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src/Cortex-M4-M3/FastMathFunctions/arm_sin_q15.c@0:1014af42efd9, 2011-03-10 (annotated)

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

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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_sin_q15.c
simon	0:1014af42efd9	9	*
simon	0:1014af42efd9	10	* Description: Fast sine calculation for Q15 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 sin
simon	0:1014af42efd9	35	* @{
simon	0:1014af42efd9	36	*/
simon	0:1014af42efd9	37
simon	0:1014af42efd9	38
simon	0:1014af42efd9	39	/**
simon	0:1014af42efd9	40	* \par
simon	0:1014af42efd9	41	* Example code for Generation of Q15 Sin Table:
simon	0:1014af42efd9	42	* \par
simon	0:1014af42efd9	43	* <pre>tableSize = 256;
simon	0:1014af42efd9	44	* for(n = -1; n < (tableSize + 1); n++)
simon	0:1014af42efd9	45	* {
simon	0:1014af42efd9	46	* sinTable[n+1]=sin(2pin/tableSize);
simon	0:1014af42efd9	47	* } </pre>
simon	0:1014af42efd9	48	* where pi value is 3.14159265358979
simon	0:1014af42efd9	49	* \par
simon	0:1014af42efd9	50	* Convert Floating point to Q15(Fixed point):
simon	0:1014af42efd9	51	* (sinTable[i] * pow(2, 15))
simon	0:1014af42efd9	52	* \par
simon	0:1014af42efd9	53	* rounding to nearest integer is done
simon	0:1014af42efd9	54	* sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
simon	0:1014af42efd9	55	*/
simon	0:1014af42efd9	56
simon	0:1014af42efd9	57
simon	0:1014af42efd9	58	static const q15_t sinTableQ15[259] = {
simon	0:1014af42efd9	59	0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
simon	0:1014af42efd9	60	0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
simon	0:1014af42efd9	61	0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
simon	0:1014af42efd9	62	0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
simon	0:1014af42efd9	63	0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
simon	0:1014af42efd9	64	0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
simon	0:1014af42efd9	65	0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
simon	0:1014af42efd9	66	0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
simon	0:1014af42efd9	67	0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
simon	0:1014af42efd9	68	0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
simon	0:1014af42efd9	69	0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
simon	0:1014af42efd9	70	0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
simon	0:1014af42efd9	71	0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
simon	0:1014af42efd9	72	0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
simon	0:1014af42efd9	73	0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
simon	0:1014af42efd9	74	0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
simon	0:1014af42efd9	75	0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
simon	0:1014af42efd9	76	0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
simon	0:1014af42efd9	77	0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
simon	0:1014af42efd9	78	0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
simon	0:1014af42efd9	79	0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
simon	0:1014af42efd9	80	0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
simon	0:1014af42efd9	81	0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
simon	0:1014af42efd9	82	0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
simon	0:1014af42efd9	83	0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
simon	0:1014af42efd9	84	0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
simon	0:1014af42efd9	85	0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
simon	0:1014af42efd9	86	0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
simon	0:1014af42efd9	87	0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
simon	0:1014af42efd9	88	0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
simon	0:1014af42efd9	89	0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
simon	0:1014af42efd9	90	0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
simon	0:1014af42efd9	91	0xfcdc, 0x0, 0x324
simon	0:1014af42efd9	92	};
simon	0:1014af42efd9	93
simon	0:1014af42efd9	94
simon	0:1014af42efd9	95	/**
simon	0:1014af42efd9	96	* @brief Fast approximation to the trigonometric sine function for Q15 data.
simon	0:1014af42efd9	97	* @param[in] x Scaled input value in radians.
simon	0:1014af42efd9	98	* @return sin(x).
simon	0:1014af42efd9	99	*
simon	0:1014af42efd9	100	* The Q15 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
simon	0:1014af42efd9	101	*/
simon	0:1014af42efd9	102
simon	0:1014af42efd9	103	q15_t arm_sin_q15(
simon	0:1014af42efd9	104	q15_t x)
simon	0:1014af42efd9	105	{
simon	0:1014af42efd9	106	q31_t sinVal; /* Temporary variables output */
simon	0:1014af42efd9	107	q15_t tablePtr; / Pointer to table */
simon	0:1014af42efd9	108	q15_t fract, in, in2; /* Temporary variables for input, output */
simon	0:1014af42efd9	109	q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
simon	0:1014af42efd9	110	q15_t a, b, c, d; /* Four nearest output values */
simon	0:1014af42efd9	111	q15_t fractCube, fractSquare; /* Temporary values for fractional value */
simon	0:1014af42efd9	112	q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */
simon	0:1014af42efd9	113	q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */
simon	0:1014af42efd9	114	int32_t index; /* Index variable */
simon	0:1014af42efd9	115
simon	0:1014af42efd9	116	in = x;
simon	0:1014af42efd9	117
simon	0:1014af42efd9	118	/* Calculate the nearest index */
simon	0:1014af42efd9	119	index = (int32_t) in / tableSpacing;
simon	0:1014af42efd9	120
simon	0:1014af42efd9	121	/* Calculate the nearest value of input */
simon	0:1014af42efd9	122	in2 = (q15_t) ((index) * tableSpacing);
simon	0:1014af42efd9	123
simon	0:1014af42efd9	124	/* Calculation of fractional value */
simon	0:1014af42efd9	125	fract = (in - in2) << 8;
simon	0:1014af42efd9	126
simon	0:1014af42efd9	127	/* fractSquare = fract * fract */
simon	0:1014af42efd9	128	fractSquare = (q15_t) ((fract * fract) >> 15);
simon	0:1014af42efd9	129
simon	0:1014af42efd9	130	/* fractCube = fract * fract * fract */
simon	0:1014af42efd9	131	fractCube = (q15_t) ((fractSquare * fract) >> 15);
simon	0:1014af42efd9	132
simon	0:1014af42efd9	133	/* Initialise table pointer */
simon	0:1014af42efd9	134	tablePtr = (q15_t *) & sinTableQ15[index];
simon	0:1014af42efd9	135
simon	0:1014af42efd9	136	/* Cubic interpolation process */
simon	0:1014af42efd9	137	/* Calculation of wa */
simon	0:1014af42efd9	138	/* wa = -(oneBy6)fractCube + (fractSquare >> 1u) - (0x2AAA)fract; */
simon	0:1014af42efd9	139	wa = (q31_t) oneBy6 *fractCube;
simon	0:1014af42efd9	140	wa += (q31_t) 0x2AAA * fract;
simon	0:1014af42efd9	141	wa = -(wa >> 15);
simon	0:1014af42efd9	142	wa += ((q31_t) fractSquare >> 1u);
simon	0:1014af42efd9	143
simon	0:1014af42efd9	144	/* Read first nearest value of output from the sin table */
simon	0:1014af42efd9	145	a = *tablePtr++;
simon	0:1014af42efd9	146
simon	0:1014af42efd9	147	/* sinVal = a * wa */
simon	0:1014af42efd9	148	sinVal = a * wa;
simon	0:1014af42efd9	149
simon	0:1014af42efd9	150	/* Calculation of wb */
simon	0:1014af42efd9	151	wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
simon	0:1014af42efd9	152	(((q31_t) fract >> 1u) - 0x7FFF);
simon	0:1014af42efd9	153
simon	0:1014af42efd9	154	/* Read second nearest value of output from the sin table */
simon	0:1014af42efd9	155	b = *tablePtr++;
simon	0:1014af42efd9	156
simon	0:1014af42efd9	157	/* sinVal += bwb /
simon	0:1014af42efd9	158	sinVal += b * wb;
simon	0:1014af42efd9	159
simon	0:1014af42efd9	160
simon	0:1014af42efd9	161	/* Calculation of wc */
simon	0:1014af42efd9	162	wc = -(q31_t) fractCube + fractSquare;
simon	0:1014af42efd9	163	wc = (wc >> 1u) + fract;
simon	0:1014af42efd9	164
simon	0:1014af42efd9	165	/* Read third nearest value of output from the sin table */
simon	0:1014af42efd9	166	c = *tablePtr++;
simon	0:1014af42efd9	167
simon	0:1014af42efd9	168	/* sinVal += cwc /
simon	0:1014af42efd9	169	sinVal += c * wc;
simon	0:1014af42efd9	170
simon	0:1014af42efd9	171	/* Calculation of wd */
simon	0:1014af42efd9	172	/* wd = (oneBy6)fractCube - (oneBy6)fract; */
simon	0:1014af42efd9	173	fractCube = fractCube - fract;
simon	0:1014af42efd9	174	wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
simon	0:1014af42efd9	175
simon	0:1014af42efd9	176	/* Read fourth nearest value of output from the sin table */
simon	0:1014af42efd9	177	d = *tablePtr++;
simon	0:1014af42efd9	178
simon	0:1014af42efd9	179	/* sinVal += dwd; /
simon	0:1014af42efd9	180	sinVal += d * wd;
simon	0:1014af42efd9	181
simon	0:1014af42efd9	182	/* Return the output value in 1.15(q15) format */
simon	0:1014af42efd9	183	return ((q15_t) (sinVal >> 15u));
simon	0:1014af42efd9	184
simon	0:1014af42efd9	185	}
simon	0:1014af42efd9	186
simon	0:1014af42efd9	187	/**
simon	0:1014af42efd9	188	* @} end of sin group
simon	0:1014af42efd9	189	*/

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Type:	Library
Created:	10 Mar 2011
Imports:	907
Forks:	1
Commits:	3
Dependents:	5
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src/Cortex-M4-M3/FastMathFunctions/arm_sin_q15.c@0:1014af42efd9, 2011-03-10 (annotated)

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