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49 lines
1.6 KiB
C++
49 lines
1.6 KiB
C++
#pragma once
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// Copyright (c) 2024-2026 Tarik Moussa.
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// SPDX-License-Identifier: MIT
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// Ported from de.varylab.discreteconformal.util.DiscreteEllipticUtility (Java).
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// Only the pure-math subset (no HDS required).
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#include <complex>
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#include <cmath>
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namespace conformallab {
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// Move tau into the fundamental domain of the modular group SL(2,Z):
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// |Re(tau)| <= 0.5, Im(tau) >= 0, Re(tau) >= 0, |tau| >= 1
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//
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// Algorithm: iteratively apply
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// 1. T-shift: Re > 0.5 or Re < 0 → Re -= sign(Re)
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// 2. Im-flip: Im < 0 → Im = -Im
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// 3. Re-flip: Re < 0 → Re = -Re
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// 4. S-invert: |tau| < 1 → tau = 1/tau
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//
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/// Normalise a complex modulus `τ` into the standard fundamental
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/// domain of an elliptic curve (`|τ| ≥ 1`, `0 ≤ Re τ ≤ ½`, `Im τ ≥ 0`).
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/// Same as Java `DiscreteEllipticUtility.normalizeModulus(Complex)`.
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inline std::complex<double> normalizeModulus(std::complex<double> tau) {
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int maxIter = 100;
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while (--maxIter > 0) {
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double re = tau.real();
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double im = tau.imag();
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// exit when all conditions satisfied
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if (std::abs(re) <= 0.5 && im >= 0.0 && re >= 0.0 && std::abs(tau) >= 1.0)
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break;
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if (std::abs(re) > 0.5)
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re -= (re > 0.0 ? 1.0 : -1.0); // signum shift
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if (im < 0.0)
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im = -im;
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if (re < 0.0)
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re = -re;
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tau = std::complex<double>(re, im);
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if (std::abs(tau) < 1.0)
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tau = 1.0 / tau; // S-transformation: invert
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}
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return tau;
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}
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} // namespace conformallab
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