/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 12. March 2014
* $Revision: V1.4.4
*
* Project: CMSIS DSP Library
* Title: arm_sin_f32.c
*
* Description: Fast sine calculation for floating-point values.
* Fast cosine calculation for floating-point values.
*
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* - Neither the name of ARM LIMITED nor the names of its contributors
* may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */
#include <stdint.h>
#include <nanohub_math.h>
#define FAST_MATH_TABLE_SIZE 512
typedef float float32_t;
/**
* \par
* Example code for the generation of the floating-point sine table:
* <pre>
* tableSize = 512;
* for(n = 0; n < (tableSize + 1); n++)
* {
* sinTable[n]=sin(2*pi*n/tableSize);
* }</pre>
* \par
* where pi value is 3.14159265358979
*/
static const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1] = {
0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f,
0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f,
0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f, 0.19509032f, 0.20711138f,
0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f,
0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f,
0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f, 0.47139674f, 0.48218377f,
0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f,
0.61523159f, 0.62485949f, 0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f,
0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f, 0.70710678f, 0.71573083f,
0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f,
0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f,
0.81758481f, 0.82458930f, 0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f,
0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f, 0.88192126f, 0.88763962f,
0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f,
0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f,
0.94952818f, 0.95330604f, 0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f,
0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f, 0.98078528f, 0.98310549f,
0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f,
0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f,
0.99969882f, 0.99992470f, 1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f,
0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f, 0.99518473f, 0.99390697f,
0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f,
0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f,
0.96377607f, 0.96043052f, 0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f,
0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f, 0.92387953f, 0.91911385f,
0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f,
0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f,
0.84485357f, 0.83822471f, 0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f,
0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f, 0.77301045f, 0.76516727f,
0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f,
0.65317284f, 0.64383154f, 0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f,
0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f, 0.55557023f, 0.54532499f,
0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f,
0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f,
0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f,
0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f, 0.29028468f, 0.27851969f,
0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f,
0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f,
0.12241068f, 0.11022221f, 0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f,
0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f, 0.00000000f, -0.01227154f,
-0.02454123f, -0.03680722f, -0.04906767f, -0.06132074f, -0.07356456f,
-0.08579731f, -0.09801714f, -0.11022221f, -0.12241068f, -0.13458071f,
-0.14673047f, -0.15885814f, -0.17096189f, -0.18303989f, -0.19509032f,
-0.20711138f, -0.21910124f, -0.23105811f, -0.24298018f, -0.25486566f,
-0.26671276f, -0.27851969f, -0.29028468f, -0.30200595f, -0.31368174f,
-0.32531029f, -0.33688985f, -0.34841868f, -0.35989504f, -0.37131719f,
-0.38268343f, -0.39399204f, -0.40524131f, -0.41642956f, -0.42755509f,
-0.43861624f, -0.44961133f, -0.46053871f, -0.47139674f, -0.48218377f,
-0.49289819f, -0.50353838f, -0.51410274f, -0.52458968f, -0.53499762f,
-0.54532499f, -0.55557023f, -0.56573181f, -0.57580819f, -0.58579786f,
-0.59569930f, -0.60551104f, -0.61523159f, -0.62485949f, -0.63439328f,
-0.64383154f, -0.65317284f, -0.66241578f, -0.67155895f, -0.68060100f,
-0.68954054f, -0.69837625f, -0.70710678f, -0.71573083f, -0.72424708f,
-0.73265427f, -0.74095113f, -0.74913639f, -0.75720885f, -0.76516727f,
-0.77301045f, -0.78073723f, -0.78834643f, -0.79583690f, -0.80320753f,
-0.81045720f, -0.81758481f, -0.82458930f, -0.83146961f, -0.83822471f,
-0.84485357f, -0.85135519f, -0.85772861f, -0.86397286f, -0.87008699f,
-0.87607009f, -0.88192126f, -0.88763962f, -0.89322430f, -0.89867447f,
-0.90398929f, -0.90916798f, -0.91420976f, -0.91911385f, -0.92387953f,
-0.92850608f, -0.93299280f, -0.93733901f, -0.94154407f, -0.94560733f,
-0.94952818f, -0.95330604f, -0.95694034f, -0.96043052f, -0.96377607f,
-0.96697647f, -0.97003125f, -0.97293995f, -0.97570213f, -0.97831737f,
-0.98078528f, -0.98310549f, -0.98527764f, -0.98730142f, -0.98917651f,
-0.99090264f, -0.99247953f, -0.99390697f, -0.99518473f, -0.99631261f,
-0.99729046f, -0.99811811f, -0.99879546f, -0.99932238f, -0.99969882f,
-0.99992470f, -1.00000000f, -0.99992470f, -0.99969882f, -0.99932238f,
-0.99879546f, -0.99811811f, -0.99729046f, -0.99631261f, -0.99518473f,
-0.99390697f, -0.99247953f, -0.99090264f, -0.98917651f, -0.98730142f,
-0.98527764f, -0.98310549f, -0.98078528f, -0.97831737f, -0.97570213f,
-0.97293995f, -0.97003125f, -0.96697647f, -0.96377607f, -0.96043052f,
-0.95694034f, -0.95330604f, -0.94952818f, -0.94560733f, -0.94154407f,
-0.93733901f, -0.93299280f, -0.92850608f, -0.92387953f, -0.91911385f,
-0.91420976f, -0.90916798f, -0.90398929f, -0.89867447f, -0.89322430f,
-0.88763962f, -0.88192126f, -0.87607009f, -0.87008699f, -0.86397286f,
-0.85772861f, -0.85135519f, -0.84485357f, -0.83822471f, -0.83146961f,
-0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f,
-0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f,
-0.74913639f, -0.74095113f, -0.73265427f, -0.72424708f, -0.71573083f,
-0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f,
-0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f,
-0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f,
-0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f,
-0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f,
-0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f,
-0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f,
-0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f,
-0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f,
-0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f,
-0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f,
-0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f,
-0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f
};
/**
* @ingroup groupFastMath
*/
/**
* @defgroup sin Sine
*
* Computes the trigonometric sine function using a combination of table lookup
* and cubic interpolation. There are separate functions for
* Q15, Q31, and floating-point data types.
* The input to the floating-point version is in radians while the
* fixed-point Q15 and Q31 have a scaled input with the range
* [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
* value of 2*pi wraps around to 0.
*
* The implementation is based on table lookup using 256 values together with cubic interpolation.
* The steps used are:
* -# Calculation of the nearest integer table index
* -# Fetch the four table values a, b, c, and d
* -# Compute the fractional portion (fract) of the table index.
* -# Calculation of wa, wb, wc, wd
* -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
*
* where
* <pre>
* a=Table[index-1];
* b=Table[index+0];
* c=Table[index+1];
* d=Table[index+2];
* </pre>
* and
* <pre>
* wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
* wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
* wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
* wd=(1/6)*fract.^3 - (1/6)*fract;
* </pre>
*/
/**
* @addtogroup sin
* @{
*/
/**
* @brief Fast approximation to the trigonometric sine function for floating-point data.
* @param[in] x input value in radians.
* @return sin(x).
*/
float32_t arm_sin_f32(
float32_t x)
{
float32_t sinVal, fract, in; /* Temporary variables for input, output */
uint16_t index; /* Index variable */
float32_t a, b; /* Two nearest output values */
int32_t n;
float32_t findex;
/* input x is in radians */
/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
in = x * 0.159154943092f;
/* Calculation of floor value of input */
n = (int32_t) in;
/* Make negative values towards -infinity */
if(x < 0.0f)
{
n--;
}
/* Map input value to [0 1] */
in = in - (float32_t) n;
/* Calculation of index of the table */
findex = (float32_t) FAST_MATH_TABLE_SIZE * in;
index = ((uint16_t)findex) & 0x1ff;
/* fractional value calculation */
fract = findex - (float32_t) index;
/* Read two nearest values of input value from the sin table */
a = sinTable_f32[index];
b = sinTable_f32[index+1];
/* Linear interpolation process */
sinVal = (1.0f-fract)*a + fract*b;
/* Return the output value */
return (sinVal);
}
/**
* @defgroup cos Cosine
*
* Computes the trigonometric cosine function using a combination of table lookup
* and cubic interpolation. There are separate functions for
* Q15, Q31, and floating-point data types.
* The input to the floating-point version is in radians while the
* fixed-point Q15 and Q31 have a scaled input with the range
* [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a
* value of 2*pi wraps around to 0.
*
* The implementation is based on table lookup using 256 values together with cubic interpolation.
* The steps used are:
* -# Calculation of the nearest integer table index
* -# Fetch the four table values a, b, c, and d
* -# Compute the fractional portion (fract) of the table index.
* -# Calculation of wa, wb, wc, wd
* -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
*
* where
* <pre>
* a=Table[index-1];
* b=Table[index+0];
* c=Table[index+1];
* d=Table[index+2];
* </pre>
* and
* <pre>
* wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
* wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
* wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
* wd=(1/6)*fract.^3 - (1/6)*fract;
* </pre>
*/
/**
* @addtogroup cos
* @{
*/
/**
* @brief Fast approximation to the trigonometric cosine function for floating-point data.
* @param[in] x input value in radians.
* @return cos(x).
*/
float32_t arm_cos_f32(
float32_t x)
{
float32_t cosVal, fract, in; /* Temporary variables for input, output */
uint16_t index; /* Index variable */
float32_t a, b; /* Two nearest output values */
int32_t n;
float32_t findex;
/* input x is in radians */
/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi, add 0.25 (pi/2) to read sine table */
in = x * 0.159154943092f + 0.25f;
/* Calculation of floor value of input */
n = (int32_t) in;
/* Make negative values towards -infinity */
if(in < 0.0f)
{
n--;
}
/* Map input value to [0 1] */
in = in - (float32_t) n;
/* Calculation of index of the table */
findex = (float32_t) FAST_MATH_TABLE_SIZE * in;
index = ((uint16_t)findex) & 0x1ff;
/* fractional value calculation */
fract = findex - (float32_t) index;
/* Read two nearest values of input value from the cos table */
a = sinTable_f32[index];
b = sinTable_f32[index+1];
/* Linear interpolation process */
cosVal = (1.0f-fract)*a + fract*b;
/* Return the output value */
return (cosVal);
}
/**
* @} end of cos group
*/