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fixed cos sin

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veclavtlica
2026-09-11 15:09:47 +03:00
parent adfae10938
commit 6d7fe7392a
10 changed files with 345 additions and 6 deletions
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Common/fixed.c
+62 -3
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@@ -1,8 +1,14 @@
/*
Fixed point arithmetic.
https://github.com/howerj/q/blob/master/q.c
*/
#include "fixed.h"
#include "bits.h"
#include <assert.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <tgmath.h>
// 4-bit LUT (16 entries) for the normalized range [0.5, 2.0)
// It stores the initial guess scaled to Q16.16.
@@ -10,6 +16,22 @@ static const uint32_t com_fixed_sqrt_lut[16] = {
46340, 49547, 52521, 55314, 57954, 60464, 62862, 65161,
67373, 69508, 71572, 73572, 75514, 77402, 79240, 81033};
/* 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_fixed_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_fixed_t com_fixed_sqrt(com_fixed_t a) {
// 1. Handle sign and edge cases
assert(a >= 0);
@@ -18,11 +40,11 @@ com_fixed_t com_fixed_sqrt(com_fixed_t a) {
// 2. Normalize input to the range [0.5, 2.0) to maximize LUT precision
// clz = count leading zeros. On modern hardware, use __builtin_clz
int leading_zeros = com_bits_needed(a);
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
int shift = (31 - leading_zeros) - COM_FIXED_FRACBITS;
int32_t shift = (31 - leading_zeros) - COM_FIXED_FRACBITS;
// Normalize shift to always be even so we can cleanly pull out 2^(shift/2)
if (shift & 1)
@@ -69,3 +91,40 @@ void com_fixed_print(com_fixed_t a) {
printf("%d.%04u\n", int_part, decimal_val);
}
void com_fixed_run_tests(void) {
com_fixed_print(com_fixed_sqrt(COM_FIXED_FRACUNIT * 2));
com_fixed_print(com_fixed_sqrt(COM_FIXED_FRACUNIT * 3));
com_fixed_print(com_fixed_sqrt(COM_FIXED_FRACUNIT * 4));
com_fixed_print(com_fixed_sqrt(COM_FIXED_FRACUNIT * 200));
com_fixed_print(com_fixed_sqrt(COM_FIXED_FRACUNIT * 1000));
com_fixed_print(COM_FIXED_PI);
com_fixed_print(com_fixed_div(COM_FIXED_PI + 234, COM_FIXED_PI2) << 2);
double max_sin_deviation = 0.0f;
com_fixed_t sin_accumulator = -COM_FIXED_PI * 4;
com_fixed_t sin_test_step = (COM_FIXED_PI << 1) >> 10;
for (int i = 0; i < 1024 * 32; ++i) {
com_fixed_t sin = com_fixed_sin(sin_accumulator);
double deviation = fabs(sin(com_fixed_as_float(sin_accumulator)) -
com_fixed_as_float(sin));
if (deviation > max_sin_deviation)
max_sin_deviation = deviation;
sin_accumulator += sin_test_step;
}
printf("max sin deviation: %f\n", max_sin_deviation);
double max_cos_deviation = 0.0f;
com_fixed_t cos_accumulator = -COM_FIXED_PI * 4;
com_fixed_t cos_test_step = (COM_FIXED_PI << 1) >> 10;
for (int i = 0; i < 1024 * 32; ++i) {
com_fixed_t cos = com_fixed_cos(cos_accumulator);
double deviation = fabs(cos(com_fixed_as_float(cos_accumulator)) -
com_fixed_as_float(cos));
if (deviation > max_cos_deviation)
max_cos_deviation = deviation;
cos_accumulator += cos_test_step;
}
printf("max cos deviation: %f\n", max_cos_deviation);
}