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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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.gitignore
+4
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@@ -1,4 +1,8 @@
**/*.o
**/*.err
**/*.EXE
**/*.exe
*.sublime-*
Player/player
Master/master
Common/bits.h
-1
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@@ -9,7 +9,6 @@
/* Alternitive semntic: nearest upper power of two */
static inline int com_bits_needed(uint32_t v) {
#ifdef COM_DEF_COMPILE_MODERN
/* Use intrinsic, required for fast sqrt impl */
return v == 0 ? 1 : 32 - __builtin_clz(v);
#else
#endif
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);
}
Common/fixed.h
+63 -1
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@@ -7,12 +7,22 @@
#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;
}
@@ -30,9 +40,61 @@ 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);
}
/* Approximate square root using Newton-Raphson in 2 iterations over small LUT*/
/* 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
Common/mat.h
+50
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@@ -134,4 +134,54 @@ static inline com_mat_t com_mat_reoder(com_mat_t a) {
return result;
}
/* TODO: move to .c file */
/* Produces a view matrix needed for camera work. */
static inline com_mat_t com_mat_look_at(com_vec_t pos, com_vec_t up,
com_vec_t target) {
com_vec_t const r = com_vec_nrm(com_vec_crs(target, up));
com_vec_t const u = com_vec_crs(r, target);
com_mat_t result;
result.a[0] = r.s.x;
result.a[1] = u.s.x;
result.a[2] = -target.s.x;
result.a[3] = 0;
result.a[4] = r.s.y;
result.a[5] = u.s.y;
result.a[6] = -target.s.y;
result.a[7] = 0;
result.a[8] = r.s.z;
result.a[9] = u.s.z;
result.a[10] = -target.s.z;
result.a[11] = 0;
result.a[12] = -com_vec_dot(r, pos);
result.a[13] = -com_vec_dot(u, pos);
result.a[14] = com_vec_dot(target, pos);
result.a[15] = COM_FIXED_FRACUNIT;
return result;
}
/* TODO: move to .c file */
/* Produces a projection matrix needed for camera work. */
static inline com_mat_t com_mat_perspective(uint16_t rwidth, uint16_t rheight,
com_fixed_t nearz, com_fixed_t farz,
com_fixed_t fov) {
com_mat_t result = {0};
// com_fixed_t const aspect = com_fixed_div(rwidth, rheight);
// const float f = 1.0f / tanf(camera->fov * 0.5f);
// const float fn = 1.0f / (CAMERA_NEAR_Z - camera->far_z);
// result.row[0].x = f / aspect;
// result.row[1].y = f;
// result.row[2].z = (CAMERA_NEAR_Z + camera->far_z) * fn;
// result.row[2].w = -1.0f;
// result.row[3].z = 2.0f * CAMERA_NEAR_Z * camera->far_z * fn;
// return result;
}
#endif
Common/vec.h
+6
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@@ -20,6 +20,12 @@ typedef union {
} s;
} com_vec_t;
static inline com_vec_t com_vec_identity(void) {
return (com_vec_t){.s = {.x = COM_FIXED_FRACUNIT,
.y = COM_FIXED_FRACUNIT,
.z = COM_FIXED_FRACUNIT}};
}
static inline com_vec_t com_vec_add(com_vec_t a, com_vec_t b) {
return (com_vec_t){.s = {.x = com_fixed_add(a.s.x, b.s.x),
.y = com_fixed_add(a.s.y, b.s.y),
Helpers/fixedgen.out
+135
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@@ -0,0 +1,135 @@
#define COM_FIXED_PI (com_fixed_t)205887
#define COM_FIXED_PI2 (com_fixed_t)411774
#define COM_FIXED_PIHALF (com_fixed_t)102943
static 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 };
Helpers/fixedgen.py
Executable
+19
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@@ -0,0 +1,19 @@
#!/usr/bin/env python3
# Generator for sin/cos fixed point LUT tables.
import math
def generate_pi():
print(f"#define COM_FIXED_PI (com_fixed_t){int(math.pi * (1 << 16))}\n")
print(f"#define COM_FIXED_PI2 (com_fixed_t){int(math.pi*2 * (1 << 16))}\n")
print(f"#define COM_FIXED_PIHALF (com_fixed_t){int(math.pi/2 * (1 << 16))}\n")
# Idea is to generate only one quadrant, as the values repeat later with different sign and order.
def generate_sin_table(n_entries=128):
r = []
for n in range(n_entries):
r += [math.sin(math.pi*n/(n_entries*2))]
# r[n_entries-1]=1 # Make it converge to unit precisely
print(f"static const uint16_t com_fixed_sin_lut[{n_entries}] =", "{", ",\n".join((str(int(a * (1 << 16))) for a in r)), "};\n")
generate_pi()
generate_sin_table()
Player/Display/x11.c
+5
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@@ -38,6 +38,11 @@ extern int plr_display_x11_main(int argc, char *argv[]) {
com_fixed_print(t0.a[4]);
com_fixed_print(t1.a[4]);
com_vec_t v0 = com_mat_vec_project(com_mat_reoder(m0), com_vec_identity());
com_fixed_print(v0.a[0]);
com_fixed_run_tests();
Display *display = XOpenDisplay(NULL);
if (NULL == display) {
fprintf(stderr, "Failed to initialize display");
Player/Makefile
+1 -1
View File
@@ -1,5 +1,5 @@
CC=clang
CFLAGS=-lX11 -Wall -std=c99 -g3 -O3 -fno-inline -msse2
CFLAGS=-lX11 -Wall -std=c99 -g3 -O3 -fno-inline -msse2 -lm
DEPS = Display/display.h ../Common/lzw.h ../Common/mat.h ../Common/vec.h ../Common/fixed.h ../Common/def.h ../Common/bits.h
OBJ = ../Common/lzw.o ../Common/fixed.o
LINUX = main.o Display/x11.o