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src/Cortex-M4-M3/FastMathFunctions/arm_cos_q31.c@0:1014af42efd9, 2011-03-10 (annotated)

Committer:: simon
Date:: Thu Mar 10 15:07:50 2011 +0000
Revision:: 0:1014af42efd9

Who changed what in which revision?

User	Revision	Line number	New contents of line
simon	0:1014af42efd9	1	/* ----------------------------------------------------------------------
simon	0:1014af42efd9	2	* Copyright (C) 2010 ARM Limited. All rights reserved.
simon	0:1014af42efd9	3	*
simon	0:1014af42efd9	4	* $Date: 29. November 2010
simon	0:1014af42efd9	5	* $Revision: V1.0.3
simon	0:1014af42efd9	6	*
simon	0:1014af42efd9	7	* Project: CMSIS DSP Library
simon	0:1014af42efd9	8	* Title: arm_cos_q31.c
simon	0:1014af42efd9	9	*
simon	0:1014af42efd9	10	* Description: Fast cosine calculation for Q31 values.
simon	0:1014af42efd9	11	*
simon	0:1014af42efd9	12	* Target Processor: Cortex-M4/Cortex-M3
simon	0:1014af42efd9	13	*
simon	0:1014af42efd9	14	* Version 1.0.3 2010/11/29
simon	0:1014af42efd9	15	* Re-organized the CMSIS folders and updated documentation.
simon	0:1014af42efd9	16	*
simon	0:1014af42efd9	17	* Version 1.0.2 2010/11/11
simon	0:1014af42efd9	18	* Documentation updated.
simon	0:1014af42efd9	19	*
simon	0:1014af42efd9	20	* Version 1.0.1 2010/10/05
simon	0:1014af42efd9	21	* Production release and review comments incorporated.
simon	0:1014af42efd9	22	*
simon	0:1014af42efd9	23	* Version 1.0.0 2010/09/20
simon	0:1014af42efd9	24	* Production release and review comments incorporated.
simon	0:1014af42efd9	25	* -------------------------------------------------------------------- */
simon	0:1014af42efd9	26
simon	0:1014af42efd9	27	#include "arm_math.h"
simon	0:1014af42efd9	28
simon	0:1014af42efd9	29	/**
simon	0:1014af42efd9	30	* @ingroup groupFastMath
simon	0:1014af42efd9	31	*/
simon	0:1014af42efd9	32
simon	0:1014af42efd9	33	/**
simon	0:1014af42efd9	34	* @addtogroup cos
simon	0:1014af42efd9	35	* @{
simon	0:1014af42efd9	36	*/
simon	0:1014af42efd9	37
simon	0:1014af42efd9	38	/**
simon	0:1014af42efd9	39	* \par
simon	0:1014af42efd9	40	* Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps
simon	0:1014af42efd9	41	* First Generate cos values in floating point:
simon	0:1014af42efd9	42	* tableSize = 256;
simon	0:1014af42efd9	43	* <pre>for(n = -1; n < (tableSize + 1); n++)
simon	0:1014af42efd9	44	* {
simon	0:1014af42efd9	45	* cosTable[n+1]= cos(2pin/tableSize);
simon	0:1014af42efd9	46	* } </pre>
simon	0:1014af42efd9	47	* where pi value is 3.14159265358979
simon	0:1014af42efd9	48	* \par
simon	0:1014af42efd9	49	* Secondly Convert Floating point to Q31(Fixed point):
simon	0:1014af42efd9	50	* (cosTable[i] * pow(2, 31))
simon	0:1014af42efd9	51	* \par
simon	0:1014af42efd9	52	* Finally Rounding to nearest integer is done
simon	0:1014af42efd9	53	* cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);
simon	0:1014af42efd9	54	*/
simon	0:1014af42efd9	55
simon	0:1014af42efd9	56
simon	0:1014af42efd9	57	static const q31_t cosTableQ31[259] = {
simon	0:1014af42efd9	58	0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
simon	0:1014af42efd9	59	0x7f0991c4, 0x7e9d55fc,
simon	0:1014af42efd9	60	0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
simon	0:1014af42efd9	61	0x798a23b1, 0x78848414,
simon	0:1014af42efd9	62	0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
simon	0:1014af42efd9	63	0x6f5f02b2, 0x6dca0d14,
simon	0:1014af42efd9	64	0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
simon	0:1014af42efd9	65	0x60ec3830, 0x5ed77c8a,
simon	0:1014af42efd9	66	0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
simon	0:1014af42efd9	67	0x4ebfe8a5, 0x4c3fdff4,
simon	0:1014af42efd9	68	0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
simon	0:1014af42efd9	69	0x398cdd32, 0x36ba2014,
simon	0:1014af42efd9	70	0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
simon	0:1014af42efd9	71	0x2223a4c5, 0x1f19f97b,
simon	0:1014af42efd9	72	0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
simon	0:1014af42efd9	73	0x96a9049, 0x647d97c,
simon	0:1014af42efd9	74	0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
simon	0:1014af42efd9	75	0xed37ef91,
simon	0:1014af42efd9	76	0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
simon	0:1014af42efd9	77	0xd7d946d8, 0xd4e0cb15,
simon	0:1014af42efd9	78	0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
simon	0:1014af42efd9	79	0xc0e8b648, 0xbe31e19b,
simon	0:1014af42efd9	80	0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
simon	0:1014af42efd9	81	0xac64d510, 0xaa0a5b2e,
simon	0:1014af42efd9	82	0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
simon	0:1014af42efd9	83	0x9b1776da, 0x99307ee0,
simon	0:1014af42efd9	84	0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
simon	0:1014af42efd9	85	0x8daad37b, 0x8c4a142f,
simon	0:1014af42efd9	86	0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
simon	0:1014af42efd9	87	0x84a2fc62, 0x83d60412,
simon	0:1014af42efd9	88	0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
simon	0:1014af42efd9	89	0x8058c94c, 0x80277872,
simon	0:1014af42efd9	90	0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
simon	0:1014af42efd9	91	0x80f66e3c, 0x8162aa04,
simon	0:1014af42efd9	92	0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
simon	0:1014af42efd9	93	0x8675dc4f, 0x877b7bec,
simon	0:1014af42efd9	94	0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
simon	0:1014af42efd9	95	0x90a0fd4e, 0x9235f2ec,
simon	0:1014af42efd9	96	0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
simon	0:1014af42efd9	97	0x9f13c7d0, 0xa1288376,
simon	0:1014af42efd9	98	0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
simon	0:1014af42efd9	99	0xb140175b, 0xb3c0200c,
simon	0:1014af42efd9	100	0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
simon	0:1014af42efd9	101	0xc67322ce, 0xc945dfec,
simon	0:1014af42efd9	102	0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
simon	0:1014af42efd9	103	0xdddc5b3b, 0xe0e60685,
simon	0:1014af42efd9	104	0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
simon	0:1014af42efd9	105	0xf6956fb7, 0xf9b82684,
simon	0:1014af42efd9	106	0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
simon	0:1014af42efd9	107	0x12c8106f,
simon	0:1014af42efd9	108	0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
simon	0:1014af42efd9	109	0x2826b928, 0x2b1f34eb,
simon	0:1014af42efd9	110	0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
simon	0:1014af42efd9	111	0x3f1749b8, 0x41ce1e65,
simon	0:1014af42efd9	112	0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
simon	0:1014af42efd9	113	0x539b2af0, 0x55f5a4d2,
simon	0:1014af42efd9	114	0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
simon	0:1014af42efd9	115	0x64e88926, 0x66cf8120,
simon	0:1014af42efd9	116	0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
simon	0:1014af42efd9	117	0x72552c85, 0x73b5ebd1,
simon	0:1014af42efd9	118	0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
simon	0:1014af42efd9	119	0x7b5d039e, 0x7c29fbee,
simon	0:1014af42efd9	120	0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
simon	0:1014af42efd9	121	0x7fa736b4, 0x7fd8878e,
simon	0:1014af42efd9	122	0x7ff62182, 0x7fffffff, 0x7ff62182
simon	0:1014af42efd9	123	};
simon	0:1014af42efd9	124
simon	0:1014af42efd9	125	/**
simon	0:1014af42efd9	126	* @brief Fast approximation to the trigonometric cosine function for Q31 data.
simon	0:1014af42efd9	127	* @param[in] x Scaled input value in radians.
simon	0:1014af42efd9	128	* @return cos(x).
simon	0:1014af42efd9	129	*
simon	0:1014af42efd9	130	* The Q31 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
simon	0:1014af42efd9	131	*/
simon	0:1014af42efd9	132
simon	0:1014af42efd9	133	q31_t arm_cos_q31(
simon	0:1014af42efd9	134	q31_t x)
simon	0:1014af42efd9	135	{
simon	0:1014af42efd9	136	q31_t cosVal, fract, in, in2; /* Temporary variables for input, output */
simon	0:1014af42efd9	137	q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
simon	0:1014af42efd9	138	q31_t a, b, c, d; /* Four nearest output values */
simon	0:1014af42efd9	139	q31_t tablePtr; / Pointer to table */
simon	0:1014af42efd9	140	q31_t fractCube, fractSquare; /* Temporary values for fractional value */
simon	0:1014af42efd9	141	q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */
simon	0:1014af42efd9	142	q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */
simon	0:1014af42efd9	143	q31_t temp; /* Temporary variable for intermediate process */
simon	0:1014af42efd9	144	uint32_t index; /* Index variable */
simon	0:1014af42efd9	145
simon	0:1014af42efd9	146	in = x;
simon	0:1014af42efd9	147
simon	0:1014af42efd9	148	/* Calculate the nearest index */
simon	0:1014af42efd9	149	index = in / tableSpacing;
simon	0:1014af42efd9	150
simon	0:1014af42efd9	151	/* Calculate the nearest value of input */
simon	0:1014af42efd9	152	in2 = ((q31_t) index) * tableSpacing;
simon	0:1014af42efd9	153
simon	0:1014af42efd9	154	/* Calculation of fractional value */
simon	0:1014af42efd9	155	fract = (in - in2) << 8;
simon	0:1014af42efd9	156
simon	0:1014af42efd9	157	/* fractSquare = fract * fract */
simon	0:1014af42efd9	158	fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
simon	0:1014af42efd9	159	fractSquare = fractSquare << 1;
simon	0:1014af42efd9	160
simon	0:1014af42efd9	161	/* fractCube = fract * fract * fract */
simon	0:1014af42efd9	162	fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
simon	0:1014af42efd9	163	fractCube = fractCube << 1;
simon	0:1014af42efd9	164
simon	0:1014af42efd9	165	/* Initialise table pointer */
simon	0:1014af42efd9	166	tablePtr = (q31_t *) & cosTableQ31[index];
simon	0:1014af42efd9	167
simon	0:1014af42efd9	168	/* Cubic interpolation process */
simon	0:1014af42efd9	169	/* Calculation of wa */
simon	0:1014af42efd9	170	/* wa = -(oneBy6)fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)fract; */
simon	0:1014af42efd9	171	wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
simon	0:1014af42efd9	172	temp = 0x2AAAAAAA;
simon	0:1014af42efd9	173	wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
simon	0:1014af42efd9	174	wa = -(wa << 1u);
simon	0:1014af42efd9	175	wa += (fractSquare >> 1u);
simon	0:1014af42efd9	176
simon	0:1014af42efd9	177	/* Read first nearest value of output from the cos table */
simon	0:1014af42efd9	178	a = *tablePtr++;
simon	0:1014af42efd9	179
simon	0:1014af42efd9	180	/* cosVal = awa /
simon	0:1014af42efd9	181	cosVal = ((q31_t) (((q63_t) a * wa) >> 32));
simon	0:1014af42efd9	182
simon	0:1014af42efd9	183	/* q31(1.31) Fixed point value of 1 */
simon	0:1014af42efd9	184	temp = 0x7FFFFFFF;
simon	0:1014af42efd9	185
simon	0:1014af42efd9	186	/* Calculation of wb */
simon	0:1014af42efd9	187	wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
simon	0:1014af42efd9	188	/* Read second nearest value of output from the cos table */
simon	0:1014af42efd9	189	b = *tablePtr++;
simon	0:1014af42efd9	190
simon	0:1014af42efd9	191	/* cosVal += bwb /
simon	0:1014af42efd9	192	cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32);
simon	0:1014af42efd9	193
simon	0:1014af42efd9	194	/* Calculation of wc */
simon	0:1014af42efd9	195	wc = -fractCube + fractSquare;
simon	0:1014af42efd9	196	wc = (wc >> 1u) + fract;
simon	0:1014af42efd9	197	/* Read third nearest values of output value from the cos table */
simon	0:1014af42efd9	198	c = *tablePtr++;
simon	0:1014af42efd9	199
simon	0:1014af42efd9	200	/* cosVal += cwc /
simon	0:1014af42efd9	201	cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32);
simon	0:1014af42efd9	202
simon	0:1014af42efd9	203	/* Calculation of wd */
simon	0:1014af42efd9	204	/* wd = (oneBy6)fractCube - (oneBy6)fract; */
simon	0:1014af42efd9	205	fractCube = fractCube - fract;
simon	0:1014af42efd9	206	wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
simon	0:1014af42efd9	207	wd = (wd << 1u);
simon	0:1014af42efd9	208
simon	0:1014af42efd9	209	/* Read fourth nearest value of output from the cos table */
simon	0:1014af42efd9	210	d = *tablePtr++;
simon	0:1014af42efd9	211
simon	0:1014af42efd9	212	/* cosVal += dwd; /
simon	0:1014af42efd9	213	cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32);
simon	0:1014af42efd9	214
simon	0:1014af42efd9	215	/* convert cosVal in 2.30 format to 1.31 format */
simon	0:1014af42efd9	216	return (cosVal << 1u);
simon	0:1014af42efd9	217
simon	0:1014af42efd9	218	}
simon	0:1014af42efd9	219
simon	0:1014af42efd9	220	/**
simon	0:1014af42efd9	221	* @} end of cos group
simon	0:1014af42efd9	222	*/

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Type:	Library
Created:	10 Mar 2011
Imports:	907
Forks:	1
Commits:	3
Dependents:	5
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Followers:	35

src/Cortex-M4-M3/FastMathFunctions/arm_cos_q31.c@0:1014af42efd9, 2011-03-10 (annotated)

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