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 /*

  * 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 */