/* 
 * jidctint.c 
 * 
 * Copyright (C) 1991-1998, 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 slow-but-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 an algorithm described in 
 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 
 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 
 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 
 * The primary algorithm described there uses 11 multiplies and 29 adds. 
 * We use their alternate method with 12 multiplies and 32 adds. 
 * The advantage of this method is that no data path contains more than one 
 * multiplication; this allows a very simple and accurate implementation in 
 * scaled fixed-point arithmetic, with a minimal number of shifts. 
 */ 
 
#define JPEG_INTERNALS 
#include "jinclude.h" 
#include "jpeglib.h" 
#include "jdct.h"		/* Private declarations for DCT subsystem */ 
 
#ifdef DCT_ISLOW_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 
 
 
/* 
 * The poop on this scaling stuff is as follows: 
 * 
 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N) 
 * larger than the true IDCT outputs.  The final outputs are therefore 
 * a factor of N larger than desired; since N=8 this can be cured by 
 * a simple right shift at the end of the algorithm.  The advantage of 
 * this arrangement is that we save two multiplications per 1-D IDCT, 
 * because the y0 and y4 inputs need not be divided by sqrt(N). 
 * 
 * We have to do addition and subtraction of the integer inputs, which 
 * is no problem, and multiplication by fractional constants, which is 
 * a problem to do in integer arithmetic.  We multiply all the constants 
 * by CONST_SCALE and convert them to integer constants (thus retaining 
 * CONST_BITS bits of precision in the constants).  After doing a 
 * multiplication we have to divide the product by CONST_SCALE, with proper 
 * rounding, to produce the correct output.  This division can be done 
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting 
 * as long as possible so that partial sums can be added together with 
 * full fractional precision. 
 * 
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 
 * they are represented to better-than-integral precision.  These outputs 
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 
 * with the recommended scaling.  (To scale up 12-bit sample data further, an 
 * intermediate INT32 array would be needed.) 
 * 
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis 
 * shows that the values given below are the most effective. 
 */ 
 
#if BITS_IN_JSAMPLE == 8 
#define CONST_BITS  13 
#define PASS1_BITS  2 
#else 
#define CONST_BITS  13 
#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 == 13 
#define FIX_0_298631336  ((INT32)  2446)	/* FIX(0.298631336) */ 
#define FIX_0_390180644  ((INT32)  3196)	/* FIX(0.390180644) */ 
#define FIX_0_541196100  ((INT32)  4433)	/* FIX(0.541196100) */ 
#define FIX_0_765366865  ((INT32)  6270)	/* FIX(0.765366865) */ 
#define FIX_0_899976223  ((INT32)  7373)	/* FIX(0.899976223) */ 
#define FIX_1_175875602  ((INT32)  9633)	/* FIX(1.175875602) */ 
#define FIX_1_501321110  ((INT32)  12299)	/* FIX(1.501321110) */ 
#define FIX_1_847759065  ((INT32)  15137)	/* FIX(1.847759065) */ 
#define FIX_1_961570560  ((INT32)  16069)	/* FIX(1.961570560) */ 
#define FIX_2_053119869  ((INT32)  16819)	/* FIX(2.053119869) */ 
#define FIX_2_562915447  ((INT32)  20995)	/* FIX(2.562915447) */ 
#define FIX_3_072711026  ((INT32)  25172)	/* FIX(3.072711026) */ 
#else 
#define FIX_0_298631336  FIX(0.298631336) 
#define FIX_0_390180644  FIX(0.390180644) 
#define FIX_0_541196100  FIX(0.541196100) 
#define FIX_0_765366865  FIX(0.765366865) 
#define FIX_0_899976223  FIX(0.899976223) 
#define FIX_1_175875602  FIX(1.175875602) 
#define FIX_1_501321110  FIX(1.501321110) 
#define FIX_1_847759065  FIX(1.847759065) 
#define FIX_1_961570560  FIX(1.961570560) 
#define FIX_2_053119869  FIX(2.053119869) 
#define FIX_2_562915447  FIX(2.562915447) 
#define FIX_3_072711026  FIX(3.072711026) 
#endif 
 
 
/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. 
 * For 8-bit samples with the recommended scaling, all the variable 
 * and constant values involved are no more than 16 bits wide, so a 
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 
 * For 12-bit samples, a full 32-bit multiplication will be needed. 
 */ 
 
#if BITS_IN_JSAMPLE == 8 
#define MULTIPLY(var,const)  MULTIPLY16C16(var,const) 
#else 
#define MULTIPLY(var,const)  ((var) * (const)) 
#endif 
 
 
/* Dequantize a coefficient by multiplying it by the multiplier-table 
 * entry; produce an int result.  In this module, both inputs and result 
 * are 16 bits or less, so either int or short multiply will work. 
 */ 
 
#define DEQUANTIZE(coef,quantval)  (((ISLOW_MULT_TYPE) (coef)) * (quantval)) 
 
 
/* 
 * Perform dequantization and inverse DCT on one block of coefficients. 
 */ 
 
GLOBAL(void) 
jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr, 
		 JCOEFPTR coef_block, 
		 JSAMPARRAY output_buf, JDIMENSION output_col) 
{ 
  INT32 tmp0, tmp1, tmp2, tmp3; 
  INT32 tmp10, tmp11, tmp12, tmp13; 
  INT32 z1, z2, z3, z4, z5; 
  JCOEFPTR inptr; 
  ISLOW_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 
 
  /* Pass 1: process columns from input, store into work array. */ 
  /* Note results are scaled up by sqrt(8) compared to a true IDCT; */ 
  /* furthermore, we scale the results by 2**PASS1_BITS. */ 
 
  inptr = coef_block; 
  quantptr = (ISLOW_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 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS; 
       
      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: reverse the even part of the forward DCT. */ 
    /* The rotator is sqrt(2)*c(-6). */ 
     
    z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 
    z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 
     
    z1 = MULTIPLY(z2 + z3, FIX_0_541196100); 
    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); 
    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); 
     
    z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 
    z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 
 
    tmp0 = (z2 + z3) << CONST_BITS; 
    tmp1 = (z2 - z3) << CONST_BITS; 
     
    tmp10 = tmp0 + tmp3; 
    tmp13 = tmp0 - tmp3; 
    tmp11 = tmp1 + tmp2; 
    tmp12 = tmp1 - tmp2; 
     
    /* Odd part per figure 8; the matrix is unitary and hence its 
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively. 
     */ 
     
    tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 
    tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 
    tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 
    tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 
     
    z1 = tmp0 + tmp3; 
    z2 = tmp1 + tmp2; 
    z3 = tmp0 + tmp2; 
    z4 = tmp1 + tmp3; 
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 
     
    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 
    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 
    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 
    tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 
     
    z3 += z5; 
    z4 += z5; 
     
    tmp0 += z1 + z3; 
    tmp1 += z2 + z4; 
    tmp2 += z2 + z3; 
    tmp3 += z1 + z4; 
     
    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ 
     
    wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS); 
    wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS); 
    wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS); 
    wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS); 
    wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS); 
    wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS); 
    wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS); 
    wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS); 
     
    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[(int) DESCALE((INT32) 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: reverse the even part of the forward DCT. */ 
    /* The rotator is sqrt(2)*c(-6). */ 
     
    z2 = (INT32) wsptr[2]; 
    z3 = (INT32) wsptr[6]; 
     
    z1 = MULTIPLY(z2 + z3, FIX_0_541196100); 
    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); 
    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); 
     
    tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS; 
    tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS; 
     
    tmp10 = tmp0 + tmp3; 
    tmp13 = tmp0 - tmp3; 
    tmp11 = tmp1 + tmp2; 
    tmp12 = tmp1 - tmp2; 
     
    /* Odd part per figure 8; the matrix is unitary and hence its 
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively. 
     */ 
     
    tmp0 = (INT32) wsptr[7]; 
    tmp1 = (INT32) wsptr[5]; 
    tmp2 = (INT32) wsptr[3]; 
    tmp3 = (INT32) wsptr[1]; 
     
    z1 = tmp0 + tmp3; 
    z2 = tmp1 + tmp2; 
    z3 = tmp0 + tmp2; 
    z4 = tmp1 + tmp3; 
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 
     
    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 
    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 
    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 
    tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 
     
    z3 += z5; 
    z4 += z5; 
     
    tmp0 += z1 + z3; 
    tmp1 += z2 + z4; 
    tmp2 += z2 + z3; 
    tmp3 += z1 + z4; 
     
    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ 
     
    outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
    outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0, 
					  CONST_BITS+PASS1_BITS+3) 
			    & RANGE_MASK]; 
     
    wsptr += DCTSIZE;		/* advance pointer to next row */ 
  } 
} 
 
#endif /* DCT_ISLOW_SUPPORTED */ 
