/* 
 * jidctfst.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 fast, not so accurate integer implementation of the 
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine 
 * must also perform dequantization of the input coefficients. 
 * 
 * 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 fixed-point math, 
 * accuracy is lost due to imprecise representation of the scaled 
 * quantization values.  The smaller the quantization table entry, the less 
 * precise the scaled value, so this implementation does worse with high- 
 * quality-setting files than with low-quality ones. 
 */ 
 
#define JPEG_INTERNALS 
#include "jinclude.h" 
#include "jpeglib.h" 
#include "jdct.h"		/* Private declarations for DCT subsystem */ 
 
#ifdef DCT_IFAST_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 
 
 
/* Scaling decisions are generally the same as in the LL&M algorithm; 
 * see jidctint.c for more details.  However, we choose to descale 
 * (right shift) multiplication products as soon as they are formed, 
 * rather than carrying additional fractional bits into subsequent additions. 
 * This compromises accuracy slightly, but it lets us save a few shifts. 
 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 
 * everywhere except in the multiplications proper; this saves a good deal 
 * of work on 16-bit-int machines. 
 * 
 * The dequantized coefficients are not integers because the AA&N scaling 
 * factors have been incorporated.  We represent them scaled up by PASS1_BITS, 
 * so that the first and second IDCT rounds have the same input scaling. 
 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to 
 * avoid a descaling shift; this compromises accuracy rather drastically 
 * for small quantization table entries, but it saves a lot of shifts. 
 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, 
 * so we use a much larger scaling factor to preserve accuracy. 
 * 
 * A final compromise is to represent the multiplicative constants to only 
 * 8 fractional bits, rather than 13.  This saves some shifting work on some 
 * machines, and may also reduce the cost of multiplication (since there 
 * are fewer one-bits in the constants). 
 */ 
 
#if BITS_IN_JSAMPLE == 8 
#define CONST_BITS  8 
#define PASS1_BITS  2 
#else 
#define CONST_BITS  8 
#define PASS1_BITS  1		/* lose a little precision to avoid overflow */ 
#endif 
 
/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 
 * causing a lot of useless floating-point operations at run time. 
 * To get around this we use the following pre-calculated constants. 
 * If you change CONST_BITS you may want to add appropriate values. 
 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 
 */ 
 
#if CONST_BITS == 8 
#define FIX_1_082392200  ((INT32)  277)		/* FIX(1.082392200) */ 
#define FIX_1_414213562  ((INT32)  362)		/* FIX(1.414213562) */ 
#define FIX_1_847759065  ((INT32)  473)		/* FIX(1.847759065) */ 
#define FIX_2_613125930  ((INT32)  669)		/* FIX(2.613125930) */ 
#else 
#define FIX_1_082392200  FIX(1.082392200) 
#define FIX_1_414213562  FIX(1.414213562) 
#define FIX_1_847759065  FIX(1.847759065) 
#define FIX_2_613125930  FIX(2.613125930) 
#endif 
 
 
/* We can gain a little more speed, with a further compromise in accuracy, 
 * by omitting the addition in a descaling shift.  This yields an incorrectly 
 * rounded result half the time... 
 */ 
 
#ifndef USE_ACCURATE_ROUNDING 
#undef DESCALE 
#define DESCALE(x,n)  RIGHT_SHIFT(x, n) 
#endif 
 
 
/* Multiply a DCTELEM variable by an INT32 constant, and immediately 
 * descale to yield a DCTELEM result. 
 */ 
 
#define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 
 
 
/* Dequantize a coefficient by multiplying it by the multiplier-table 
 * entry; produce a DCTELEM result.  For 8-bit data a 16x16->16 
 * multiplication will do.  For 12-bit data, the multiplier table is 
 * declared INT32, so a 32-bit multiply will be used. 
 */ 
 
#if BITS_IN_JSAMPLE == 8 
#define DEQUANTIZE(coef,quantval)  (((IFAST_MULT_TYPE) (coef)) * (quantval)) 
#else 
#define DEQUANTIZE(coef,quantval)  \ 
	DESCALE((coef)*(quantval), IFAST_SCALE_BITS-PASS1_BITS) 
#endif 
 
 
/* Like DESCALE, but applies to a DCTELEM and produces an int. 
 * We assume that int right shift is unsigned if INT32 right shift is. 
 */ 
 
#ifdef RIGHT_SHIFT_IS_UNSIGNED 
#define ISHIFT_TEMPS	DCTELEM ishift_temp; 
#if BITS_IN_JSAMPLE == 8 
#define DCTELEMBITS  16		/* DCTELEM may be 16 or 32 bits */ 
#else 
#define DCTELEMBITS  32		/* DCTELEM must be 32 bits */ 
#endif 
#define IRIGHT_SHIFT(x,shft)  \ 
    ((ishift_temp = (x)) < 0 ? \ 
     (ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \ 
     (ishift_temp >> (shft))) 
#else 
#define ISHIFT_TEMPS 
#define IRIGHT_SHIFT(x,shft)	((x) >> (shft)) 
#endif 
 
#ifdef USE_ACCURATE_ROUNDING 
#define IDESCALE(x,n)  ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n)) 
#else 
#define IDESCALE(x,n)  ((int) IRIGHT_SHIFT(x, n)) 
#endif 
 
 
/* 
 * Perform dequantization and inverse DCT on one block of coefficients. 
 */ 
 
GLOBAL(void) 
jpeg_idct_ifast (j_decompress_ptr cinfo, jpeg_component_info * compptr, 
		 JCOEFPTR coef_block, 
		 JSAMPARRAY output_buf, JDIMENSION output_col) 
{ 
  DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 
  DCTELEM tmp10, tmp11, tmp12, tmp13; 
  DCTELEM z5, z10, z11, z12, z13; 
  JCOEFPTR inptr; 
  IFAST_MULT_TYPE * quantptr; 
  int * wsptr; 
  JSAMPROW outptr; 
  JSAMPLE *range_limit = IDCT_range_limit(cinfo); 
  int ctr; 
  int workspace[DCTSIZE2];	/* buffers data between passes */ 
  SHIFT_TEMPS			/* for DESCALE */ 
  ISHIFT_TEMPS			/* for IDESCALE */ 
 
  /* Pass 1: process columns from input, store into work array. */ 
 
  inptr = coef_block; 
  quantptr = (IFAST_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 */ 
      int dcval = (int) 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 = MULTIPLY(tmp1 - tmp3, FIX_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 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 
 
    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 
    tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 
    tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 
 
    tmp6 = tmp12 - tmp7;	/* phase 2 */ 
    tmp5 = tmp11 - tmp6; 
    tmp4 = tmp10 + tmp5; 
 
    wsptr[DCTSIZE*0] = (int) (tmp0 + tmp7); 
    wsptr[DCTSIZE*7] = (int) (tmp0 - tmp7); 
    wsptr[DCTSIZE*1] = (int) (tmp1 + tmp6); 
    wsptr[DCTSIZE*6] = (int) (tmp1 - tmp6); 
    wsptr[DCTSIZE*2] = (int) (tmp2 + tmp5); 
    wsptr[DCTSIZE*5] = (int) (tmp2 - tmp5); 
    wsptr[DCTSIZE*4] = (int) (tmp3 + tmp4); 
    wsptr[DCTSIZE*3] = (int) (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, */ 
  /* and also undo the PASS1_BITS scaling. */ 
 
  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). 
     * On machines with very fast multiplication, it's possible that the 
     * test takes more time than it's worth.  In that case this section 
     * may be commented out. 
     */ 
     
#ifndef NO_ZERO_ROW_TEST 
    if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && 
	wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { 
      /* AC terms all zero */ 
      JSAMPLE dcval = range_limit[IDESCALE(wsptr[0], PASS1_BITS+3) 
				  & RANGE_MASK]; 
       
      outptr[0] = dcval; 
      outptr[1] = dcval; 
      outptr[2] = dcval; 
      outptr[3] = dcval; 
      outptr[4] = dcval; 
      outptr[5] = dcval; 
      outptr[6] = dcval; 
      outptr[7] = dcval; 
 
      wsptr += DCTSIZE;		/* advance pointer to next row */ 
      continue; 
    } 
#endif 
     
    /* Even part */ 
 
    tmp10 = ((DCTELEM) wsptr[0] + (DCTELEM) wsptr[4]); 
    tmp11 = ((DCTELEM) wsptr[0] - (DCTELEM) wsptr[4]); 
 
    tmp13 = ((DCTELEM) wsptr[2] + (DCTELEM) wsptr[6]); 
    tmp12 = MULTIPLY((DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562) 
	    - tmp13; 
 
    tmp0 = tmp10 + tmp13; 
    tmp3 = tmp10 - tmp13; 
    tmp1 = tmp11 + tmp12; 
    tmp2 = tmp11 - tmp12; 
 
    /* Odd part */ 
 
    z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; 
    z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; 
    z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; 
    z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; 
 
    tmp7 = z11 + z13;		/* phase 5 */ 
    tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ 
 
    z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ 
    tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ 
    tmp12 = MULTIPLY(z10, - FIX_2_613125930) + z5; /* -2*(c2+c6) */ 
 
    tmp6 = tmp12 - tmp7;	/* phase 2 */ 
    tmp5 = tmp11 - tmp6; 
    tmp4 = tmp10 + tmp5; 
 
    /* Final output stage: scale down by a factor of 8 and range-limit */ 
 
    outptr[0] = range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[7] = range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[1] = range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[6] = range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[2] = range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[5] = range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[4] = range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[3] = range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS+3) 
			    & RANGE_MASK]; 
 
    wsptr += DCTSIZE;		/* advance pointer to next row */ 
  } 
} 
 
#endif /* DCT_IFAST_SUPPORTED */ 
