1 /* ----------------------------------------------------------------------
2 * Copyright (C) 2010 ARM Limited. All rights reserved.
7 * Project: CMSIS DSP Library
10 * Description: Fast sine calculation for Q15 values.
12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
14 * Version 1.0.10 2011/7/15
15 * Big Endian support added and Merged M0 and M3/M4 Source code.
17 * Version 1.0.3 2010/11/29
18 * Re-organized the CMSIS folders and updated documentation.
20 * Version 1.0.2 2010/11/11
21 * Documentation updated.
23 * Version 1.0.1 2010/10/05
24 * Production release and review comments incorporated.
26 * Version 1.0.0 2010/09/20
27 * Production release and review comments incorporated.
28 * -------------------------------------------------------------------- */
33 * @ingroup groupFastMath
44 * Example code for Generation of Q15 Sin Table:
46 * <pre>tableSize = 256;
47 * for(n = -1; n < (tableSize + 1); n++)
49 * sinTable[n+1]=sin(2*pi*n/tableSize);
51 * where pi value is 3.14159265358979
53 * Convert Floating point to Q15(Fixed point):
54 * (sinTable[i] * pow(2, 15))
56 * rounding to nearest integer is done
57 * sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
61 static const q15_t sinTableQ15[259] = {
62 0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
63 0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
64 0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
65 0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
66 0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
67 0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
68 0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
69 0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
70 0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
71 0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
72 0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
73 0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
74 0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
75 0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
76 0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
77 0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
78 0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
79 0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
80 0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
81 0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
82 0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
83 0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
84 0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
85 0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
86 0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
87 0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
88 0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
89 0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
90 0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
91 0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
92 0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
93 0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
99 * @brief Fast approximation to the trigonometric sine function for Q15 data.
100 * @param[in] x Scaled input value in radians.
103 * The Q15 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
109 q31_t sinVal; /* Temporary variables output */
110 q15_t *tablePtr; /* Pointer to table */
111 q15_t fract, in, in2; /* Temporary variables for input, output */
112 q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
113 q15_t a, b, c, d; /* Four nearest output values */
114 q15_t fractCube, fractSquare; /* Temporary values for fractional value */
115 q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */
116 q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */
117 int32_t index; /* Index variable */
121 /* Calculate the nearest index */
122 index = (int32_t) in / tableSpacing;
124 /* Calculate the nearest value of input */
125 in2 = (q15_t) ((index) * tableSpacing);
127 /* Calculation of fractional value */
128 fract = (in - in2) << 8;
130 /* fractSquare = fract * fract */
131 fractSquare = (q15_t) ((fract * fract) >> 15);
133 /* fractCube = fract * fract * fract */
134 fractCube = (q15_t) ((fractSquare * fract) >> 15);
136 /* Initialise table pointer */
137 tablePtr = (q15_t *) & sinTableQ15[index];
139 /* Cubic interpolation process */
140 /* Calculation of wa */
141 /* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
142 wa = (q31_t) oneBy6 *fractCube;
143 wa += (q31_t) 0x2AAA *fract;
145 wa += ((q31_t) fractSquare >> 1u);
147 /* Read first nearest value of output from the sin table */
150 /* sinVal = a * wa */
153 /* Calculation of wb */
154 wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
155 (((q31_t) fract >> 1u) - 0x7FFF);
157 /* Read second nearest value of output from the sin table */
164 /* Calculation of wc */
165 wc = -(q31_t) fractCube + fractSquare;
166 wc = (wc >> 1u) + fract;
168 /* Read third nearest value of output from the sin table */
174 /* Calculation of wd */
175 /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
176 fractCube = fractCube - fract;
177 wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
179 /* Read fourth nearest value of output from the sin table */
182 /* sinVal += d*wd; */
185 /* Return the output value in 1.15(q15) format */
186 return ((q15_t) (sinVal >> 15u));
191 * @} end of sin group