/* Copyright (C) 1996, MPEG Software Simulation Group. All Rights Reserved. *//* * Disclaimer of Warranty * * These software programs are available to the user without any license fee or * royalty on an "as is" basis.  The MPEG Software Simulation Group disclaims * any and all warranties, whether express, implied, or statuary, including any * implied warranties or merchantability or of fitness for a particular * purpose.  In no event shall the copyright-holder be liable for any * incidental, punitive, or consequential damages of any kind whatsoever * arising from the use of these programs. * * This disclaimer of warranty extends to the user of these programs and user's * customers, employees, agents, transferees, successors, and assigns. * * The MPEG Software Simulation Group does not represent or warrant that the * programs furnished hereunder are free of infringement of any third-party * patents. * * Commercial implementations of MPEG-1 and MPEG-2 video, including shareware, * are subject to royalty fees to patent holders.  Many of these patents are * general enough such that they are unavoidable regardless of implementation * design. * *//* This routine is a slow-but-accurate integer implementation of the * forward DCT (Discrete Cosine Transform). Taken from the IJG software * * 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 an algorithm described in *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. * The primary algorithm described there uses 11 multiplies and 29 adds. * We use their alternate method with 12 multiplies and 32 adds. * The advantage of this method is that no data path contains more than one * multiplication; this allows a very simple and accurate implementation in * scaled fixed-point arithmetic, with a minimal number of shifts. * * The poop on this scaling stuff is as follows: * * Each 1-D DCT step produces outputs which are a factor of sqrt(N) * larger than the true DCT outputs.  The final outputs are therefore * a factor of N larger than desired; since N=8 this can be cured by * a simple right shift at the end of the algorithm.  The advantage of * this arrangement is that we save two multiplications per 1-D DCT, * because the y0 and y4 outputs need not be divided by sqrt(N). * In the IJG code, this factor of 8 is removed by the quantization step * (in jcdctmgr.c), here it is removed. * * We have to do addition and subtraction of the integer inputs, which * is no problem, and multiplication by fractional constants, which is * a problem to do in integer arithmetic.  We multiply all the constants * by CONST_SCALE and convert them to integer constants (thus retaining * CONST_BITS bits of precision in the constants).  After doing a * multiplication we have to divide the product by CONST_SCALE, with proper * rounding, to produce the correct output.  This division can be done * cheaply as a right shift of CONST_BITS bits.  We postpone shifting * as long as possible so that partial sums can be added together with * full fractional precision. * * The outputs of the first pass are scaled up by PASS1_BITS bits so that * they are represented to better-than-integral precision.  These outputs * require 8 + PASS1_BITS + 3 bits; this fits in a 16-bit word * with the recommended scaling.  (For 12-bit sample data, the intermediate * array is INT32 anyway.) * * To avoid overflow of the 32-bit intermediate results in pass 2, we must * have 8 + CONST_BITS + PASS1_BITS <= 26.  Error analysis * shows that the values given below are the most effective. * * 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... */#include "fdct.h"#define USE_ACCURATE_ROUNDING#define RIGHT_SHIFT(x, shft)  ((x) >> (shft))#ifdef USE_ACCURATE_ROUNDING#define ONE ((int) 1)#define DESCALE(x, n)  RIGHT_SHIFT((x) + (ONE << ((n) - 1)), n)#else#define DESCALE(x, n)  RIGHT_SHIFT(x, n)#endif#define CONST_BITS  13#define PASS1_BITS  2#define FIX_0_298631336  ((int)  2446)	/* FIX(0.298631336) */#define FIX_0_390180644  ((int)  3196)	/* FIX(0.390180644) */#define FIX_0_541196100  ((int)  4433)	/* FIX(0.541196100) */#define FIX_0_765366865  ((int)  6270)	/* FIX(0.765366865) */#define FIX_0_899976223  ((int)  7373)	/* FIX(0.899976223) */#define FIX_1_175875602  ((int)  9633)	/* FIX(1.175875602) */#define FIX_1_501321110  ((int) 12299)	/* FIX(1.501321110) */#define FIX_1_847759065  ((int) 15137)	/* FIX(1.847759065) */#define FIX_1_961570560  ((int) 16069)	/* FIX(1.961570560) */#define FIX_2_053119869  ((int) 16819)	/* FIX(2.053119869) */#define FIX_2_562915447  ((int) 20995)	/* FIX(2.562915447) */#define FIX_3_072711026  ((int) 25172)	/* FIX(3.072711026) */// function pointerfdctFuncPtr fdct;/* * Perform an integer forward DCT on one block of samples. */void fdct_int32(short * const block){  int tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;  int tmp10, tmp11, tmp12, tmp13;  int z1, z2, z3, z4, z5;  short *blkptr;  int *dataptr;  int data[64];  int i;  /* Pass 1: process rows. */  /* Note results are scaled up by sqrt(8) compared to a true DCT; */  /* furthermore, we scale the results by 2**PASS1_BITS. */  dataptr = data;  blkptr = block;  for (i = 0; i < 8; i++)  {    tmp0 = blkptr[0] + blkptr[7];    tmp7 = blkptr[0] - blkptr[7];    tmp1 = blkptr[1] + blkptr[6];    tmp6 = blkptr[1] - blkptr[6];    tmp2 = blkptr[2] + blkptr[5];    tmp5 = blkptr[2] - blkptr[5];    tmp3 = blkptr[3] + blkptr[4];    tmp4 = blkptr[3] - blkptr[4];    /* Even part per LL&M figure 1 --- note that published figure is faulty;     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".     */    tmp10 = tmp0 + tmp3;    tmp13 = tmp0 - tmp3;    tmp11 = tmp1 + tmp2;    tmp12 = tmp1 - tmp2;    dataptr[0] = (tmp10 + tmp11) << PASS1_BITS;    dataptr[4] = (tmp10 - tmp11) << PASS1_BITS;    z1 = (tmp12 + tmp13) * FIX_0_541196100;    dataptr[2] = DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS - PASS1_BITS);    dataptr[6] = DESCALE(z1 + tmp12 * (-FIX_1_847759065), CONST_BITS - PASS1_BITS);    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).     * cK represents cos(K*pi/16).     * i0..i3 in the paper are tmp4..tmp7 here.     */    z1 = tmp4 + tmp7;    z2 = tmp5 + tmp6;    z3 = tmp4 + tmp6;    z4 = tmp5 + tmp7;    z5 = (z3 + z4) * FIX_1_175875602; /* sqrt(2) * c3 */    tmp4 *= FIX_0_298631336; /* sqrt(2) * (-c1+c3+c5-c7) */    tmp5 *= FIX_2_053119869; /* sqrt(2) * ( c1+c3-c5+c7) */    tmp6 *= FIX_3_072711026; /* sqrt(2) * ( c1+c3+c5-c7) */    tmp7 *= FIX_1_501321110; /* sqrt(2) * ( c1+c3-c5-c7) */    z1 *= -FIX_0_899976223; /* sqrt(2) * (c7-c3) */    z2 *= -FIX_2_562915447; /* sqrt(2) * (-c1-c3) */    z3 *= -FIX_1_961570560; /* sqrt(2) * (-c3-c5) */    z4 *= -FIX_0_390180644; /* sqrt(2) * (c5-c3) */    z3 += z5;    z4 += z5;    dataptr[7] = DESCALE(tmp4 + z1 + z3, CONST_BITS - PASS1_BITS);    dataptr[5] = DESCALE(tmp5 + z2 + z4, CONST_BITS - PASS1_BITS);    dataptr[3] = DESCALE(tmp6 + z2 + z3, CONST_BITS - PASS1_BITS);    dataptr[1] = DESCALE(tmp7 + z1 + z4, CONST_BITS - PASS1_BITS);    dataptr += 8;		/* advance pointer to next row */    blkptr += 8;  }  /* Pass 2: process columns.   * We remove the PASS1_BITS scaling, but leave the results scaled up   * by an overall factor of 8.   */  dataptr = data;  for (i = 0; i < 8; i++)  {    tmp0 = dataptr[0] + dataptr[56];    tmp7 = dataptr[0] - dataptr[56];    tmp1 = dataptr[8] + dataptr[48];    tmp6 = dataptr[8] - dataptr[48];    tmp2 = dataptr[16] + dataptr[40];    tmp5 = dataptr[16] - dataptr[40];    tmp3 = dataptr[24] + dataptr[32];    tmp4 = dataptr[24] - dataptr[32];    /* Even part per LL&M figure 1 --- note that published figure is faulty;     * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".     */    tmp10 = tmp0 + tmp3;    tmp13 = tmp0 - tmp3;    tmp11 = tmp1 + tmp2;    tmp12 = tmp1 - tmp2;    dataptr[0] = DESCALE(tmp10 + tmp11, PASS1_BITS);    dataptr[32] = DESCALE(tmp10 - tmp11, PASS1_BITS);    z1 = (tmp12 + tmp13) * FIX_0_541196100;    dataptr[16] = DESCALE(z1 + tmp13 * FIX_0_765366865, CONST_BITS + PASS1_BITS);    dataptr[48] = DESCALE(z1 + tmp12 * (-FIX_1_847759065), CONST_BITS + PASS1_BITS);    /* Odd part per figure 8 --- note paper omits factor of sqrt(2).     * cK represents cos(K*pi/16).     * i0..i3 in the paper are tmp4..tmp7 here.     */    z1 = tmp4 + tmp7;    z2 = tmp5 + tmp6;    z3 = tmp4 + tmp6;    z4 = tmp5 + tmp7;    z5 = (z3 + z4) * FIX_1_175875602; /* sqrt(2) * c3 */    tmp4 *= FIX_0_298631336; /* sqrt(2) * (-c1+c3+c5-c7) */    tmp5 *= FIX_2_053119869; /* sqrt(2) * ( c1+c3-c5+c7) */    tmp6 *= FIX_3_072711026; /* sqrt(2) * ( c1+c3+c5-c7) */    tmp7 *= FIX_1_501321110; /* sqrt(2) * ( c1+c3-c5-c7) */    z1 *= -FIX_0_899976223; /* sqrt(2) * (c7-c3) */    z2 *= -FIX_2_562915447; /* sqrt(2) * (-c1-c3) */    z3 *= -FIX_1_961570560; /* sqrt(2) * (-c3-c5) */    z4 *= -FIX_0_390180644; /* sqrt(2) * (c5-c3) */    z3 += z5;    z4 += z5;    dataptr[56] = DESCALE(tmp4 + z1 + z3, CONST_BITS + PASS1_BITS);    dataptr[40] = DESCALE(tmp5 + z2 + z4, CONST_BITS + PASS1_BITS);    dataptr[24] = DESCALE(tmp6 + z2 + z3, CONST_BITS + PASS1_BITS);    dataptr[8] = DESCALE(tmp7 + z1 + z4, CONST_BITS + PASS1_BITS);    dataptr++;			/* advance pointer to next column */  }  /* descale */  for (i = 0; i < 64; i++)    block[i] = (short int) DESCALE(data[i], 3);}