/* ---------------------------------------------------------------------- * Copyright (C) 2010-2014 ARM Limited. All rights reserved. * * $Date: 12. March 2014 * $Revision: V1.4.4 * * Project: CMSIS DSP Library * Title: arm_cos_f32.c * * Description: 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 "arm_math.h" #include "arm_common_tables.h" /** * @ingroup groupFastMath */ /** * @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 a*wa + b*wb + c*wc + d*wd * * where *
    
 *    a=Table[index-1];    
 *    b=Table[index+0];    
 *    c=Table[index+1];    
 *    d=Table[index+2];    
 * 
* and *
    
 *    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;    
 * 
*/ /** * @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 */