00001 /*
00002  * jfdctint.c
00003  *
00004  * Copyright (C) 1991-1996, Thomas G. Lane.
00005  * This file is part of the Independent JPEG Group's software.
00006  * For conditions of distribution and use, see the accompanying README file.
00007  *
00008  * This file contains a slow-but-accurate integer implementation of the
00009  * forward DCT (Discrete Cosine Transform).
00010  *
00011  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
00012  * on each column.  Direct algorithms are also available, but they are
00013  * much more complex and seem not to be any faster when reduced to code.
00014  *
00015  * This implementation is based on an algorithm described in
00016  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
00017  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
00018  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
00019  * The primary algorithm described there uses 11 multiplies and 29 adds.
00020  * We use their alternate method with 12 multiplies and 32 adds.
00021  * The advantage of this method is that no data path contains more than one
00022  * multiplication; this allows a very simple and accurate implementation in
00023  * scaled fixed-point arithmetic, with a minimal number of shifts.
00024  */
00025 
00026 #define JPEG_INTERNALS
00027 #include "jinclude.h"
00028 #include "jpeglib.h"
00029 #include "jdct.h"               /* Private declarations for DCT subsystem */
00030 
00031 #ifdef DCT_ISLOW_SUPPORTED
00032 
00033 
00034 /*
00035  * This module is specialized to the case DCTSIZE = 8.
00036  */
00037 
00038 #if DCTSIZE != 8
00039   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
00040 #endif
00041 
00042 
00043 /*
00044  * The poop on this scaling stuff is as follows:
00045  *
00046  * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
00047  * larger than the true DCT outputs.  The final outputs are therefore
00048  * a factor of N larger than desired; since N=8 this can be cured by
00049  * a simple right shift at the end of the algorithm.  The advantage of
00050  * this arrangement is that we save two multiplications per 1-D DCT,
00051  * because the y0 and y4 outputs need not be divided by sqrt(N).
00052  * In the IJG code, this factor of 8 is removed by the quantization step
00053  * (in jcdctmgr.c), NOT in this module.
00054  *
00055  * We have to do addition and subtraction of the integer inputs, which
00056  * is no problem, and multiplication by fractional constants, which is
00057  * a problem to do in integer arithmetic.  We multiply all the constants
00058  * by CONST_SCALE and convert them to integer constants (thus retaining
00059  * CONST_BITS bits of precision in the constants).  After doing a
00060  * multiplication we have to divide the product by CONST_SCALE, with proper
00061  * rounding, to produce the correct output.  This division can be done
00062  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
00063  * as long as possible so that partial sums can be added together with
00064  * full fractional precision.
00065  *
00066  * The outputs of the first pass are scaled up by PASS1_BITS bits so that
00067  * they are represented to better-than-integral precision.  These outputs
00068  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
00069  * with the recommended scaling.  (For 12-bit sample data, the intermediate
00070  * array is INT32 anyway.)
00071  *
00072  * To avoid overflow of the 32-bit intermediate results in pass 2, we must
00073  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
00074  * shows that the values given below are the most effective.
00075  */
00076 
00077 #if BITS_IN_JSAMPLE == 8
00078 #define CONST_BITS  13
00079 #define PASS1_BITS  2
00080 #else
00081 #define CONST_BITS  13
00082 #define PASS1_BITS  1           /* lose a little precision to avoid overflow */
00083 #endif
00084 
00085 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
00086  * causing a lot of useless floating-point operations at run time.
00087  * To get around this we use the following pre-calculated constants.
00088  * If you change CONST_BITS you may want to add appropriate values.
00089  * (With a reasonable C compiler, you can just rely on the FIX() macro...)
00090  */
00091 
00092 #if CONST_BITS == 13
00093 #define FIX_0_298631336  ((INT32)  2446)        /* FIX(0.298631336) */
00094 #define FIX_0_390180644  ((INT32)  3196)        /* FIX(0.390180644) */
00095 #define FIX_0_541196100  ((INT32)  4433)        /* FIX(0.541196100) */
00096 #define FIX_0_765366865  ((INT32)  6270)        /* FIX(0.765366865) */
00097 #define FIX_0_899976223  ((INT32)  7373)        /* FIX(0.899976223) */
00098 #define FIX_1_175875602  ((INT32)  9633)        /* FIX(1.175875602) */
00099 #define FIX_1_501321110  ((INT32)  12299)       /* FIX(1.501321110) */
00100 #define FIX_1_847759065  ((INT32)  15137)       /* FIX(1.847759065) */
00101 #define FIX_1_961570560  ((INT32)  16069)       /* FIX(1.961570560) */
00102 #define FIX_2_053119869  ((INT32)  16819)       /* FIX(2.053119869) */
00103 #define FIX_2_562915447  ((INT32)  20995)       /* FIX(2.562915447) */
00104 #define FIX_3_072711026  ((INT32)  25172)       /* FIX(3.072711026) */
00105 #else
00106 #define FIX_0_298631336  FIX(0.298631336)
00107 #define FIX_0_390180644  FIX(0.390180644)
00108 #define FIX_0_541196100  FIX(0.541196100)
00109 #define FIX_0_765366865  FIX(0.765366865)
00110 #define FIX_0_899976223  FIX(0.899976223)
00111 #define FIX_1_175875602  FIX(1.175875602)
00112 #define FIX_1_501321110  FIX(1.501321110)
00113 #define FIX_1_847759065  FIX(1.847759065)
00114 #define FIX_1_961570560  FIX(1.961570560)
00115 #define FIX_2_053119869  FIX(2.053119869)
00116 #define FIX_2_562915447  FIX(2.562915447)
00117 #define FIX_3_072711026  FIX(3.072711026)
00118 #endif
00119 
00120 
00121 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
00122  * For 8-bit samples with the recommended scaling, all the variable
00123  * and constant values involved are no more than 16 bits wide, so a
00124  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
00125  * For 12-bit samples, a full 32-bit multiplication will be needed.
00126  */
00127 
00128 #if BITS_IN_JSAMPLE == 8
00129 #define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
00130 #else
00131 #define MULTIPLY(var,const)  ((var) * (const))
00132 #endif
00133 
00134 
00135 /*
00136  * Perform the forward DCT on one block of samples.
00137  */
00138 
00139 GLOBAL(void)
00140 jpeg_fdct_islow (DCTELEM * data)
00141 {
00142   INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
00143   INT32 tmp10, tmp11, tmp12, tmp13;
00144   INT32 z1, z2, z3, z4, z5;
00145   DCTELEM *dataptr;
00146   int ctr;
00147   SHIFT_TEMPS
00148 
00149   /* Pass 1: process rows. */
00150   /* Note results are scaled up by sqrt(8) compared to a true DCT; */
00151   /* furthermore, we scale the results by 2**PASS1_BITS. */
00152 
00153   dataptr = data;
00154   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
00155     tmp0 = dataptr[0] + dataptr[7];
00156     tmp7 = dataptr[0] - dataptr[7];
00157     tmp1 = dataptr[1] + dataptr[6];
00158     tmp6 = dataptr[1] - dataptr[6];
00159     tmp2 = dataptr[2] + dataptr[5];
00160     tmp5 = dataptr[2] - dataptr[5];
00161     tmp3 = dataptr[3] + dataptr[4];
00162     tmp4 = dataptr[3] - dataptr[4];
00163     
00164     /* Even part per LL&M figure 1 --- note that published figure is faulty;
00165      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
00166      */
00167     
00168     tmp10 = tmp0 + tmp3;
00169     tmp13 = tmp0 - tmp3;
00170     tmp11 = tmp1 + tmp2;
00171     tmp12 = tmp1 - tmp2;
00172     
00173     dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
00174     dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
00175     
00176     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
00177     dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
00178                                    CONST_BITS-PASS1_BITS);
00179     dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
00180                                    CONST_BITS-PASS1_BITS);
00181     
00182     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
00183      * cK represents cos(K*pi/16).
00184      * i0..i3 in the paper are tmp4..tmp7 here.
00185      */
00186     
00187     z1 = tmp4 + tmp7;
00188     z2 = tmp5 + tmp6;
00189     z3 = tmp4 + tmp6;
00190     z4 = tmp5 + tmp7;
00191     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
00192     
00193     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
00194     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
00195     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
00196     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
00197     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
00198     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
00199     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
00200     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
00201     
00202     z3 += z5;
00203     z4 += z5;
00204     
00205     dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
00206     dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
00207     dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
00208     dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
00209     
00210     dataptr += DCTSIZE;         /* advance pointer to next row */
00211   }
00212 
00213   /* Pass 2: process columns.
00214    * We remove the PASS1_BITS scaling, but leave the results scaled up
00215    * by an overall factor of 8.
00216    */
00217 
00218   dataptr = data;
00219   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
00220     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
00221     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
00222     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
00223     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
00224     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
00225     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
00226     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
00227     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
00228     
00229     /* Even part per LL&M figure 1 --- note that published figure is faulty;
00230      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
00231      */
00232     
00233     tmp10 = tmp0 + tmp3;
00234     tmp13 = tmp0 - tmp3;
00235     tmp11 = tmp1 + tmp2;
00236     tmp12 = tmp1 - tmp2;
00237     
00238     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
00239     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
00240     
00241     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
00242     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
00243                                            CONST_BITS+PASS1_BITS);
00244     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
00245                                            CONST_BITS+PASS1_BITS);
00246     
00247     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
00248      * cK represents cos(K*pi/16).
00249      * i0..i3 in the paper are tmp4..tmp7 here.
00250      */
00251     
00252     z1 = tmp4 + tmp7;
00253     z2 = tmp5 + tmp6;
00254     z3 = tmp4 + tmp6;
00255     z4 = tmp5 + tmp7;
00256     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
00257     
00258     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
00259     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
00260     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
00261     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
00262     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
00263     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
00264     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
00265     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
00266     
00267     z3 += z5;
00268     z4 += z5;
00269     
00270     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
00271                                            CONST_BITS+PASS1_BITS);
00272     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
00273                                            CONST_BITS+PASS1_BITS);
00274     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
00275                                            CONST_BITS+PASS1_BITS);
00276     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
00277                                            CONST_BITS+PASS1_BITS);
00278     
00279     dataptr++;                  /* advance pointer to next column */
00280   }
00281 }
00282 
00283 #endif /* DCT_ISLOW_SUPPORTED */