DSP库中的arm_sin_q31函数是查表实现，精度略低，大概到11到12个bit

eric2013

原始数据：
0x00000000, 0x04000000, 0x08000000, 0x0C000000,
  0x10000000, 0x14000000, 0x18000000, 0x1C000000,
  0x20000000, 0x24000000,


理论结果：
0x00000000, 0x0C8BD35E, 0x18F8B83C, 0x25280C5D,
  0x30FBC54D, 0x3C56BA70, 0x471CECE6, 0x5133CC94,
  0x5A827999, 0x62F201AC,


实际求得结果：

eric2013

实现代码：

1. /* ----------------------------------------------------------------------
   
2. * Project:      CMSIS DSP Library
   
3. * Title:        arm_sin_q31.c
   
4. * Description:  Fast sine calculation for Q31 values
   
5. *
   
6. * $Date:        18. March 2019
   
7. * $Revision:    V1.6.0
   
8. *
   
9. * Target Processor: Cortex-M cores
   
10. * -------------------------------------------------------------------- */
    
11. /*
    
12. * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
    
13. *
    
14. * SPDX-License-Identifier: Apache-2.0
    
15. *
    
16. * Licensed under the Apache License, Version 2.0 (the License); you may
    
17. * not use this file except in compliance with the License.
    
18. * You may obtain a copy of the License at
    
19. *
    
20. * www.apache.org/licenses/LICENSE-2.0
    
21. *
    
22. * Unless required by applicable law or agreed to in writing, software
    
23. * distributed under the License is distributed on an AS IS BASIS, WITHOUT
    
24. * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    
25. * See the License for the specific language governing permissions and
    
26. * limitations under the License.
    
27. */
    
28. 
    
29. #include "arm_math.h"
    
30. #include "arm_common_tables.h"
    
31. 
    
32. /**
    
33.   @ingroup groupFastMath
    
34. */
    
35. 
    
36. /**
    
37.   @addtogroup sin
    
38.   @{
    
39. */
    
40. 
    
41. /**
    
42.   @brief         Fast approximation to the trigonometric sine function for Q31 data.
    
43.   @param[in]     x  Scaled input value in radians
    
44.   @return        sin(x)
    
45. 
    
46.   The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*PI).
    
47. */
    
48. 
    
49. q31_t arm_sin_q31(
    
50.   q31_t x)
    
51. {
    
52.   q31_t sinVal;                                  /* Temporary variables for input, output */
    
53.   int32_t index;                                 /* Index variable */
    
54.   q31_t a, b;                                    /* Two nearest output values */
    
55.   q31_t fract;                                   /* Temporary values for fractional values */
    
56. 
    
57.   if (x < 0)
    
58.   { /* convert negative numbers to corresponding positive ones */
    
59.     x = (uint32_t)x + 0x80000000;
    
60.   }
    
61. 
    
62.   /* Calculate the nearest index */
    
63.   index = (uint32_t)x >> FAST_MATH_Q31_SHIFT;
    
64. 
    
65.   /* Calculation of fractional value */
    
66.   fract = (x - (index << FAST_MATH_Q31_SHIFT)) << 9;
    
67. 
    
68.   /* Read two nearest values of input value from the sin table */
    
69.   a = sinTable_q31[index];
    
70.   b = sinTable_q31[index+1];
    
71. 
    
72.   /* Linear interpolation process */
    
73.   sinVal = (q63_t) (0x80000000 - fract) * a >> 32;
    
74.   sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) fract * b)) >> 32);
    
75. 
    
76.   /* Return output value */
    
77.   return (sinVal << 1);
    
78. }
    
79. 
    
80. /**
    
81.   @} end of sin group
    
82. */
    

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