Diff: cmsis_dsp/TransformFunctions/arm_dct4_q31.c

Revision:

1:fdd22bb7aa52

Child:

2:da51fb522205

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cmsis_dsp/TransformFunctions/arm_dct4_q31.c	Wed Nov 28 12:30:09 2012 +0000
@@ -0,0 +1,387 @@
+/* ----------------------------------------------------------------------    
+* Copyright (C) 2010 ARM Limited. All rights reserved.    
+*    
+* $Date:        15. February 2012  
+* $Revision:     V1.1.0  
+*    
+* Project:         CMSIS DSP Library    
+* Title:        arm_dct4_q31.c    
+*    
+* Description:    Processing function of DCT4 & IDCT4 Q31.    
+*    
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*  
+* Version 1.1.0 2012/02/15 
+*    Updated with more optimizations, bug fixes and minor API changes.  
+*   
+* Version 1.0.10 2011/7/15  
+*    Big Endian support added and Merged M0 and M3/M4 Source code.   
+*    
+* Version 1.0.3 2010/11/29   
+*    Re-organized the CMSIS folders and updated documentation.    
+*     
+* Version 1.0.2 2010/11/11    
+*    Documentation updated.     
+*    
+* Version 1.0.1 2010/10/05     
+*    Production release and review comments incorporated.    
+*    
+* Version 1.0.0 2010/09/20     
+*    Production release and review comments incorporated.    
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**    
+ * @addtogroup DCT4_IDCT4    
+ * @{    
+ */
+
+/**    
+ * @brief Processing function for the Q31 DCT4/IDCT4.   
+ * @param[in]       *S             points to an instance of the Q31 DCT4 structure.   
+ * @param[in]       *pState        points to state buffer.   
+ * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.   
+ * @return none.   
+ * \par Input an output formats:    
+ * Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process,    
+ * as the conversion from DCT2 to DCT4 involves one subtraction.    
+ * Internally inputs are downscaled in the RFFT process function to avoid overflows.    
+ * Number of bits downscaled, depends on the size of the transform.    
+ * The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:     
+ *    
+ * \image html dct4FormatsQ31Table.gif    
+ */
+
+void arm_dct4_q31(
+  const arm_dct4_instance_q31 * S,
+  q31_t * pState,
+  q31_t * pInlineBuffer)
+{
+  uint16_t i;                                    /* Loop counter */
+  q31_t *weights = S->pTwiddle;                  /* Pointer to the Weights table */
+  q31_t *cosFact = S->pCosFactor;                /* Pointer to the cos factors table */
+  q31_t *pS1, *pS2, *pbuff;                      /* Temporary pointers for input buffer and pState buffer */
+  q31_t in;                                      /* Temporary variable */
+
+
+  /* DCT4 computation involves DCT2 (which is calculated using RFFT)    
+   * along with some pre-processing and post-processing.    
+   * Computational procedure is explained as follows:    
+   * (a) Pre-processing involves multiplying input with cos factor,    
+   *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))    
+   *              where,    
+   *                 r(n) -- output of preprocessing    
+   *                 u(n) -- input to preprocessing(actual Source buffer)    
+   * (b) Calculation of DCT2 using FFT is divided into three steps:    
+   *                  Step1: Re-ordering of even and odd elements of input.    
+   *                  Step2: Calculating FFT of the re-ordered input.    
+   *                  Step3: Taking the real part of the product of FFT output and weights.    
+   * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:    
+   *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *                        where,    
+   *                           Y4 -- DCT4 output,   Y2 -- DCT2 output    
+   * (d) Multiplying the output with the normalizing factor sqrt(2/N).    
+   */
+
+        /*-------- Pre-processing ------------*/
+  /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
+  arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N);
+  arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N);
+
+  /* ----------------------------------------------------------------    
+   * Step1: Re-ordering of even and odd elements as    
+   *             pState[i] =  pInlineBuffer[2*i] and    
+   *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2    
+   ---------------------------------------------------------------------*/
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
+  pS2 = pState + (S->N - 1u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+#ifndef ARM_MATH_CM0
+
+  /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+  /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
+  i = S->Nby2 >> 2u;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    *pS1++ = *pbuff++;
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = S->N >> 2u;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.    
+   * Compute 4 outputs at a time */
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
+
+  /*----------------------------------------------------------------------    
+   *  Step3: Multiply the FFT output with the weights.    
+   *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
+
+  /* The output of complex multiplication is in 3.29 format.    
+   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
+  arm_shift_q31(pState, 2, pState, S->N * 2);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
+  i = (S->N - 1u) >> 2u;
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ >> 1u;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.    
+   ** a second loop below computes the remaining 1 to 3 samples. */
+  do
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.    
+   ** No loop unrolling is used. */
+  i = (S->N - 1u) % 0x4u;
+
+  while(i > 0u)
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+
+        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter to N/4 instead of N for loop unrolling */
+  i = S->N >> 2u;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+#else
+
+  /* Run the below code for Cortex-M0 */
+
+  /* Initializing the loop counter to N/2 */
+  i = S->Nby2;
+
+  do
+  {
+    /* Re-ordering of even and odd elements */
+    /* pState[i] =  pInlineBuffer[2*i] */
+    *pS1++ = *pbuff++;
+    /* pState[N-i-1] = pInlineBuffer[2*i+1] */
+    *pS2-- = *pbuff++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+  /* pbuff initialized to input buffer */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Initializing the loop counter */
+  i = S->N;
+
+  do
+  {
+    /* Writing the re-ordered output back to inplace input buffer */
+    *pbuff++ = *pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+
+  /* ---------------------------------------------------------    
+   *     Step2: Calculate RFFT for N-point input    
+   * ---------------------------------------------------------- */
+  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
+  arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
+
+  /*----------------------------------------------------------------------    
+   *  Step3: Multiply the FFT output with the weights.    
+   *----------------------------------------------------------------------*/
+  arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
+
+  /* The output of complex multiplication is in 3.29 format.    
+   * Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
+  arm_shift_q31(pState, 2, pState, S->N * 2);
+
+  /* ----------- Post-processing ---------- */
+  /* DCT-IV can be obtained from DCT-II by the equation,    
+   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)    
+   *       Hence, Y4(0) = Y2(0)/2  */
+  /* Getting only real part from the output and Converting to DCT-IV */
+
+  /* pbuff initialized to input buffer. */
+  pbuff = pInlineBuffer;
+
+  /* pS1 initialized to pState */
+  pS1 = pState;
+
+  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
+  in = *pS1++ >> 1u;
+  /* input buffer acts as inplace, so output values are stored in the input itself. */
+  *pbuff++ = in;
+
+  /* pState pointer is incremented twice as the real values are located alternatively in the array */
+  pS1++;
+
+  /* Initializing the loop counter */
+  i = (S->N - 1u);
+
+  while(i > 0u)
+  {
+    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
+    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
+    in = *pS1++ - in;
+    *pbuff++ = in;
+    /* points to the next real value */
+    pS1++;
+
+    /* Decrement the loop counter */
+    i--;
+  }
+
+
+        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
+
+  /* Initializing the loop counter */
+  i = S->N;
+
+  /* pbuff initialized to the pInlineBuffer(now contains the output values) */
+  pbuff = pInlineBuffer;
+
+  do
+  {
+    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
+    in = *pbuff;
+    *pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
+
+    /* Decrement the loop counter */
+    i--;
+  } while(i > 0u);
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/**    
+   * @} end of DCT4_IDCT4 group    
+   */