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arm_sin_q31.c
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/ lib / src / stm32f4 / CPU / CMSIS / DSP_Lib / Source / FastMathFunctions / arm_sin_q31.c
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/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_sin_q31.c
*
* Description: Fast sine calculation for Q31 values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFastMath
*/
/**
* @addtogroup sin
* @{
*/
/**
* \par
* Tables generated are in Q31(1.31 Fixed point format)
* Generation of sin values in floating point:
* <pre>tableSize = 256;
* for(n = -1; n < (tableSize + 1); n++)
* {
* sinTable[n+1]= sin(2*pi*n/tableSize);
* } </pre>
* where pi value is 3.14159265358979
* \par
* Convert Floating point to Q31(Fixed point):
* (sinTable[i] * pow(2, 31))
* \par
* rounding to nearest integer is done
* sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
*/
static const q31_t sinTableQ31[259] = {
0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
0x12c8106f,
0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
0x2826b928, 0x2b1f34eb,
0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
0x3f1749b8, 0x41ce1e65,
0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
0x539b2af0, 0x55f5a4d2,
0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
0x64e88926, 0x66cf8120,
0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
0x72552c85, 0x73b5ebd1,
0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
0x7b5d039e, 0x7c29fbee,
0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
0x7fa736b4, 0x7fd8878e,
0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
0x7f0991c4, 0x7e9d55fc,
0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
0x798a23b1, 0x78848414,
0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
0x6f5f02b2, 0x6dca0d14,
0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
0x60ec3830, 0x5ed77c8a,
0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
0x4ebfe8a5, 0x4c3fdff4,
0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
0x398cdd32, 0x36ba2014,
0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
0x2223a4c5, 0x1f19f97b,
0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
0x96a9049, 0x647d97c,
0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
0xed37ef91,
0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
0xd7d946d8, 0xd4e0cb15,
0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
0xc0e8b648, 0xbe31e19b,
0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
0xac64d510, 0xaa0a5b2e,
0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
0x9b1776da, 0x99307ee0,
0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
0x8daad37b, 0x8c4a142f,
0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
0x84a2fc62, 0x83d60412,
0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
0x8058c94c, 0x80277872,
0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
0x80f66e3c, 0x8162aa04,
0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
0x8675dc4f, 0x877b7bec,
0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
0x90a0fd4e, 0x9235f2ec,
0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
0x9f13c7d0, 0xa1288376,
0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
0xb140175b, 0xb3c0200c,
0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
0xc67322ce, 0xc945dfec,
0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
0xdddc5b3b, 0xe0e60685,
0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
0xf6956fb7, 0xf9b82684,
0xfcdbd541, 0x0, 0x3242abf
};
/**
* @brief Fast approximation to the trigonometric sine function for Q31 data.
* @param[in] x Scaled input value in radians.
* @return sin(x).
*
* The Q31 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
*/
q31_t arm_sin_q31(
q31_t x)
{
q31_t sinVal, in, in2; /* Temporary variables for input, output */
uint32_t index; /* Index variables */
q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
q31_t a, b, c, d; /* Four nearest output values */
q31_t *tablePtr; /* Pointer to table */
q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */
q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */
q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */
q31_t temp; /* Temporary variable for intermediate process */
in = x;
/* Calculate the nearest index */
index = (uint32_t) in / (uint32_t) tableSpacing;
/* Calculate the nearest value of input */
in2 = (q31_t) index *tableSpacing;
/* Calculation of fractional value */
fract = (in - in2) << 8;
/* fractSquare = fract * fract */
fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
fractSquare = fractSquare << 1;
/* fractCube = fract * fract * fract */
fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
fractCube = fractCube << 1;
/* Initialise table pointer */
tablePtr = (q31_t *) & sinTableQ31[index];
/* Cubic interpolation process */
/* Calculation of wa */
/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
temp = 0x2AAAAAAA;
wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
wa = -(wa << 1u);
wa += (fractSquare >> 1u);
/* Read first nearest value of output from the sin table */
a = *tablePtr++;
/* sinVal = a*wa */
sinVal = ((q31_t) (((q63_t) a * wa) >> 32));
/* q31(1.31) Fixed point value of 1 */
temp = 0x7FFFFFFF;
/* Calculation of wb */
wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
/* Read second nearest value of output from the sin table */
b = *tablePtr++;
/* sinVal += b*wb */
sinVal = (q31_t) ((((q63_t) sinVal << 32) + (q63_t) b * (wb)) >> 32);
/* Calculation of wc */
wc = -fractCube + fractSquare;
wc = (wc >> 1u) + fract;
/* Read third nearest value of output from the sin table */
c = *tablePtr++;
/* sinVal += c*wc */
sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) c * wc)) >> 32);
/* Calculation of wd */
/* wd = (oneBy6) * fractCube - (oneBy6) * fract; */
fractCube = fractCube - fract;
wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
wd = (wd << 1u);
/* Read fourth nearest value of output from the sin table */
d = *tablePtr++;
/* sinVal += d*wd; */
sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) d * wd)) >> 32);
/* convert sinVal in 2.30 format to 1.31 format */
return (sinVal << 1u);
}
/**
* @} end of sin group
*/