/*
 * ============================
 * FFTW3 Transform Types (Summary)
 * ============================
 *
 * 1. Complex-to-Complex (C2C)
 * ---------------------------
 * - Input:  Complex[]
 * - Output: Complex[]
 * - Use:    General-purpose FFT
 * - API:    fftwf_plan_dft_1d / 2d / 3d / many
 *
 * 2. Real-to-Complex (R2C)
 * ------------------------
 * - Input:  Real[]
 * - Output: Complex[] (half-spectrum)
 * - Use:    Signal processing, time series
 * - API:    fftwf_plan_dft_r2c_1d / 2d / 3d / many
 *
 * 3. Complex-to-Real (C2R)
 * ------------------------
 * - Input:  Complex[] (half-spectrum)
 * - Output: Real[]
 * - Use:    Inverse of R2C
 * - API:    fftwf_plan_dft_c2r_1d / 2d / 3d / many
 *
 * 4. Real-to-Real (R2R)
 * ---------------------
 * - Input:  Real[]
 * - Output: Real[]
 * - Use:    DCT/DST for PDEs, image compression
 * - Types:
 *     FFTW_REDFT00  → DCT-I
 *     FFTW_REDFT01  → DCT-II (used in JPEG)
 *     FFTW_REDFT10  → DCT-III
 *     FFTW_REDFT11  → DCT-IV
 *     FFTW_RODFT00  → DST-I
 *     FFTW_RODFT01  → DST-II
 *     FFTW_RODFT10  → DST-III
 *     FFTW_RODFT11  → DST-IV
 *     FFTW_R2HC     → Real-to-halfcomplex
 *     FFTW_HC2R     → Halfcomplex-to-real
 *     FFTW_DHT      → Hartley Transform
 * - API:    fftwf_plan_r2r_1d / 2d / 3d / guru / many
 *
 * 5. Split-Complex Transforms
 * ---------------------------
 * - Input/Output: Separate real and imaginary arrays
 * - Use:  Specialized memory layouts
 * - API:  fftwf_plan_guru_split_dft, split_r2c, split_c2r
 *
 * ============================
 * FFTW is fast because:
 * - Auto-tuned plan selection
 * - SIMD and cache-aware
 * - Wisdom reuse
 * - Multithreading support
 * - Custom codelets per architecture
 * ============================
 */