use crate::math::{PI, PI_2, PI_NEG_2};
/// Computes the four quadrant arctangent of self (y) and other (x) in radians.
///
/// * Average error of 0.00231 radians.
/// * Largest error of 0.00488 radians.
/// * Speedup of 20.67x over f32.atan2(y);
pub fn atan2(y: f32, x: f32) -> f32 {
const CONST: f32 = 0.28087f32; // Trial and error
if x == 0f32 {
if y > 0f32 {
return PI_2;
}
if y == 0f32 {
return 0f32;
}
return PI_NEG_2;
}
let z: f32 = y / x;
let atan: f32;
if z.abs() < 1f32 {
atan = z / (z * z * CONST + 1f32);
if x < 0f32 {
if y < 0f32 {
return atan - PI;
}
return atan + PI;
}
return atan;
}
atan = PI_2 - z / (z * z + CONST);
if y < 0f32 {
return atan - PI;
}
atan
}
const SIN_BITS: i32 = 11i32;
const SIN_MASK: i32 = !(-1i32 << SIN_BITS);
const SIN_COUNT: i32 = SIN_MASK + 1i32;
const RAD_FULL: f32 = PI * 2f32;
const DEG_FULL: f32 = 360f32;
const RAD_INDEX: f32 = (SIN_COUNT as f32) / RAD_FULL;
const DEG_INDEX: f32 = (SIN_COUNT as f32) / DEG_FULL;
const SIZE: usize = SIN_COUNT as usize;
/// Computes the sine of a number. Input in radians, output in radians.
///
/// * Average error of 0.00060 radians.
/// * Largest error of 0.00229 radians.
/// * Speedup of 30x over f32.sin();
pub fn sin_rad(rad: f32) -> f32 {
unsafe { *SIN.get_unchecked((((rad * RAD_INDEX) as i32) & SIN_MASK) as usize) }
}
/// Computes the cosine of a number. Input in radians, output in radians.
///
/// * Average error of 0.00060 radians.
/// * Largest error of 0.00229 radians.
/// * Speedup of 30x over f32.cos();
pub fn cos_rad(rad: f32) -> f32 {
unsafe { *COS.get_unchecked((((rad * RAD_INDEX) as i32) & SIN_MASK) as usize) }
}
/// Computes the sine of a number. Input in degrees, output in radians.
///
/// * Average error of 0.00060 radians.
/// * Largest error of 0.00229 radians.
/// * Speedup of 30x over f32.sin();
pub fn sin_deg(deg: f32) -> f32 {
unsafe { *SIN.get_unchecked((((deg * DEG_INDEX) as i32) & SIN_MASK) as usize) }
}
/// Computes the cosine of a number. Input in degrees, output in radians.
///
/// * Average error of 0.00060 radians.
/// * Largest error of 0.00229 radians.
/// * Speedup of 30x over f32.cos();
pub fn cos_deg(deg: f32) -> f32 {
unsafe { *COS.get_unchecked((((deg * DEG_INDEX) as i32) & SIN_MASK) as usize) }
}
// Tokenization is skipped for long lines
#[rustfmt::skip] #[allow(clippy::all)] static SIN: [f32; SIZE] = [0f32, 0.004601926f32, 0.0076698293f32, 0.010737659f32, 0.0138053885f32, 0.016872989f32, 0.019940428f32, 0.023007682f32, 0.026074719f32, 0.02914151f32, 0.03220803f32, 0.035274237f32, 0.03834012f32, 0.041405644f32, 0.044470772f32, 0.047535487f32, 0.05059975f32, 0.05366354f32, 0.05672682f32, 0.059789572f32, 0.06285176f32, 0.06591336f32, 0.06897433f32, 0.07203466f32, 0.075094305f32, 0.078153245f32, 0.08121145f32, 0.08426889f32, 0.087325536f32, 0.09038136f32, 0.09343634f32, 0.096490435f32, 0.099543616f32, 0.10259587f32, 0.105647154f32, 0.108697444f32, 0.11174671f32, 0.11479493f32, 0.11784206f32, 0.12088809f32, 0.12393298f32, 0.1269767f32, 0.13001922f32, 0.13306053f32, 0.13610058f32, 0.13913935f32, 0.1421768f32, 0.14521293f32, 0.14824769f32, 0.15128104f32, 0.15431298f32, 0.15734346f32, 0.16037247f32, 0.16339995f32, 0.1664259f32, 0.1694503f32, 0.17247309f32, 0.17549427f32, 0.17851378f32, 0.18153162f32, 0.18454774f32, 0.18756212f32, 0.19057477f32, 0.19358559f32, 0.19659461f32, 0.19960175f32, 0.20260705f32, 0.20561042f32, 0.20861185f32, 0.21161133f32, 0.21460882f32, 0.21760428f32, 0.2205977f32, 0.22358905f32, 0.22657827f32, 0.22956537f32, 0.23255032f32, 0.23553306f32, 0.2385136f32, 0.24149188f32, 0.2444679f32, 0.24744162f32, 0.250413f32, 0.25338206f32, 0.2563487f32, 0.25931293f32, 0.2622747f32, 0.26523405f32, 0.26819086f32, 0.27114516f32, 0.27409694f32, 0.2770461f32, 0.27999264f32, 0.28293657f32, 0.28587785f32, 0.2888164f32, 0.29175228f32, 0.2946854f32, 0.29761574f32, 0.30054325f32, 0.30346796f32, 0.3063898f32, 0.30930877f32, 0.3122248f32, 0.31513795f32, 0.3180481f32, 0.32095525f32, 0.32385936f32, 0.32676047f32, 0.32965845f32, 0.3325534f32, 0.33544517f32, 0.33833376f32, 0.34121922f32, 0.34410143f32, 0.34698042f32, 0.34985614f32, 0.35272858f32, 0.35559767f32, 0.3584634f32, 0.3613258f32, 0.3641848f32, 0.36704037f32, 0.36989245f32, 0.37274107f32, 0.37558618f32, 0.37842774f32, 0.3812658f32, 0.3841002f32, 0.38693103f32, 0.38975817f32, 0.39258167f32, 0.3954015f32, 0.39821756f32, 0.4010299f32, 0.4038385f32, 0.40664324f32, 0.40944415f32, 0.41224125f32, 0.41503444f32, 0.4178237f32, 0.4206091f32, 0.42339048f32, 0.4261679f32, 0.4289413f32, 0.43171066f32, 0.434476f32, 0.43723717f32, 0.43999428f32, 0.44274724f32, 0.44549602f32, 0.4482406f32, 0.450981f32, 0.45371714f32, 0.45644897f32, 0.45917657f32, 0.46189982f32, 0.46461868f32, 0.46733323f32, 0.47004336f32, 0.47274905f32, 0.47545028f32, 0.47814706f32, 0.4808393f32, 0.4835271f32, 0.4862103f32, 0.48888892f32, 0.49156293f32, 0.49423233f32, 0.4968971f32, 0.4995571f32, 0.50221246f32, 0.50486314f32, 0.507509f32, 0.51015013f32, 0.51278645f32, 0.5154179f32, 0.5180445f32, 0.52066624f32, 0.5232831f32, 0.52589506f32, 0.52850205f32, 0.531104f32, 0.533701f32, 0.53629297f32, 0.53887993f32, 0.54146177f32, 0.54403853f32, 0.5466102f32, 0.5491767f32, 0.55173796f32, 0.5542941f32, 0.55684507f32, 0.5593907f32, 0.56193113f32, 0.5644663f32, 0.5669961f32, 0.56952053f32, 0.5720396f32, 0.5745534f32, 0.5770617f32, 0.5795646f32, 0.582062f32, 0.58455396f32, 0.58704036f32, 0.5895213f32, 0.5919967f32, 0.5944665f32, 0.59693074f32, 0.5993893f32, 0.6018423f32, 0.60428953f32, 0.6067311f32, 0.60916704f32, 0.6115972f32, 0.6140216f32, 0.6164402f32, 0.61885303f32, 0.62126f32, 0.6236611f32, 0.6260564f32, 0.6284458f32, 0.6308293f32, 0.6332068f32, 0.63557833f32, 0.6379439f32, 0.6403035f32, 0.64265704f32, 0.6450046f32, 0.647346f32, 0.6496813f32, 0.65201056f32, 0.6543336f32, 0.65665054f32, 0.6589613f32, 0.66126585f32, 0.6635642f32, 0.66585624f32, 0.6681421f32, 0.67042154f32, 0.6726948f32, 0.6749617f32, 0.6772222f32, 0.6794763f32, 0.68172413f32, 0.68396544f32, 0.6862003f32, 0.68842876f32, 0.6906507f32, 0.6928662f32, 0.69507515f32, 0.69727755f32, 0.6994734f32, 0.7016626f32, 0.70384526f32, 0.70602125f32, 0.7081907f32, 0.7103534f32, 0.7125094f32, 0.7146587f32, 0.7168013f32, 0.71893716f32, 0.72106624f32, 0.7231885f32, 0.725304f32, 0.72741264f32, 0.7295144f32, 0.7316094f32, 0.7336975f32, 0.7357786f32, 0.7378528f32, 0.73992014f32, 0.74198043f32, 0.74403375f32, 0.7460801f32, 0.7481194f32, 0.75015163f32, 0.7521769f32, 0.754195f32, 0.75620604f32, 0.7582099f32, 0.7602067f32, 0.7621963f32, 0.76417875f32, 0.766154f32, 0.7681221f32, 0.7700829f32, 0.7720364f32, 0.7739827f32, 0.7759217f32, 0.7778534f32, 0.7797778f32, 0.7816948f32, 0.78360456f32, 0.78550684f32, 0.78740174f32, 0.78928924f32, 0.79116935f32, 0.793042f32, 0.79490715f32, 0.79676485f32, 0.798615f32, 0.80045766f32, 0.8022928f32, 0.8041204f32, 0.8059404f32, 0.80775285f32, 0.8095577f32, 0.8113549f32, 0.81314445f32, 0.8149263f32, 0.8167006f32, 0.81846714f32, 0.820226f32, 0.82197714f32, 0.8237205f32, 0.82545614f32, 0.827184f32, 0.82890415f32, 0.8306164f32, 0.83232087f32, 0.8340175f32, 0.8357063f32, 0.8373872f32, 0.83906025f32, 0.84072536f32, 0.8423826f32, 0.8440319f32, 0.84567326f32, 0.84730667f32, 0.8489321f32, 0.8505495f32, 0.8521589f32, 0.8537603f32, 0.8553537f32, 0.856939f32, 0.8585163f32, 0.8600854f32, 0.86164653f32, 0.8631994f32, 0.86474425f32, 0.866281f32, 0.8678095f32, 0.86932987f32, 0.8708421f32, 0.87234604f32, 0.8738419f32, 0.87532943f32, 0.87680876f32, 0.8782798f32, 0.8797426f32, 0.88119715f32, 0.8826434f32, 0.88408124f32, 0.88551086f32, 0.88693213f32, 0.88834506f32, 0.8897496f32, 0.89114577f32, 0.89253354f32, 0.893913f32, 0.89528394f32, 0.8966465f32, 0.8980006f32, 0.8993463f32, 0.90068346f32, 0.90201217f32, 0.90333235f32, 0.9046441f32, 0.90594727f32, 0.907242f32, 0.90852815f32, 0.9098057f32, 0.91107476f32, 0.9123352f32, 0.9135871f32, 0.9148303f32, 0.916065f32, 0.91729105f32, 0.9185084f32, 0.9197172f32, 0.9209172f32, 0.92210865f32, 0.92329144f32, 0.9244655f32, 0.9256308f32, 0.9267875f32, 0.9279354f32, 0.9290746f32, 0.93020505f32, 0.93132675f32, 0.9324396f32, 0.9335438f32, 0.93463916f32, 0.9357257f32, 0.93680346f32, 0.93787235f32, 0.9389325f32, 0.9399838f32, 0.9410262f32, 0.94205976f32, 0.9430845f32, 0.94410026f32, 0.9451072f32, 0.94610524f32, 0.9470944f32, 0.94807464f32, 0.9490459f32, 0.9500082f32, 0.95096165f32, 0.95190614f32, 0.95284164f32, 0.9537682f32, 0.95468575f32, 0.95559436f32, 0.9564939f32, 0.9573845f32, 0.9582661f32, 0.95913863f32, 0.9600022f32, 0.9608567f32, 0.9617021f32, 0.9625385f32, 0.9633658f32, 0.96418405f32, 0.96499324f32, 0.9657934f32, 0.9665844f32, 0.9673663f32, 0.9681391f32, 0.9689028f32, 0.9696574f32, 0.97040284f32, 0.9711392f32, 0.97186637f32, 0.97258437f32, 0.97329324f32, 0.97399294f32, 0.9746835f32, 0.97536486f32, 0.9760371f32, 0.97670007f32, 0.97735393f32, 0.9779985f32, 0.97863394f32, 0.97926015f32, 0.9798771f32, 0.9804849f32, 0.9810834f32, 0.9816727f32, 0.9822527f32, 0.98282355f32, 0.9833851f32, 0.98393744f32, 0.98448044f32, 0.98501426f32, 0.9855387f32, 0.98605394f32, 0.9865599f32, 0.98705655f32, 0.98754394f32, 0.988022f32, 0.9884908f32, 0.98895025f32, 0.98940045f32, 0.9898413f32, 0.9902728f32, 0.990695f32, 0.99110794f32, 0.99151146f32, 0.9919057f32, 0.9922906f32, 0.9926661f32, 0.99303234f32, 0.99338925f32, 0.99373674f32, 0.9940749f32, 0.99440366f32, 0.99472314f32, 0.9950332f32, 0.9953339f32, 0.99562526f32, 0.99590725f32, 0.9961798f32, 0.99644303f32, 0.9966969f32, 0.9969414f32, 0.99717647f32, 0.99740213f32, 0.99761844f32, 0.9978254f32, 0.99802285f32, 0.998211f32, 0.9983897f32, 0.99855906f32, 0.99871904f32, 0.99886954f32, 0.9990107f32, 0.9991424f32, 0.9992648f32, 0.99937767f32, 0.9994812f32, 0.9995753f32, 0.99966f32, 0.9997353f32, 0.99980116f32, 0.99985766f32, 0.9999047f32, 0.99994236f32, 0.9999706f32, 0.9999894f32, 0.9999988f32, 1f32, 0.9999894f32, 0.9999706f32, 0.99994236f32, 0.9999047f32, 0.99985766f32, 0.99980116f32, 0.9997353f32, 0.99966f32, 0.9995753f32, 0.9994812f32, 0.99937767f32, 0.9992647f32, 0.9991424f32, 0.9990107f32, 0.99886954f32, 0.99871904f32, 0.99855906f32, 0.9983897f32, 0.998211f32, 0.99802285f32, 0.9978253f32, 0.99761844f32, 0.99740213f32, 0.9971764f32, 0.9969413f32, 0.9966969f32, 0.99644303f32, 0.9961798f32, 0.99590725f32, 0.99562526f32, 0.9953339f32, 0.9950332f32, 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0.95096165f32, 0.9500082f32, 0.9490459f32, 0.9480746f32, 0.9470944f32, 0.94610524f32, 0.94510716f32, 0.94410026f32, 0.9430844f32, 0.9420597f32, 0.94102615f32, 0.9399837f32, 0.9389325f32, 0.93787235f32, 0.9368034f32, 0.9357256f32, 0.93463916f32, 0.93354374f32, 0.9324396f32, 0.9313267f32, 0.930205f32, 0.9290746f32, 0.92793536f32, 0.92678744f32, 0.9256308f32, 0.9244654f32, 0.9232914f32, 0.92210865f32, 0.9209172f32, 0.91971713f32, 0.9185084f32, 0.917291f32, 0.916065f32, 0.9148303f32, 0.91358703f32, 0.91233516f32, 0.9110747f32, 0.90980566f32, 0.90852815f32, 0.907242f32, 0.9059473f32, 0.9046441f32, 0.90333235f32, 0.90201217f32, 0.9006834f32, 0.89934623f32, 0.8980006f32, 0.89664644f32, 0.8952839f32, 0.8939129f32, 0.89253354f32, 0.8911457f32, 0.8897495f32, 0.888345f32, 0.8869321f32, 0.8855108f32, 0.8840812f32, 0.8826433f32, 0.88119704f32, 0.8797425f32, 0.87827975f32, 0.87680864f32, 0.8753293f32, 0.87384176f32, 0.8723461f32, 0.8708421f32, 0.86932987f32, 0.86780953f32, 0.866281f32, 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-0.0046017645f32, -0.0015338097f32, ];
#[rustfmt::skip] #[allow(clippy::all)] static COS: [f32; SIZE] = [1f32, 0.9999894f32, 0.9999706f32, 0.99994236f32, 0.9999047f32, 0.99985766f32, 0.99980116f32, 0.9997353f32, 0.99966f32, 0.9995753f32, 0.9994812f32, 0.99937767f32, 0.9992648f32, 0.9991424f32, 0.9990107f32, 0.99886954f32, 0.99871904f32, 0.99855906f32, 0.9983897f32, 0.998211f32, 0.99802285f32, 0.9978253f32, 0.99761844f32, 0.99740213f32, 0.9971764f32, 0.9969413f32, 0.9966969f32, 0.99644303f32, 0.9961798f32, 0.99590725f32, 0.99562526f32, 0.9953339f32, 0.9950332f32, 0.99472314f32, 0.99440366f32, 0.9940749f32, 0.99373674f32, 0.9933892f32, 0.99303234f32, 0.9926661f32, 0.9922906f32, 0.9919057f32, 0.99151146f32, 0.99110794f32, 0.990695f32, 0.9902728f32, 0.9898413f32, 0.98940045f32, 0.98895025f32, 0.9884908f32, 0.988022f32, 0.98754394f32, 0.98705655f32, 0.9865599f32, 0.98605394f32, 0.9855387f32, 0.98501426f32, 0.98448044f32, 0.98393744f32, 0.9833851f32, 0.98282355f32, 0.9822527f32, 0.9816727f32, 0.9810834f32, 0.98048484f32, 0.9798771f32, 0.97926015f32, 0.97863394f32, 0.9779985f32, 0.9773539f32, 0.97670007f32, 0.9760371f32, 0.97536486f32, 0.9746835f32, 0.97399294f32, 0.97329324f32, 0.97258437f32, 0.9718663f32, 0.97113913f32, 0.97040284f32, 0.96965736f32, 0.9689028f32, 0.9681391f32, 0.9673663f32, 0.9665844f32, 0.9657934f32, 0.96499324f32, 0.96418405f32, 0.9633658f32, 0.9625385f32, 0.96170205f32, 0.9608566f32, 0.9600021f32, 0.95913863f32, 0.9582661f32, 0.9573845f32, 0.9564939f32, 0.9555943f32, 0.95468575f32, 0.9537682f32, 0.95284164f32, 0.95190614f32, 0.95096165f32, 0.9500082f32, 0.9490459f32, 0.9480746f32, 0.9470944f32, 0.94610524f32, 0.94510716f32, 0.94410026f32, 0.9430844f32, 0.94205976f32, 0.94102615f32, 0.9399837f32, 0.9389325f32, 0.93787235f32, 0.93680346f32, 0.9357257f32, 0.9346391f32, 0.9335438f32, 0.9324396f32, 0.9313267f32, 0.930205f32, 0.9290746f32, 0.92793536f32, 0.9267875f32, 0.9256308f32, 0.9244655f32, 0.9232914f32, 0.92210865f32, 0.9209172f32, 0.91971713f32, 0.9185084f32, 0.917291f32, 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