/*
    Doom-inspired Q15.16 format used for most of everything.
    https://hackmd.io/9uRB9YbTSBW4Qz_2b8TyDw#Examples-2-DOOM
*/

#ifndef COM_FIXED_H
#define COM_FIXED_H

#include <stdint.h>
#include <stdio.h>

#define COM_FIXED_FRACBITS 16
#define COM_FIXED_FRACUNIT (1 << COM_FIXED_FRACBITS)
#define COM_FIXED_FRACHALF (COM_FIXED_FRACUNIT >> 1)
#define COM_FIXED_FRACQRTR (COM_FIXED_FRACHALF >> 1)

#define COM_FIXED_PI (com_fixed_t)205887
#define COM_FIXED_PI2 (com_fixed_t)411774
#define COM_FIXED_PIHALF (com_fixed_t)102943
#define COM_FIXED_PIONEANDAHALF (COM_FIXED_PI + COM_FIXED_PIHALF)

typedef int32_t com_fixed_t;

extern const uint16_t com_fixed_sin_lut[128];

static inline com_fixed_t com_fixed_add(com_fixed_t a, com_fixed_t b) {
  return a + b;
}

static inline com_fixed_t com_fixed_sub(com_fixed_t a, com_fixed_t b) {
  return a - b;
}

static inline com_fixed_t com_fixed_mul(com_fixed_t a, com_fixed_t b) {
  return (com_fixed_t)(((int64_t)a * (int64_t)b) >> COM_FIXED_FRACBITS);
}

/* Note: this does not clamp for over/underflow cases */
static inline com_fixed_t com_fixed_div(com_fixed_t a, com_fixed_t b) {
  return (com_fixed_t)(((int64_t)a << COM_FIXED_FRACBITS) / (int64_t)b);
}

/* Is supposed to be only used for debugging, not in real code. */
/* Because of that we default to maximum precision here. */
static inline double com_fixed_as_float(com_fixed_t a) {
  return (a >> COM_FIXED_FRACBITS) * (double)1.0 +
         (a & 0xFFFF) * (double)(1.0 / COM_FIXED_FRACUNIT);
}

/* Approximated square root by Newton-Raphson in 2 iterations over small LUT. */
com_fixed_t com_fixed_sqrt(com_fixed_t a);

/* Approximated using LUT. */
/* TODO: test whether linearly interpolated version could be default. */
/*       things like camera movement can be jarring if done without.*/
/* https://namoseley.wordpress.com/2015/07/26/sincos-generation-using-table-lookup-and-iterpolation/
 */
static inline com_fixed_t com_fixed_sin(com_fixed_t a) {
  int32_t sign = 1;

  /* Wrap to (-Pi2,+Pi2) */
  com_fixed_t q = a % COM_FIXED_PI2;

  /* Wrap to [0,+Pi2) */
  if (q < 0)
    q = COM_FIXED_PI2 + q;

  /* Limit to [0,+1) */
  q = com_fixed_div(q, COM_FIXED_PI2);

  /* Handle cases of 3rd and 4th quadrant. */
  if (q >= COM_FIXED_FRACHALF) {
    q -= COM_FIXED_FRACHALF;
    sign = -1;
  }

  /* Finally clculate the index into LUT. */
  uint16_t const idx = q >= COM_FIXED_FRACQRTR ? 255 - (q >> 7) : q >> 7;

  return com_fixed_sin_lut[idx] * sign;
}

/* Implemented over sin, as to share one single LUT. */
/* Additionally, optimizer probably can collapse some math for combined sincos
 * case. */
static inline com_fixed_t com_fixed_cos(com_fixed_t a) {
  return com_fixed_sin(a + COM_FIXED_PIHALF);
}

static inline void com_fixed_sincos(com_fixed_t a, com_fixed_t *restrict s,
                                    com_fixed_t *restrict c) {
  *s = com_fixed_sin(a);
  *c = com_fixed_cos(a);
}

void com_fixed_print(com_fixed_t a);

void com_fixed_run_tests(void);

#endif