michael@0: /*
michael@0:  * jfdctflt.c
michael@0:  *
michael@0:  * Copyright (C) 1994-1996, Thomas G. Lane.
michael@0:  * This file is part of the Independent JPEG Group's software.
michael@0:  * For conditions of distribution and use, see the accompanying README file.
michael@0:  *
michael@0:  * This file contains a floating-point implementation of the
michael@0:  * forward DCT (Discrete Cosine Transform).
michael@0:  *
michael@0:  * This implementation should be more accurate than either of the integer
michael@0:  * DCT implementations.  However, it may not give the same results on all
michael@0:  * machines because of differences in roundoff behavior.  Speed will depend
michael@0:  * on the hardware's floating point capacity.
michael@0:  *
michael@0:  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
michael@0:  * on each column.  Direct algorithms are also available, but they are
michael@0:  * much more complex and seem not to be any faster when reduced to code.
michael@0:  *
michael@0:  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
michael@0:  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
michael@0:  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
michael@0:  * JPEG textbook (see REFERENCES section in file README).  The following code
michael@0:  * is based directly on figure 4-8 in P&M.
michael@0:  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
michael@0:  * possible to arrange the computation so that many of the multiplies are
michael@0:  * simple scalings of the final outputs.  These multiplies can then be
michael@0:  * folded into the multiplications or divisions by the JPEG quantization
michael@0:  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
michael@0:  * to be done in the DCT itself.
michael@0:  * The primary disadvantage of this method is that with a fixed-point
michael@0:  * implementation, accuracy is lost due to imprecise representation of the
michael@0:  * scaled quantization values.  However, that problem does not arise if
michael@0:  * we use floating point arithmetic.
michael@0:  */
michael@0: 
michael@0: #define JPEG_INTERNALS
michael@0: #include "jinclude.h"
michael@0: #include "jpeglib.h"
michael@0: #include "jdct.h"		/* Private declarations for DCT subsystem */
michael@0: 
michael@0: #ifdef DCT_FLOAT_SUPPORTED
michael@0: 
michael@0: 
michael@0: /*
michael@0:  * This module is specialized to the case DCTSIZE = 8.
michael@0:  */
michael@0: 
michael@0: #if DCTSIZE != 8
michael@0:   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
michael@0: #endif
michael@0: 
michael@0: 
michael@0: /*
michael@0:  * Perform the forward DCT on one block of samples.
michael@0:  */
michael@0: 
michael@0: GLOBAL(void)
michael@0: jpeg_fdct_float (FAST_FLOAT * data)
michael@0: {
michael@0:   FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
michael@0:   FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
michael@0:   FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
michael@0:   FAST_FLOAT *dataptr;
michael@0:   int ctr;
michael@0: 
michael@0:   /* Pass 1: process rows. */
michael@0: 
michael@0:   dataptr = data;
michael@0:   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
michael@0:     tmp0 = dataptr[0] + dataptr[7];
michael@0:     tmp7 = dataptr[0] - dataptr[7];
michael@0:     tmp1 = dataptr[1] + dataptr[6];
michael@0:     tmp6 = dataptr[1] - dataptr[6];
michael@0:     tmp2 = dataptr[2] + dataptr[5];
michael@0:     tmp5 = dataptr[2] - dataptr[5];
michael@0:     tmp3 = dataptr[3] + dataptr[4];
michael@0:     tmp4 = dataptr[3] - dataptr[4];
michael@0:     
michael@0:     /* Even part */
michael@0:     
michael@0:     tmp10 = tmp0 + tmp3;	/* phase 2 */
michael@0:     tmp13 = tmp0 - tmp3;
michael@0:     tmp11 = tmp1 + tmp2;
michael@0:     tmp12 = tmp1 - tmp2;
michael@0:     
michael@0:     dataptr[0] = tmp10 + tmp11; /* phase 3 */
michael@0:     dataptr[4] = tmp10 - tmp11;
michael@0:     
michael@0:     z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
michael@0:     dataptr[2] = tmp13 + z1;	/* phase 5 */
michael@0:     dataptr[6] = tmp13 - z1;
michael@0:     
michael@0:     /* Odd part */
michael@0: 
michael@0:     tmp10 = tmp4 + tmp5;	/* phase 2 */
michael@0:     tmp11 = tmp5 + tmp6;
michael@0:     tmp12 = tmp6 + tmp7;
michael@0: 
michael@0:     /* The rotator is modified from fig 4-8 to avoid extra negations. */
michael@0:     z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
michael@0:     z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
michael@0:     z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
michael@0:     z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
michael@0: 
michael@0:     z11 = tmp7 + z3;		/* phase 5 */
michael@0:     z13 = tmp7 - z3;
michael@0: 
michael@0:     dataptr[5] = z13 + z2;	/* phase 6 */
michael@0:     dataptr[3] = z13 - z2;
michael@0:     dataptr[1] = z11 + z4;
michael@0:     dataptr[7] = z11 - z4;
michael@0: 
michael@0:     dataptr += DCTSIZE;		/* advance pointer to next row */
michael@0:   }
michael@0: 
michael@0:   /* Pass 2: process columns. */
michael@0: 
michael@0:   dataptr = data;
michael@0:   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
michael@0:     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
michael@0:     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
michael@0:     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
michael@0:     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
michael@0:     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
michael@0:     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
michael@0:     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
michael@0:     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
michael@0:     
michael@0:     /* Even part */
michael@0:     
michael@0:     tmp10 = tmp0 + tmp3;	/* phase 2 */
michael@0:     tmp13 = tmp0 - tmp3;
michael@0:     tmp11 = tmp1 + tmp2;
michael@0:     tmp12 = tmp1 - tmp2;
michael@0:     
michael@0:     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
michael@0:     dataptr[DCTSIZE*4] = tmp10 - tmp11;
michael@0:     
michael@0:     z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
michael@0:     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
michael@0:     dataptr[DCTSIZE*6] = tmp13 - z1;
michael@0:     
michael@0:     /* Odd part */
michael@0: 
michael@0:     tmp10 = tmp4 + tmp5;	/* phase 2 */
michael@0:     tmp11 = tmp5 + tmp6;
michael@0:     tmp12 = tmp6 + tmp7;
michael@0: 
michael@0:     /* The rotator is modified from fig 4-8 to avoid extra negations. */
michael@0:     z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
michael@0:     z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
michael@0:     z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
michael@0:     z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
michael@0: 
michael@0:     z11 = tmp7 + z3;		/* phase 5 */
michael@0:     z13 = tmp7 - z3;
michael@0: 
michael@0:     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
michael@0:     dataptr[DCTSIZE*3] = z13 - z2;
michael@0:     dataptr[DCTSIZE*1] = z11 + z4;
michael@0:     dataptr[DCTSIZE*7] = z11 - z4;
michael@0: 
michael@0:     dataptr++;			/* advance pointer to next column */
michael@0:   }
michael@0: }
michael@0: 
michael@0: #endif /* DCT_FLOAT_SUPPORTED */