/* 
 * jidctflt.c 
 * 
 * Copyright (C) 1994-1998, Thomas G. Lane. 
 * This file is part of the Independent JPEG Group's software. 
 * For conditions of distribution and use, see the accompanying README file. 
 * 
 * This file contains a floating-point implementation of the 
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine 
 * must also perform dequantization of the input coefficients. 
 * 
 * This implementation should be more accurate than either of the integer 
 * IDCT implementations.  However, it may not give the same results on all 
 * machines because of differences in roundoff behavior.  Speed will depend 
 * on the hardware's floating point capacity. 
 * 
 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT 
 * on each row (or vice versa, but it's more convenient to emit a row at 
 * a time).  Direct algorithms are also available, but they are much more 
 * complex and seem not to be any faster when reduced to code. 
 * 
 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 
 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in 
 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 
 * JPEG textbook (see REFERENCES section in file README).  The following code 
 * is based directly on figure 4-8 in P&M. 
 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 
 * possible to arrange the computation so that many of the multiplies are 
 * simple scalings of the final outputs.  These multiplies can then be 
 * folded into the multiplications or divisions by the JPEG quantization 
 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds 
 * to be done in the DCT itself. 
 * The primary disadvantage of this method is that with a fixed-point 
 * implementation, accuracy is lost due to imprecise representation of the 
 * scaled quantization values.  However, that problem does not arise if 
 * we use floating point arithmetic. 
 */ 
 
#define JPEG_INTERNALS 
#include "jinclude.h" 
#include "jpeglib.h" 
#include "jdct.h"		/* Private declarations for DCT subsystem */ 
 
#ifdef DCT_FLOAT_SUPPORTED 
 
 
/* 
 * This module is specialized to the case DCTSIZE = 8. 
 */ 
 
#if DCTSIZE != 8 
  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 
#endif 
 
 
/* Dequantize a coefficient by multiplying it by the multiplier-table 
 * entry; produce a float result. 
 */ 
 
#define DEQUANTIZE(coef,quantval)  (((FAST_FLOAT) (coef)) * (quantval)) 
 
 
/* 
 * Perform dequantization and inverse DCT on one block of coefficients. 
 */ 
 
GLOBAL(void) 
jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr, 
		 JCOEFPTR coef_block, 
		 JSAMPARRAY output_buf, JDIMENSION output_col) 
{ 
  FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 
  FAST_FLOAT tmp10, tmp11, tmp12, tmp13; 
  FAST_FLOAT z5, z10, z11, z12, z13; 
  JCOEFPTR inptr; 
  FLOAT_MULT_TYPE * quantptr; 
  FAST_FLOAT * wsptr; 
  JSAMPROW outptr; 
  JSAMPLE *range_limit = IDCT_range_limit(cinfo); 
  int ctr; 
  FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */ 
  SHIFT_TEMPS 
 
  /* Pass 1: process columns from input, store into work array. */ 
 
  inptr = coef_block; 
  quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table; 
  wsptr = workspace; 
  for (ctr = DCTSIZE; ctr > 0; ctr--) { 
    /* Due to quantization, we will usually find that many of the input 
     * coefficients are zero, especially the AC terms.  We can exploit this 
     * by short-circuiting the IDCT calculation for any column in which all 
     * the AC terms are zero.  In that case each output is equal to the 
     * DC coefficient (with scale factor as needed). 
     * With typical images and quantization tables, half or more of the 
     * column DCT calculations can be simplified this way. 
     */ 
     
    if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 
	inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 
	inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 
	inptr[DCTSIZE*7] == 0) { 
      /* AC terms all zero */ 
      FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 
       
      wsptr[DCTSIZE*0] = dcval; 
      wsptr[DCTSIZE*1] = dcval; 
      wsptr[DCTSIZE*2] = dcval; 
      wsptr[DCTSIZE*3] = dcval; 
      wsptr[DCTSIZE*4] = dcval; 
      wsptr[DCTSIZE*5] = dcval; 
      wsptr[DCTSIZE*6] = dcval; 
      wsptr[DCTSIZE*7] = dcval; 
       
      inptr++;			/* advance pointers to next column */ 
      quantptr++; 
      wsptr++; 
      continue; 
    } 
     
    /* Even part */ 
 
    tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 
    tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 
    tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 
    tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 
 
    tmp10 = tmp0 + tmp2;	/* phase 3 */ 
    tmp11 = tmp0 - tmp2; 
 
    tmp13 = tmp1 + tmp3;	/* phases 5-3 */ 
    tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */ 
 
    tmp0 = tmp10 + tmp13;	/* phase 2 */ 
    tmp3 = tmp10 - tmp13; 
    tmp1 = tmp11 + tmp12; 
    tmp2 = tmp11 - tmp12; 
     
    /* Odd part */ 
 
    tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 
    tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 
    tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 
    tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 
 
    z13 = tmp6 + tmp5;		/* phase 6 */ 
    z10 = tmp6 - tmp5; 
    z11 = tmp4 + tmp7; 
    z12 = tmp4 - tmp7; 
 
    tmp7 = z11 + z13;		/* phase 5 */ 
    tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ 
 
    z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ 
    tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ 
    tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ 
 
    tmp6 = tmp12 - tmp7;	/* phase 2 */ 
    tmp5 = tmp11 - tmp6; 
    tmp4 = tmp10 + tmp5; 
 
    wsptr[DCTSIZE*0] = tmp0 + tmp7; 
    wsptr[DCTSIZE*7] = tmp0 - tmp7; 
    wsptr[DCTSIZE*1] = tmp1 + tmp6; 
    wsptr[DCTSIZE*6] = tmp1 - tmp6; 
    wsptr[DCTSIZE*2] = tmp2 + tmp5; 
    wsptr[DCTSIZE*5] = tmp2 - tmp5; 
    wsptr[DCTSIZE*4] = tmp3 + tmp4; 
    wsptr[DCTSIZE*3] = tmp3 - tmp4; 
 
    inptr++;			/* advance pointers to next column */ 
    quantptr++; 
    wsptr++; 
  } 
   
  /* Pass 2: process rows from work array, store into output array. */ 
  /* Note that we must descale the results by a factor of 8 == 2**3. */ 
 
  wsptr = workspace; 
  for (ctr = 0; ctr < DCTSIZE; ctr++) { 
    outptr = output_buf[ctr] + output_col; 
    /* Rows of zeroes can be exploited in the same way as we did with columns. 
     * However, the column calculation has created many nonzero AC terms, so 
     * the simplification applies less often (typically 5% to 10% of the time). 
     * And testing floats for zero is relatively expensive, so we don't bother. 
     */ 
     
    /* Even part */ 
 
    tmp10 = wsptr[0] + wsptr[4]; 
    tmp11 = wsptr[0] - wsptr[4]; 
 
    tmp13 = wsptr[2] + wsptr[6]; 
    tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13; 
 
    tmp0 = tmp10 + tmp13; 
    tmp3 = tmp10 - tmp13; 
    tmp1 = tmp11 + tmp12; 
    tmp2 = tmp11 - tmp12; 
 
    /* Odd part */ 
 
    z13 = wsptr[5] + wsptr[3]; 
    z10 = wsptr[5] - wsptr[3]; 
    z11 = wsptr[1] + wsptr[7]; 
    z12 = wsptr[1] - wsptr[7]; 
 
    tmp7 = z11 + z13; 
    tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); 
 
    z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ 
    tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ 
    tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ 
 
    tmp6 = tmp12 - tmp7; 
    tmp5 = tmp11 - tmp6; 
    tmp4 = tmp10 + tmp5; 
 
    /* Final output stage: scale down by a factor of 8 and range-limit */ 
 
    outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3) 
			    & RANGE_MASK]; 
    outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3) 
			    & RANGE_MASK]; 
    outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3) 
			    & RANGE_MASK]; 
    outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3) 
			    & RANGE_MASK]; 
    outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3) 
			    & RANGE_MASK]; 
    outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3) 
			    & RANGE_MASK]; 
    outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3) 
			    & RANGE_MASK]; 
    outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3) 
			    & RANGE_MASK]; 
     
    wsptr += DCTSIZE;		/* advance pointer to next row */ 
  } 
} 
 
#endif /* DCT_FLOAT_SUPPORTED */ 
