brightstone/Common/fix.c

/*
    Fixed point arithmetic.
    https://github.com/howerj/q/blob/master/q.c
*/

#include "fix.h"
#include "def.h"
#include "std.h"
#include "time.h"
#include <stdbool.h>
#include <stdint.h>

// 4-bit LUT (16 entries) for the normalized range [0.5, 2.0)
// It stores the initial guess scaled to Q16.16.
static const uint32_t com_fix_sqrt_lut[16] = {
    46340, 49547, 52521, 55314, 57954, 60464, 62862, 65161,
    67373, 69508, 71572, 73572, 75514, 77402, 79240, 81033};

/* TODO: Test performance of uint_fast16_t here. */
/* Used for other quadrants as well as cosine eval, all from the same table. */
/* Only fractional part is present, reducing the cache footprint. */
const uint16_t com_fix_sin_lut[128] = {
    0,     804,   1608,  2412,  3215,  4018,  4821,  5622,  6423,  7223,  8022,
    8819,  9616,  10410, 11204, 11995, 12785, 13573, 14359, 15142, 15923, 16702,
    17479, 18253, 19024, 19792, 20557, 21319, 22078, 22833, 23586, 24334, 25079,
    25820, 26557, 27291, 28020, 28745, 29465, 30181, 30893, 31600, 32302, 32999,
    33692, 34379, 35061, 35738, 36409, 37075, 37736, 38390, 39039, 39682, 40319,
    40950, 41575, 42194, 42806, 43412, 44011, 44603, 45189, 45768, 46340, 46906,
    47464, 48015, 48558, 49095, 49624, 50146, 50660, 51166, 51665, 52155, 52639,
    53114, 53581, 54040, 54491, 54933, 55368, 55794, 56212, 56621, 57022, 57414,
    57797, 58172, 58538, 58895, 59243, 59583, 59913, 60235, 60547, 60850, 61144,
    61429, 61705, 61971, 62228, 62475, 62714, 62942, 63162, 63371, 63571, 63762,
    63943, 64115, 64276, 64428, 64571, 64703, 64826, 64939, 65043, 65136, 65220,
    65294, 65358, 65412, 65457, 65491, 65516, 65531};

com_fix_t com_fix_sqrt(com_fix_t a) {
  // 1. Handle sign and edge cases
  com_std_assert(a >= 0);
  if (a == 0)
    return 0;

  // 2. Normalize input to the range [0.5, 2.0) to maximize LUT precision
  // clz = count leading zeros. On modern hardware, use __builtin_clz
  uint32_t leading_zeros = __builtin_clz(a);

  // Calculate how much we need to shift to place the highest bit properly
  // We want the value to land squarely within an optimal window
  int32_t shift = (31 - leading_zeros) - COM_FIX_FRACBITS;

  // Normalize shift to always be even so we can cleanly pull out 2^(shift/2)
  if (shift & 1)
    shift -= 1;

  uint32_t normalized_a;
  if (shift > 0) {
    normalized_a = a >> shift;
  } else {
    normalized_a = a << (-shift);
  }

  // 3. LUT Lookup using 4 MSBs of the normalized value
  // Extracted index corresponds to the interval [0.5, 2.0)
  uint32_t lut_index = (normalized_a >> (COM_FIX_FRACBITS - 3)) & 0xF;
  uint64_t x = com_fix_sqrt_lut[lut_index];

  // 4. Newton-Raphson Iterations: x = 0.5 * (x + normalized_a / x)
  // We upscale to 64-bit to prevent intermediate overflow during division
  x = (x + ((uint64_t)normalized_a << COM_FIX_FRACBITS) / x) >>
      1; // Iteration 1
  x = (x + ((uint64_t)normalized_a << COM_FIX_FRACBITS) / x) >>
      1; // Iteration 2

  // 5. Denormalize back to the target scale: result = x * 2^(shift / 2)
  int32_t final_shift = shift / 2;
  if (final_shift > 0) {
    return (int32_t)(x << final_shift);
  } else {
    return (int32_t)(x >> (-final_shift));
  }
}

void com_fix_print(com_fix_t a) {
  if (a < 0) {
    com_std_printf("-");
    a = -a;
  }
  int32_t int_part = a >> 16;
  int32_t frac_part = a & 0xFFFF;

  // Convert fractional 16-bit part to a decimal value (up to 4 decimal places)
  uint32_t decimal_val = (frac_part * 10000) >> 16;

  com_std_printf("%d.%04u\n", int_part, decimal_val);
}

void com_fix_run_bench(void) {
  uint64_t start = com_timer_count_ns();
  for (int i = 5000000; i--;) {
    com_fix_t sqrt = com_fix_sqrt(i);
    COM_DEF_PROFILE_SINK(sqrt);
  }
  com_timer_profile(start, "fixed: sqrt");

  start = com_timer_count_ns();
  for (int i = 50000000; i--;) {
    com_fix_t sin = com_fix_sin(i);
    COM_DEF_PROFILE_SINK(sin);
  }
  com_timer_profile(start, "fixed: sin");

  start = com_timer_count_ns();
  for (int i = 50000000; i--;) {
    com_fix_t cos = com_fix_cos(i);
    COM_DEF_PROFILE_SINK(cos);
  }
  com_timer_profile(start, "fixed: cos");

  start = com_timer_count_ns();
  for (int i = 50000000; i--;) {
    com_fix_t sin, cos;
    com_fix_sincos(i, &sin, &cos);
    com_fix_t sinv = sin;
    com_fix_t cosv = cos;
    COM_DEF_PROFILE_SINK(sinv);
    COM_DEF_PROFILE_SINK(cosv);
  }
  com_timer_profile(start, "fixed: sincos");
}

void com_fix_run_tests(void) {
  // {
  //   double max_sqrt_deviation = 0.0f;
  //   com_fix_t sqrt_accumulator = 0;
  //   com_fix_t sqrt_test_step = COM_FIX_FRACUNIT >> 2; /* Quarter step */
  //   for (int i = 0; i < COM_FIX_FRACUNIT << 1; ++i) {
  //     com_fix_t sqrt = com_fix_sqrt(sqrt_accumulator);
  //     double const deviation =
  //         com_std_sqrt(com_fix_as_float(sqrt_accumulator)) -
  //         com_fix_as_float(sqrt);
  //     if (deviation > max_sqrt_deviation)
  //       max_sqrt_deviation = deviation;
  //     sqrt_accumulator += sqrt_test_step;
  //   }
  //   com_std_printf("max sqrt deviation: %f\n", max_sqrt_deviation);
  // }

  // {
  //   double max_sin_deviation = 0.0f;
  //   com_fix_t sin_accumulator = -COM_FIX_PI * 4;
  //   com_fix_t sin_test_step = (COM_FIX_PI << 1) >> 10;
  //   for (int i = 0; i < 1024 * 32; ++i) {
  //     com_fix_t sin = com_fix_sin(sin_accumulator);
  //     double const deviation =
  //         com_std_fabs(com_std_sin(com_fix_as_float(sin_accumulator)) -
  //                      com_fix_as_float(sin));
  //     if (deviation > max_sin_deviation)
  //       max_sin_deviation = deviation;
  //     sin_accumulator += sin_test_step;
  //   }
  //   com_std_printf("max sin deviation: %f\n", max_sin_deviation);
  // }

  // {
  //   double max_cos_deviation = 0.0f;
  //   com_fix_t cos_accumulator = -COM_FIX_PI * 4;
  //   com_fix_t cos_test_step = (COM_FIX_PI << 1) >> 10;
  //   for (int i = 0; i < 1024 * 32; ++i) {
  //     com_fix_t cos = com_fix_cos(cos_accumulator);
  //     double const deviation =
  //         com_std_fabs(com_std_cos(com_fix_as_float(cos_accumulator)) -
  //                      com_fix_as_float(cos));
  //     if (deviation > max_cos_deviation)
  //       max_cos_deviation = deviation;
  //     cos_accumulator += cos_test_step;
  //   }
  //   com_std_printf("max cos deviation: %f\n", max_cos_deviation);
  // }

  // {
  //   double max_sin_deviation = 0.0f;
  //   double max_cos_deviation = 0.0f;
  //   com_fix_t sincos_accumulator = -COM_FIX_PI * 4;
  //   com_fix_t sincos_test_step = (COM_FIX_PI << 1) >> 10;
  //   for (int i = 0; i < 1024 * 32; ++i) {
  //     com_fix_t sin, cos;
  //     com_fix_sincos(sincos_accumulator, &sin, &cos);
  //     double const sin_deviation =
  //         com_std_fabs(com_std_sin(com_fix_as_float(sincos_accumulator)) -
  //                      com_fix_as_float(sin));
  //     double const cos_deviation =
  //         com_std_fabs(com_std_cos(com_fix_as_float(sincos_accumulator)) -
  //                      com_fix_as_float(cos));
  //     if (sin_deviation > max_sin_deviation)
  //       max_sin_deviation = sin_deviation;
  //     if (cos_deviation > max_cos_deviation)
  //       max_cos_deviation = cos_deviation;
  //     sincos_accumulator += sincos_test_step;
  //   }
  //   com_std_printf("max sincos deviations: %f %f\n", max_sin_deviation,
  //                  max_cos_deviation);
  // }
}