arm_cos_q31.c
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| text/x-c
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CLexer
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r16 | /* ---------------------------------------------------------------------- | ||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 29. November 2010 | ||||
* $Revision: V1.0.3 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_cos_q31.c | ||||
* | ||||
* Description: Fast cosine calculation for Q31 values. | ||||
* | ||||
* Target Processor: Cortex-M4/Cortex-M3 | ||||
* | ||||
* 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 cos | ||||
* @{ | ||||
*/ | ||||
/** | ||||
* \par | ||||
* Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps | ||||
* First Generate cos values in floating point: | ||||
* tableSize = 256; | ||||
* <pre>for(n = -1; n < (tableSize + 1); n++) | ||||
* { | ||||
* cosTable[n+1]= cos(2*pi*n/tableSize); | ||||
* } </pre> | ||||
* where pi value is 3.14159265358979 | ||||
* \par | ||||
* Secondly Convert Floating point to Q31(Fixed point): | ||||
* (cosTable[i] * pow(2, 31)) | ||||
* \par | ||||
* Finally Rounding to nearest integer is done | ||||
* cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5); | ||||
*/ | ||||
static const q31_t cosTableQ31[259] = { | ||||
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, 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 | ||||
}; | ||||
/** | ||||
* @brief Fast approximation to the trigonometric cosine function for Q31 data. | ||||
* @param[in] x Scaled input value in radians. | ||||
* @return cos(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_cos_q31( | ||||
q31_t x) | ||||
{ | ||||
q31_t cosVal, fract, in, in2; /* Temporary variables for input, output */ | ||||
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 fractCube, fractSquare; /* Temporary values for fractional value */ | ||||
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 */ | ||||
uint32_t index; /* Index variable */ | ||||
in = x; | ||||
/* Calculate the nearest index */ | ||||
index = in / 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 *) & cosTableQ31[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 cos table */ | ||||
a = *tablePtr++; | ||||
/* cosVal = a*wa */ | ||||
cosVal = ((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 cos table */ | ||||
b = *tablePtr++; | ||||
/* cosVal += b*wb */ | ||||
cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32); | ||||
/* Calculation of wc */ | ||||
wc = -fractCube + fractSquare; | ||||
wc = (wc >> 1u) + fract; | ||||
/* Read third nearest values of output value from the cos table */ | ||||
c = *tablePtr++; | ||||
/* cosVal += c*wc */ | ||||
cosVal = (q31_t) ((((q63_t) cosVal << 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 cos table */ | ||||
d = *tablePtr++; | ||||
/* cosVal += d*wd; */ | ||||
cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32); | ||||
/* convert cosVal in 2.30 format to 1.31 format */ | ||||
return (cosVal << 1u); | ||||
} | ||||
/** | ||||
* @} end of cos group | ||||
*/ | ||||