// Math for Game Programmers: Fast and Funky 1D Nonlinear Transformations
//   https://www.youtube.com/watch?v=mr5xkf6zSzk
//
// Thread safety: Safe for concurrent use (no shared state, pure functions).
// Macros: Namespaced INTERP_* variants are collision-safe. Legacy un-prefixed
//   names are provided via #ifndef guard — if your code already defines e.g.
//   "mix", the library will not override it.

#ifndef INTERPOLATE_H
#define INTERPOLATE_H

// Namespaced macros (safe from collisions). Use these in new code.
#ifndef INTERP_FLIP
#define INTERP_FLIP(x) (1.0 - (double)(x))
#endif
#ifndef INTERP_SCALE
#define INTERP_SCALE(a, t) ((double)(t) * (double)(a))
#endif
#ifndef INTERP_REVERSE_SCALE
#define INTERP_REVERSE_SCALE(a, t) ((1.0 - (double)(t)) * (double)(a))
#endif
#ifndef INTERP_MIX
#define INTERP_MIX(a, b, b_weight) ((double)(a) + (double)(b_weight) * ((double)(b) - (double)(a)))
#endif
#ifndef INTERP_CROSSFADE
#define INTERP_CROSSFADE(a, b, t) ((double)(a) + (double)(t) * ((double)(b) - (double)(a)))
#endif

#ifndef INTERP_SMOOTH_START_2
#define INTERP_SMOOTH_START_2(t) ((double)(t) * (double)(t))
#endif
#ifndef INTERP_SMOOTH_START_3
#define INTERP_SMOOTH_START_3(t) (INTERP_SMOOTH_START_2(t) * (double)(t))
#endif
#ifndef INTERP_SMOOTH_START_4
#define INTERP_SMOOTH_START_4(t) (INTERP_SMOOTH_START_3(t) * (double)(t))
#endif
#ifndef INTERP_SMOOTH_START_5
#define INTERP_SMOOTH_START_5(t) (INTERP_SMOOTH_START_4(t) * (double)(t))
#endif
#ifndef INTERP_SMOOTH_START_6
#define INTERP_SMOOTH_START_6(t) (INTERP_SMOOTH_START_5(t) * (double)(t))
#endif

#ifndef INTERP_SMOOTH_STOP_2
#define INTERP_SMOOTH_STOP_2(t) (INTERP_FLIP(INTERP_SMOOTH_START_2(INTERP_FLIP(t))))
#endif
#ifndef INTERP_SMOOTH_STOP_3
#define INTERP_SMOOTH_STOP_3(t) (INTERP_FLIP(INTERP_SMOOTH_START_3(INTERP_FLIP(t))))
#endif
#ifndef INTERP_SMOOTH_STOP_4
#define INTERP_SMOOTH_STOP_4(t) (INTERP_FLIP(INTERP_SMOOTH_START_4(INTERP_FLIP(t))))
#endif
#ifndef INTERP_SMOOTH_STOP_5
#define INTERP_SMOOTH_STOP_5(t) (INTERP_FLIP(INTERP_SMOOTH_START_5(INTERP_FLIP(t))))
#endif
#ifndef INTERP_SMOOTH_STOP_6
#define INTERP_SMOOTH_STOP_6(t) (INTERP_FLIP(INTERP_SMOOTH_START_6(INTERP_FLIP(t))))
#endif

#ifndef INTERP_SMOOTH_STEP_3
#define INTERP_SMOOTH_STEP_3(t) (INTERP_CROSSFADE(INTERP_SMOOTH_START_2(t), INTERP_SMOOTH_STOP_2(t), (double)(t)))
#endif

#ifndef INTERP_ARCH_2
#define INTERP_ARCH_2(t) (INTERP_SCALE(INTERP_FLIP(t), (double)(t)))
#endif
#ifndef INTERP_SMOOTH_START_ARCH_3
#define INTERP_SMOOTH_START_ARCH_3(t) (INTERP_SCALE(INTERP_ARCH_2(t), (double)(t)))
#endif
#ifndef INTERP_SMOOTH_STOP_ARCH_3
#define INTERP_SMOOTH_STOP_ARCH_3(t) (INTERP_REVERSE_SCALE(INTERP_ARCH_2(t), (double)(t)))
#endif

// Legacy macro names — alias to namespaced variants when not already defined by user.
#ifndef flip
#define flip(x) INTERP_FLIP(x)
#endif
#ifndef scale
#define scale(a, t) INTERP_SCALE(a, t)
#endif
#ifndef reverse_scale
#define reverse_scale(a, t) INTERP_REVERSE_SCALE(a, t)
#endif
#ifndef mix
#define mix(a, b, b_weight) INTERP_MIX(a, b, b_weight)
#endif
#ifndef crossfade
#define crossfade(a, b, t) INTERP_CROSSFADE(a, b, t)
#endif

#ifndef smooth_start_2
#define smooth_start_2(t) INTERP_SMOOTH_START_2(t)
#endif
#ifndef smooth_start_3
#define smooth_start_3(t) INTERP_SMOOTH_START_3(t)
#endif
#ifndef smooth_start_4
#define smooth_start_4(t) INTERP_SMOOTH_START_4(t)
#endif
#ifndef smooth_start_5
#define smooth_start_5(t) INTERP_SMOOTH_START_5(t)
#endif
#ifndef smooth_start_6
#define smooth_start_6(t) INTERP_SMOOTH_START_6(t)
#endif

#ifndef smooth_stop_2
#define smooth_stop_2(t) INTERP_SMOOTH_STOP_2(t)
#endif
#ifndef smooth_stop_3
#define smooth_stop_3(t) INTERP_SMOOTH_STOP_3(t)
#endif
#ifndef smooth_stop_4
#define smooth_stop_4(t) INTERP_SMOOTH_STOP_4(t)
#endif
#ifndef smooth_stop_5
#define smooth_stop_5(t) INTERP_SMOOTH_STOP_5(t)
#endif
#ifndef smooth_stop_6
#define smooth_stop_6(t) INTERP_SMOOTH_STOP_6(t)
#endif

#ifndef smooth_step_3
#define smooth_step_3(t) INTERP_SMOOTH_STEP_3(t)
#endif

#ifndef arch_2
#define arch_2(t) INTERP_ARCH_2(t)
#endif
#ifndef smooth_start_arch_3
#define smooth_start_arch_3(t) INTERP_SMOOTH_START_ARCH_3(t)
#endif
#ifndef smooth_stop_arch_3
#define smooth_stop_arch_3(t) INTERP_SMOOTH_STOP_ARCH_3(t)
#endif

/* Function wrappers for debuggability (use these instead of macros when debugging) */
#ifdef __cplusplus
extern "C" {
#endif

double interpolate_flip(double t);
double interpolate_scale(double a, double t);
double interpolate_reverse_scale(double a, double t);
double interpolate_mix(double a, double b, double b_weight);
double interpolate_crossfade(double a, double b, double t);
double interpolate_smooth_start_2(double t);
double interpolate_smooth_start_3(double t);
double interpolate_smooth_start_4(double t);
double interpolate_smooth_start_5(double t);
double interpolate_smooth_start_6(double t);
double interpolate_smooth_stop_2(double t);
double interpolate_smooth_stop_3(double t);
double interpolate_smooth_stop_4(double t);
double interpolate_smooth_stop_5(double t);
double interpolate_smooth_stop_6(double t);
double interpolate_smooth_step_3(double t);
double interpolate_arch_2(double t);
double interpolate_smooth_start_arch_3(double t);
double interpolate_smooth_stop_arch_3(double t);

#ifdef __cplusplus
}
#endif

#endif

#ifdef INTERPOLATE_IMPLEMENTATION
#ifndef INTERPOLATE_IMPLEMENTED
#define INTERPOLATE_IMPLEMENTED

double interpolate_flip(double t) { return flip(t); }
double interpolate_scale(double a, double t) { return scale(a, t); }
double interpolate_reverse_scale(double a, double t) { return reverse_scale(a, t); }
double interpolate_mix(double a, double b, double b_weight) { return mix(a, b, b_weight); }
double interpolate_crossfade(double a, double b, double t) { return crossfade(a, b, t); }
double interpolate_smooth_start_2(double t) { return smooth_start_2(t); }
double interpolate_smooth_start_3(double t) { return smooth_start_3(t); }
double interpolate_smooth_start_4(double t) { return smooth_start_4(t); }
double interpolate_smooth_start_5(double t) { return smooth_start_5(t); }
double interpolate_smooth_start_6(double t) { return smooth_start_6(t); }
double interpolate_smooth_stop_2(double t) { return smooth_stop_2(t); }
double interpolate_smooth_stop_3(double t) { return smooth_stop_3(t); }
double interpolate_smooth_stop_4(double t) { return smooth_stop_4(t); }
double interpolate_smooth_stop_5(double t) { return smooth_stop_5(t); }
double interpolate_smooth_stop_6(double t) { return smooth_stop_6(t); }
double interpolate_smooth_step_3(double t) { return smooth_step_3(t); }
double interpolate_arch_2(double t) { return arch_2(t); }
double interpolate_smooth_start_arch_3(double t) { return smooth_start_arch_3(t); }
double interpolate_smooth_stop_arch_3(double t) { return smooth_stop_arch_3(t); }

#endif /* INTERPOLATE_IMPLEMENTED */
#endif // INTERPOLATE_IMPLEMENTATION