1 /* ----------------------------------------------------------------------
2 * Copyright (C) 2010-2014 ARM Limited. All rights reserved.
3 *
4 * $Date: 12. March 2014
5 * $Revision: V1.4.4
6 *
7 * Project: CMSIS DSP Library
8 * Title: arm_sin_f32.c
9 *
10 * Description: Fast sine calculation for floating-point values.
11 * Fast cosine calculation for floating-point values.
12 *
13 *
14 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
15 *
16 * Redistribution and use in source and binary forms, with or without
17 * modification, are permitted provided that the following conditions
18 * are met:
19 * - Redistributions of source code must retain the above copyright
20 * notice, this list of conditions and the following disclaimer.
21 * - Redistributions in binary form must reproduce the above copyright
22 * notice, this list of conditions and the following disclaimer in
23 * the documentation and/or other materials provided with the
24 * distribution.
25 * - Neither the name of ARM LIMITED nor the names of its contributors
26 * may be used to endorse or promote products derived from this
27 * software without specific prior written permission.
28 *
29 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
30 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
31 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
32 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
33 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
34 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
35 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
36 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
37 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
38 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
39 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
40 * POSSIBILITY OF SUCH DAMAGE.
41 * -------------------------------------------------------------------- */
42
43 #include <stdint.h>
44 #include <nanohub_math.h>
45
46 #define FAST_MATH_TABLE_SIZE 512
47 typedef float float32_t;
48
49 /**
50 * \par
51 * Example code for the generation of the floating-point sine table:
52 * <pre>
53 * tableSize = 512;
54 * for(n = 0; n < (tableSize + 1); n++)
55 * {
56 * sinTable[n]=sin(2*pi*n/tableSize);
57 * }</pre>
58 * \par
59 * where pi value is 3.14159265358979
60 */
61
62 static const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1] = {
63 0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f,
64 0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f,
65 0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f, 0.19509032f, 0.20711138f,
66 0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
67 0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f,
68 0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f,
69 0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f, 0.47139674f, 0.48218377f,
70 0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
71 0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f,
72 0.61523159f, 0.62485949f, 0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f,
73 0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f, 0.70710678f, 0.71573083f,
74 0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f,
75 0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f,
76 0.81758481f, 0.82458930f, 0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f,
77 0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f, 0.88192126f, 0.88763962f,
78 0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f,
79 0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f,
80 0.94952818f, 0.95330604f, 0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f,
81 0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f, 0.98078528f, 0.98310549f,
82 0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f,
83 0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f,
84 0.99969882f, 0.99992470f, 1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f,
85 0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f, 0.99518473f, 0.99390697f,
86 0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f,
87 0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f,
88 0.96377607f, 0.96043052f, 0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f,
89 0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f, 0.92387953f, 0.91911385f,
90 0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f,
91 0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f,
92 0.84485357f, 0.83822471f, 0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f,
93 0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f, 0.77301045f, 0.76516727f,
94 0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
95 0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f,
96 0.65317284f, 0.64383154f, 0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f,
97 0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f, 0.55557023f, 0.54532499f,
98 0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f,
99 0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f,
100 0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f,
101 0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f, 0.29028468f, 0.27851969f,
102 0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f,
103 0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f,
104 0.12241068f, 0.11022221f, 0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f,
105 0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f, 0.00000000f, -0.01227154f,
106 -0.02454123f, -0.03680722f, -0.04906767f, -0.06132074f, -0.07356456f,
107 -0.08579731f, -0.09801714f, -0.11022221f, -0.12241068f, -0.13458071f,
108 -0.14673047f, -0.15885814f, -0.17096189f, -0.18303989f, -0.19509032f,
109 -0.20711138f, -0.21910124f, -0.23105811f, -0.24298018f, -0.25486566f,
110 -0.26671276f, -0.27851969f, -0.29028468f, -0.30200595f, -0.31368174f,
111 -0.32531029f, -0.33688985f, -0.34841868f, -0.35989504f, -0.37131719f,
112 -0.38268343f, -0.39399204f, -0.40524131f, -0.41642956f, -0.42755509f,
113 -0.43861624f, -0.44961133f, -0.46053871f, -0.47139674f, -0.48218377f,
114 -0.49289819f, -0.50353838f, -0.51410274f, -0.52458968f, -0.53499762f,
115 -0.54532499f, -0.55557023f, -0.56573181f, -0.57580819f, -0.58579786f,
116 -0.59569930f, -0.60551104f, -0.61523159f, -0.62485949f, -0.63439328f,
117 -0.64383154f, -0.65317284f, -0.66241578f, -0.67155895f, -0.68060100f,
118 -0.68954054f, -0.69837625f, -0.70710678f, -0.71573083f, -0.72424708f,
119 -0.73265427f, -0.74095113f, -0.74913639f, -0.75720885f, -0.76516727f,
120 -0.77301045f, -0.78073723f, -0.78834643f, -0.79583690f, -0.80320753f,
121 -0.81045720f, -0.81758481f, -0.82458930f, -0.83146961f, -0.83822471f,
122 -0.84485357f, -0.85135519f, -0.85772861f, -0.86397286f, -0.87008699f,
123 -0.87607009f, -0.88192126f, -0.88763962f, -0.89322430f, -0.89867447f,
124 -0.90398929f, -0.90916798f, -0.91420976f, -0.91911385f, -0.92387953f,
125 -0.92850608f, -0.93299280f, -0.93733901f, -0.94154407f, -0.94560733f,
126 -0.94952818f, -0.95330604f, -0.95694034f, -0.96043052f, -0.96377607f,
127 -0.96697647f, -0.97003125f, -0.97293995f, -0.97570213f, -0.97831737f,
128 -0.98078528f, -0.98310549f, -0.98527764f, -0.98730142f, -0.98917651f,
129 -0.99090264f, -0.99247953f, -0.99390697f, -0.99518473f, -0.99631261f,
130 -0.99729046f, -0.99811811f, -0.99879546f, -0.99932238f, -0.99969882f,
131 -0.99992470f, -1.00000000f, -0.99992470f, -0.99969882f, -0.99932238f,
132 -0.99879546f, -0.99811811f, -0.99729046f, -0.99631261f, -0.99518473f,
133 -0.99390697f, -0.99247953f, -0.99090264f, -0.98917651f, -0.98730142f,
134 -0.98527764f, -0.98310549f, -0.98078528f, -0.97831737f, -0.97570213f,
135 -0.97293995f, -0.97003125f, -0.96697647f, -0.96377607f, -0.96043052f,
136 -0.95694034f, -0.95330604f, -0.94952818f, -0.94560733f, -0.94154407f,
137 -0.93733901f, -0.93299280f, -0.92850608f, -0.92387953f, -0.91911385f,
138 -0.91420976f, -0.90916798f, -0.90398929f, -0.89867447f, -0.89322430f,
139 -0.88763962f, -0.88192126f, -0.87607009f, -0.87008699f, -0.86397286f,
140 -0.85772861f, -0.85135519f, -0.84485357f, -0.83822471f, -0.83146961f,
141 -0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f,
142 -0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f,
143 -0.74913639f, -0.74095113f, -0.73265427f, -0.72424708f, -0.71573083f,
144 -0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f,
145 -0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f,
146 -0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f,
147 -0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f,
148 -0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f,
149 -0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f,
150 -0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f,
151 -0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f,
152 -0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f,
153 -0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f,
154 -0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f,
155 -0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f,
156 -0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f
157 };
158
159 /**
160 * @ingroup groupFastMath
161 */
162
163 /**
164 * @defgroup sin Sine
165 *
166 * Computes the trigonometric sine function using a combination of table lookup
167 * and cubic interpolation. There are separate functions for
168 * Q15, Q31, and floating-point data types.
169 * The input to the floating-point version is in radians while the
170 * fixed-point Q15 and Q31 have a scaled input with the range
171 * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
172 * value of 2*pi wraps around to 0.
173 *
174 * The implementation is based on table lookup using 256 values together with cubic interpolation.
175 * The steps used are:
176 * -# Calculation of the nearest integer table index
177 * -# Fetch the four table values a, b, c, and d
178 * -# Compute the fractional portion (fract) of the table index.
179 * -# Calculation of wa, wb, wc, wd
180 * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
181 *
182 * where
183 * <pre>
184 * a=Table[index-1];
185 * b=Table[index+0];
186 * c=Table[index+1];
187 * d=Table[index+2];
188 * </pre>
189 * and
190 * <pre>
191 * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
192 * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
193 * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
194 * wd=(1/6)*fract.^3 - (1/6)*fract;
195 * </pre>
196 */
197
198 /**
199 * @addtogroup sin
200 * @{
201 */
202
203 /**
204 * @brief Fast approximation to the trigonometric sine function for floating-point data.
205 * @param[in] x input value in radians.
206 * @return sin(x).
207 */
208
arm_sin_f32(float32_t x)209 float32_t arm_sin_f32(
210 float32_t x)
211 {
212 float32_t sinVal, fract, in; /* Temporary variables for input, output */
213 uint16_t index; /* Index variable */
214 float32_t a, b; /* Two nearest output values */
215 int32_t n;
216 float32_t findex;
217
218 /* input x is in radians */
219 /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
220 in = x * 0.159154943092f;
221
222 /* Calculation of floor value of input */
223 n = (int32_t) in;
224
225 /* Make negative values towards -infinity */
226 if(x < 0.0f)
227 {
228 n--;
229 }
230
231 /* Map input value to [0 1] */
232 in = in - (float32_t) n;
233
234 /* Calculation of index of the table */
235 findex = (float32_t) FAST_MATH_TABLE_SIZE * in;
236 index = ((uint16_t)findex) & 0x1ff;
237
238 /* fractional value calculation */
239 fract = findex - (float32_t) index;
240
241 /* Read two nearest values of input value from the sin table */
242 a = sinTable_f32[index];
243 b = sinTable_f32[index+1];
244
245 /* Linear interpolation process */
246 sinVal = (1.0f-fract)*a + fract*b;
247
248 /* Return the output value */
249 return (sinVal);
250 }
251
252 /**
253 * @defgroup cos Cosine
254 *
255 * Computes the trigonometric cosine function using a combination of table lookup
256 * and cubic interpolation. There are separate functions for
257 * Q15, Q31, and floating-point data types.
258 * The input to the floating-point version is in radians while the
259 * fixed-point Q15 and Q31 have a scaled input with the range
260 * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
261 * value of 2*pi wraps around to 0.
262 *
263 * The implementation is based on table lookup using 256 values together with cubic interpolation.
264 * The steps used are:
265 * -# Calculation of the nearest integer table index
266 * -# Fetch the four table values a, b, c, and d
267 * -# Compute the fractional portion (fract) of the table index.
268 * -# Calculation of wa, wb, wc, wd
269 * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
270 *
271 * where
272 * <pre>
273 * a=Table[index-1];
274 * b=Table[index+0];
275 * c=Table[index+1];
276 * d=Table[index+2];
277 * </pre>
278 * and
279 * <pre>
280 * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
281 * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
282 * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
283 * wd=(1/6)*fract.^3 - (1/6)*fract;
284 * </pre>
285 */
286
287 /**
288 * @addtogroup cos
289 * @{
290 */
291
292 /**
293 * @brief Fast approximation to the trigonometric cosine function for floating-point data.
294 * @param[in] x input value in radians.
295 * @return cos(x).
296 */
297
arm_cos_f32(float32_t x)298 float32_t arm_cos_f32(
299 float32_t x)
300 {
301 float32_t cosVal, fract, in; /* Temporary variables for input, output */
302 uint16_t index; /* Index variable */
303 float32_t a, b; /* Two nearest output values */
304 int32_t n;
305 float32_t findex;
306
307 /* input x is in radians */
308 /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi, add 0.25 (pi/2) to read sine table */
309 in = x * 0.159154943092f + 0.25f;
310
311 /* Calculation of floor value of input */
312 n = (int32_t) in;
313
314 /* Make negative values towards -infinity */
315 if(in < 0.0f)
316 {
317 n--;
318 }
319
320 /* Map input value to [0 1] */
321 in = in - (float32_t) n;
322
323 /* Calculation of index of the table */
324 findex = (float32_t) FAST_MATH_TABLE_SIZE * in;
325 index = ((uint16_t)findex) & 0x1ff;
326
327 /* fractional value calculation */
328 fract = findex - (float32_t) index;
329
330 /* Read two nearest values of input value from the cos table */
331 a = sinTable_f32[index];
332 b = sinTable_f32[index+1];
333
334 /* Linear interpolation process */
335 cosVal = (1.0f-fract)*a + fract*b;
336
337 /* Return the output value */
338 return (cosVal);
339 }
340
341 /**
342 * @} end of cos group
343 */
344