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 floating-point values.
12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
14 * Redistribution and use in source and binary forms, with or without
15 * modification, are permitted provided that the following conditions
17 * - Redistributions of source code must retain the above copyright
18 * notice, this list of conditions and the following disclaimer.
19 * - Redistributions in binary form must reproduce the above copyright
20 * notice, this list of conditions and the following disclaimer in
21 * the documentation and/or other materials provided with the
23 * - Neither the name of ARM LIMITED nor the names of its contributors
24 * may be used to endorse or promote products derived from this
25 * software without specific prior written permission.
27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
38 * POSSIBILITY OF SUCH DAMAGE.
39 * -------------------------------------------------------------------- */
43 * @ingroup groupFastMath
47 * @defgroup cos Cosine
49 * Computes the trigonometric cosine function using a combination of table lookup
50 * and cubic interpolation. There are separate functions for
51 * Q15, Q31, and floating-point data types.
52 * The input to the floating-point version is in radians while the
53 * fixed-point Q15 and Q31 have a scaled input with the range
54 * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
55 * value of 2*pi wraps around to 0.
57 * The implementation is based on table lookup using 256 values together with cubic interpolation.
59 * -# Calculation of the nearest integer table index
60 * -# Fetch the four table values a, b, c, and d
61 * -# Compute the fractional portion (fract) of the table index.
62 * -# Calculation of wa, wb, wc, wd
63 * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
74 * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
75 * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
76 * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
77 * wd=(1/6)*fract.^3 - (1/6)*fract;
89 * <b>Example code for Generation of Cos Table:</b>
92 * for(n = -1; n < (tableSize + 2); n++)
94 * cosTable[n+1]= cos(2*pi*n/tableSize);
96 * where pi value is 3.14159265358979
99 static const float32_t cosTable[260] = {
100 0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
101 0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
102 0.992479562759399410f, 0.989176511764526370f,
103 0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
104 0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
105 0.949528157711029050f, 0.941544055938720700f,
106 0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
107 0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
108 0.870086967945098880f, 0.857728600502014160f,
109 0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
110 0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
111 0.757208824157714840f, 0.740951120853424070f,
112 0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
113 0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
114 0.615231573581695560f, 0.595699310302734380f,
115 0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
116 0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
117 0.449611335992813110f, 0.427555084228515630f,
118 0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
119 0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
120 0.266712754964828490f, 0.242980182170867920f,
121 0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
122 0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
123 0.073564566671848297f, 0.049067676067352295f,
124 0.024541229009628296f, 0.000000000000000061f, -0.024541229009628296f,
125 -0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
126 -0.122410677373409270f, -0.146730467677116390f,
127 -0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
128 -0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
129 -0.313681751489639280f, -0.336889863014221190f,
130 -0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
131 -0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
132 -0.492898195981979370f, -0.514102756977081300f,
133 -0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
134 -0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
135 -0.653172850608825680f, -0.671558976173400880f,
136 -0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
137 -0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
138 -0.788346409797668460f, -0.803207516670227050f,
139 -0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
140 -0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
141 -0.893224298954010010f, -0.903989315032958980f,
142 -0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
143 -0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
144 -0.963776051998138430f, -0.970031261444091800f,
145 -0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
146 -0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
147 -0.997290432453155520f, -0.998795449733734130f,
148 -0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
149 -0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
150 -0.992479562759399410f, -0.989176511764526370f,
151 -0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
152 -0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
153 -0.949528157711029050f, -0.941544055938720700f,
154 -0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
155 -0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
156 -0.870086967945098880f, -0.857728600502014160f,
157 -0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
158 -0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
159 -0.757208824157714840f, -0.740951120853424070f,
160 -0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
161 -0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
162 -0.615231573581695560f, -0.595699310302734380f,
163 -0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
164 -0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
165 -0.449611335992813110f, -0.427555084228515630f,
166 -0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
167 -0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
168 -0.266712754964828490f, -0.242980182170867920f,
169 -0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
170 -0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
171 -0.073564566671848297f, -0.049067676067352295f,
172 -0.024541229009628296f, -0.000000000000000184f, 0.024541229009628296f,
173 0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
174 0.122410677373409270f, 0.146730467677116390f,
175 0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
176 0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
177 0.313681751489639280f, 0.336889863014221190f,
178 0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
179 0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
180 0.492898195981979370f, 0.514102756977081300f,
181 0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
182 0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
183 0.653172850608825680f, 0.671558976173400880f,
184 0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
185 0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
186 0.788346409797668460f, 0.803207516670227050f,
187 0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
188 0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
189 0.893224298954010010f, 0.903989315032958980f,
190 0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
191 0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
192 0.963776051998138430f, 0.970031261444091800f,
193 0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
194 0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
195 0.997290432453155520f, 0.998795449733734130f,
196 0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
197 0.998795449733734130f
201 * @brief Fast approximation to the trigonometric cosine function for floating-point data.
202 * @param[in] x input value in radians.
207 float32_t arm_cos_f32(
210 float32_t cosVal, fract, in;
212 uint32_t tableSize = (uint32_t) TABLE_SIZE;
213 float32_t wa, wb, wc, wd;
214 float32_t a, b, c, d;
217 float32_t fractsq, fractby2, fractby6, fractby3, fractsqby2;
218 float32_t oneminusfractby2;
219 float32_t frby2xfrsq, frby6xfrsq;
221 /* input x is in radians */
222 /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
223 in = x * 0.159154943092f;
225 /* Calculation of floor value of input */
228 /* Make negative values towards -infinity */
234 /* Map input value to [0 1] */
235 in = in - (float32_t) n;
237 /* Calculation of index of the table */
238 index = (uint32_t) (tableSize * in);
240 /* fractional value calculation */
241 fract = ((float32_t) tableSize * in) - (float32_t) index;
243 /* Checking min and max index of table */
253 /* Initialise table pointer */
254 tablePtr = (float32_t *) & cosTable[index];
256 /* Read four nearest values of input value from the cos table */
262 /* Cubic interpolation process */
263 fractsq = fract * fract;
264 fractby2 = fract * 0.5f;
265 fractby6 = fract * 0.166666667f;
266 fractby3 = fract * 0.3333333333333f;
267 fractsqby2 = fractsq * 0.5f;
268 frby2xfrsq = (fractby2) * fractsq;
269 frby6xfrsq = (fractby6) * fractsq;
270 oneminusfractby2 = 1.0f - fractby2;
271 wb = fractsqby2 - fractby3;
272 wc = (fractsqby2 + fract);
273 wa = wb - frby6xfrsq;
274 wb = frby2xfrsq - fractsq;
276 wc = wc - frby2xfrsq;
277 wd = (frby6xfrsq) - fractby6;
278 wb = wb + oneminusfractby2;
280 /* Calculate cos value */
281 cosVal = (cosVal + (b * wb)) + ((c * wc) + (d * wd));
283 /* Return the output value */
289 * @} end of cos group