use std::f32::consts::PI;
use std::f32::consts::TAU;
use std::fmt;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Mul;
#[derive(Debug, Eq, PartialEq, Clone, Copy)]
pub struct FixedPointPhase {
pub value: i32,
}
impl From<&FixedPointPhase> for f32 {
fn from(x: &FixedPointPhase) -> Self {
(x.value as f32) * (PI / FixedPointPhase::TWO_TO_THE_31)
}
}
impl fmt::Display for FixedPointPhase {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
let x: f32 = self.into();
write!(f, "{}({:#x})", x, self.value)
}
}
impl Add for FixedPointPhase {
type Output = Self;
fn add(self, other: Self) -> Self {
Self {
value: self.value.wrapping_add(other.value),
}
}
}
impl Add<f32> for FixedPointPhase {
type Output = Self;
fn add(self, other: f32) -> Self {
self + FixedPointPhase::new(other)
}
}
impl AddAssign for FixedPointPhase {
fn add_assign(&mut self, other: Self) {
self.value = self.value.wrapping_add(other.value);
}
}
impl Mul<i32> for FixedPointPhase {
type Output = Self;
fn mul(self, other: i32) -> Self {
FixedPointPhase {
value: self.value.wrapping_mul(other),
}
}
}
impl FixedPointPhase {
const WORDBITS: u32 = 32;
const NBITS: u32 = 10;
const ACCUM_MASK: u32 = ((1 << (FixedPointPhase::WORDBITS - FixedPointPhase::NBITS)) - 1);
const TWO_TO_THE_31: f32 = 2147483648.0;
pub fn new(x: f32) -> Self {
let d = (x / TAU + 0.5).floor() as i32;
let x = x - (d as f32) * TAU;
let value = (x * FixedPointPhase::TWO_TO_THE_31 / PI) as i32;
FixedPointPhase { value }
}
pub fn sin(&self) -> f32 {
let ux: u32 = self.value as u32;
let index = (ux >> (FixedPointPhase::WORDBITS - FixedPointPhase::NBITS)) as usize;
FixedPointPhase::S_SINE_TABLE[index][0] * ((ux & FixedPointPhase::ACCUM_MASK) as f32)
+ FixedPointPhase::S_SINE_TABLE[index][1]
}
pub fn cos(&self) -> f32 {
let ux: u32 = (self.value as u32).wrapping_add(0x40000000);
let index = (ux >> (FixedPointPhase::WORDBITS - FixedPointPhase::NBITS)) as usize;
FixedPointPhase::S_SINE_TABLE[index][0] * ((ux & FixedPointPhase::ACCUM_MASK) as f32)
+ FixedPointPhase::S_SINE_TABLE[index][1]
}
#[allow(clippy::excessive_precision)]
const S_SINE_TABLE: [[f32; 2]; 1 << FixedPointPhase::NBITS] = [
[1.462908899582504e-09, 0.000000000000000e+00],
[1.462853821889299e-09, 6.135884647725872e-03],
[1.462743668576535e-09, 1.227153828286288e-02],
[1.462578443791421e-09, 1.840672990151965e-02],
[1.462358153754576e-09, 2.454122851719949e-02],
[1.462082806759796e-09, 3.067480316949683e-02],
[1.461752413173738e-09, 3.680722293279286e-02],
[1.461366985435540e-09, 4.293825692494962e-02],
[1.460926538056327e-09, 4.906767431600274e-02],
[1.460431087618708e-09, 5.519524433685186e-02],
[1.459880652776101e-09, 6.132073628794915e-02],
[1.459275254252073e-09, 6.744391954798490e-02],
[1.458614914839525e-09, 7.356456358257031e-02],
[1.457899659399885e-09, 7.968243795291696e-02],
[1.457129514862092e-09, 8.579731232451281e-02],
[1.456304510221670e-09, 9.190895647579396e-02],
[1.455424676539561e-09, 9.801714030681258e-02],
[1.454490046941024e-09, 1.041216338478999e-01],
[1.453500656614323e-09, 1.102222072683244e-01],
[1.452456542809451e-09, 1.163186308849450e-01],
[1.451357744836691e-09, 1.224106751708585e-01],
[1.450204304065186e-09, 1.284981107640406e-01],
[1.448996263921306e-09, 1.345807084759822e-01],
[1.447733669887093e-09, 1.406582393003174e-01],
[1.446416569498500e-09, 1.467304744214457e-01],
[1.445045012343608e-09, 1.527971852231470e-01],
[1.443619050060775e-09, 1.588581432971887e-01],
[1.442138736336656e-09, 1.649131204519250e-01],
[1.440604126904254e-09, 1.709618887208885e-01],
[1.439015279540716e-09, 1.770042203713726e-01],
[1.437372254065277e-09, 1.830398879130061e-01],
[1.435675112336899e-09, 1.890686641063174e-01],
[1.433923918252015e-09, 1.950903219712905e-01],
[1.432118737742074e-09, 2.011046347959103e-01],
[1.430259638771149e-09, 2.071113761446983e-01],
[1.428346691333216e-09, 2.131103198672379e-01],
[1.426379967449695e-09, 2.191012401066887e-01],
[1.424359541166604e-09, 2.250839113082899e-01],
[1.422285488551876e-09, 2.310581082278522e-01],
[1.420157887692400e-09, 2.370236059402383e-01],
[1.417976818691155e-09, 2.429801798478312e-01],
[1.415742363664161e-09, 2.489276056889901e-01],
[1.413454606737380e-09, 2.548656595464935e-01],
[1.411113634043567e-09, 2.607941178559702e-01],
[1.408719533719009e-09, 2.667127574143157e-01],
[1.406272395900267e-09, 2.726213553880957e-01],
[1.403772312720636e-09, 2.785196893219365e-01],
[1.401219378306918e-09, 2.844075371468990e-01],
[1.398613688775567e-09, 2.902846771888409e-01],
[1.395955342229358e-09, 2.961508881767612e-01],
[1.393244438753570e-09, 3.020059492511319e-01],
[1.390481080412114e-09, 3.078496399722132e-01],
[1.387665371243942e-09, 3.136817403283521e-01],
[1.384797417258841e-09, 3.195020307442669e-01],
[1.381877326433739e-09, 3.253102920893130e-01],
[1.378905208708310e-09, 3.311063056857338e-01],
[1.375881175981207e-09, 3.368898533168934e-01],
[1.372805342105461e-09, 3.426607172354924e-01],
[1.369677822884547e-09, 3.484186801717661e-01],
[1.366498736067770e-09, 3.541635253416645e-01],
[1.363268201345953e-09, 3.598950364550140e-01],
[1.359986340346888e-09, 3.656129977236608e-01],
[1.356653276630805e-09, 3.713171938695950e-01],
[1.353269135685687e-09, 3.770074101330558e-01],
[1.349834044922455e-09, 3.826834322806173e-01],
[1.346348133670440e-09, 3.883450466132535e-01],
[1.342811533172131e-09, 3.939920399743852e-01],
[1.339224376578606e-09, 3.996241997579039e-01],
[1.335586798944265e-09, 4.052413139161772e-01],
[1.331898937221815e-09, 4.108431709680320e-01],
[1.328160930257228e-09, 4.164295600067165e-01],
[1.324372918784288e-09, 4.220002707078411e-01],
[1.320535045419559e-09, 4.275550933372964e-01],
[1.316647454656711e-09, 4.330938187591503e-01],
[1.312710292861422e-09, 4.386162384435209e-01],
[1.308723708265572e-09, 4.441221444744288e-01],
[1.304687850961821e-09, 4.496113295576239e-01],
[1.300602872897917e-09, 4.550835870283904e-01],
[1.296468927870966e-09, 4.605387108593275e-01],
[1.292286171521700e-09, 4.659764956681063e-01],
[1.288054761328471e-09, 4.713967367252024e-01],
[1.283774856601514e-09, 4.767992299616036e-01],
[1.279446618476844e-09, 4.821837719764931e-01],
[1.275070209910126e-09, 4.875501600449075e-01],
[1.270645795670723e-09, 4.928981921253692e-01],
[1.266173542335286e-09, 4.982276668674933e-01],
[1.261653618281671e-09, 5.035383836195678e-01],
[1.257086193682450e-09, 5.088301424361090e-01],
[1.252471440498532e-09, 5.141027440853885e-01],
[1.247809532472813e-09, 5.193559900569341e-01],
[1.243100645123464e-09, 5.245896825690044e-01],
[1.238344955737523e-09, 5.298036245760344e-01],
[1.233542643363834e-09, 5.349976197760548e-01],
[1.228693888806899e-09, 5.401714726180816e-01],
[1.223798874619550e-09, 5.453249883094801e-01],
[1.218857785096278e-09, 5.504579728232972e-01],
[1.213870806266271e-09, 5.555702329055674e-01],
[1.208838125886583e-09, 5.606615760825878e-01],
[1.203759933434647e-09, 5.657318106681659e-01],
[1.198636420101655e-09, 5.707807457708350e-01],
[1.193467778784934e-09, 5.758081913010425e-01],
[1.188254204080907e-09, 5.808139579783058e-01],
[1.182995892277682e-09, 5.857978573383388e-01],
[1.177693041347820e-09, 5.907597017401474e-01],
[1.172345850940616e-09, 5.956993043730946e-01],
[1.166954522374703e-09, 6.006164792639334e-01],
[1.161519258630623e-09, 6.055110412838081e-01],
[1.156040264342986e-09, 6.103828061552252e-01],
[1.150517745792821e-09, 6.152315904589911e-01],
[1.144951910899825e-09, 6.200572116411174e-01],
[1.139342969214470e-09, 6.248594880196940e-01],
[1.133691131910381e-09, 6.296382387917295e-01],
[1.127996611775918e-09, 6.343932840399586e-01],
[1.122259623206610e-09, 6.391244447396153e-01],
[1.116480382196810e-09, 6.438315427651733e-01],
[1.110659106331654e-09, 6.485144008970526e-01],
[1.104796014778906e-09, 6.531728428282912e-01],
[1.098891328280697e-09, 6.578066931711836e-01],
[1.092945269145088e-09, 6.624157774638835e-01],
[1.086958061237803e-09, 6.669999221769725e-01],
[1.080929929973898e-09, 6.715589547199929e-01],
[1.074861102309128e-09, 6.760927034479466e-01],
[1.068751806731371e-09, 6.806009976677565e-01],
[1.062602273252160e-09, 6.850836676446934e-01],
[1.056412733397972e-09, 6.895405446087663e-01],
[1.050183420201466e-09, 6.939714607610767e-01],
[1.043914568192806e-09, 6.983762492801359e-01],
[1.037606413390681e-09, 7.027547443281458e-01],
[1.031259193293520e-09, 7.071067810572427e-01],
[1.024873146870679e-09, 7.114321956157034e-01],
[1.018448514553096e-09, 7.157308251541148e-01],
[1.011985538224661e-09, 7.200025078315043e-01],
[1.005484461212609e-09, 7.242470828214339e-01],
[9.989455282789665e-10, 7.284643903180539e-01],
[9.923689856107905e-10, 7.326542715421209e-01],
[9.857550808112170e-10, 7.368165687469751e-01],
[9.791040628900650e-10, 7.409511252244793e-01],
[9.724161822542557e-10, 7.450577853109192e-01],
[9.656916906988912e-10, 7.491363943928633e-01],
[9.589308413971959e-10, 7.531867989129853e-01],
[9.521338888913055e-10, 7.572088463758445e-01],
[9.453010890826585e-10, 7.612023853536271e-01],
[9.384326992223078e-10, 7.651672654918477e-01],
[9.315289779012860e-10, 7.691033375150101e-01],
[9.245901850407323e-10, 7.730104532322277e-01],
[9.176165818823365e-10, 7.768884655428019e-01],
[9.106084309782543e-10, 7.807372284417612e-01],
[9.035659961814723e-10, 7.845565970253577e-01],
[8.964895426356170e-10, 7.883464274965233e-01],
[8.893793367652408e-10, 7.921065771702825e-01],
[8.822356462654715e-10, 7.958369044791258e-01],
[8.750587400922988e-10, 7.995372689783381e-01],
[8.678488884521710e-10, 8.032075313512876e-01],
[8.606063627919368e-10, 8.068475534146706e-01],
[8.533314357885487e-10, 8.104571981237139e-01],
[8.460243813389244e-10, 8.140363295773342e-01],
[8.386854745495451e-10, 8.175848130232554e-01],
[8.313149917260522e-10, 8.211025148630814e-01],
[8.239132103630834e-10, 8.245893026573261e-01],
[8.164804091333399e-10, 8.280450451304002e-01],
[8.090168678777144e-10, 8.314696121755525e-01],
[8.015228675943046e-10, 8.348628748597694e-01],
[7.939986904279592e-10, 8.382247054286289e-01],
[7.864446196597152e-10, 8.415549773111103e-01],
[7.788609396960255e-10, 8.448535651243595e-01],
[7.712479360582235e-10, 8.481203446784097e-01],
[7.636058953715121e-10, 8.513551929808573e-01],
[7.559351053544544e-10, 8.545579882414919e-01],
[7.482358548079632e-10, 8.577286098768823e-01],
[7.405084336044481e-10, 8.608669385149160e-01],
[7.327531326769622e-10, 8.639728559992937e-01],
[7.249702440081918e-10, 8.670462453939777e-01],
[7.171600606194971e-10, 8.700869909875942e-01],
[7.093228765599009e-10, 8.730949782977905e-01],
[7.014589868949188e-10, 8.760700940755445e-01],
[6.935686876955208e-10, 8.790122263094288e-01],
[6.856522760270671e-10, 8.819212642298275e-01],
[6.777100499379789e-10, 8.847970983131074e-01],
[6.697423084485687e-10, 8.876396202857406e-01],
[6.617493515397899e-10, 8.904487231283816e-01],
[6.537314801419611e-10, 8.932243010798961e-01],
[6.456889961233841e-10, 8.959662496413431e-01],
[6.376222022790941e-10, 8.986744655799088e-01],
[6.295314023192924e-10, 9.013488469327942e-01],
[6.214169008579643e-10, 9.039892930110528e-01],
[6.132790034015773e-10, 9.065957044033821e-01],
[6.051180163373800e-10, 9.091679829798665e-01],
[5.969342469218625e-10, 9.117060318956715e-01],
[5.887280032693477e-10, 9.142097555946899e-01],
[5.804995943402911e-10, 9.166790598131396e-01],
[5.722493299296081e-10, 9.191138515831125e-01],
[5.639775206551068e-10, 9.215140392360748e-01],
[5.556844779457087e-10, 9.238795324063178e-01],
[5.473705140297754e-10, 9.262102420343608e-01],
[5.390359419234357e-10, 9.285060803703034e-01],
[5.306810754184889e-10, 9.307669609771302e-01],
[5.223062290710754e-10, 9.329927987339640e-01],
[5.139117181893161e-10, 9.351835098392717e-01],
[5.054978588218234e-10, 9.373390118140181e-01],
[4.970649677456849e-10, 9.394592235047723e-01],
[4.886133624544984e-10, 9.415440650867625e-01],
[4.801433611463023e-10, 9.435934580668817e-01],
[4.716552827120074e-10, 9.456073252866422e-01],
[4.631494467229042e-10, 9.475855909250817e-01],
[4.546261734189096e-10, 9.495281805016170e-01],
[4.460857836964177e-10, 9.514350208788487e-01],
[4.375285990963351e-10, 9.533060402653141e-01],
[4.289549417918254e-10, 9.551411682181910e-01],
[4.203651345761336e-10, 9.569403356459493e-01],
[4.117595008508066e-10, 9.587034748109520e-01],
[4.031383646129612e-10, 9.604305193320064e-01],
[3.945020504435582e-10, 9.621214041868623e-01],
[3.858508834949088e-10, 9.637760657146607e-01],
[3.771851894786302e-10, 9.653944416183301e-01],
[3.685052946531527e-10, 9.669764709669327e-01],
[3.598115258115960e-10, 9.685220941979578e-01],
[3.511042102694873e-10, 9.700312531195641e-01],
[3.423836758523208e-10, 9.715038909127713e-01],
[3.336502508832488e-10, 9.729399521335991e-01],
[3.249042641708265e-10, 9.743393827151539e-01],
[3.161460449964917e-10, 9.757021299696653e-01],
[3.073759231022829e-10, 9.770281425904696e-01],
[2.985942286782925e-10, 9.783173706539410e-01],
[2.898012923503584e-10, 9.795697656213717e-01],
[2.809974451675703e-10, 9.807852803407989e-01],
[2.721830185898024e-10, 9.819638690487806e-01],
[2.633583444752197e-10, 9.831054873721181e-01],
[2.545237550678371e-10, 9.842100923295267e-01],
[2.456795829849199e-10, 9.852776423332542e-01],
[2.368261612045696e-10, 9.863080971906463e-01],
[2.279638230531239e-10, 9.873014181056600e-01],
[2.190929021925573e-10, 9.882575676803244e-01],
[2.102137326080935e-10, 9.891765099161482e-01],
[2.013266485954199e-10, 9.900582102154760e-01],
[1.924319847481680e-10, 9.909026353827898e-01],
[1.835300759455251e-10, 9.917097536259590e-01],
[1.746212573392116e-10, 9.924795345574384e-01],
[1.657058643412515e-10, 9.932119491954108e-01],
[1.567842326111878e-10, 9.939069699648789e-01],
[1.478566980433767e-10, 9.945645706987039e-01],
[1.389235967544681e-10, 9.951847266385896e-01],
[1.299852650706196e-10, 9.957674144360156e-01],
[1.210420395150567e-10, 9.963126121531154e-01],
[1.120942567951023e-10, 9.968202992635034e-01],
[1.031422537897619e-10, 9.972904566530466e-01],
[9.418636753680700e-11, 9.977230666205853e-01],
[8.522693522041346e-11, 9.981181128785984e-01],
[7.626429415803239e-11, 9.984755805538179e-01],
[6.729878178813478e-11, 9.987954561877876e-01],
[5.833073565708242e-11, 9.990777277373710e-01],
[4.936049340684595e-11, 9.993223845752035e-01],
[4.038839276190232e-11, 9.995294174900936e-01],
[3.141477151682045e-11, 9.996988186873690e-01],
[2.243996752334399e-11, 9.998305817891704e-01],
[1.346431867776521e-11, 9.999247018346915e-01],
[4.488162908219557e-12, 9.999811752803658e-01],
[-4.488161838152247e-12, 1.000000000000000e+00],
[-1.346431760775084e-11, 9.999811752848540e-01],
[-2.243996645340903e-11, 9.999247018436677e-01],
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