Jacobi Elliptic Functions in the Complex PlaneComputing π with the Bailey-Borwein-Plouffe FormulaAdaptive Contouring in Fragment ShadersGrouping Points with Principal Component AnalysisDomain Coloring with Adaptive ContouringDouble Compound Pendulums3D Reaction-DiffusionQuasicrystals2D (Non-physical) N-body Gravity with Poisson's EquationPeriodic Planar Three-Body OrbitseasesFinding Roots in the Complex Planeglsl-complexglsl-complex-auto-differentiationpolynomial-rootsutilsIntegration
complex-auto-differentiation
function creal (a) {
return a[0];
}
function cimag(a) {
return a[1];
}
function ccreateS () {
return [0, 0]
}
function ccreateD () {
return [0, 0, 0, 0]
}
function cfromValuesD (a, b, c, d) {
return [a, b, c, d]
}
function cfromValuesS (a, b) {
return [a, b]
}
function csetValuesD (out, a, b, c, d) {
out[0] = a
out[1] = b
out[2] = c
out[3] = d
return out
}
function csetValuesS (out, a, b) {
out[0] = a
out[1] = b
return out
}
function ccopyS (out, a) {
out[0] = a[0]
out[1] = a[1]
return out
}
function ccopyD (out, a) {
out[0] = a[0]
out[1] = a[1]
out[2] = a[2]
out[3] = a[3]
return out
}
function cscaleS (out, a, s) {
out[0] = a[0] * s
out[1] = a[1] * s
return out
}
function cscaleD (out, a, s) {
out[0] = a[0] * s
out[1] = a[1] * s
out[2] = a[2] * s
out[3] = a[3] * s
return out
}
function caddSS (out, a, b) {
out[0] = a[0] + b[0]
out[1] = a[1] + b[1]
return out
}
function caddSD (out, a, b) {
out[0] = a[0] + b[0]
out[1] = a[1] + b[1]
out[2] = b[2]
out[3] = b[3]
return out
}
function caddDS (out, a, b) {
out[0] = a[0] + b[0]
out[1] = a[1] + b[1]
out[2] = a[2]
out[3] = a[3]
return out
}
function caddDD (out, a, b) {
out[0] = a[0] + b[0]
out[1] = a[1] + b[1]
out[2] = a[2] + b[2]
out[3] = a[3] + b[3]
return out
}
function csubSS (out, a, b) {
out[0] = a[0] - b[0]
out[1] = a[1] - b[1]
return out
}
function csubSD (out, a, b) {
out[0] = a[0] - b[0]
out[1] = a[1] - b[1]
out[2] = -b[2]
out[3] = -b[3]
return out
}
function csubDS (out, a, b) {
out[0] = a[0] - b[0]
out[1] = a[1] - b[1]
out[2] = a[2]
out[3] = a[3]
return out
}
function csubDD (out, a, b) {
out[0] = a[0] - b[0]
out[1] = a[1] - b[1]
out[2] = a[2] - b[2]
out[3] = a[3] - b[3]
return out
}
function cmulSS (out, a, b) {
var ar = a[0], ai = a[1]
var br = b[0], bi = b[1]
out[0] = ar * br - ai * bi
out[1] = ar * bi + ai * br
return out
}
function cmulSD (out, a, b) {
var ar = a[0], ai = a[1]
var br = b[0], bi = b[1], bu = b[2], bv = b[3]
out[0] = ar * br - ai * bi
out[1] = ar * bi + ai * br
out[2] = ar * bu - ai * bv
out[3] = ar * bv + ai * bu
return out;
}
//function cmulDS (out, a, b) {
// var ar = a[0], ai = a[1], au = a[2], av = a[3]
// var br = b[0], bi = b[1]
// out[0] = -a[1]
// out[1] = a[0]
// out[2] = -a[3]
// out[3] = a[2]
// return out;
//}
function cmulDS (out, a, b) {
var ar = a[0], ai = a[1], au = a[2], av = a[3]
var br = b[0], bi = b[1]
out[0] = ar * br - ai * bi
out[1] = ar * bi + ai * br
out[2] = au * br - av * bi
out[3] = au * bi + av * br
return out;
}
function cmulDD (out, a, b) {
var ar = a[0], ai = a[1], dar = a[2], av = a[3]
var br = b[0], bi = b[1], bu = b[2], bv = b[3]
out[0] = ar * br - ai * bi;
out[1] = ar * bi + ai * br;
out[2] = ar * bu - ai * bv + dar * br - av * bi;
out[3] = ar * bv + ai * bu + dar * bi + av * br;
return out;
}
function cinvS (out, b) {
var br = b[0], bi = b[1]
var e, f;
if (Math.abs(br) >= Math.abs(bi)) {
e = bi / br
f = 1 / (br + bi * e)
out[0] = f
out[1] = -e * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[0] = e * f
out[1] = -f
}
return out
}
function cdivSS (out, a, b) {
var ar = a[0], ai = a[1]
var br = b[0], bi = b[1]
var e, f;
if (Math.abs(br) >= Math.abs(bi)) {
e = bi / br
f = 1 / (br + bi * e)
out[0] = (ar + ai * e) * f
out[1] = (ai - ar * e) * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[0] = (ar * e + ai) * f
out[1] = (ai * e - ar) * f
}
return out
}
function cdivSD (out, a, b) {
var ar = a[0], ai = a[1]
var br = b[0], bi = b[1], dbr = b[2], dbi = b[3]
var aobr, aobi
var e, f
var r = Math.abs(br) >= Math.abs(bi)
if (r) {
e = bi / br
f = 1 / (br + bi * e)
out[0] = aobr = (ar + ai * e) * f
out[1] = aobi = (ai - ar * e) * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[0] = aobr = (ar * e + ai) * f
out[1] = aobi = (ai * e - ar) * f
}
// Compute the differential - a * db / b^2 but instead as
// -((a / b) * db) / b
var numr = aobr * dbr - aobi * dbi
var numi = aobr * dbi + aobi * dbr
if (r) {
e = bi / br
f = 1 / (br + bi * e)
out[2] = -(numr + numi * e) * f
out[3] = -(numi - numr * e) * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[2] = -(numr * e + numi) * f
out[3] = -(numi * e - numr) * f
}
return out
}
function cdivDS (out, a, b) {
var ar = a[0], ai = a[1], dar = a[2], dai = a[3]
var br = b[0], bi = b[1]
var aobr, aobi
var e, f
var r = Math.abs(br) >= Math.abs(bi)
if (r) {
e = bi / br
f = 1 / (br + bi * e)
out[0] = aobr = (ar + ai * e) * f
out[1] = aobi = (ai - ar * e) * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[0] = aobr = (ar * e + ai) * f
out[1] = aobi = (ai * e - ar) * f
}
// Compute the differential da / b
if (r) {
e = bi / br
f = 1 / (br + bi * e)
out[2] = (dar + dai * e) * f
out[3] = (dai - dar * e) * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[2] = (dar * e + dai) * f
out[3] = (dai * e - dar) * f
}
return out
}
function cdivDD (out, a, b) {
var ar = a[0], ai = a[1], au = a[2], av = a[3]
var br = b[0], bi = b[1], bu = b[2], bv = b[3]
var aobr, aobi
var e, f
var r = Math.abs(br) >= Math.abs(bi)
if (r) {
e = bi / br
f = 1 / (br + bi * e)
out[0] = aobr = (ar + ai * e) * f
out[1] = aobi = (ai - ar * e) * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[0] = aobr = (ar * e + ai) * f
out[1] = aobi = (ai * e - ar) * f
}
// Compute the differential (b * da - a * db) / b^2 but instead as
// (da - (a / b) * db) / b so that we use the result we've already
// computed and avoid floating point overflow
var numr = au - aobr * bu + aobi * bv
var numi = av - aobr * bv - aobi * bu
if (r) {
e = bi / br
f = 1 / (br + bi * e)
out[2] = (numr + numi * e) * f
out[3] = (numi - numr * e) * f
} else {
e = br / bi
f = 1 / (br * e + bi)
out[2] = (numr * e + numi) * f
out[3] = (numi * e - numr) * f
}
return out
}
function csqrS (out, a) {
var ar = a[0]
var ai = a[1]
out[0] = ar * ar - ai * ai
out[1] = 2.0 * ar * ai
return out
}
function csqrD (out, a) {
var ar = a[0], ai = a[1], au = a[2], av = a[3]
out[0] = ar * ar - ai * ai
out[1] = 2 * ar * ai
out[2] = 2 * (ar * au - ai * av)
out[3] = 2 * (ar * av + ai * au)
return out;
}
function csqrtD (out, a) {
var ar = a[0], ai = a[1], au = a[2], av = a[3]
var mod = Math.hypot(ar, ai)
var br, bi
var c = Math.sqrt(2 * (mod + ar))
var d = Math.sqrt(2 * (mod - ar))
br = ar >= 0 ? 0.5 * c : Math.abs(ai) / d
bi = ar <= 0 ? 0.5 * d : Math.abs(ai) / c
bi = ai < 0 ? -bi : bi
out[0] = br
out[1] = bi
var e, f;
if (Math.abs(br) >= Math.abs(bi)) {
e = bi / br
f = 0.5 / (br + bi * e)
out[2] = (au + av * e) * f
out[3] = (av - au * e) * f
} else {
e = br / bi
f = 0.5 / (br * e + bi)
out[2] = (au * e + av) * f
out[3] = (av * e - au) * f
}
return out
}
function csqrtAltD(out, a) {
var ar = -a[0],
ai = -a[1],
au = -a[2],
av = -a[3];
var mod = Math.hypot(ar, ai);
var br, bi;
var c = Math.sqrt(2 * (mod + ar));
var d = Math.sqrt(2 * (mod - ar));
br = ar >= 0 ? 0.5 * c : Math.abs(ai) / d;
bi = ar <= 0 ? 0.5 * d : Math.abs(ai) / c;
bi = ai < 0 ? -bi : bi;
out[0] = -bi;
out[1] = br;
var e, f;
if (Math.abs(br) >= Math.abs(bi)) {
e = bi / br;
f = 0.5 / (br + bi * e);
out[2] = -(av - au * e) * f;
out[3] = (au + av * e) * f;
} else {
e = br / bi;
f = 0.5 / (br * e + bi);
out[2] = -(av * e - au) * f;
out[3] = (au * e + av) * f;
}
return out;
}
function csqrtS (out, a) {
var ar = a[0], ai = a[1], au = a[2], av = a[3]
var mod = Math.hypot(ar, ai)
var br, bi
if (ar >= 0) {
br = 0.5 * Math.sqrt(2 * (mod + ar))
} else {
br = Math.abs(ai) / Math.sqrt(2 * (mod - ar))
}
if (ar <= 0) {
bi = 0.5 * Math.sqrt(2 * (mod - ar))
} else {
bi = Math.abs(ai) / Math.sqrt(2 * (mod + ar))
}
out[0] = br
out[1] = bi = ai < 0 ? -bi : bi
return out
}
function cexpS (out, a) {
var ai = a[1]
var e = Math.exp(a[0])
out[0] = e * Math.cos(ai)
out[1] = e * Math.sin(ai)
return out
}
function cexpD (out, a) {
var ar = a[0], ai = a[1], au = a[2], av = a[3]
var e = Math.exp(ar)
var re = e * Math.cos(ai)
var im = e * Math.sin(ai)
out[0] = re
out[1] = im
out[2] = re * au - im * av
out[3] = re * av + im * au
return out
}
function csinhcoshD (sinhOut, coshOut, a) {
var ar = a[0], ai = a[1], dar = a[2], dai = a[3]
var e = Math.exp(ar)
var c = 0.5 * Math.cos(ai)
var s = 0.5 * Math.sin(ai)
var epr = c * e
var epi = s * e
var emr = c / e
var emi = -s / e
var epu = epr * dar - epi * dai
var epv = epr * dai + epi * dar
var emu = emr * dar - emi * dai
var emv = emr * dai + emi * dar
var sr = sinhOut[0] = epr - emr
var si = sinhOut[1] = epi - emi
var cr = coshOut[0] = epr + emr
var ci = coshOut[1] = epi + emi
sinhOut[2] = cr * dar - ci * dai
sinhOut[3] = cr * dai + ci * dar
coshOut[2] = sr * dar - si * dai
coshOut[3] = sr * dai + si * dar
}
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