| /* ---------------------------------------------------------------------- |
| * Copyright (C) 2010 ARM Limited. All rights reserved. |
| * |
| * $Date: 15. July 2011 |
| * $Revision: V1.0.10 |
| * |
| * Project: CMSIS DSP Library |
| * Title: arm_cos_q31.c |
| * |
| * Description: Fast cosine 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 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, 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 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 */ |
| 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 |
| */ |
