/* * 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 */