| /* ---------------------------------------------------------------------- |
| * 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 |
| */ |