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 /*

  * jfdctfst.c

  *

  * Copyright (C) 1994-1996, 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

  * forward DCT (Discrete Cosine Transform).

  *

  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT

  * on each column.  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 jfdctint.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.

  *

  * Again to save a few shifts, the intermediate results between pass 1 and

  * pass 2 are not upscaled, but are represented only to integral precision.

  *

  * 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).

  */

 #define CONST_BITS  8

 /* 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_0_382683433  ((INT32)   98)		/* FIX(0.382683433) */

 #define FIX_0_541196100  ((INT32)  139)		/* FIX(0.541196100) */

 #define FIX_0_707106781  ((INT32)  181)		/* FIX(0.707106781) */

 #define FIX_1_306562965  ((INT32)  334)		/* FIX(1.306562965) */

 #else

 #define FIX_0_382683433  FIX(0.382683433)

 #define FIX_0_541196100  FIX(0.541196100)

 #define FIX_0_707106781  FIX(0.707106781)

 #define FIX_1_306562965  FIX(1.306562965)

 #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))

 /*

  * Perform the forward DCT on one block of samples.

  */

 GLOBAL(void)

 jpeg_fdct_ifast (DCTELEM * data)

 {

   DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

   DCTELEM tmp10, tmp11, tmp12, tmp13;

   DCTELEM z1, z2, z3, z4, z5, z11, z13;

   DCTELEM *dataptr;

   int ctr;

   SHIFT_TEMPS

   /* Pass 1: process rows. */

   dataptr = data;

   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {

     tmp0 = dataptr[0] + dataptr[7];

     tmp7 = dataptr[0] - dataptr[7];

     tmp1 = dataptr[1] + dataptr[6];

     tmp6 = dataptr[1] - dataptr[6];

     tmp2 = dataptr[2] + dataptr[5];

     tmp5 = dataptr[2] - dataptr[5];

     tmp3 = dataptr[3] + dataptr[4];

     tmp4 = dataptr[3] - dataptr[4];

     /* Even part */

     tmp10 = tmp0 + tmp3;	/* phase 2 */

     tmp13 = tmp0 - tmp3;

     tmp11 = tmp1 + tmp2;

     tmp12 = tmp1 - tmp2;

     dataptr[0] = tmp10 + tmp11; /* phase 3 */

     dataptr[4] = tmp10 - tmp11;

     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */

     dataptr[2] = tmp13 + z1;	/* phase 5 */

     dataptr[6] = tmp13 - z1;

     /* Odd part */

     tmp10 = tmp4 + tmp5;	/* phase 2 */

     tmp11 = tmp5 + tmp6;

     tmp12 = tmp6 + tmp7;

     /* The rotator is modified from fig 4-8 to avoid extra negations. */

     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */

     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */

     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */

     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */

     z11 = tmp7 + z3;		/* phase 5 */

     z13 = tmp7 - z3;

     dataptr[5] = z13 + z2;	/* phase 6 */

     dataptr[3] = z13 - z2;

     dataptr[1] = z11 + z4;

     dataptr[7] = z11 - z4;

     dataptr += DCTSIZE;		/* advance pointer to next row */

   }

   /* Pass 2: process columns. */

   dataptr = data;

   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {

     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];

     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];

     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];

     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];

     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];

     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];

     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];

     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];

     /* Even part */

     tmp10 = tmp0 + tmp3;	/* phase 2 */

     tmp13 = tmp0 - tmp3;

     tmp11 = tmp1 + tmp2;

     tmp12 = tmp1 - tmp2;

     dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */

     dataptr[DCTSIZE*4] = tmp10 - tmp11;

     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */

     dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */

     dataptr[DCTSIZE*6] = tmp13 - z1;

     /* Odd part */

     tmp10 = tmp4 + tmp5;	/* phase 2 */

     tmp11 = tmp5 + tmp6;

     tmp12 = tmp6 + tmp7;

     /* The rotator is modified from fig 4-8 to avoid extra negations. */

     z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */

     z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */

     z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */

     z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */

     z11 = tmp7 + z3;		/* phase 5 */

     z13 = tmp7 - z3;

     dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */

     dataptr[DCTSIZE*3] = z13 - z2;

     dataptr[DCTSIZE*1] = z11 + z4;

     dataptr[DCTSIZE*7] = z11 - z4;

     dataptr++;			/* advance pointer to next column */

   }

 }

 #endif /* DCT_IFAST_SUPPORTED */