1 /* ----------------------------------------------------------------------
2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
4 * $Date: 17. January 2013
7 * Project: CMSIS DSP Library
10 * Description: Fast cosine calculation for Q15 values.
12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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44 * @ingroup groupFastMath
54 * Table values are in Q15 (1.15 fixed-point format) and generation is done in
55 * three steps. First, generate cos values in floating point:
58 * for(n = -1; n < (tableSize + 1); n++)
60 * cosTable[n+1]= cos(2*pi*n/tableSize);
62 * where pi value is 3.14159265358979
64 * Second, convert floating-point to Q15 (fixed-point):
65 * (cosTable[i] * pow(2, 15))
67 * Finally, round to the nearest integer value:
68 * cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);
71 static const q15_t cosTableQ15[259] = {
72 0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
73 0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
74 0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
75 0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
76 0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
77 0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
78 0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
79 0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
80 0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
81 0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
82 0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
83 0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
84 0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
85 0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
86 0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
87 0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
88 0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
89 0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
90 0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
91 0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
92 0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
93 0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
94 0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
95 0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
96 0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
97 0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
98 0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
99 0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
100 0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
101 0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
102 0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
103 0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
104 0x7ff6, 0x7fff, 0x7ff6
109 * @brief Fast approximation to the trigonometric cosine function for Q15 data.
110 * @param[in] x Scaled input value in radians.
113 * The Q15 input value is in the range [0 +0.9999] and is mapped to a radian
114 * value in the range [0 2*pi).
120 q31_t cosVal; /* Temporary variable for output */
121 q15_t *tablePtr; /* Pointer to table */
122 q15_t in, in2; /* Temporary variables for input */
123 q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
124 q15_t a, b, c, d; /* Four nearest output values */
125 q15_t fract, fractCube, fractSquare; /* Variables for fractional value */
126 q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */
127 q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */
128 int32_t index; /* Index variable */
132 /* Calculate the nearest index */
133 index = (int32_t) in / tableSpacing;
135 /* Calculate the nearest value of input */
136 in2 = (q15_t) index *tableSpacing;
138 /* Calculation of fractional value */
139 fract = (in - in2) << 8;
141 /* fractSquare = fract * fract */
142 fractSquare = (q15_t) ((fract * fract) >> 15);
144 /* fractCube = fract * fract * fract */
145 fractCube = (q15_t) ((fractSquare * fract) >> 15);
147 /* Checking min and max index of table */
157 /* Initialise table pointer */
158 tablePtr = (q15_t *) & cosTableQ15[index];
160 /* Cubic interpolation process */
161 /* Calculation of wa */
162 /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
163 wa = (q31_t) oneBy6 *fractCube;
164 wa += (q31_t) 0x2AAA *fract;
166 wa += (fractSquare >> 1u);
168 /* Read first nearest value of output from the cos table */
171 /* cosVal = a * wa */
174 /* Calculation of wb */
175 wb = (((fractCube >> 1u) - fractSquare) - (fract >> 1u)) + 0x7FFF;
177 /* Read second nearest value of output from the cos table */
183 /* Calculation of wc */
184 wc = -(q31_t) fractCube + fractSquare;
185 wc = (wc >> 1u) + fract;
187 /* Read third nearest value of output from the cos table */
193 /* Calculation of wd */
194 /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
195 fractCube = fractCube - fract;
196 wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
198 /* Read fourth nearest value of output from the cos table */
201 /* cosVal += d*wd; */
204 /* Convert output value in 1.15(q15) format and saturate */
205 cosVal = __SSAT((cosVal >> 15), 16);
207 /* Return the output value in 1.15(q15) format */
208 return ((q15_t) cosVal);
213 * @} end of cos group