Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Replace sine table with 5th order approximation #27

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
jserv merged 1 commit into sysprog21:main from ndsl7109256:shrinkSineTable
Aug 9, 2024
Merged
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 2 additions & 0 deletions include/twin.h
View file Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1042,6 +1042,8 @@ twin_fixed_t twin_cos(twin_angle_t a);

twin_fixed_t twin_tan(twin_angle_t a);

void twin_sincos(twin_angle_t a, twin_fixed_t *sin, twin_fixed_t *cos);

/*
* widget.c
*/
Expand Down
4 changes: 2 additions & 2 deletions src/matrix.c
View file Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -100,8 +100,8 @@ twin_point_t _twin_matrix_expand(twin_matrix_t *matrix)
void twin_matrix_rotate(twin_matrix_t *m, twin_angle_t a)
{
twin_matrix_t t;
twin_fixed_t c=twin_cos(a);
twin_fixed_ts=twin_sin(a);
twin_fixed_t c, s;
twin_sincos(a, &s, &c);

t.m[0][0] = c;
t.m[0][1] = s;
Expand Down
14 changes: 10 additions & 4 deletions src/path.c
View file Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -134,6 +134,13 @@ void twin_path_draw(twin_path_t *path, twin_fixed_t x, twin_fixed_t y)
_twin_matrix_y(&path->state.matrix, x, y));
}

static void twin_path_draw_polar(twin_path_t *path, twin_angle_t deg)
{
twin_fixed_t s, c;
twin_sincos(deg, &s, &c);
twin_path_draw(path, c, s);
}

void twin_path_rdraw(twin_path_t *path, twin_fixed_t dx, twin_fixed_t dy)
{
twin_spoint_t here = _twin_path_current_spoint(path);
Expand Down Expand Up @@ -218,14 +225,13 @@ void twin_path_arc(twin_path_t *path,
twin_angle_t last = (start + extent - inc + epsilon) & ~(step - 1);

if (first != start)
twin_path_draw(path, twin_cos(start), twin_sin(start));
twin_path_draw_polar(path, start);

for (twin_angle_t a = first; a != last; a += inc)
twin_path_draw(path, twin_cos(a), twin_sin(a));
twin_path_draw_polar(path, a);

if (last != start + extent)
twin_path_draw(path, twin_cos(start + extent),
twin_sin(start + extent));
twin_path_draw_polar(path, start + extent);

twin_path_set_matrix(path, save);
}
Expand Down
216 changes: 69 additions & 147 deletions src/trig.c
View file Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -6,167 +6,28 @@

#include "twin_private.h"

#define TWIN_LOG2_SIN 10

/*
* construction:
int s = 10; for (int i = 0; i < (1 << s); i++) {
if (i % 8 == 0) printf ("\n ");
printf (" 0x%04x,", floor (sin(pi/2 * i / (1 << s)) * 2**16 + 0.5));
}
*/

static const uint16_t _twin_sin_table[1 << TWIN_LOG2_SIN] = {
0x0000, 0x0065, 0x00c9, 0x012e, 0x0192, 0x01f7, 0x025b, 0x02c0, 0x0324,
0x0389, 0x03ed, 0x0452, 0x04b6, 0x051b, 0x057f, 0x05e4, 0x0648, 0x06ad,
0x0711, 0x0776, 0x07da, 0x083f, 0x08a3, 0x0908, 0x096c, 0x09d1, 0x0a35,
0x0a9a, 0x0afe, 0x0b62, 0x0bc7, 0x0c2b, 0x0c90, 0x0cf4, 0x0d59, 0x0dbd,
0x0e21, 0x0e86, 0x0eea, 0x0f4e, 0x0fb3, 0x1017, 0x107b, 0x10e0, 0x1144,
0x11a8, 0x120d, 0x1271, 0x12d5, 0x1339, 0x139e, 0x1402, 0x1466, 0x14ca,
0x152e, 0x1593, 0x15f7, 0x165b, 0x16bf, 0x1723, 0x1787, 0x17eb, 0x1850,
0x18b4, 0x1918, 0x197c, 0x19e0, 0x1a44, 0x1aa8, 0x1b0c, 0x1b70, 0x1bd4,
0x1c38, 0x1c9b, 0x1cff, 0x1d63, 0x1dc7, 0x1e2b, 0x1e8f, 0x1ef3, 0x1f56,
0x1fba, 0x201e, 0x2082, 0x20e5, 0x2149, 0x21ad, 0x2210, 0x2274, 0x22d7,
0x233b, 0x239f, 0x2402, 0x2466, 0x24c9, 0x252d, 0x2590, 0x25f4, 0x2657,
0x26ba, 0x271e, 0x2781, 0x27e4, 0x2848, 0x28ab, 0x290e, 0x2971, 0x29d5,
0x2a38, 0x2a9b, 0x2afe, 0x2b61, 0x2bc4, 0x2c27, 0x2c8a, 0x2ced, 0x2d50,
0x2db3, 0x2e16, 0x2e79, 0x2edc, 0x2f3f, 0x2fa1, 0x3004, 0x3067, 0x30ca,
0x312c, 0x318f, 0x31f1, 0x3254, 0x32b7, 0x3319, 0x337c, 0x33de, 0x3440,
0x34a3, 0x3505, 0x3568, 0x35ca, 0x362c, 0x368e, 0x36f1, 0x3753, 0x37b5,
0x3817, 0x3879, 0x38db, 0x393d, 0x399f, 0x3a01, 0x3a63, 0x3ac5, 0x3b27,
0x3b88, 0x3bea, 0x3c4c, 0x3cae, 0x3d0f, 0x3d71, 0x3dd2, 0x3e34, 0x3e95,
0x3ef7, 0x3f58, 0x3fba, 0x401b, 0x407c, 0x40de, 0x413f, 0x41a0, 0x4201,
0x4262, 0x42c3, 0x4324, 0x4385, 0x43e6, 0x4447, 0x44a8, 0x4509, 0x456a,
0x45cb, 0x462b, 0x468c, 0x46ec, 0x474d, 0x47ae, 0x480e, 0x486f, 0x48cf,
0x492f, 0x4990, 0x49f0, 0x4a50, 0x4ab0, 0x4b10, 0x4b71, 0x4bd1, 0x4c31,
0x4c90, 0x4cf0, 0x4d50, 0x4db0, 0x4e10, 0x4e70, 0x4ecf, 0x4f2f, 0x4f8e,
0x4fee, 0x504d, 0x50ad, 0x510c, 0x516c, 0x51cb, 0x522a, 0x5289, 0x52e8,
0x5348, 0x53a7, 0x5406, 0x5464, 0x54c3, 0x5522, 0x5581, 0x55e0, 0x563e,
0x569d, 0x56fc, 0x575a, 0x57b9, 0x5817, 0x5875, 0x58d4, 0x5932, 0x5990,
0x59ee, 0x5a4c, 0x5aaa, 0x5b08, 0x5b66, 0x5bc4, 0x5c22, 0x5c80, 0x5cde,
0x5d3b, 0x5d99, 0x5df6, 0x5e54, 0x5eb1, 0x5f0f, 0x5f6c, 0x5fc9, 0x6026,
0x6084, 0x60e1, 0x613e, 0x619b, 0x61f8, 0x6254, 0x62b1, 0x630e, 0x636b,
0x63c7, 0x6424, 0x6480, 0x64dd, 0x6539, 0x6595, 0x65f2, 0x664e, 0x66aa,
0x6706, 0x6762, 0x67be, 0x681a, 0x6876, 0x68d1, 0x692d, 0x6989, 0x69e4,
0x6a40, 0x6a9b, 0x6af6, 0x6b52, 0x6bad, 0x6c08, 0x6c63, 0x6cbe, 0x6d19,
0x6d74, 0x6dcf, 0x6e2a, 0x6e85, 0x6edf, 0x6f3a, 0x6f94, 0x6fef, 0x7049,
0x70a3, 0x70fe, 0x7158, 0x71b2, 0x720c, 0x7266, 0x72c0, 0x731a, 0x7373,
0x73cd, 0x7427, 0x7480, 0x74da, 0x7533, 0x758d, 0x75e6, 0x763f, 0x7698,
0x76f1, 0x774a, 0x77a3, 0x77fc, 0x7855, 0x78ad, 0x7906, 0x795f, 0x79b7,
0x7a10, 0x7a68, 0x7ac0, 0x7b18, 0x7b70, 0x7bc8, 0x7c20, 0x7c78, 0x7cd0,
0x7d28, 0x7d7f, 0x7dd7, 0x7e2f, 0x7e86, 0x7edd, 0x7f35, 0x7f8c, 0x7fe3,
0x803a, 0x8091, 0x80e8, 0x813f, 0x8195, 0x81ec, 0x8243, 0x8299, 0x82f0,
0x8346, 0x839c, 0x83f2, 0x8449, 0x849f, 0x84f5, 0x854a, 0x85a0, 0x85f6,
0x864c, 0x86a1, 0x86f7, 0x874c, 0x87a1, 0x87f6, 0x884c, 0x88a1, 0x88f6,
0x894a, 0x899f, 0x89f4, 0x8a49, 0x8a9d, 0x8af2, 0x8b46, 0x8b9a, 0x8bef,
0x8c43, 0x8c97, 0x8ceb, 0x8d3f, 0x8d93, 0x8de6, 0x8e3a, 0x8e8d, 0x8ee1,
0x8f34, 0x8f88, 0x8fdb, 0x902e, 0x9081, 0x90d4, 0x9127, 0x9179, 0x91cc,
0x921f, 0x9271, 0x92c4, 0x9316, 0x9368, 0x93ba, 0x940c, 0x945e, 0x94b0,
0x9502, 0x9554, 0x95a5, 0x95f7, 0x9648, 0x969a, 0x96eb, 0x973c, 0x978d,
0x97de, 0x982f, 0x9880, 0x98d0, 0x9921, 0x9972, 0x99c2, 0x9a12, 0x9a63,
0x9ab3, 0x9b03, 0x9b53, 0x9ba3, 0x9bf2, 0x9c42, 0x9c92, 0x9ce1, 0x9d31,
0x9d80, 0x9dcf, 0x9e1e, 0x9e6d, 0x9ebc, 0x9f0b, 0x9f5a, 0x9fa8, 0x9ff7,
0xa045, 0xa094, 0xa0e2, 0xa130, 0xa17e, 0xa1cc, 0xa21a, 0xa268, 0xa2b5,
0xa303, 0xa350, 0xa39e, 0xa3eb, 0xa438, 0xa485, 0xa4d2, 0xa51f, 0xa56c,
0xa5b8, 0xa605, 0xa652, 0xa69e, 0xa6ea, 0xa736, 0xa782, 0xa7ce, 0xa81a,
0xa866, 0xa8b2, 0xa8fd, 0xa949, 0xa994, 0xa9df, 0xaa2a, 0xaa76, 0xaac1,
0xab0b, 0xab56, 0xaba1, 0xabeb, 0xac36, 0xac80, 0xacca, 0xad14, 0xad5e,
0xada8, 0xadf2, 0xae3c, 0xae85, 0xaecf, 0xaf18, 0xaf62, 0xafab, 0xaff4,
0xb03d, 0xb086, 0xb0ce, 0xb117, 0xb160, 0xb1a8, 0xb1f0, 0xb239, 0xb281,
0xb2c9, 0xb311, 0xb358, 0xb3a0, 0xb3e8, 0xb42f, 0xb477, 0xb4be, 0xb505,
0xb54c, 0xb593, 0xb5da, 0xb620, 0xb667, 0xb6ad, 0xb6f4, 0xb73a, 0xb780,
0xb7c6, 0xb80c, 0xb852, 0xb898, 0xb8dd, 0xb923, 0xb968, 0xb9ae, 0xb9f3,
0xba38, 0xba7d, 0xbac1, 0xbb06, 0xbb4b, 0xbb8f, 0xbbd4, 0xbc18, 0xbc5c,
0xbca0, 0xbce4, 0xbd28, 0xbd6b, 0xbdaf, 0xbdf2, 0xbe36, 0xbe79, 0xbebc,
0xbeff, 0xbf42, 0xbf85, 0xbfc7, 0xc00a, 0xc04c, 0xc08f, 0xc0d1, 0xc113,
0xc155, 0xc197, 0xc1d8, 0xc21a, 0xc25c, 0xc29d, 0xc2de, 0xc31f, 0xc360,
0xc3a1, 0xc3e2, 0xc423, 0xc463, 0xc4a4, 0xc4e4, 0xc524, 0xc564, 0xc5a4,
0xc5e4, 0xc624, 0xc663, 0xc6a3, 0xc6e2, 0xc721, 0xc761, 0xc7a0, 0xc7de,
0xc81d, 0xc85c, 0xc89a, 0xc8d9, 0xc917, 0xc955, 0xc993, 0xc9d1, 0xca0f,
0xca4d, 0xca8a, 0xcac7, 0xcb05, 0xcb42, 0xcb7f, 0xcbbc, 0xcbf9, 0xcc35,
0xcc72, 0xccae, 0xcceb, 0xcd27, 0xcd63, 0xcd9f, 0xcddb, 0xce17, 0xce52,
0xce8e, 0xcec9, 0xcf04, 0xcf3f, 0xcf7a, 0xcfb5, 0xcff0, 0xd02a, 0xd065,
0xd09f, 0xd0d9, 0xd113, 0xd14d, 0xd187, 0xd1c1, 0xd1fa, 0xd234, 0xd26d,
0xd2a6, 0xd2df, 0xd318, 0xd351, 0xd38a, 0xd3c2, 0xd3fb, 0xd433, 0xd46b,
0xd4a3, 0xd4db, 0xd513, 0xd54b, 0xd582, 0xd5ba, 0xd5f1, 0xd628, 0xd65f,
0xd696, 0xd6cd, 0xd703, 0xd73a, 0xd770, 0xd7a6, 0xd7dc, 0xd812, 0xd848,
0xd87e, 0xd8b4, 0xd8e9, 0xd91e, 0xd954, 0xd989, 0xd9be, 0xd9f2, 0xda27,
0xda5c, 0xda90, 0xdac4, 0xdaf8, 0xdb2c, 0xdb60, 0xdb94, 0xdbc8, 0xdbfb,
0xdc2f, 0xdc62, 0xdc95, 0xdcc8, 0xdcfb, 0xdd2d, 0xdd60, 0xdd92, 0xddc5,
0xddf7, 0xde29, 0xde5b, 0xde8c, 0xdebe, 0xdef0, 0xdf21, 0xdf52, 0xdf83,
0xdfb4, 0xdfe5, 0xe016, 0xe046, 0xe077, 0xe0a7, 0xe0d7, 0xe107, 0xe137,
0xe167, 0xe196, 0xe1c6, 0xe1f5, 0xe224, 0xe253, 0xe282, 0xe2b1, 0xe2df,
0xe30e, 0xe33c, 0xe36b, 0xe399, 0xe3c7, 0xe3f4, 0xe422, 0xe450, 0xe47d,
0xe4aa, 0xe4d7, 0xe504, 0xe531, 0xe55e, 0xe58b, 0xe5b7, 0xe5e3, 0xe610,
0xe63c, 0xe667, 0xe693, 0xe6bf, 0xe6ea, 0xe716, 0xe741, 0xe76c, 0xe797,
0xe7c2, 0xe7ec, 0xe817, 0xe841, 0xe86b, 0xe895, 0xe8bf, 0xe8e9, 0xe913,
0xe93c, 0xe966, 0xe98f, 0xe9b8, 0xe9e1, 0xea0a, 0xea32, 0xea5b, 0xea83,
0xeaab, 0xead4, 0xeafc, 0xeb23, 0xeb4b, 0xeb73, 0xeb9a, 0xebc1, 0xebe8,
0xec0f, 0xec36, 0xec5d, 0xec83, 0xecaa, 0xecd0, 0xecf6, 0xed1c, 0xed42,
0xed68, 0xed8d, 0xedb3, 0xedd8, 0xedfd, 0xee22, 0xee47, 0xee6b, 0xee90,
0xeeb4, 0xeed9, 0xeefd, 0xef21, 0xef45, 0xef68, 0xef8c, 0xefaf, 0xefd2,
0xeff5, 0xf018, 0xf03b, 0xf05e, 0xf080, 0xf0a3, 0xf0c5, 0xf0e7, 0xf109,
0xf12b, 0xf14c, 0xf16e, 0xf18f, 0xf1b1, 0xf1d2, 0xf1f3, 0xf213, 0xf234,
0xf254, 0xf275, 0xf295, 0xf2b5, 0xf2d5, 0xf2f5, 0xf314, 0xf334, 0xf353,
0xf372, 0xf391, 0xf3b0, 0xf3cf, 0xf3ed, 0xf40c, 0xf42a, 0xf448, 0xf466,
0xf484, 0xf4a2, 0xf4bf, 0xf4dd, 0xf4fa, 0xf517, 0xf534, 0xf551, 0xf56e,
0xf58a, 0xf5a6, 0xf5c3, 0xf5df, 0xf5fb, 0xf616, 0xf632, 0xf64e, 0xf669,
0xf684, 0xf69f, 0xf6ba, 0xf6d5, 0xf6ef, 0xf70a, 0xf724, 0xf73e, 0xf758,
0xf772, 0xf78c, 0xf7a5, 0xf7bf, 0xf7d8, 0xf7f1, 0xf80a, 0xf823, 0xf83b,
0xf854, 0xf86c, 0xf885, 0xf89d, 0xf8b4, 0xf8cc, 0xf8e4, 0xf8fb, 0xf913,
0xf92a, 0xf941, 0xf958, 0xf96e, 0xf985, 0xf99b, 0xf9b2, 0xf9c8, 0xf9de,
0xf9f3, 0xfa09, 0xfa1f, 0xfa34, 0xfa49, 0xfa5e, 0xfa73, 0xfa88, 0xfa9c,
0xfab1, 0xfac5, 0xfad9, 0xfaed, 0xfb01, 0xfb15, 0xfb28, 0xfb3c, 0xfb4f,
0xfb62, 0xfb75, 0xfb88, 0xfb9a, 0xfbad, 0xfbbf, 0xfbd1, 0xfbe3, 0xfbf5,
0xfc07, 0xfc18, 0xfc2a, 0xfc3b, 0xfc4c, 0xfc5d, 0xfc6e, 0xfc7f, 0xfc8f,
0xfca0, 0xfcb0, 0xfcc0, 0xfcd0, 0xfcdf, 0xfcef, 0xfcfe, 0xfd0e, 0xfd1d,
0xfd2c, 0xfd3b, 0xfd49, 0xfd58, 0xfd66, 0xfd74, 0xfd83, 0xfd90, 0xfd9e,
0xfdac, 0xfdb9, 0xfdc7, 0xfdd4, 0xfde1, 0xfdee, 0xfdfa, 0xfe07, 0xfe13,
0xfe1f, 0xfe2b, 0xfe37, 0xfe43, 0xfe4f, 0xfe5a, 0xfe66, 0xfe71, 0xfe7c,
0xfe87, 0xfe91, 0xfe9c, 0xfea6, 0xfeb0, 0xfeba, 0xfec4, 0xfece, 0xfed8,
0xfee1, 0xfeeb, 0xfef4, 0xfefd, 0xff06, 0xff0e, 0xff17, 0xff1f, 0xff28,
0xff30, 0xff38, 0xff3f, 0xff47, 0xff4e, 0xff56, 0xff5d, 0xff64, 0xff6b,
0xff71, 0xff78, 0xff7e, 0xff85, 0xff8b, 0xff91, 0xff96, 0xff9c, 0xffa2,
0xffa7, 0xffac, 0xffb1, 0xffb6, 0xffbb, 0xffbf, 0xffc4, 0xffc8, 0xffcc,
0xffd0, 0xffd4, 0xffd7, 0xffdb, 0xffde, 0xffe1, 0xffe4, 0xffe7, 0xffea,
0xffec, 0xffef, 0xfff1, 0xfff3, 0xfff5, 0xfff7, 0xfff8, 0xfffa, 0xfffb,
0xfffc, 0xfffd, 0xfffe, 0xffff, 0xffff, 0xffff, 0xffff,
};

/*
* angles are measured from -2048 .. 2048
*/

twin_fixed_t twin_sin(twin_angle_t a)
{
twin_fixed_t sin;

/* limit to [0..360) */
a = a & (TWIN_ANGLE_360 - 1);
/* special case for 90 degrees - no room in table */
if ((a & ~(TWIN_ANGLE_180)) == TWIN_ANGLE_90)
sin = TWIN_FIXED_ONE;
else {
/* mirror second and third quadrant values across y axis */
if (a & TWIN_ANGLE_90)
a = TWIN_ANGLE_180 - a;
sin = _twin_sin_table[a & (TWIN_ANGLE_90 - 1)];
}
/* mirror third and fourth quadrant values across x axis */
if (a & TWIN_ANGLE_180)
sin = -sin;
return sin;
twin_fixed_t sin_val = 0;
twin_sincos(a, &sin_val, NULL);
return sin_val;
}

twin_fixed_t twin_cos(twin_angle_t a)
{
return twin_sin(a + TWIN_ANGLE_90);
twin_fixed_t cos_val = 0;
twin_sincos(a, NULL, &cos_val);
return cos_val;
}

twin_fixed_t twin_tan(twin_angle_t a)
Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Is it possible to calculate tan(x) without divisions?

Copy link
Collaborator Author

@ndsl7109256 ndsl7109256 Aug 8, 2024

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I think we could use Taylor series expansion to calculate tan(x) without using division, but as x approaches 90 degrees, the error would become very large. I'm not sure if this is suitable for use in this project.

Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I think we could use Taylor series expansion to calculate tan(x) without using division, but as x approaches 90 degrees, the error would become very large. I'm not sure if this is suitable for use in this project.

TWIN_FIXED_MAX can be set for $tan(\pi/2)$ while TWIN_FIXED_MIN can be set for $tan(-\pi/2)$.

Copy link
Collaborator Author

@ndsl7109256 ndsl7109256 Aug 8, 2024

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

image

Though we could set $tan( \pi /2)$ to TWIN_FIXED_MAX directly. However, we still suffer significant error when angle is closed to $\pi/2$. Should we just neglect the error here?

Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

@jouae, Can you comment this? Can CORDIC algorithm be applied to tan(x)?

Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I need to spend some time studying the principles of CORDIC.

See https://github.com/Max-Gulda/Cordic-Math/blob/main/lib/cordicMath/src/cordic-math.c#L290-L332

Copy link
Collaborator

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Perhaps we can improve the division about $\frac{x}{y}$

see https://hackmd.io/@sysprog/linux-intdiv

Copy link
Collaborator Author

@ndsl7109256 ndsl7109256 Aug 9, 2024

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Perhaps we can improve the division about x y

see https://hackmd.io/@sysprog/linux-intdiv

@jouae Thanks for the follow-up!
The divisor we use (x calculated in CORDIC or cos calculated in current way) varies for different angles. Is it possible to improve by the mentioned techniques?
Could you provide a more detailed explanation of your idea? Thanks!

jouae reacted with thumbs up emoji
Copy link
Collaborator

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

@ndsl7109256
Sure, leave it to me, dude.

Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

@jouae, Create a new GitHub issue when this pull request is merged.

{
twin_fixed_t s=twin_sin(a);
twin_fixed_tc=twin_cos(a);
twin_fixed_t s, c;
twin_sincos(a, &s, &c);

if (c == 0) {
if (s > 0)
Expand All @@ -178,3 +39,64 @@ twin_fixed_t twin_tan(twin_angle_t a)
return 0;
return ((s << 15) / c) << 1;
}

static inline twin_fixed_t sin_poly(twin_angle_t x)
{
/* S(x) = x * 2^(-n) * (A1 - 2 ^ (q-p) * x * (2^-n) * x * 2^(-n) * (B1 - 2 ^
* (-r) * x * 2 ^ (-n) * C1 * x)) * 2 ^ (a-q)
* @n: the angle scale
* @A: the amplitude
* @p,q,r: the scaling factor
*
* A1 = 2^q * a5, B1 = 2 ^ p * b5, C1 = 2 ^ (r+p-n) * c5
* where a5, b5, c5 are the coefficients for 5th-order polynomial
* a5 = 4 * (3 / pi - 9 / 16)
* b5 = 2 * a5 - 5 / 2
* c5 = a5 - 3 / 2
*/
const uint64_t A = 16, n = 10, p = 32, q = 31, r = 3;
const uint64_t A1 = 3370945099, B1 = 2746362156, C1 = 2339369;
uint64_t y = (C1 * x) >> n;
y = B1 - ((x * y) >> r);
y = x * (y >> n);
y = x * (y >> n);
y = A1 - (y >> (p - q));
y = x * (y >> n);
y = (y + (1UL << (q - A - 1))) >> (q - A); // Rounding
return y;
}

void twin_sincos(twin_angle_t a, twin_fixed_t *sin, twin_fixed_t *cos)
{
twin_fixed_t sin_val = 0, cos_val = 0;

/* limit to [0..360) */
a = a & (TWIN_ANGLE_360 - 1);
int c = a > TWIN_ANGLE_90 && a < TWIN_ANGLE_270;
/* special case for 90 degrees */
if ((a & ~(TWIN_ANGLE_180)) == TWIN_ANGLE_90) {
sin_val = TWIN_FIXED_ONE;
cos_val = 0;
} else {
/* mirror second and third quadrant values across y axis */
if (a & TWIN_ANGLE_90)
a = TWIN_ANGLE_180 - a;
twin_angle_t x = a & (TWIN_ANGLE_90 - 1);
if (sin)
sin_val = sin_poly(x);
if (cos)
cos_val = sin_poly(TWIN_ANGLE_90 - x);
}
if (sin) {
/* mirror third and fourth quadrant values across x axis */
if (a & TWIN_ANGLE_180)
sin_val = -sin_val;
*sin = sin_val;
}
if (cos) {
/* mirror first and fourth quadrant values across y axis */
if (c)
cos_val = -cos_val;
*cos = cos_val;
}
}

AltStyle によって変換されたページ (->オリジナル) /