/* 
 * 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 */ 
