Diff: cmsis_dsp/FastMathFunctions/arm_cos_q31.c

Revision:

5:3762170b6d4d

Parent:

3:7a284390b0ce

--- a/cmsis_dsp/FastMathFunctions/arm_cos_q31.c	Mon Jun 23 09:30:09 2014 +0100
+++ b/cmsis_dsp/FastMathFunctions/arm_cos_q31.c	Fri Nov 20 08:45:18 2015 +0000
@@ -1,24 +1,24 @@
-/* ----------------------------------------------------------------------    
-* Copyright (C) 2010-2013 ARM Limited. All rights reserved.    
-*    
-* $Date:        17. January 2013
-* $Revision: 	V1.4.1
-*    
-* Project: 	    CMSIS DSP Library    
-* Title:		arm_cos_q31.c    
-*    
-* Description:	Fast cosine calculation for Q31 values.   
-*    
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
+*
+* $Date:        07. September 2015
+* $Revision:    V.1.4.5 a
+*
+* Project:      CMSIS DSP Library
+* Title:        arm_cos_q31.c
+*
+* Description: Fast cosine calculation for Q31 values.
+*
 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
-*  
-* Redistribution and use in source and binary forms, with or without 
+*
+* 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 
+*     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
@@ -27,7 +27,7 @@
 * 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 
+* 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;
@@ -35,113 +35,26 @@
 * 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.   
+* POSSIBILITY OF SUCH DAMAGE.
 * -------------------------------------------------------------------- */
 
 #include "arm_math.h"
-
-/**    
- * @ingroup groupFastMath    
- */
-
- /**    
- * @addtogroup cos    
- * @{    
- */
+#include "arm_common_tables.h"
 
-/**    
- * \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:    
- * <pre>
- * tableSize = 256;      
- * for(n = -1; n < (tableSize + 1); n++)    
- * {    
- *	cosTable[n+1]= cos(2*pi*n/tableSize);    
- * } </pre>     
- * where pi value is  3.14159265358979    
- * \par    
- * Second, convert floating-point to Q31 (Fixed point):
- *	(cosTable[i] * pow(2, 31))    
- * \par    
- * Finally, round to the nearest integer value:
- * 	cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);    
+/**
+ * @ingroup groupFastMath
  */
 
+ /**
+ * @addtogroup cos
+ * @{
+ */
 
-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).   
- *   
+/**
+ * @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 +0.9999] and is mapped to a radian
  * value in the range [0 2*pi).
  */
@@ -149,101 +62,35 @@
 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 */
-  int32_t index;                                 /* Index variable */
-
-  in = x;
-
-  /* Calculate the nearest index */
-  index = in / tableSpacing;
-
-  /* Calculate the nearest value of input */
-  in2 = ((q31_t) index) * tableSpacing;
+  q31_t cosVal;                                  /* Temporary variables for input, output */
+  int32_t index;                                 /* Index variables */
+  q31_t a, b;                                    /* Four nearest output values */
+  q31_t fract;                                   /* Temporary values for fractional values */
 
-  /* 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;
-
-  /* Checking min and max index of table */
-  if(index < 0)
-  {
-    index = 0;
-  }
-  else if(index > 256)
-  {
-    index = 256;
+  /* add 0.25 (pi/2) to read sine table */
+  x = (uint32_t)x + 0x20000000;
+  if(x < 0)
+  {   /* convert negative numbers to corresponding positive ones */
+      x = (uint32_t)x + 0x80000000;
   }
 
-  /* 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);
+  /* Calculate the nearest index */
+  index = (uint32_t)x >> FAST_MATH_Q31_SHIFT;
 
-  /* 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++;
+  /* Calculation of fractional value */
+  fract = (x - (index << FAST_MATH_Q31_SHIFT)) << 9;
 
-  /*      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);
+  /* Read two nearest values of input value from the sin table */
+  a = sinTable_q31[index];
+  b = sinTable_q31[index+1];
 
-  /* Calculation of wd */
-  /* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
-  fractCube = fractCube - fract;
-  wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
-  wd = (wd << 1u);
+  /* Linear interpolation process */
+  cosVal = (q63_t)(0x80000000-fract)*a >> 32;
+  cosVal = (q31_t)((((q63_t)cosVal << 32) + ((q63_t)fract*b)) >> 32);
 
-  /* 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 (__QADD(cosVal, cosVal));
-
+  return cosVal << 1;
 }
 
-/**    
- * @} end of cos group    
+/**
+ * @} end of cos group
  */