791207762334), FloatOrd(0.9762499171030283), 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FloatOrd(1.0814932709982863), FloatOrd(1.0830640673250813), FloatOrd(1.0846348636518761), FloatOrd(1.0862056599786711), FloatOrd(1.087776456305466), FloatOrd(1.089347252632261), FloatOrd(1.0909180489590558), FloatOrd(1.0924888452858508), FloatOrd(1.0940596416126456), FloatOrd(1.0956304379394404), FloatOrd(1.0972012342662354), FloatOrd(1.0987720305930302), FloatOrd(1.1003428269198252), FloatOrd(1.10191362324662), FloatOrd(1.103484419573415), FloatOrd(1.1050552159002098), FloatOrd(1.1066260122270049), FloatOrd(1.1081968085537997), FloatOrd(1.1097676048805944), FloatOrd(1.1113384012073895), FloatOrd(1.1129091975341843), FloatOrd(1.1144799938609793), FloatOrd(1.116050790187774), FloatOrd(1.117621586514569), FloatOrd(1.119192382841364), FloatOrd(1.1207631791681587), FloatOrd(1.1223339754949537), FloatOrd(1.1239047718217485), FloatOrd(1.1254755681485435), FloatOrd(1.1270463644753383), FloatOrd(1.1286171608021334), FloatOrd(1.1301879571289282), FloatOrd(1.1317587534557232), 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FloatOrd(1.2370021073509812), FloatOrd(1.238572903677776), FloatOrd(1.240143700004571), FloatOrd(1.2417144963313658), FloatOrd(1.2432852926581608), FloatOrd(1.2448560889849556), FloatOrd(1.2464268853117506), FloatOrd(1.2479976816385454), FloatOrd(1.2495684779653404), FloatOrd(1.2511392742921352), FloatOrd(1.25271007061893), FloatOrd(1.254280866945725), FloatOrd(1.2558516632725198), FloatOrd(1.2574224595993149), FloatOrd(1.2589932559261097), FloatOrd(1.2605640522529047), FloatOrd(1.2621348485796995), FloatOrd(1.2637056449064945), FloatOrd(1.2652764412332893), FloatOrd(1.266847237560084), FloatOrd(1.2684180338868791), FloatOrd(1.269988830213674), FloatOrd(1.271559626540469), FloatOrd(1.2731304228672637), FloatOrd(1.2747012191940588), FloatOrd(1.2762720155208536), FloatOrd(1.2778428118476486), FloatOrd(1.2794136081744434), FloatOrd(1.2809844045012382), FloatOrd(1.2825552008280332), FloatOrd(1.284125997154828), FloatOrd(1.285696793481623), FloatOrd(1.2872675898084178), 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FloatOrd(1.3406746649194443), FloatOrd(1.3422454612462393), FloatOrd(1.3438162575730341), FloatOrd(1.345387053899829), FloatOrd(1.346957850226624), FloatOrd(1.3485286465534188), FloatOrd(1.3500994428802138), FloatOrd(1.3516702392070086), FloatOrd(1.3532410355338036), FloatOrd(1.3548118318605984), FloatOrd(1.3563826281873934), FloatOrd(1.3579534245141882), FloatOrd(1.359524220840983), FloatOrd(1.361095017167778), FloatOrd(1.3626658134945728), FloatOrd(1.3642366098213679), FloatOrd(1.3658074061481627), FloatOrd(1.3673782024749577), FloatOrd(1.3689489988017525), FloatOrd(1.3705197951285473), FloatOrd(1.3720905914553423), FloatOrd(1.373661387782137), FloatOrd(1.375232184108932), FloatOrd(1.376802980435727), FloatOrd(1.378373776762522), FloatOrd(1.3799445730893167), FloatOrd(1.3815153694161117), FloatOrd(1.3830861657429065), FloatOrd(1.3846569620697013), FloatOrd(1.3862277583964964), FloatOrd(1.3877985547232912), FloatOrd(1.3893693510500862), FloatOrd(1.390940147376881), FloatOrd(1.392510943703676), FloatOrd(1.3940817400304708), FloatOrd(1.3956525363572658), FloatOrd(1.3972233326840606), FloatOrd(1.3987941290108554), FloatOrd(1.4003649253376504), FloatOrd(1.4019357216644452), FloatOrd(1.4035065179912403), FloatOrd(1.405077314318035), FloatOrd(1.40664811064483), FloatOrd(1.4082189069716249), FloatOrd(1.40978970329842), FloatOrd(1.4113604996252147), FloatOrd(1.4129312959520095), FloatOrd(1.4145020922788045), FloatOrd(1.4160728886055993), FloatOrd(1.4176436849323943), FloatOrd(1.4192144812591891), FloatOrd(1.4207852775859842), FloatOrd(1.422356073912779), FloatOrd(1.4239268702395738), FloatOrd(1.4254976665663688), FloatOrd(1.4270684628931636), FloatOrd(1.4286392592199586), FloatOrd(1.4302100555467534), FloatOrd(1.4317808518735484), FloatOrd(1.4333516482003432), FloatOrd(1.4349224445271382), FloatOrd(1.436493240853933), FloatOrd(1.4380640371807278), FloatOrd(1.4396348335075229), FloatOrd(1.4412056298343177), FloatOrd(1.4427764261611127), FloatOrd(1.4443472224879075), FloatOrd(1.4459180188147025), FloatOrd(1.4474888151414973), FloatOrd(1.4490596114682923), FloatOrd(1.4506304077950871), FloatOrd(1.452201204121882), FloatOrd(1.453772000448677), FloatOrd(1.4553427967754717), FloatOrd(1.4569135931022668), FloatOrd(1.4584843894290616), FloatOrd(1.4600551857558566), FloatOrd(1.4616259820826514), FloatOrd(1.4631967784094462), FloatOrd(1.4647675747362412), FloatOrd(1.466338371063036), FloatOrd(1.467909167389831), FloatOrd(1.4694799637166258), FloatOrd(1.4710507600434208), FloatOrd(1.4726215563702156), FloatOrd(1.4741923526970107), FloatOrd(1.4757631490238055), FloatOrd(1.4773339453506003), FloatOrd(1.4789047416773953), FloatOrd(1.48047553800419), FloatOrd(1.482046334330985), FloatOrd(1.48361713065778), FloatOrd(1.485187926984575), FloatOrd(1.4867587233113697), FloatOrd(1.4883295196381647), FloatOrd(1.4899003159649595), FloatOrd(1.4914711122917543), FloatOrd(1.4930419086185494), FloatOrd(1.4946127049453442), FloatOrd(1.4961835012721392), FloatOrd(1.497754297598934), FloatOrd(1.499325093925729), FloatOrd(1.5008958902525238), FloatOrd(1.5024666865793186), FloatOrd(1.5040374829061136), FloatOrd(1.5056082792329084), FloatOrd(1.5071790755597034), FloatOrd(1.5087498718864982), FloatOrd(1.5103206682132932), FloatOrd(1.511891464540088), FloatOrd(1.513462260866883), FloatOrd(1.5150330571936779), FloatOrd(1.5166038535204727), FloatOrd(1.5181746498472677), FloatOrd(1.5197454461740625), FloatOrd(1.5213162425008575), FloatOrd(1.5228870388276523), FloatOrd(1.5244578351544473), FloatOrd(1.5260286314812421), FloatOrd(1.5275994278080371), FloatOrd(1.529170224134832), FloatOrd(1.5307410204616267), FloatOrd(1.5323118167884218), FloatOrd(1.5338826131152166), FloatOrd(1.5354534094420116), FloatOrd(1.5370242057688064), FloatOrd(1.5385950020956014), FloatOrd(1.5401657984223962), FloatOrd(1.5417365947491912), FloatOrd(1.543307391075986), FloatOrd(1.5448781874027808), FloatOrd(1.5464489837295758), FloatOrd(1.5480197800563706), FloatOrd(1.5495905763831657), FloatOrd(1.5511613727099605), FloatOrd(1.5527321690367555), FloatOrd(1.5543029653635503), FloatOrd(1.555873761690345), FloatOrd(1.55744455801714), FloatOrd(1.559015354343935), FloatOrd(1.56058615067073), FloatOrd(1.5621569469975247), FloatOrd(1.5637277433243197), FloatOrd(1.5652985396511145), FloatOrd(1.5668693359779096), FloatOrd(1.5684401323047044)]; pub const SIN_F64_VALUES: [f64; 1000] = [0.0, 0.001570795680830879, 0.0031415874858795635, 0.004712371539373423, 0.006283143965558951, 0.007853900888711334, 0.009424638433144006, 0.010995352723218223, 0.012566039883352607, 0.014136696038032734, 0.015707317311820675, 0.01727789982936457, 0.018848439715408175, 0.020418933094800456, 0.02198937609250511, 0.023559764833610154, 0.02513009544333748, 0.026700364047052408, 0.028270566770273252, 0.02984069973868089, 0.03141075907812829, 0.03298074091465013, 0.03455064137447227, 0.0361204565840214, 0.03769018266993454, 0.03925981575906861, 0.040829351978509995, 0.042398787455584105, 0.04396811831786491, 0.0455373406931845, 0.047106450709642665, 0.048675444495616414, 0.050244318179769556, 0.051813067891062235, 0.053381689758760474, 0.054950179912445746, 0.05651853448202453, 0.05808674959773781, 0.059654821390170705, 0.06122274599026192, 0.06279051952931337, 0.06435813813899972, 0.06592559795137785, 0.06749289509889653, 0.0690600257144058, 0.07062698593116667, 0.0721937718828606, 0.07376037970359897, 0.07532680552793272, 0.07689304549086184, 0.07845909572784494, 0.08002495237480871, 0.08159061156815754, 0.08315606944478302, 0.08472132214207345, 0.08628636579792338, 0.08785119655074318, 0.08941581053946852, 0.09098020390356992, 0.09254437278306225, 0.09410831331851433, 0.0956720216510583, 0.09723549392239933, 0.09879872627482501, 0.1003617148512149, 0.10192445579505004, 0.10348694525042253, 0.10504917936204494, 0.10661115427525991, 0.10817286613604961, 0.10973431109104527, 0.11129548528753667, 0.11285638487348168, 0.11441700599751574, 0.11597734480896137, 0.11753739745783766, 0.11909716009486974, 0.1206566288714984, 0.12221579993988944, 0.12377466945294324, 0.12533323356430426, 0.12689148842837042, 0.12844943020030286, 0.13000705503603502, 0.1315643590922825, 0.13312133852655234, 0.1346779894971526, 0.13623430816320173, 0.13779029068463808, 0.13934593322222952, 0.14090123193758267, 0.14245618299315263, 0.14401078255225216, 0.14556502677906147, 0.14711891183863737, 0.148672433896923, 0.15022558912075706, 0.15177837367788347, 0.15333078373696063, 0.15488281546757113, 0.15643446504023087, 0.15798572862639884, 0.1595366023984863, 0.16108708252986642, 0.16263716519488358, 0.16418684656886295, 0.1657361228281197, 0.16728499014996873, 0.1688334447127339, 0.17038148269575742, 0.17192910027940955, 0.1734762936450977, 0.17502305897527606, 0.1765693924534549, 0.17811529026421014, 0.17966074859319253, 0.18120576362713736, 0.18275033155387355, 0.18429444856233332, 0.1858381108425614, 0.18738131458572463, 0.18892405598412113, 0.1904663312311899, 0.19200813652152002, 0.19354946805086026, 0.19509032201612825, 0.19663069461542007, 0.19817058204801935, 0.19970998051440703, 0.20124888621627035, 0.2027872953565125, 0.20432520413926183, 0.20586260876988133, 0.2073995054549779, 0.2089358904024117, 0.21047175982130567, 0.21200710992205463, 0.2135419369163349, 0.21507623701711337, 0.21661000643865713, 0.21814324139654254, 0.2196759381076648, 0.2212080927902471, 0.22273970166385015, 0.22427076094938117, 0.2258012668691037, 0.22733121564664643, 0.22886060350701293, 0.23038942667659057, 0.2319176813831603, 0.23344536385590542, 0.23497247032542135, 0.2364989970237247, 0.23802494018426254, 0.23955029604192185, 0.24107506083303865, 0.24259923079540743, 0.2441228021682903, 0.24564577119242634, 0.2471681341100409, 0.2486898871648548, 0.25021102660209366, 0.25173154866849706, 0.2532514496123281, 0.25477072568338216, 0.25628937313299666, 0.25780738821405985, 0.25932476718102054, 0.26084150628989694, 0.26235760179828604, 0.26387304996537286, 0.2653878470519398, 0.26690198932037557, 0.2684154730346846, 0.2699282944604964, 0.27144044986507426, 0.2729519355173252, 0.2744627476878087, 0.27597288264874575, 0.2774823366740285, 0.2789911060392293, 0.28049918702160953, 0.28200657590012945, 0.28351326895545675, 0.2850192624699761, 0.2865245527277983, 0.2880291360147692, 0.2895330086184791, 0.2910361668282718, 0.292538606935254, 0.294040325232304, 0.29554131801408107, 0.2970415815770349, 0.2985411122194142, 0.30003990624127624, 0.3015379599444957, 0.30303526963277394, 0.3045318316116483, 0.30602764218850076, 0.3075226976725674, 0.3090169943749474, 0.31051052860861234, 0.31200329668841487, 0.3134952949310981, 0.3149865196553048, 0.31647696718158613, 0.31796663383241097, 0.31945551593217497, 0.3209436098072095, 0.3224309117857909, 0.3239174181981494, 0.3254031253764782, 0.32688802965494246, 0.32837212736968857, 0.3298554148588529, 0.331337888462571, 0.3328195445229867, 0.33430037938426077, 0.33578038939258065, 0.33725957089616865, 0.3387379202452914, 0.3402154337922689, 0.3416921078914833, 0.3431679388993882, 0.34464292317451706, 0.34611705707749296, 0.34759033697103703, 0.3490627592199776, 0.350534320191259, 0.352005016253951, 0.35347484377925714, 0.35494379914052415, 0.35641187871325075, 0.3578790788750964, 0.35934539600589066, 0.3608108264876418, 0.3622753667045457, 0.363739013042995, 0.3652017618915878, 0.3666636096411368, 0.368124552684678, 0.36958458741747957, 0.371043710237051, 0.3725019175431518, 0.37395920573780045, 0.3754155712252831, 0.37687101041216264, 0.3783255197072877, 0.3797790955218011, 0.3812317342691491, 0.3826834323650898, 0.38413418622770257, 0.38558399227739654, 0.38703284693691936, 0.38848074663136606, 0.38992768778818826, 0.3913736668372024, 0.39281868021059896, 0.394262724342951, 0.3957057956712232, 0.3971478906347806, 0.3985890056753972, 0.4000291372372648, 0.40146828176700194, 0.40290643571366264, 0.404343595528745, 0.4057797576662, 0.4072149185824403, 0.40864907473634904, 0.4100822225892885, 0.4115143586051088, 0.4129454792501566, 0.41437558099328414, 0.4158046603058574, 0.4172327136617653, 0.4186597375374281, 0.42008572841180625, 0.4215106827664091, 0.4229345970853033, 0.4243574678551219, 0.42577929156507266, 0.427200064706947, 0.4286197837751284, 0.4300384452666011, 0.43145604568095897, 0.43287258152041397, 0.43428804928980463, 0.435702445496605, 0.4371157666509329, 0.43852800926555907, 0.43993916985591514, 0.4413492449401027, 0.4427582310389015, 0.4441661246757786, 0.4455729223768963, 0.44697862067112115, 0.44838321609003223, 0.4497867051679302, 0.4511890844418451, 0.45259035045154544, 0.4539904997395468, 0.4553895288511199, 0.45678743433429947, 0.4581842127398928, 0.45957986062148787, 0.46097437453546236, 0.4623677510409918, 0.4637599867000582, 0.46515107807745837, 0.4665410217408127, 0.4679298142605734, 0.4693174522100329, 0.4707039321653326, 0.4720892507054709, 0.4734734044123121, 0.4748563898705946, 0.4762382036679391, 0.4776188423948575, 0.478998302644761, 0.4803765810139686, 0.4817536741017153, 0.4831295785101609, 0.484504290844398, 0.48587780771246064, 0.4872501257253323, 0.4886212414969549, 0.48999115164423657, 0.4913598527870601, 0.49272734154829156, 0.49409361455378836, 0.4954586684324076, 0.49682249981601456, 0.4981851053394908, 0.49954648164074283, 0.5009066253607098, 0.5022655331433725, 0.5036232016357608, 0.5049796274879629, 0.5063348073531325, 0.5076887378874985, 0.5090414157503713, 0.5103928376041531, 0.5117430001143449, 0.5130918999495547, 0.5144395337815064, 0.5157858982850475, 0.5171309901381572, 0.5184748060219553, 0.5198173426207096, 0.5211585966218443, 0.5224985647159488, 0.523837243596785, 0.5251746299612957, 0.526510720509613, 0.5278455119450665, 0.5291790009741907, 0.530511184306734, 0.5318420586556667, 0.5331716207371886, 0.5344998672707373, 0.5358267949789967, 0.5371524005879043, 0.5384766808266602, 0.5397996324277347, 0.5411212521268759, 0.5424415366631188, 0.5437604827787924, 0.5450780872195286, 0.5463943467342691, 0.5477092580752745, 0.5490228179981318, 0.5503350232617624, 0.5516458706284303, 0.5529553568637499, 0.554263478736694, 0.5555702330196022, 0.556875616488188, 0.5581796259215475, 0.559482258102167, 0.5607835098159312, 0.5620833778521306, 0.5633818590034704, 0.564678950066077, 0.5659746478395076, 0.5672689491267565, 0.5685618507342639, 0.5698533494719238, 0.5711434421530912, 0.5724321255945909, 0.5737193966167244, 0.5750052520432786, 0.5762896887015329, 0.5775727034222676, 0.5788542930397714, 0.5801344543918494, 0.5814131843198306, 0.5826904796685761, 0.5839663372864865, 0.5852407540255101, 0.5865137267411501, 0.5877852522924731, 0.5890553275421161, 0.5903239493562945, 0.5915911146048104, 0.5928568201610592, 0.5941210629020386, 0.595383839708355, 0.5966451474642323, 0.5979049830575188, 0.5991633433796958, 0.600420225325884, 0.6016756257948523, 0.6029295416890247, 0.6041819699144885, 0.6054329073810014, 0.6066823510019997, 0.6079302976946054, 0.6091767443796341, 0.6104216879816026, 0.6116651254287361, 0.6129070536529765, 0.6141474695899893, 0.6153863701791715, 0.6166237523636591, 0.6178596130903343, 0.619093949309834, 0.620326757976556, 0.6215580360486677, 0.6227877804881126, 0.6240159882606185, 0.6252426563357052, 0.6264677816866908, 0.6276913612907006, 0.628913392128673, 0.6301338711853691, 0.6313527954493777, 0.6325701619131244, 0.6337859675728786, 0.6350002094287607, 0.6362128844847494, 0.6374239897486897, 0.6386335222322997, 0.6398414789511784, 0.6410478569248126, 0.6422526531765844, 0.6434558647337789, 0.6446574886275913, 0.6458575218931341, 0.6470559615694443, 0.6482528046994914, 0.6494480483301837, 0.6506416895123764, 0.6518337253008788, 0.6530241527544608, 0.6542129689358611, 0.6554001709117939, 0.6565857557529565, 0.6577697205340359, 0.658952062333717, 0.6601327782346886, 0.6613118653236518, 0.6624893206913265, 0.6636651414324585, 0.664839324645827, 0.6660118674342517, 0.6671827669045997, 0.668352020167793, 0.6695196243388155, 0.67068557653672, 0.6718498738846352, 0.6730125135097733, 0.6741734925434365, 0.6753328081210245, 0.6764904573820413, 0.6776464374701023, 0.6788007455329417, 0.6799533787224192, 0.6811043341945269, 0.6822536091093965, 0.6834012006313064, 0.6845471059286887, 0.685691322174136, 0.6868338465444083, 0.6879746762204404, 0.6891138083873485, 0.6902512402344372, 0.6913869689552065, 0.6925209917473585, 0.693653305812805, 0.6947839083576735, 0.6959127965923144, 0.6970399677313084, 0.6981654189934726, 0.6992891476018682, 0.7004111507838063, 0.7015314257708557, 0.7026499697988492, 0.7037667801078906, 0.7048818539423615, 0.7059951885509279, 0.7071067811865475, 0.708216629106476, 0.7093247295722739, 0.7104310798498135, 0.7115356772092853, 0.7126385189252055, 0.7137396022764213, 0.7148389245461194, 0.7159364830218311, 0.7170322749954402, 0.7181262977631888, 0.7192185486256846, 0.7203090248879069, 0.7213977238592142, 0.7224846428533499, 0.7235697791884493, 0.7246531301870467, 0.7257346931760809, 0.7268144654869029, 0.7278924444552817, 0.7289686274214116, 0.7300430117299178, 0.7311155947298641, 0.7321863737747585, 0.7332553462225601, 0.7343225094356856, 0.7353878607810158, 0.7364513976299024, 0.7375131173581739, 0.7385730173461422, 0.7396310949786097, 0.7406873476448749, 0.7417417727387392, 0.7427943676585137, 0.743845129807025, 0.744894056591622, 0.7459411454241821, 0.7469863937211177, 0.7480297989033825, 0.749071358396478, 0.7501110696304596, 0.7511489300399432, 0.7521849370641114, 0.75321908814672, 0.7542513807361038, 0.7552818122851837, 0.756310380251472, 0.7573370820970796, 0.7583619152887219, 0.7593848772977246, 0.7604059656000309, 0.7614251776762069, 0.7624425110114479, 0.7634579630955851, 0.7644715314230917, 0.7654832134930881, 0.7664930068093498, 0.7675009088803121, 0.7685069172190767, 0.769511029343418, 0.7705132427757893, 0.7715135550433284, 0.7725119636778645, 0.7735084662159233, 0.7745030601987338, 0.7754957431722345, 0.7764865126870786, 0.7774753662986409, 0.7784623015670235, 0.7794473160570615, 0.7804304073383297, 0.7814115729851482, 0.7823908105765881, 0.7833681176964782, 0.7843434919334101, 0.785316930880745, 0.7862884321366189, 0.7872579933039492, 0.7882256119904401, 0.7891912858085884, 0.7901550123756904, 0.7911167893138462, 0.7920766142499671, 0.7930344848157802, 0.7939903986478353, 0.79494435338751, 0.7958963466810158, 0.796846376179404, 0.797794439538571, 0.798740534419265, 0.7996846584870906, 0.8006268094125157, 0.8015669848708765, 0.8025051825423837, 0.8034414001121276, 0.8043756352700845, 0.805307885711122, 0.8062381491350047, 0.8071664232464003, 0.8080927057548846, 0.8090169943749475, 0.8099392868259987, 0.8108595808323734, 0.8117778741233377, 0.812694164433094, 0.813608449500787, 0.8145207270705094, 0.8154309948913069, 0.8163392507171839, 0.8172454923071099, 0.8181497174250234, 0.8190519238398392, 0.8199521093254524, 0.8208502716607448, 0.8217464086295903, 0.8226405180208598, 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0.9985741811195097, 0.998656800905955, 0.9987369566060175, 0.9988146480219211, 0.99888987496197, 0.9989626372405491, 0.9990329346781247, 0.999100767101245, 0.9991661343425401, 0.9992290362407229, 0.9992894726405892, 0.9993474433930183, 0.9994029483549729, 0.9994559873895001, 0.9995065603657316, 0.9995546671588833, 0.9996003076502565, 0.999643481727238, 0.9996841892832999, 0.9997224302180006, 0.999758204436984, 0.9997915118519811, 0.999822352380809, 0.9998507259473718, 0.9998766324816606, 0.9999000719197535, 0.9999210442038161, 0.9999395492821014, 0.9999555871089498, 0.9999691576447897, 0.9999802608561371, 0.999988896715596, 0.9999950652018582, 0.9999987662997035]; diff --git a/src/lookup/lookup_table.rs b/src/lookup/lookup_table.rs index f32c826..db34478 100644 --- a/src/lookup/lookup_table.rs +++ b/src/lookup/lookup_table.rs @@ -1,75 +1,25 @@ use std::f32::consts as f32_consts; use std::f64::consts as f64_consts; +use std::cmp::Ordering; +use num_traits::identities::One; +use num_traits::ops::wrapping::WrappingSub; use num_traits::float::{Float, FloatConst}; + +use crate::{ + impl_fbitfbit_lookup_table, + impl_cycling_fbitfbit_lookup_table, +}; use crate::lookup::TABLE_SIZE; +use crate::lookup::ordinal_float::FloatOrd; use crate::lookup::const_tables::*; -// 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( - input: [T; TABLE_SIZE], - mut map_target: [FloatOrd; TABLE_SIZE], -) -> () { - // let mut map_target = [FloatOrd::::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(pub T); -impl FloatOrd { - pub fn new() -> Self { - FloatOrd(T::zero()) - } -} -impl Eq for FloatOrd {} -impl Ord for FloatOrd { - fn cmp(&self, other: &Self) -> std::cmp::Ordering { - self.partial_cmp(other).unwrap_or(std::cmp::Ordering::Equal) - } -} - #[derive(Debug, Clone)] pub struct FloatLookupTable where T1: Float, T2: Float, + FloatOrd: Ord, { keys: [FloatOrd; TABLE_SIZE], values: [T2; TABLE_SIZE], @@ -78,6 +28,7 @@ impl FloatLookupTable where T1: Float, T2: Float, + FloatOrd: Ord, { pub fn new(keys: [T1; TABLE_SIZE], values: [T2; TABLE_SIZE]) -> Self { FloatLookupTable { @@ -86,20 +37,22 @@ where } } - pub fn get_next(&self, key: T1) -> T2 { + 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 { + let mut mid: usize; + + while lower_bound < upper_bound { + mid = lower_bound + (upper_bound - lower_bound) / 2; if self.keys[mid] < ord_key { - lower_bound = mid; + lower_bound = mid + 1; } else { upper_bound = mid; } - mid = (lower_bound + upper_bound) / 2; } - self.values[mid] + self.values[upper_bound] } pub fn lookup(&self, key: T1) -> T2 { @@ -117,27 +70,30 @@ pub struct CyclingFloatLookupTable where T1: Float, T2: Float, + FloatOrd: Ord, { lookup_table: FloatLookupTable, lower_bound: T1, - upper_bound: T1, + range: T1, } impl CyclingFloatLookupTable where T1: Float, T2: Float, + FloatOrd: Ord, { 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, - upper_bound, + lower_bound: lower_bound, + range: upper_bound - lower_bound, } } pub fn lookup(&self, key: T1) -> T2 { - let key = (key % (self.upper_bound - self.lower_bound)) + self.lower_bound; - self.lookup_table.lookup(key) + self.lookup_table.lookup( + (key % self.range) + self.lower_bound + ) } } impl_cycling_fbitfbit_lookup_table!(f32, f32); @@ -146,19 +102,19 @@ impl_cycling_fbitfbit_lookup_table!(f32, f64); impl_cycling_fbitfbit_lookup_table!(f64, f32); - #[derive(Debug, Clone)] pub struct EndoSinLookupTable where T: Float + FloatConst, + FloatOrd: Ord, { lookup_table: CyclingFloatLookupTable, } impl EndoSinLookupTable where T: Float + FloatConst, + FloatOrd: Ord, { - #[allow(dead_code)] pub fn lookup(&self, key: T) -> T { if key < T::zero() { -self.lookup(-key) @@ -166,28 +122,30 @@ where self.lookup_table.lookup(key) } else if key < T::PI() { self.lookup_table.lookup(T::PI() - key) - } else { + } else if key < T::TAU() { // obviously, mod is slow so we want to avoid it until this would start recursing deeply -self.lookup(key - T::PI()) + } else { + -self.lookup(key % T::PI()) } } } impl EndoSinLookupTable { pub const fn new() -> Self { - const UPPER_BOUND: f32 = f32_consts::PI; - EndoSinLookupTable { - lookup_table: CyclingFloatLookupTable::::new_const(SIN_F32_KEYS, SIN_F32_VALUES, 0.0f32, UPPER_BOUND), + lookup_table: CyclingFloatLookupTable::::new_const( + SIN_F32_KEYS, SIN_F32_VALUES, 0.0f32, f32_consts::PI + ), } } } impl EndoSinLookupTable { pub const fn new() -> Self { - let upper_bound = f64_consts::PI; - EndoSinLookupTable { - lookup_table: CyclingFloatLookupTable::::new_const(SIN_F64_KEYS, SIN_F64_VALUES, 0.0f64, upper_bound), + lookup_table: CyclingFloatLookupTable::::new_const( + SIN_F64_KEYS, SIN_F64_VALUES, 0.0f64, f64_consts::PI + ), } } } @@ -202,9 +160,8 @@ where } impl EndoCosLookupTable where - T: Float + FloatConst + std::fmt::Debug, + T: Float + FloatConst, { - #[allow(dead_code)] pub fn lookup(&self, key: T) -> T { self.lookup_table.lookup(key + T::FRAC_PI_2()) } diff --git a/src/lookup/mod.rs b/src/lookup/mod.rs index ada5f00..d37bf0f 100644 --- a/src/lookup/mod.rs +++ b/src/lookup/mod.rs @@ -1,6 +1,7 @@ -mod const_tables; +pub mod const_tables; pub mod lookup_table; +pub(crate) mod ordinal_float; -pub use const_tables::*; +pub use lookup_table::*; include!("config.rs"); \ No newline at end of file diff --git a/src/lookup/ordinal_float.rs b/src/lookup/ordinal_float.rs new file mode 100644 index 0000000..bcb99a1 --- /dev/null +++ b/src/lookup/ordinal_float.rs @@ -0,0 +1,16 @@ +use num_traits::float::Float; + +#[derive(Default, Debug, Clone, Copy, PartialEq, PartialOrd)] +pub struct FloatOrd(pub T); +impl FloatOrd { + #[allow(dead_code)] + pub fn new() -> Self { + FloatOrd(T::zero()) + } +} +impl Eq for FloatOrd {} +impl Ord for FloatOrd { + fn cmp(&self, other: &Self) -> std::cmp::Ordering { + self.partial_cmp(other).unwrap_or(std::cmp::Ordering::Equal) + } +} \ No newline at end of file diff --git a/src/macros/lookup.rs b/src/macros/lookup.rs new file mode 100644 index 0000000..f9904e2 --- /dev/null +++ b/src/macros/lookup.rs @@ -0,0 +1,30 @@ +mod lookup_table { + #[macro_export] + macro_rules! impl_fbitfbit_lookup_table { + ($key_type:ty, $value_type:ty) => { + impl FloatLookupTable<$key_type, $value_type> { + pub const fn new_const(keys: [FloatOrd<$key_type>; TABLE_SIZE], values: [$value_type; TABLE_SIZE]) -> Self { + FloatLookupTable { + keys: keys, + values: values, + } + } + } + }; + } + + #[macro_export] + macro_rules! impl_cycling_fbitfbit_lookup_table { + ($key_type:ty, $value_type:ty) => { + impl CyclingFloatLookupTable<$key_type, $value_type> { + pub const fn new_const(keys: [FloatOrd<$key_type>; TABLE_SIZE], values: [$value_type; TABLE_SIZE], lower_bound: $key_type, range: $key_type) -> Self { + CyclingFloatLookupTable { + lookup_table: FloatLookupTable::<$key_type, $value_type>::new_const(keys, values), + lower_bound: lower_bound, + range: range, + } + } + } + }; + } +} \ No newline at end of file diff --git a/src/macros/mod.rs b/src/macros/mod.rs new file mode 100644 index 0000000..83d58e1 --- /dev/null +++ b/src/macros/mod.rs @@ -0,0 +1 @@ +mod lookup; \ No newline at end of file diff --git a/src/tests.rs b/src/tests.rs deleted file mode 100644 index a5629a0..0000000 --- a/src/tests.rs +++ /dev/null @@ -1,174 +0,0 @@ -//tests.rs - -use num_traits::Float; - -fn calculate_percentage_error(vector1: &[T], vector2: &[T]) -> T - where T: Float + std::ops::AddAssign, -{ - let n = vector1.len(); - assert_eq!(n, vector2.len(), "Vectors must have equal lengths."); - - let mut total_error = T::zero(); - for i in 0..n { - let diff = (vector1[i] - vector2[i]).abs(); - let error = diff / if vector1[i] == T::zero() { T::min_positive_value() } else { vector1[i] }; - total_error += error; - } - - let average_error = total_error / T::from(n).unwrap(); - let percentage_error = average_error * T::from(100).expect("Cannot convert 100 to type T"); - percentage_error -} - -#[cfg(test)] -mod tests { - mod f64_error { - use crate::*; - use super::super::calculate_percentage_error; - use once_cell::sync::Lazy; - - const TOLERANCE: f64 = 2.5; - - static X: Lazy> = Lazy::new(|| { - (-10000..10000) - .map(|a| (a as f64) / 1000.) - .collect::>() - }); - - #[test] - fn pow2() -> Result<(), Box> { - let percentage_error = calculate_percentage_error( - &X.iter().map(|&x| x.fast_pow2()).collect::>(), - &X.iter().map(|&x| 2.0f64.powf(x)).collect::>() - ); - assert!(!percentage_error.is_nan(), "fast_pow2 percentage error is NaN"); - assert!( - percentage_error < TOLERANCE, - "fast_pow2 percentage error: {0}", - percentage_error - ); - Ok(()) - } - - #[test] - fn exp() -> Result<(), Box> { - let percentage_error = calculate_percentage_error( - &X.iter().map(|&x| x.fast_exp()).collect::>(), - &X.iter().map(|&x| x.exp()).collect::>() - ); - assert!(!percentage_error.is_nan(), "fast_exp percentage error is NaN"); - assert!( - percentage_error < TOLERANCE, - "fast_exp percentage error: {0}", - percentage_error - ); - Ok(()) - } - - #[test] - fn cos() -> Result<(), Box> { - let percentage_error = calculate_percentage_error( - &X.iter().map(|&x| x.fast_cos()).collect::>(), - &X.iter().map(|&x| x.cos()).collect::>() - ); - assert!(!percentage_error.is_nan(), "fast_cos percentage error is NaN"); - assert!( - percentage_error < TOLERANCE, - "fast_cos percentage error: {0}", - percentage_error - ); - // lookup - let percentage_error = calculate_percentage_error( - &X.iter().map(|&x| x.lookup_cos()).collect::>(), - &X.iter().map(|&x| x.cos()).collect::>() - ); - assert!(!percentage_error.is_nan(), "lookup_cos percentage error is NaN"); - assert!( - percentage_error < TOLERANCE, - "lookup_cos percentage error: {0}", - percentage_error - ); - Ok(()) - } - - #[test] - fn sigmoid() -> Result<(), Box> { - let percentage_error = calculate_percentage_error( - &X.iter().map(|&x| x.fast_sigmoid()).collect::>(), - &X.iter().map(|&x| sigmoid_builtin_f64(x)).collect::>() - ); - assert!(!percentage_error.is_nan(), "fast_sigmoid percentage error is NaN"); - assert!( - percentage_error < TOLERANCE, - "fast_sigmoid percentage error: {0}", - percentage_error - ); - Ok(()) - } - } - - mod f32_error { - use crate::*; - use super::super::calculate_percentage_error; - use once_cell::sync::Lazy; - - const TOLERANCE: f32 = 2.5; - - static X: Lazy> = Lazy::new(|| { - (-10000..10000) - .map(|a| (a as f32) / 1000.) - .collect::>() - }); - - #[test] - fn pow2() -> Result<(), Box> { - assert!( - calculate_percentage_error( - &X.iter().map(|&x| x.fast_pow2()).collect::>(), - &X.iter().map(|&x| 2.0f32.powf(x)).collect::>() - ) < TOLERANCE - ); - Ok(()) - } - - #[test] - fn exp() -> Result<(), Box> { - assert!( - calculate_percentage_error( - &X.iter().map(|&x| x.fast_exp()).collect::>(), - &X.iter().map(|&x| x.exp()).collect::>() - ) < TOLERANCE - ); - Ok(()) - } - - #[test] - fn cos() -> Result<(), Box> { - assert!( - calculate_percentage_error( - &X.iter().map(|&x| x.fast_cos()).collect::>(), - &X.iter().map(|&x| x.cos()).collect::>() - ) < TOLERANCE - ); - // lookup - assert!( - calculate_percentage_error( - &X.iter().map(|&x| x.lookup_cos()).collect::>(), - &X.iter().map(|&x| x.cos()).collect::>() - ) < TOLERANCE - ); - Ok(()) - } - - #[test] - fn sigmoid() -> Result<(), Box> { - assert!( - calculate_percentage_error( - &X.iter().map(|&x| x.fast_sigmoid()).collect::>(), - &X.iter().map(|&x| sigmoid_builtin_f32(x)).collect::>() - ) < TOLERANCE - ); - Ok(()) - } - } -} \ No newline at end of file diff --git a/src/tests/accuracy/comparisons.rs b/src/tests/accuracy/comparisons.rs new file mode 100644 index 0000000..e2c2298 --- /dev/null +++ b/src/tests/accuracy/comparisons.rs @@ -0,0 +1,130 @@ +#[cfg(test)] + +use super::exact; + +use num_traits::Float; + +fn calculate_percentage_error(vector1: &[T], vector2: &[T]) -> T + where T: Float, +{ + let n = vector1.len(); + assert_eq!(n, vector2.len(), "Vectors must have equal lengths."); + + let mut total_error = T::zero(); + for i in 0..n { + let diff = (vector1[i] - vector2[i]).abs(); + let error = diff / if vector1[i] == T::zero() { T::min_positive_value() } else { vector1[i] }; + total_error = total_error + error; + } + + let average_error = total_error / T::from(n).unwrap(); + let percentage_error = average_error * T::from(100).expect("Cannot convert 100 to type T"); + percentage_error +} + +macro_rules! panic_if_nan_or_print { + ($x:expr, $varname:expr) => { + if $x.is_nan() { + Err(format!("{} is NaN!", $varname))? + } else { + println!("{}: {}%", $varname, $x); + Ok($x) + } + } +} + +pub mod f64 { + use crate::*; + use super::exact; + use super::calculate_percentage_error; + + include!("x.rs"); + + pub fn pow2() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F64.iter().map(|&x| x.fast_pow2()).collect::>(), + &X_F64.iter().map(|&x| exact::f64::pow2(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_pow2 percentage error") + } + + pub fn exp() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F64.iter().map(|&x| x.fast_exp()).collect::>(), + &X_F64.iter().map(|&x| exact::f64::exp(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_exp percentage error") + } + + pub fn cos() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F64.iter().map(|&x| x.fast_cos()).collect::>(), + &X_F64.iter().map(|&x| exact::f64::cos(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_cos percentage error") + } + + pub fn cos_lookup() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F64.iter().map(|&x| x.lookup_cos()).collect::>(), + &X_F64.iter().map(|&x| exact::f64::cos(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "lookup_cos percentage error") + } + + pub fn sigmoid() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F64.iter().map(|&x| x.fast_sigmoid()).collect::>(), + &X_F64.iter().map(|&x| exact::f64::sigmoid(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_sigmoid percentage error") + } +} + +pub mod f32 { + use crate::*; + use super::exact; + use super::calculate_percentage_error; + + include!("x.rs"); + + pub fn pow2() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F32.iter().map(|&x| x.fast_pow2()).collect::>(), + &X_F32.iter().map(|&x| exact::f32::pow2(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_pow2 percentage error") + } + + pub fn exp() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F32.iter().map(|&x| x.fast_exp()).collect::>(), + &X_F32.iter().map(|&x| exact::f32::exp(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_exp percentage error") + } + + pub fn cos() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F32.iter().map(|&x| x.fast_cos()).collect::>(), + &X_F32.iter().map(|&x| exact::f32::cos(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_cos percentage error") + } + + pub fn cos_lookup() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F32.iter().map(|&x| x.lookup_cos()).collect::>(), + &X_F32.iter().map(|&x| exact::f32::cos(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "lookup_cos percentage error") + } + + pub fn sigmoid() -> Result> { + let percentage_error = calculate_percentage_error( + &X_F32.iter().map(|&x| x.fast_sigmoid()).collect::>(), + &X_F32.iter().map(|&x| exact::f32::sigmoid(x)).collect::>() + ); + panic_if_nan_or_print!(percentage_error, "fast_sigmoid percentage error") + } +} \ No newline at end of file diff --git a/src/tests/accuracy/config.rs b/src/tests/accuracy/config.rs new file mode 100644 index 0000000..9827ec3 --- /dev/null +++ b/src/tests/accuracy/config.rs @@ -0,0 +1,3 @@ +const X_MIN: f64 = -10.0; +const X_MAX: f64 = 10.0; +const X_SIZE: usize = 20000; \ No newline at end of file diff --git a/src/tests/accuracy/exact.rs b/src/tests/accuracy/exact.rs new file mode 100644 index 0000000..ed5c4c4 --- /dev/null +++ b/src/tests/accuracy/exact.rs @@ -0,0 +1,35 @@ +pub mod f64 { + pub fn pow2(n: f64) -> f64 { + 2.0f64.powf(n) + } + + pub fn exp(n: f64) -> f64 { + n.exp() + } + + pub fn cos(n: f64) -> f64 { + n.cos() + } + + pub fn sigmoid(n: f64) -> f64 { + (1. + (-n).exp()).recip() + } +} + +pub mod f32 { + pub fn pow2(n: f32) -> f32 { + 2.0f32.powf(n) + } + + pub fn exp(n: f32) -> f32 { + n.exp() + } + + pub fn cos(n: f32) -> f32 { + n.cos() + } + + pub fn sigmoid(n: f32) -> f32 { + (1. + (-n).exp()).recip() + } +} \ No newline at end of file diff --git a/src/tests/accuracy/mod.rs b/src/tests/accuracy/mod.rs new file mode 100644 index 0000000..f2fecaa --- /dev/null +++ b/src/tests/accuracy/mod.rs @@ -0,0 +1,4 @@ +mod exact; + +mod comparisons; +pub use comparisons::*; \ No newline at end of file diff --git a/src/tests/accuracy/x.rs b/src/tests/accuracy/x.rs new file mode 100644 index 0000000..7f4b9ee --- /dev/null +++ b/src/tests/accuracy/x.rs @@ -0,0 +1,6 @@ +#[cfg(test)] +#[allow(dead_code)] +pub const X_F32: [f32; 20000] = [-10.0, -9.999, -9.998, -9.997, -9.996, -9.995, -9.994, -9.993, -9.992, -9.991, -9.99, -9.989, -9.988, -9.987, -9.986, -9.985, -9.984, -9.983, -9.982, -9.981, -9.98, -9.979, -9.978, -9.977, -9.976, -9.975, -9.974, -9.973, -9.972, -9.971, -9.97, -9.969, -9.968, 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9.485001, 9.486, 9.4869995, 9.488001, 9.489, 9.49, 9.490999, 9.492001, 9.493, 9.4939995, 9.495001, 9.496, 9.497, 9.497999, 9.499001, 9.5, 9.500999, 9.502001, 9.503, 9.504, 9.504999, 9.5060005, 9.507, 9.507999, 9.509001, 9.51, 9.511, 9.511999, 9.5130005, 9.514, 9.514999, 9.516001, 9.517, 9.518, 9.518999, 9.52, 9.521, 9.521999, 9.523001, 9.524, 9.525, 9.525999, 9.527, 9.528, 9.528999, 9.530001, 9.531, 9.532, 9.533001, 9.534, 9.535, 9.535999, 9.537001, 9.538, 9.539, 9.540001, 9.541, 9.542, 9.542999, 9.544001, 9.545, 9.546, 9.547001, 9.548, 9.549, 9.549999, 9.551001, 9.552, 9.5529995, 9.554001, 9.555, 9.556, 9.556999, 9.558001, 9.559, 9.559999, 9.561001, 9.562, 9.563, 9.563999, 9.565001, 9.566, 9.566999, 9.568001, 9.569, 9.57, 9.570999, 9.5720005, 9.573, 9.573999, 9.575001, 9.576, 9.577, 9.577999, 9.579, 9.58, 9.580999, 9.582001, 9.583, 9.584, 9.584999, 9.586, 9.587, 9.587999, 9.589001, 9.59, 9.591, 9.591999, 9.593, 9.594, 9.594999, 9.596001, 9.597, 9.598, 9.599001, 9.6, 9.601, 9.601999, 9.603001, 9.604, 9.605, 9.606001, 9.607, 9.608, 9.608999, 9.610001, 9.611, 9.6119995, 9.613001, 9.614, 9.615, 9.615999, 9.617001, 9.618, 9.6189995, 9.620001, 9.621, 9.622, 9.622999, 9.624001, 9.625, 9.625999, 9.627001, 9.628, 9.629, 9.629999, 9.6310005, 9.632, 9.632999, 9.634001, 9.635, 9.636, 9.636999, 9.6380005, 9.639, 9.639999, 9.641001, 9.642, 9.643, 9.643999, 9.645, 9.646, 9.646999, 9.648001, 9.649, 9.65, 9.650999, 9.652, 9.653, 9.653999, 9.655001, 9.656, 9.657, 9.658001, 9.659, 9.66, 9.660999, 9.662001, 9.663, 9.664, 9.665001, 9.666, 9.667, 9.667999, 9.669001, 9.67, 9.671, 9.672001, 9.673, 9.674, 9.674999, 9.676001, 9.677, 9.6779995, 9.679001, 9.68, 9.681, 9.681999, 9.683001, 9.684, 9.684999, 9.686001, 9.687, 9.688, 9.688999, 9.690001, 9.691, 9.691999, 9.693001, 9.694, 9.695, 9.695999, 9.6970005, 9.698, 9.698999, 9.700001, 9.701, 9.702, 9.702999, 9.704, 9.705, 9.705999, 9.707001, 9.708, 9.709, 9.709999, 9.711, 9.712, 9.712999, 9.714001, 9.715, 9.716, 9.716999, 9.718, 9.719, 9.719999, 9.721001, 9.722, 9.723, 9.724001, 9.725, 9.726, 9.726999, 9.728001, 9.729, 9.73, 9.731001, 9.732, 9.733, 9.733999, 9.735001, 9.736, 9.7369995, 9.738001, 9.739, 9.74, 9.740999, 9.742001, 9.743, 9.7439995, 9.745001, 9.746, 9.747, 9.747999, 9.749001, 9.75, 9.750999, 9.752001, 9.753, 9.754, 9.754999, 9.7560005, 9.757, 9.757999, 9.759001, 9.76, 9.761, 9.761999, 9.7630005, 9.764, 9.764999, 9.766001, 9.767, 9.768, 9.768999, 9.77, 9.771, 9.771999, 9.773001, 9.774, 9.775, 9.775999, 9.777, 9.778, 9.778999, 9.780001, 9.781, 9.782, 9.783001, 9.784, 9.785, 9.785999, 9.787001, 9.788, 9.789, 9.790001, 9.791, 9.792, 9.792999, 9.794001, 9.795, 9.796, 9.797001, 9.798, 9.799, 9.799999, 9.801001, 9.802, 9.8029995, 9.804001, 9.805, 9.806, 9.806999, 9.808001, 9.809, 9.809999, 9.811001, 9.812, 9.813, 9.813999, 9.815001, 9.816, 9.816999, 9.818001, 9.819, 9.82, 9.820999, 9.8220005, 9.823, 9.823999, 9.825001, 9.826, 9.827, 9.827999, 9.829, 9.83, 9.830999, 9.832001, 9.833, 9.834, 9.834999, 9.836, 9.837, 9.837999, 9.839001, 9.84, 9.841, 9.841999, 9.843, 9.844, 9.844999, 9.846001, 9.847, 9.848, 9.849001, 9.85, 9.851, 9.851999, 9.853001, 9.854, 9.855, 9.856001, 9.857, 9.858, 9.858999, 9.860001, 9.861, 9.8619995, 9.863001, 9.864, 9.865, 9.865999, 9.867001, 9.868, 9.8689995, 9.870001, 9.871, 9.872, 9.872999, 9.874001, 9.875, 9.875999, 9.877001, 9.878, 9.879, 9.879999, 9.8810005, 9.882, 9.882999, 9.884001, 9.885, 9.886, 9.886999, 9.8880005, 9.889, 9.889999, 9.891001, 9.892, 9.893, 9.893999, 9.895, 9.896, 9.896999, 9.898001, 9.899, 9.9, 9.900999, 9.902, 9.903, 9.903999, 9.905001, 9.906, 9.907, 9.908001, 9.909, 9.91, 9.910999, 9.912001, 9.913, 9.914, 9.915001, 9.916, 9.917, 9.917999, 9.919001, 9.92, 9.921, 9.922001, 9.923, 9.924, 9.924999, 9.926001, 9.927, 9.9279995, 9.929001, 9.93, 9.931, 9.931999, 9.933001, 9.934, 9.934999, 9.936001, 9.937, 9.938, 9.938999, 9.940001, 9.941, 9.941999, 9.943001, 9.944, 9.945, 9.945999, 9.9470005, 9.948, 9.948999, 9.950001, 9.951, 9.952, 9.952999, 9.954, 9.955, 9.955999, 9.957001, 9.958, 9.959, 9.959999, 9.961, 9.962, 9.962999, 9.964001, 9.965, 9.966, 9.966999, 9.968, 9.969, 9.969999, 9.971001, 9.972, 9.973, 9.974001, 9.975, 9.976, 9.976999, 9.978001, 9.979, 9.98, 9.981001, 9.982, 9.983, 9.983999, 9.985001, 9.986, 9.9869995, 9.988001, 9.989, 9.99, 9.990999, 9.992001, 9.993, 9.9939995, 9.995001, 9.996, 9.997, 9.997999, 9.999001]; +#[cfg(test)] +#[allow(dead_code)] +pub const X_F64: [f64; 20000] = [-10.0, -9.999, -9.998, -9.997, -9.996, -9.995, -9.994, -9.993, -9.992, -9.991, -9.99, -9.989, -9.988, -9.987, -9.986, -9.985, -9.984, -9.983, -9.982, -9.981, -9.98, -9.979, -9.978, -9.977, -9.976, -9.975, -9.974, -9.973, -9.972, -9.971, -9.97, -9.969, -9.968, -9.967, -9.966, -9.965, -9.964, -9.963, -9.962, -9.961, -9.96, -9.959, -9.958, -9.957, -9.956, -9.955, -9.954, -9.953, -9.952, -9.951, -9.95, -9.949, -9.948, -9.947, -9.946, -9.945, -9.944, -9.943, -9.942, -9.941, -9.94, -9.939, -9.938, -9.937, -9.936, -9.935, -9.934, -9.933, -9.932, -9.931, -9.93, -9.929, -9.928, -9.927, -9.926, -9.925, -9.924, -9.923, -9.922, -9.921, -9.92, -9.919, -9.918, -9.917, -9.916, -9.915, -9.914, -9.913, -9.912, -9.911, -9.91, -9.909, -9.908, -9.907, -9.906, -9.905, -9.904, -9.903, -9.902, -9.901, -9.9, -9.899, -9.898, -9.897, -9.896, -9.895, -9.894, -9.893, -9.892, -9.891, -9.89, -9.889, -9.888, -9.887, -9.886, -9.885, -9.884, -9.883, -9.882, -9.881, -9.88, -9.879, -9.878, -9.877, -9.876, -9.875, -9.874, -9.873, -9.872, -9.871, -9.87, -9.869, -9.868, -9.867, -9.866, -9.865, -9.864, -9.863, -9.862, -9.861, -9.86, -9.859, -9.858, -9.857, -9.856, -9.855, -9.854, -9.853, -9.852, -9.851, -9.85, -9.849, -9.848, -9.847, -9.846, -9.845, -9.844, -9.843, -9.842, -9.841, -9.84, -9.839, -9.838, -9.837, -9.836, -9.835, -9.834, -9.833, -9.832, -9.831, -9.83, -9.829, -9.828, -9.827, -9.826, -9.825, -9.824, -9.823, -9.822, -9.821, -9.82, -9.819, -9.818, -9.817, -9.816, -9.815, -9.814, -9.813, -9.812, -9.811, -9.81, -9.809, -9.808, -9.807, -9.806, -9.805, -9.804, -9.803, -9.802, -9.801, -9.8, -9.799, -9.798, -9.797, -9.796, -9.795, -9.794, -9.793, -9.792, -9.791, -9.79, -9.789, -9.788, -9.787, -9.786, -9.785, -9.784, -9.783, -9.782, -9.781, -9.78, -9.779, -9.778, -9.777, -9.776, -9.775, -9.774, -9.773, -9.772, -9.771, -9.77, -9.769, -9.768, -9.767, -9.766, -9.765, -9.764, -9.763, -9.762, -9.761, -9.76, -9.759, -9.758, -9.757, -9.756, -9.755, -9.754, -9.753, -9.752, -9.751, -9.75, -9.749, -9.748, -9.747, -9.746, -9.745, -9.744, -9.743, -9.742, -9.741, -9.74, -9.739, -9.738, -9.737, -9.736, -9.735, -9.734, -9.733, -9.732, -9.731, -9.73, -9.729, -9.728, -9.727, -9.725999999999999, -9.725, -9.724, -9.723, -9.722, -9.721, -9.72, -9.719, -9.718, -9.717, -9.716, -9.715, -9.714, -9.713, -9.712, -9.711, -9.71, -9.709, -9.708, -9.707, -9.706, -9.705, -9.704, -9.703, -9.702, -9.701, -9.7, -9.699, -9.698, -9.697, -9.696, -9.695, -9.694, -9.693, -9.692, -9.691, -9.69, -9.689, -9.688, -9.687, -9.686, -9.685, -9.684, -9.683, -9.682, -9.681, -9.68, -9.679, -9.678, -9.677, -9.676, -9.675, -9.674, -9.673, -9.672, -9.671, -9.67, -9.669, -9.668, -9.667, -9.666, -9.665, -9.664, -9.663, -9.662, -9.661, -9.66, -9.659, -9.658, -9.657, -9.656, -9.655, -9.654, -9.653, -9.652, -9.651, -9.65, -9.649000000000001, -9.648, -9.647, -9.646, -9.645, -9.644, -9.643, -9.642, -9.641, -9.64, -9.639, -9.638, -9.637, -9.636, -9.635, -9.634, -9.633, -9.632, -9.631, -9.63, -9.629, -9.628, -9.627, -9.626, -9.625, -9.624, -9.623, -9.622, -9.621, -9.62, -9.619, -9.618, -9.617, -9.616, -9.615, -9.614, -9.613, -9.612, -9.611, -9.61, -9.609, -9.608, -9.607, -9.606, -9.605, -9.604, -9.603, -9.602, -9.600999999999999, -9.6, -9.599, -9.598, -9.597, -9.596, -9.595, -9.594, -9.593, -9.592, -9.591, -9.59, -9.589, -9.588, -9.587, -9.586, -9.585, -9.584, -9.583, -9.582, -9.581, -9.58, -9.579, -9.578, -9.577, -9.576, -9.575, -9.574, -9.573, -9.572, -9.571, -9.57, -9.569, -9.568, -9.567, -9.566, -9.565, -9.564, -9.563, -9.562, -9.561, -9.56, -9.559, -9.558, -9.557, -9.556, -9.555, -9.554, -9.553, -9.552, -9.551, -9.55, -9.549, -9.548, -9.547, -9.546, -9.545, -9.544, -9.543, -9.542, -9.541, -9.54, -9.539, -9.538, -9.537, -9.536, -9.535, -9.534, -9.533, -9.532, -9.531, -9.53, -9.529, -9.528, -9.527, -9.526, -9.525, -9.524000000000001, -9.523, -9.522, -9.521, -9.52, -9.519, -9.518, -9.517, -9.516, -9.515, -9.514, -9.513, -9.512, -9.511, -9.51, -9.509, -9.508, -9.507, -9.506, -9.505, -9.504, -9.503, -9.502, -9.501, -9.5, -9.499, -9.498, -9.497, -9.496, -9.495, -9.494, -9.493, -9.492, -9.491, -9.49, -9.489, -9.488, -9.487, -9.486, -9.485, -9.484, -9.483, -9.482, -9.481, -9.48, -9.479, -9.478, -9.477, -9.475999999999999, -9.475, -9.474, -9.473, -9.472, -9.471, -9.47, -9.469, -9.468, -9.467, -9.466, -9.465, -9.464, -9.463, -9.462, -9.461, -9.46, -9.459, -9.458, -9.457, -9.456, -9.455, -9.454, -9.453, -9.452, -9.451, -9.45, -9.449, -9.448, -9.447, -9.446, -9.445, -9.443999999999999, -9.443, -9.442, -9.441, -9.44, -9.439, -9.438, -9.437, 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2.0, + "exp_fast": 2.0, + "cos_fast": 1.0, + "cos_lk": 1.0, + "sigmoid_fast": 1.0 +} \ No newline at end of file diff --git a/src/tests/tolerance.rs b/src/tests/tolerance.rs new file mode 100644 index 0000000..cfe6287 --- /dev/null +++ b/src/tests/tolerance.rs @@ -0,0 +1,50 @@ +use super::accuracy; +use serde_json; + +fn get_tolerance(key: &str) -> Result +where + T: serde::de::DeserializeOwned +{ + let json: serde_json::Value = + serde_json::from_str( + include_str!("tolerance.json") + )?; + let value = serde_json::value::from_value( + json[key].clone() + )?; + Ok(value) +} + +macro_rules! test_within_tolerance { + ($function:ident, $t:ty, $test_name:ident) => { + #[test] + fn $test_name() -> Result<(), Box> { + let tolerance: $t = get_tolerance::<$t>(stringify!($test_name))?; + let percentage_error: $t = $function()?; + assert!(percentage_error < tolerance); + Ok(()) + } + }; +} + +mod f64 { + use super::{accuracy, get_tolerance}; + use accuracy::f64::*; + + test_within_tolerance!(pow2, f64, pow2_fast); + test_within_tolerance!(exp, f64, exp_fast); + test_within_tolerance!(cos, f64, cos_fast); + test_within_tolerance!(cos_lookup, f64, cos_lk); + test_within_tolerance!(sigmoid, f64, sigmoid_fast); +} + +mod f32 { + use super::{accuracy, get_tolerance}; + use accuracy::f32::*; + + test_within_tolerance!(pow2, f32, pow2_fast); + test_within_tolerance!(exp, f32, exp_fast); + test_within_tolerance!(cos, f32, cos_fast); + test_within_tolerance!(cos_lookup, f32, cos_lk); + test_within_tolerance!(sigmoid, f32, sigmoid_fast); +} \ No newline at end of file diff --git a/test.rs b/test.rs new file mode 100644 index 0000000..321df64 --- /dev/null +++ b/test.rs @@ -0,0 +1,70 @@ +use std::fs::read; +use std::f64::consts as f64_consts; +use bincode::deserialize; +use once_cell::sync::Lazy; +use ndarray::prelude::*; +use optimize::*; +use num_traits::Float; + + +fn calculate_percentage_error(vector1: &[T], vector2: &[T]) -> T + where T: Float + std::ops::AddAssign, +{ + let n = vector1.len(); + assert_eq!(n, vector2.len(), "Vectors must have equal lengths."); + + let mut total_error = T::zero(); + for i in 0..n { + let diff = (vector1[i] - vector2[i]).abs(); + let error = diff / if vector1[i] == T::zero() { T::min_positive_value() } else { vector1[i] }; + total_error += error; + } + + let average_error = total_error / T::from(n).unwrap(); + let percentage_error = average_error * T::from(100).expect("Cannot convert 100 to type T"); + percentage_error +} + + +fn fast_exp(x: f64, clipp_thresh: f64, v_scale: f64, clipp_shift: f64) -> 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 * x; + let clipp = scaled_p.max(clipp_thresh); + let v = (v_scale * (clipp + clipp_shift)) as u64; + f64::from_bits(v) +} + +const Y: Lazy> = Lazy::new(|| { deserialize(&read("tmp/Y.bin").unwrap()).unwrap() } ); + +fn objective(args: ArrayView1) -> f64 { + let clipp_thresh: f64 = args[0]; + let v_scale: f64 = args[1]; + let clipp_shift: f64 = args[2]; + + let X: Vec = (-10000..10000) + .map(|a| (a as f64) / 1000.) + .collect::>(); + let Y_hat: Vec = X.iter().map(|&x| fast_exp(x, clipp_thresh, v_scale, clipp_shift)).collect::>(); + calculate_percentage_error(&(*Y), &Y_hat) +} + +fn optimize_params() { + // Create a minimizer using the builder pattern. + let minimizer = NelderMeadBuilder::default() + .xtol(1e-6f64) + .ftol(1e-6f64) + .maxiter(50000) + .build() + .unwrap(); + + // Set the starting guess + let args: Array1 = Array1::from_vec(vec![-180335.51911105003, 4524653012949098.0, 1018.1563534409383]); + + // Run the optimization + let ans = minimizer.minimize(objective, args.view()); + + // Print the optimized values + println!("Final optimized arguments: {}", ans); +} \ No newline at end of file