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_cos_f32.c
9 *
10 * Description: Fast cosine calculation for floating-point values.
11 *
12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
13 *
14 * Redistribution and use in source and binary forms, with or without
15 * modification, are permitted provided that the following conditions
16 * are met:
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
22 * distribution.
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.
26 *
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 * -------------------------------------------------------------------- */
40
41 #include "arm_math.h"
42 #include "arm_common_tables.h"
43 /**
44 * @ingroup groupFastMath
45 */
46
47 /**
48 * @defgroup cos Cosine
49 *
50 * Computes the trigonometric cosine function using a combination of table lookup
51 * and cubic interpolation. There are separate functions for
52 * Q15, Q31, and floating-point data types.
53 * The input to the floating-point version is in radians while the
54 * fixed-point Q15 and Q31 have a scaled input with the range
55 * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
56 * value of 2*pi wraps around to 0.
57 *
58 * The implementation is based on table lookup using 256 values together with cubic interpolation.
59 * The steps used are:
60 * -# Calculation of the nearest integer table index
61 * -# Fetch the four table values a, b, c, and d
62 * -# Compute the fractional portion (fract) of the table index.
63 * -# Calculation of wa, wb, wc, wd
64 * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
65 *
66 * where
67 * <pre>
68 * a=Table[index-1];
69 * b=Table[index+0];
70 * c=Table[index+1];
71 * d=Table[index+2];
72 * </pre>
73 * and
74 * <pre>
75 * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
76 * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
77 * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
78 * wd=(1/6)*fract.^3 - (1/6)*fract;
79 * </pre>
80 */
81
82 /**
83 * @addtogroup cos
84 * @{
85 */
86
87 /**
88 * @brief Fast approximation to the trigonometric cosine function for floating-point data.
89 * @param[in] x input value in radians.
90 * @return cos(x).
91 */
92
arm_cos_f32(float32_t x)93 float32_t arm_cos_f32(
94 float32_t x)
95 {
96 float32_t cosVal, fract, in; /* Temporary variables for input, output */
97 uint16_t index; /* Index variable */
98 float32_t a, b; /* Two nearest output values */
99 int32_t n;
100 float32_t findex;
101
102 /* input x is in radians */
103 /* 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 */
104 in = x * 0.159154943092f + 0.25f;
105
106 /* Calculation of floor value of input */
107 n = (int32_t) in;
108
109 /* Make negative values towards -infinity */
110 if(in < 0.0f)
111 {
112 n--;
113 }
114
115 /* Map input value to [0 1] */
116 in = in - (float32_t) n;
117
118 /* Calculation of index of the table */
119 findex = (float32_t) FAST_MATH_TABLE_SIZE * in;
120 index = ((uint16_t)findex) & 0x1ff;
121
122 /* fractional value calculation */
123 fract = findex - (float32_t) index;
124
125 /* Read two nearest values of input value from the cos table */
126 a = sinTable_f32[index];
127 b = sinTable_f32[index+1];
128
129 /* Linear interpolation process */
130 cosVal = (1.0f-fract)*a + fract*b;
131
132 /* Return the output value */
133 return (cosVal);
134 }
135
136 /**
137 * @} end of cos group
138 */
139