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/*
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 * jfdctfst.c
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 *
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 * Copyright (C) 1994-1996, Thomas G. Lane.
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 * This file is part of the Independent JPEG Group's software.
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 * For conditions of distribution and use, see the accompanying README file.
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 *
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 * This file contains a fast, not so accurate integer implementation of the
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 * forward DCT (Discrete Cosine Transform).
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 *
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 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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 * on each column.  Direct algorithms are also available, but they are
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 * much more complex and seem not to be any faster when reduced to code.
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 *
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 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
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 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
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 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
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 * JPEG textbook (see REFERENCES section in file README).  The following code
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 * is based directly on figure 4-8 in P&M.
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 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
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 * possible to arrange the computation so that many of the multiplies are
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 * simple scalings of the final outputs.  These multiplies can then be
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 * folded into the multiplications or divisions by the JPEG quantization
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 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
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 * to be done in the DCT itself.
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 * The primary disadvantage of this method is that with fixed-point math,
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 * accuracy is lost due to imprecise representation of the scaled
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 * quantization values.  The smaller the quantization table entry, the less
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 * precise the scaled value, so this implementation does worse with high-
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 * quality-setting files than with low-quality ones.
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 */
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/**
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 * @file jfdctfst.c
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 * Independent JPEG Group's fast AAN dct.
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 */
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#include <stdlib.h>
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#include <stdio.h>
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#include "common.h"
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#include "dsputil.h"
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#define DCTSIZE 8
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#define GLOBAL(x) x
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#define RIGHT_SHIFT(x, n) ((x) >> (n))
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#define SHIFT_TEMPS
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/*
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 * This module is specialized to the case DCTSIZE = 8.
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 */
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#if DCTSIZE != 8
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  Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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#endif
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/* Scaling decisions are generally the same as in the LL&M algorithm;
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 * see jfdctint.c for more details.  However, we choose to descale
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 * (right shift) multiplication products as soon as they are formed,
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 * rather than carrying additional fractional bits into subsequent additions.
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 * This compromises accuracy slightly, but it lets us save a few shifts.
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 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
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 * everywhere except in the multiplications proper; this saves a good deal
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 * of work on 16-bit-int machines.
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 *
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 * Again to save a few shifts, the intermediate results between pass 1 and
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 * pass 2 are not upscaled, but are represented only to integral precision.
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 *
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 * A final compromise is to represent the multiplicative constants to only
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 * 8 fractional bits, rather than 13.  This saves some shifting work on some
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 * machines, and may also reduce the cost of multiplication (since there
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 * are fewer one-bits in the constants).
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 */
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#define CONST_BITS  8
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/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
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 * causing a lot of useless floating-point operations at run time.
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 * To get around this we use the following pre-calculated constants.
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 * If you change CONST_BITS you may want to add appropriate values.
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 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
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 */
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#if CONST_BITS == 8
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#define FIX_0_382683433  ((int32_t)   98)                /* FIX(0.382683433) */
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#define FIX_0_541196100  ((int32_t)  139)                /* FIX(0.541196100) */
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#define FIX_0_707106781  ((int32_t)  181)                /* FIX(0.707106781) */
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#define FIX_1_306562965  ((int32_t)  334)                /* FIX(1.306562965) */
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#else
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#define FIX_0_382683433  FIX(0.382683433)
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#define FIX_0_541196100  FIX(0.541196100)
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#define FIX_0_707106781  FIX(0.707106781)
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#define FIX_1_306562965  FIX(1.306562965)
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#endif
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/* We can gain a little more speed, with a further compromise in accuracy,
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 * by omitting the addition in a descaling shift.  This yields an incorrectly
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 * rounded result half the time...
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 */
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#ifndef USE_ACCURATE_ROUNDING
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#undef DESCALE
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#define DESCALE(x,n)  RIGHT_SHIFT(x, n)
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#endif
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/* Multiply a DCTELEM variable by an int32_t constant, and immediately
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 * descale to yield a DCTELEM result.
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 */
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#define MULTIPLY(var,const)  ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
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/*
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 * Perform the forward DCT on one block of samples.
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 */
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GLOBAL(void)
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fdct_ifast (DCTELEM * data)
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{
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  DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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  DCTELEM tmp10, tmp11, tmp12, tmp13;
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  DCTELEM z1, z2, z3, z4, z5, z11, z13;
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  DCTELEM *dataptr;
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  int ctr;
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  SHIFT_TEMPS
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  /* Pass 1: process rows. */
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  dataptr = data;
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  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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    tmp0 = dataptr[0] + dataptr[7];
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    tmp7 = dataptr[0] - dataptr[7];
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    tmp1 = dataptr[1] + dataptr[6];
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    tmp6 = dataptr[1] - dataptr[6];
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    tmp2 = dataptr[2] + dataptr[5];
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    tmp5 = dataptr[2] - dataptr[5];
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    tmp3 = dataptr[3] + dataptr[4];
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    tmp4 = dataptr[3] - dataptr[4];
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    /* Even part */
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    tmp10 = tmp0 + tmp3;        /* phase 2 */
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    tmp13 = tmp0 - tmp3;
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    tmp11 = tmp1 + tmp2;
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    tmp12 = tmp1 - tmp2;
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    dataptr[0] = tmp10 + tmp11; /* phase 3 */
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    dataptr[4] = tmp10 - tmp11;
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    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
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    dataptr[2] = tmp13 + z1;        /* phase 5 */
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    dataptr[6] = tmp13 - z1;
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    /* Odd part */
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    tmp10 = tmp4 + tmp5;        /* phase 2 */
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    tmp11 = tmp5 + tmp6;
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    tmp12 = tmp6 + tmp7;
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    /* The rotator is modified from fig 4-8 to avoid extra negations. */
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    z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
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    z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
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    z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
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    z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
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    z11 = tmp7 + z3;                /* phase 5 */
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    z13 = tmp7 - z3;
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    dataptr[5] = z13 + z2;        /* phase 6 */
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    dataptr[3] = z13 - z2;
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    dataptr[1] = z11 + z4;
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    dataptr[7] = z11 - z4;
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    dataptr += DCTSIZE;                /* advance pointer to next row */
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  }
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  /* Pass 2: process columns. */
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  dataptr = data;
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  for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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    tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
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    tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
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    tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
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    tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
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    tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
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    tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
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    tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
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    tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
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    /* Even part */
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    tmp10 = tmp0 + tmp3;        /* phase 2 */
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    tmp13 = tmp0 - tmp3;
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    tmp11 = tmp1 + tmp2;
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    tmp12 = tmp1 - tmp2;
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    dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
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    dataptr[DCTSIZE*4] = tmp10 - tmp11;
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    z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
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    dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
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    dataptr[DCTSIZE*6] = tmp13 - z1;
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    /* Odd part */
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    tmp10 = tmp4 + tmp5;        /* phase 2 */
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    tmp11 = tmp5 + tmp6;
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    tmp12 = tmp6 + tmp7;
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    /* The rotator is modified from fig 4-8 to avoid extra negations. */
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    z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
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    z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
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    z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
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    z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
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    z11 = tmp7 + z3;                /* phase 5 */
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    z13 = tmp7 - z3;
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    dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
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    dataptr[DCTSIZE*3] = z13 - z2;
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    dataptr[DCTSIZE*1] = z11 + z4;
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    dataptr[DCTSIZE*7] = z11 - z4;
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    dataptr++;                        /* advance pointer to next column */
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  }
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}
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#undef GLOBAL
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#undef CONST_BITS
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#undef DESCALE
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#undef FIX_0_541196100
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#undef FIX_1_306562965