/* * 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 */