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