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arm_sin_cos_q31.c
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/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_sin_cos_q31.c
*
* Description: Cosine & Sine calculation for Q31 values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupController
*/
/**
* @addtogroup SinCos
* @{
*/
/**
* \par
* Sine Table is generated from following loop
* <pre>for(i = 0; i < 360; i++)
* {
* sinTable[i]= sin((i-180) * PI/180.0);
* } </pre>
* Convert above coefficients to fixed point 1.31 format.
*/
static const int32_t sinTableQ31[360] = {
0x0, 0xfdc41e9b, 0xfb8869ce, 0xf94d0e2e, 0xf7123849, 0xf4d814a4, 0xf29ecfb2,
0xf06695da,
0xee2f9369, 0xebf9f498, 0xe9c5e582, 0xe7939223, 0xe5632654, 0xe334cdc9,
0xe108b40d, 0xdedf047d,
0xdcb7ea46, 0xda939061, 0xd8722192, 0xd653c860, 0xd438af17, 0xd220ffc0,
0xd00ce422, 0xcdfc85bb,
0xcbf00dbe, 0xc9e7a512, 0xc7e3744b, 0xc5e3a3a9, 0xc3e85b18, 0xc1f1c224,
0xc0000000, 0xbe133b7c,
0xbc2b9b05, 0xba4944a2, 0xb86c5df0, 0xb6950c1e, 0xb4c373ee, 0xb2f7b9af,
0xb1320139, 0xaf726def,
0xadb922b7, 0xac0641fb, 0xaa59eda4, 0xa8b4471a, 0xa7156f3c, 0xa57d8666,
0xa3ecac65, 0xa263007d,
0xa0e0a15f, 0x9f65ad2d, 0x9df24175, 0x9c867b2c, 0x9b2276b0, 0x99c64fc5,
0x98722192, 0x9726069c,
0x95e218c9, 0x94a6715d, 0x937328f5, 0x92485786, 0x9126145f, 0x900c7621,
0x8efb92c2, 0x8df37f8b,
0x8cf45113, 0x8bfe1b3f, 0x8b10f144, 0x8a2ce59f, 0x89520a1a, 0x88806fc4,
0x87b826f7, 0x86f93f50,
0x8643c7b3, 0x8597ce46, 0x84f56073, 0x845c8ae3, 0x83cd5982, 0x8347d77b,
0x82cc0f36, 0x825a0a5b,
0x81f1d1ce, 0x81936daf, 0x813ee55b, 0x80f43f69, 0x80b381ac, 0x807cb130,
0x804fd23a, 0x802ce84c,
0x8013f61d, 0x8004fda0, 0x80000000, 0x8004fda0, 0x8013f61d, 0x802ce84c,
0x804fd23a, 0x807cb130,
0x80b381ac, 0x80f43f69, 0x813ee55b, 0x81936daf, 0x81f1d1ce, 0x825a0a5b,
0x82cc0f36, 0x8347d77b,
0x83cd5982, 0x845c8ae3, 0x84f56073, 0x8597ce46, 0x8643c7b3, 0x86f93f50,
0x87b826f7, 0x88806fc4,
0x89520a1a, 0x8a2ce59f, 0x8b10f144, 0x8bfe1b3f, 0x8cf45113, 0x8df37f8b,
0x8efb92c2, 0x900c7621,
0x9126145f, 0x92485786, 0x937328f5, 0x94a6715d, 0x95e218c9, 0x9726069c,
0x98722192, 0x99c64fc5,
0x9b2276b0, 0x9c867b2c, 0x9df24175, 0x9f65ad2d, 0xa0e0a15f, 0xa263007d,
0xa3ecac65, 0xa57d8666,
0xa7156f3c, 0xa8b4471a, 0xaa59eda4, 0xac0641fb, 0xadb922b7, 0xaf726def,
0xb1320139, 0xb2f7b9af,
0xb4c373ee, 0xb6950c1e, 0xb86c5df0, 0xba4944a2, 0xbc2b9b05, 0xbe133b7c,
0xc0000000, 0xc1f1c224,
0xc3e85b18, 0xc5e3a3a9, 0xc7e3744b, 0xc9e7a512, 0xcbf00dbe, 0xcdfc85bb,
0xd00ce422, 0xd220ffc0,
0xd438af17, 0xd653c860, 0xd8722192, 0xda939061, 0xdcb7ea46, 0xdedf047d,
0xe108b40d, 0xe334cdc9,
0xe5632654, 0xe7939223, 0xe9c5e582, 0xebf9f498, 0xee2f9369, 0xf06695da,
0xf29ecfb2, 0xf4d814a4,
0xf7123849, 0xf94d0e2e, 0xfb8869ce, 0xfdc41e9b, 0x0, 0x23be165, 0x4779632,
0x6b2f1d2,
0x8edc7b7, 0xb27eb5c, 0xd61304e, 0xf996a26, 0x11d06c97, 0x14060b68,
0x163a1a7e, 0x186c6ddd,
0x1a9cd9ac, 0x1ccb3237, 0x1ef74bf3, 0x2120fb83, 0x234815ba, 0x256c6f9f,
0x278dde6e, 0x29ac37a0,
0x2bc750e9, 0x2ddf0040, 0x2ff31bde, 0x32037a45, 0x340ff242, 0x36185aee,
0x381c8bb5, 0x3a1c5c57,
0x3c17a4e8, 0x3e0e3ddc, 0x40000000, 0x41ecc484, 0x43d464fb, 0x45b6bb5e,
0x4793a210, 0x496af3e2,
0x4b3c8c12, 0x4d084651, 0x4ecdfec7, 0x508d9211, 0x5246dd49, 0x53f9be05,
0x55a6125c, 0x574bb8e6,
0x58ea90c4, 0x5a82799a, 0x5c13539b, 0x5d9cff83, 0x5f1f5ea1, 0x609a52d3,
0x620dbe8b, 0x637984d4,
0x64dd8950, 0x6639b03b, 0x678dde6e, 0x68d9f964, 0x6a1de737, 0x6b598ea3,
0x6c8cd70b, 0x6db7a87a,
0x6ed9eba1, 0x6ff389df, 0x71046d3e, 0x720c8075, 0x730baeed, 0x7401e4c1,
0x74ef0ebc, 0x75d31a61,
0x76adf5e6, 0x777f903c, 0x7847d909, 0x7906c0b0, 0x79bc384d, 0x7a6831ba,
0x7b0a9f8d, 0x7ba3751d,
0x7c32a67e, 0x7cb82885, 0x7d33f0ca, 0x7da5f5a5, 0x7e0e2e32, 0x7e6c9251,
0x7ec11aa5, 0x7f0bc097,
0x7f4c7e54, 0x7f834ed0, 0x7fb02dc6, 0x7fd317b4, 0x7fec09e3, 0x7ffb0260,
0x7fffffff, 0x7ffb0260,
0x7fec09e3, 0x7fd317b4, 0x7fb02dc6, 0x7f834ed0, 0x7f4c7e54, 0x7f0bc097,
0x7ec11aa5, 0x7e6c9251,
0x7e0e2e32, 0x7da5f5a5, 0x7d33f0ca, 0x7cb82885, 0x7c32a67e, 0x7ba3751d,
0x7b0a9f8d, 0x7a6831ba,
0x79bc384d, 0x7906c0b0, 0x7847d909, 0x777f903c, 0x76adf5e6, 0x75d31a61,
0x74ef0ebc, 0x7401e4c1,
0x730baeed, 0x720c8075, 0x71046d3e, 0x6ff389df, 0x6ed9eba1, 0x6db7a87a,
0x6c8cd70b, 0x6b598ea3,
0x6a1de737, 0x68d9f964, 0x678dde6e, 0x6639b03b, 0x64dd8950, 0x637984d4,
0x620dbe8b, 0x609a52d3,
0x5f1f5ea1, 0x5d9cff83, 0x5c13539b, 0x5a82799a, 0x58ea90c4, 0x574bb8e6,
0x55a6125c, 0x53f9be05,
0x5246dd49, 0x508d9211, 0x4ecdfec7, 0x4d084651, 0x4b3c8c12, 0x496af3e2,
0x4793a210, 0x45b6bb5e,
0x43d464fb, 0x41ecc484, 0x40000000, 0x3e0e3ddc, 0x3c17a4e8, 0x3a1c5c57,
0x381c8bb5, 0x36185aee,
0x340ff242, 0x32037a45, 0x2ff31bde, 0x2ddf0040, 0x2bc750e9, 0x29ac37a0,
0x278dde6e, 0x256c6f9f,
0x234815ba, 0x2120fb83, 0x1ef74bf3, 0x1ccb3237, 0x1a9cd9ac, 0x186c6ddd,
0x163a1a7e, 0x14060b68,
0x11d06c97, 0xf996a26, 0xd61304e, 0xb27eb5c, 0x8edc7b7, 0x6b2f1d2,
0x4779632, 0x23be165,
};
/**
* \par
* Cosine Table is generated from following loop
* <pre>for(i = 0; i < 360; i++)
* {
* cosTable[i]= cos((i-180) * PI/180.0);
* } </pre>
* \par
* Convert above coefficients to fixed point 1.31 format.
*/
static const int32_t cosTableQ31[360] = {
0x80000000, 0x8004fda0, 0x8013f61d, 0x802ce84c, 0x804fd23a, 0x807cb130,
0x80b381ac, 0x80f43f69,
0x813ee55b, 0x81936daf, 0x81f1d1ce, 0x825a0a5b, 0x82cc0f36, 0x8347d77b,
0x83cd5982, 0x845c8ae3,
0x84f56073, 0x8597ce46, 0x8643c7b3, 0x86f93f50, 0x87b826f7, 0x88806fc4,
0x89520a1a, 0x8a2ce59f,
0x8b10f144, 0x8bfe1b3f, 0x8cf45113, 0x8df37f8b, 0x8efb92c2, 0x900c7621,
0x9126145f, 0x92485786,
0x937328f5, 0x94a6715d, 0x95e218c9, 0x9726069c, 0x98722192, 0x99c64fc5,
0x9b2276b0, 0x9c867b2c,
0x9df24175, 0x9f65ad2d, 0xa0e0a15f, 0xa263007d, 0xa3ecac65, 0xa57d8666,
0xa7156f3c, 0xa8b4471a,
0xaa59eda4, 0xac0641fb, 0xadb922b7, 0xaf726def, 0xb1320139, 0xb2f7b9af,
0xb4c373ee, 0xb6950c1e,
0xb86c5df0, 0xba4944a2, 0xbc2b9b05, 0xbe133b7c, 0xc0000000, 0xc1f1c224,
0xc3e85b18, 0xc5e3a3a9,
0xc7e3744b, 0xc9e7a512, 0xcbf00dbe, 0xcdfc85bb, 0xd00ce422, 0xd220ffc0,
0xd438af17, 0xd653c860,
0xd8722192, 0xda939061, 0xdcb7ea46, 0xdedf047d, 0xe108b40d, 0xe334cdc9,
0xe5632654, 0xe7939223,
0xe9c5e582, 0xebf9f498, 0xee2f9369, 0xf06695da, 0xf29ecfb2, 0xf4d814a4,
0xf7123849, 0xf94d0e2e,
0xfb8869ce, 0xfdc41e9b, 0x0, 0x23be165, 0x4779632, 0x6b2f1d2, 0x8edc7b7,
0xb27eb5c,
0xd61304e, 0xf996a26, 0x11d06c97, 0x14060b68, 0x163a1a7e, 0x186c6ddd,
0x1a9cd9ac, 0x1ccb3237,
0x1ef74bf3, 0x2120fb83, 0x234815ba, 0x256c6f9f, 0x278dde6e, 0x29ac37a0,
0x2bc750e9, 0x2ddf0040,
0x2ff31bde, 0x32037a45, 0x340ff242, 0x36185aee, 0x381c8bb5, 0x3a1c5c57,
0x3c17a4e8, 0x3e0e3ddc,
0x40000000, 0x41ecc484, 0x43d464fb, 0x45b6bb5e, 0x4793a210, 0x496af3e2,
0x4b3c8c12, 0x4d084651,
0x4ecdfec7, 0x508d9211, 0x5246dd49, 0x53f9be05, 0x55a6125c, 0x574bb8e6,
0x58ea90c4, 0x5a82799a,
0x5c13539b, 0x5d9cff83, 0x5f1f5ea1, 0x609a52d3, 0x620dbe8b, 0x637984d4,
0x64dd8950, 0x6639b03b,
0x678dde6e, 0x68d9f964, 0x6a1de737, 0x6b598ea3, 0x6c8cd70b, 0x6db7a87a,
0x6ed9eba1, 0x6ff389df,
0x71046d3e, 0x720c8075, 0x730baeed, 0x7401e4c1, 0x74ef0ebc, 0x75d31a61,
0x76adf5e6, 0x777f903c,
0x7847d909, 0x7906c0b0, 0x79bc384d, 0x7a6831ba, 0x7b0a9f8d, 0x7ba3751d,
0x7c32a67e, 0x7cb82885,
0x7d33f0ca, 0x7da5f5a5, 0x7e0e2e32, 0x7e6c9251, 0x7ec11aa5, 0x7f0bc097,
0x7f4c7e54, 0x7f834ed0,
0x7fb02dc6, 0x7fd317b4, 0x7fec09e3, 0x7ffb0260, 0x7fffffff, 0x7ffb0260,
0x7fec09e3, 0x7fd317b4,
0x7fb02dc6, 0x7f834ed0, 0x7f4c7e54, 0x7f0bc097, 0x7ec11aa5, 0x7e6c9251,
0x7e0e2e32, 0x7da5f5a5,
0x7d33f0ca, 0x7cb82885, 0x7c32a67e, 0x7ba3751d, 0x7b0a9f8d, 0x7a6831ba,
0x79bc384d, 0x7906c0b0,
0x7847d909, 0x777f903c, 0x76adf5e6, 0x75d31a61, 0x74ef0ebc, 0x7401e4c1,
0x730baeed, 0x720c8075,
0x71046d3e, 0x6ff389df, 0x6ed9eba1, 0x6db7a87a, 0x6c8cd70b, 0x6b598ea3,
0x6a1de737, 0x68d9f964,
0x678dde6e, 0x6639b03b, 0x64dd8950, 0x637984d4, 0x620dbe8b, 0x609a52d3,
0x5f1f5ea1, 0x5d9cff83,
0x5c13539b, 0x5a82799a, 0x58ea90c4, 0x574bb8e6, 0x55a6125c, 0x53f9be05,
0x5246dd49, 0x508d9211,
0x4ecdfec7, 0x4d084651, 0x4b3c8c12, 0x496af3e2, 0x4793a210, 0x45b6bb5e,
0x43d464fb, 0x41ecc484,
0x40000000, 0x3e0e3ddc, 0x3c17a4e8, 0x3a1c5c57, 0x381c8bb5, 0x36185aee,
0x340ff242, 0x32037a45,
0x2ff31bde, 0x2ddf0040, 0x2bc750e9, 0x29ac37a0, 0x278dde6e, 0x256c6f9f,
0x234815ba, 0x2120fb83,
0x1ef74bf3, 0x1ccb3237, 0x1a9cd9ac, 0x186c6ddd, 0x163a1a7e, 0x14060b68,
0x11d06c97, 0xf996a26,
0xd61304e, 0xb27eb5c, 0x8edc7b7, 0x6b2f1d2, 0x4779632, 0x23be165, 0x0,
0xfdc41e9b,
0xfb8869ce, 0xf94d0e2e, 0xf7123849, 0xf4d814a4, 0xf29ecfb2, 0xf06695da,
0xee2f9369, 0xebf9f498,
0xe9c5e582, 0xe7939223, 0xe5632654, 0xe334cdc9, 0xe108b40d, 0xdedf047d,
0xdcb7ea46, 0xda939061,
0xd8722192, 0xd653c860, 0xd438af17, 0xd220ffc0, 0xd00ce422, 0xcdfc85bb,
0xcbf00dbe, 0xc9e7a512,
0xc7e3744b, 0xc5e3a3a9, 0xc3e85b18, 0xc1f1c224, 0xc0000000, 0xbe133b7c,
0xbc2b9b05, 0xba4944a2,
0xb86c5df0, 0xb6950c1e, 0xb4c373ee, 0xb2f7b9af, 0xb1320139, 0xaf726def,
0xadb922b7, 0xac0641fb,
0xaa59eda4, 0xa8b4471a, 0xa7156f3c, 0xa57d8666, 0xa3ecac65, 0xa263007d,
0xa0e0a15f, 0x9f65ad2d,
0x9df24175, 0x9c867b2c, 0x9b2276b0, 0x99c64fc5, 0x98722192, 0x9726069c,
0x95e218c9, 0x94a6715d,
0x937328f5, 0x92485786, 0x9126145f, 0x900c7621, 0x8efb92c2, 0x8df37f8b,
0x8cf45113, 0x8bfe1b3f,
0x8b10f144, 0x8a2ce59f, 0x89520a1a, 0x88806fc4, 0x87b826f7, 0x86f93f50,
0x8643c7b3, 0x8597ce46,
0x84f56073, 0x845c8ae3, 0x83cd5982, 0x8347d77b, 0x82cc0f36, 0x825a0a5b,
0x81f1d1ce, 0x81936daf,
0x813ee55b, 0x80f43f69, 0x80b381ac, 0x807cb130, 0x804fd23a, 0x802ce84c,
0x8013f61d, 0x8004fda0,
};
/**
* @brief Q31 sin_cos function.
* @param[in] theta scaled input value in degrees
* @param[out] *pSinVal points to the processed sine output.
* @param[out] *pCosVal points to the processed cosine output.
* @return none.
*
* The Q31 input value is in the range [-1 +1) and is mapped to a degree value in the range [-180 180).
*
*/
void arm_sin_cos_q31(
q31_t theta,
q31_t * pSinVal,
q31_t * pCosVal)
{
q31_t x0; /* Nearest input value */
q31_t y0, y1; /* Nearest output values */
q31_t xSpacing = INPUT_SPACING; /* Spaing between inputs */
uint32_t i; /* Index */
q31_t oneByXSpacing; /* 1/ xSpacing value */
q31_t out; /* temporary variable */
uint32_t sign_bits; /* No.of sign bits */
uint32_t firstX = 0x80000000; /* First X value */
/* Calculation of index */
i = ((uint32_t) theta - firstX) / (uint32_t) xSpacing;
/* Calculation of first nearest input value */
x0 = (q31_t) firstX + ((q31_t) i * xSpacing);
/* Reading nearest sine output values from table */
y0 = sinTableQ31[i];
y1 = sinTableQ31[i + 1u];
/* Calculation of 1/(x1-x0) */
/* (x1-x0) is xSpacing which is fixed value */
sign_bits = 8u;
oneByXSpacing = 0x5A000000;
/* Calculation of (theta - x0)/(x1-x0) */
out =
(((q31_t) (((q63_t) (theta - x0) * oneByXSpacing) >> 32)) << sign_bits);
/* Calculation of y0 + (y1 - y0) * ((theta - x0)/(x1-x0)) */
*pSinVal = y0 + ((q31_t) (((q63_t) (y1 - y0) * out) >> 30));
/* Reading nearest cosine output values from table */
y0 = cosTableQ31[i];
y1 = cosTableQ31[i + 1u];
/* Calculation of y0 + (y1 - y0) * ((theta - x0)/(x1-x0)) */
*pCosVal = y0 + ((q31_t) (((q63_t) (y1 - y0) * out) >> 30));
}
/**
* @} end of SinCos group
*/