diff options
Diffstat (limited to 'Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c')
| -rw-r--r-- | Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c | 257 |
1 files changed, 128 insertions, 129 deletions
diff --git a/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c index 231c79a3f..87455dc0f 100644 --- a/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c +++ b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_dct4_f32.c @@ -3,13 +3,13 @@ * Title: arm_dct4_f32.c * Description: Processing function of DCT4 & IDCT4 F32 * - * $Date: 27. January 2017 - * $Revision: V.1.5.1 + * $Date: 18. March 2019 + * $Revision: V1.6.0 * * Target Processor: Cortex-M cores * -------------------------------------------------------------------- */ /* - * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved. + * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved. * * SPDX-License-Identifier: Apache-2.0 * @@ -29,109 +29,111 @@ #include "arm_math.h" /** - * @ingroup groupTransforms + @ingroup groupTransforms */ /** - * @defgroup DCT4_IDCT4 DCT Type IV Functions - * Representation of signals by minimum number of values is important for storage and transmission. - * The possibility of large discontinuity between the beginning and end of a period of a signal - * in DFT can be avoided by extending the signal so that it is even-symmetric. - * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the - * spectrum and is very widely used in signal and image coding applications. - * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions. - * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular. - * - * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal. - * Reordering of the input data makes the computation of DCT just a problem of - * computing the DFT of a real signal with a few additional operations. - * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations. - * - * DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used. - * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing. - * DCT2 implementation can be described in the following steps: - * - Re-ordering input - * - Calculating Real FFT - * - Multiplication of weights and Real FFT output and getting real part from the product. - * - * This process is explained by the block diagram below: - * \image html DCT4.gif "Discrete Cosine Transform - type-IV" - * - * \par Algorithm: - * The N-point type-IV DCT is defined as a real, linear transformation by the formula: - * \image html DCT4Equation.gif - * where <code>k = 0,1,2,.....N-1</code> - *\par - * Its inverse is defined as follows: - * \image html IDCT4Equation.gif - * where <code>n = 0,1,2,.....N-1</code> - *\par - * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N). - * The symmetry of the transform matrix indicates that the fast algorithms for the forward - * and inverse transform computation are identical. - * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both. - * - * \par Lengths supported by the transform: - * As DCT4 internally uses Real FFT, it supports all the lengths 128, 512, 2048 and 8192. - * The library provides separate functions for Q15, Q31, and floating-point data types. - * \par Instance Structure - * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure. - * A separate instance structure must be defined for each transform. - * There are separate instance structure declarations for each of the 3 supported data types. - * - * \par Initialization Functions - * There is also an associated initialization function for each data type. - * The initialization function performs the following operations: - * - Sets the values of the internal structure fields. - * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32(). - * \par - * Use of the initialization function is optional. - * However, if the initialization function is used, then the instance structure cannot be placed into a const data section. - * To place an instance structure into a const data section, the instance structure must be manually initialized. - * Manually initialize the instance structure as follows: - * <pre> - *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; - *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; - *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; - * </pre> - * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4; - * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>; - * \c pTwiddle points to the twiddle factor table; - * \c pCosFactor points to the cosFactor table; - * \c pRfft points to the real FFT instance; - * \c pCfft points to the complex FFT instance; - * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32() - * and arm_rfft_f32() respectively for details regarding static initialization. - * - * \par Fixed-Point Behavior - * Care must be taken when using the fixed-point versions of the DCT4 transform functions. - * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. - * Refer to the function specific documentation below for usage guidelines. + @defgroup DCT4_IDCT4 DCT Type IV Functions + + Representation of signals by minimum number of values is important for storage and transmission. + The possibility of large discontinuity between the beginning and end of a period of a signal + in DFT can be avoided by extending the signal so that it is even-symmetric. + Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the + spectrum and is very widely used in signal and image coding applications. + The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions. + DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular. + + DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal. + Reordering of the input data makes the computation of DCT just a problem of + computing the DFT of a real signal with a few additional operations. + This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations. + + DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used. + DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing. + DCT2 implementation can be described in the following steps: + - Re-ordering input + - Calculating Real FFT + - Multiplication of weights and Real FFT output and getting real part from the product. + + This process is explained by the block diagram below: + \image html DCT4.gif "Discrete Cosine Transform - type-IV" + + @par Algorithm + The N-point type-IV DCT is defined as a real, linear transformation by the formula: + \image html DCT4Equation.gif + where <code>k = 0, 1, 2, ..., N-1</code> + @par + Its inverse is defined as follows: + \image html IDCT4Equation.gif + where <code>n = 0, 1, 2, ..., N-1</code> + @par + The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N). + The symmetry of the transform matrix indicates that the fast algorithms for the forward + and inverse transform computation are identical. + Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both. + + @par Lengths supported by the transform: + As DCT4 internally uses Real FFT, it supports all the lengths 128, 512, 2048 and 8192. + The library provides separate functions for Q15, Q31, and floating-point data types. + + @par Instance Structure + The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure. + A separate instance structure must be defined for each transform. + There are separate instance structure declarations for each of the 3 supported data types. + + @par Initialization Functions + There is also an associated initialization function for each data type. + The initialization function performs the following operations: + - Sets the values of the internal structure fields. + - Initializes Real FFT as its process function is used internally in DCT4, by calling \ref arm_rfft_init_f32(). + @par + Use of the initialization function is optional. + However, if the initialization function is used, then the instance structure cannot be placed into a const data section. + To place an instance structure into a const data section, the instance structure must be manually initialized. + Manually initialize the instance structure as follows: + <pre> + arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; + arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; + arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; + </pre> + where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4; + \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>; + \c pTwiddle points to the twiddle factor table; + \c pCosFactor points to the cosFactor table; + \c pRfft points to the real FFT instance; + \c pCfft points to the complex FFT instance; + The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32() + and arm_rfft_f32() respectively for details regarding static initialization. + + @par Fixed-Point Behavior + Care must be taken when using the fixed-point versions of the DCT4 transform functions. + In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. + Refer to the function specific documentation below for usage guidelines. */ /** - * @addtogroup DCT4_IDCT4 - * @{ + @addtogroup DCT4_IDCT4 + @{ */ /** - * @brief Processing function for the floating-point DCT4/IDCT4. - * @param[in] *S points to an instance of the floating-point DCT4/IDCT4 structure. - * @param[in] *pState points to state buffer. - * @param[in,out] *pInlineBuffer points to the in-place input and output buffer. - * @return none. + @brief Processing function for the floating-point DCT4/IDCT4. + @param[in] S points to an instance of the floating-point DCT4/IDCT4 structure + @param[in] pState points to state buffer + @param[in,out] pInlineBuffer points to the in-place input and output buffer + @return none */ void arm_dct4_f32( const arm_dct4_instance_f32 * S, - float32_t * pState, - float32_t * pInlineBuffer) + float32_t * pState, + float32_t * pInlineBuffer) { - uint32_t i; /* Loop counter */ - float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */ - float32_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ - float32_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ - float32_t in; /* Temporary variable */ + const float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */ + const float32_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */ + float32_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */ + float32_t in; /* Temporary variable */ + uint32_t i; /* Loop counter */ /* DCT4 computation involves DCT2 (which is calculated using RFFT) @@ -153,13 +155,13 @@ void arm_dct4_f32( * (d) Multiplying the output with the normalizing factor sqrt(2/N). */ - /*-------- Pre-processing ------------*/ + /*-------- Pre-processing ------------*/ /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N); arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N); /* ---------------------------------------------------------------- - * Step1: Re-ordering of even and odd elements as, + * 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 ---------------------------------------------------------------------*/ @@ -173,12 +175,11 @@ void arm_dct4_f32( /* pbuff initialized to input buffer */ pbuff = pInlineBuffer; -#if defined (ARM_MATH_DSP) - /* Run the below code for Cortex-M4 and Cortex-M3 */ +#if defined (ARM_MATH_LOOPUNROLL) /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ - i = (uint32_t) S->Nby2 >> 2U; + 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. */ @@ -199,7 +200,7 @@ void arm_dct4_f32( *pS1++ = *pbuff++; *pS2-- = *pbuff++; - /* Decrement the loop counter */ + /* Decrement loop counter */ i--; } while (i > 0U); @@ -210,7 +211,7 @@ void arm_dct4_f32( pS1 = pState; /* Initializing the loop counter to N/4 instead of N for loop unrolling */ - i = (uint32_t) S->N >> 2U; + i = S->N >> 2U; /* Processing with loop unrolling 4 times as N is always multiple of 4. * Compute 4 outputs at a time */ @@ -231,12 +232,12 @@ void arm_dct4_f32( * Step2: Calculate RFFT for N-point input * ---------------------------------------------------------- */ /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ - arm_rfft_f32(S->pRfft, pInlineBuffer, pState); + arm_rfft_f32 (S->pRfft, pInlineBuffer, pState); - /*---------------------------------------------------------------------- - * Step3: Multiply the FFT output with the weights. - *----------------------------------------------------------------------*/ - arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_f32 (pState, weights, pState, S->N); /* ----------- Post-processing ---------- */ /* DCT-IV can be obtained from DCT-II by the equation, @@ -245,7 +246,7 @@ void arm_dct4_f32( /* 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 = ((uint32_t) S->N - 1U) >> 2U; + i = (S->N - 1U) >> 2U; /* pbuff initialized to input buffer. */ pbuff = pInlineBuffer; @@ -290,7 +291,7 @@ void arm_dct4_f32( /* If the blockSize is not a multiple of 4, compute any remaining output samples here. ** No loop unrolling is used. */ - i = ((uint32_t) S->N - 1U) % 0x4U; + i = (S->N - 1U) % 0x4U; while (i > 0U) { @@ -298,6 +299,7 @@ void arm_dct4_f32( /* 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++; @@ -306,10 +308,10 @@ void arm_dct4_f32( } - /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ /* Initializing the loop counter to N/4 instead of N for loop unrolling */ - i = (uint32_t) S->N >> 2U; + i = S->N >> 2U; /* pbuff initialized to the pInlineBuffer(now contains the output values) */ pbuff = pInlineBuffer; @@ -337,10 +339,8 @@ void arm_dct4_f32( #else - /* Run the below code for Cortex-M0 */ - /* Initializing the loop counter to N/2 */ - i = (uint32_t) S->Nby2; + i = S->Nby2; do { @@ -361,7 +361,7 @@ void arm_dct4_f32( pS1 = pState; /* Initializing the loop counter */ - i = (uint32_t) S->N; + i = S->N; do { @@ -377,12 +377,12 @@ void arm_dct4_f32( * Step2: Calculate RFFT for N-point input * ---------------------------------------------------------- */ /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ - arm_rfft_f32(S->pRfft, pInlineBuffer, pState); + arm_rfft_f32 (S->pRfft, pInlineBuffer, pState); - /*---------------------------------------------------------------------- - * Step3: Multiply the FFT output with the weights. - *----------------------------------------------------------------------*/ - arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); + /*---------------------------------------------------------------------- + * Step3: Multiply the FFT output with the weights. + *----------------------------------------------------------------------*/ + arm_cmplx_mult_cmplx_f32 (pState, weights, pState, S->N); /* ----------- Post-processing ---------- */ /* DCT-IV can be obtained from DCT-II by the equation, @@ -405,7 +405,7 @@ void arm_dct4_f32( pS1++; /* Initializing the loop counter */ - i = ((uint32_t) S->N - 1U); + i = (S->N - 1U); do { @@ -413,21 +413,20 @@ void arm_dct4_f32( /* 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 */ + /* Decrement loop counter */ i--; } while (i > 0U); + /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ - /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ - - /* Initializing the loop counter */ - i = (uint32_t) S->N; + /* Initializing loop counter */ + i = S->N; - /* pbuff initialized to the pInlineBuffer(now contains the output values) */ + /* pbuff initialized to the pInlineBuffer (now contains the output values) */ pbuff = pInlineBuffer; do @@ -436,14 +435,14 @@ void arm_dct4_f32( in = *pbuff; *pbuff++ = in * S->normalize; - /* Decrement the loop counter */ + /* Decrement loop counter */ i--; } while (i > 0U); -#endif /* #if defined (ARM_MATH_DSP) */ +#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ } /** - * @} end of DCT4_IDCT4 group - */ + @} end of DCT4_IDCT4 group + */ |