// * jfdctint.c // * // * Copyright (C) 1991-1994, 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 slow-but-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 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. #define JPEG_INTERNALS #include "JINCLUDE.h" #include "JPEGLIB.h" #include "JDCT.h" // Private declarations for DCT subsystem #ifdef DCT_ISLOW_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 // * 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), NOT in this module. // * // * 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 BITS_IN_JSAMPLE + 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 BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis // * shows that the values given below are the most effective. #if BITS_IN_JSAMPLE == 8 #define CONST_BITS 13 #define PASS1_BITS 2 #else #define CONST_BITS 13 #define PASS1_BITS 1 // lose a little precision to avoid overflow #endif // 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 == 13 #define FIX_0_298631336 ((INT32) 2446) // FIX(0.298631336) #define FIX_0_390180644 ((INT32) 3196) // FIX(0.390180644) #define FIX_0_541196100 ((INT32) 4433) // FIX(0.541196100) #define FIX_0_765366865 ((INT32) 6270) // FIX(0.765366865) #define FIX_0_899976223 ((INT32) 7373) // FIX(0.899976223) #define FIX_1_175875602 ((INT32) 9633) // FIX(1.175875602) #define FIX_1_501321110 ((INT32) 12299) // FIX(1.501321110) #define FIX_1_847759065 ((INT32) 15137) // FIX(1.847759065) #define FIX_1_961570560 ((INT32) 16069) // FIX(1.961570560) #define FIX_2_053119869 ((INT32) 16819) // FIX(2.053119869) #define FIX_2_562915447 ((INT32) 20995) // FIX(2.562915447) #define FIX_3_072711026 ((INT32) 25172) // FIX(3.072711026) #else #define FIX_0_298631336 FIX(0.298631336) #define FIX_0_390180644 FIX(0.390180644) #define FIX_0_541196100 FIX(0.541196100) #define FIX_0_765366865 FIX(0.765366865) #define FIX_0_899976223 FIX(0.899976223) #define FIX_1_175875602 FIX(1.175875602) #define FIX_1_501321110 FIX(1.501321110) #define FIX_1_847759065 FIX(1.847759065) #define FIX_1_961570560 FIX(1.961570560) #define FIX_2_053119869 FIX(2.053119869) #define FIX_2_562915447 FIX(2.562915447) #define FIX_3_072711026 FIX(3.072711026) #endif // Multiply an INT32 variable by an INT32 constant to yield an INT32 result. // * For 8-bit samples with the recommended scaling, all the variable // * and constant values involved are no more than 16 bits wide, so a // * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. // * For 12-bit samples, a full 32-bit multiplication will be needed. #if BITS_IN_JSAMPLE == 8 #define MULTIPLY(var,const) MULTIPLY16C16(var,const) #else #define MULTIPLY(var,const) ((var) * (const)) #endif // * Perform the forward DCT on one block of samples. GLOBAL void jpeg_fdct_islow (DCTELEM * data) { INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; INT32 tmp10, tmp11, tmp12, tmp13; INT32 z1, z2, z3, z4, z5; DCTELEM *dataptr; int ctr; SHIFT_TEMPS // 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; 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 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] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), CONST_BITS-PASS1_BITS); dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(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 = MULTIPLY(z3 + z4, FIX_1_175875602); // sqrt(2) * c3 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); // sqrt(2) * (-c1+c3+c5-c7) tmp5 = MULTIPLY(tmp5, FIX_2_053119869); // sqrt(2) * ( c1+c3-c5+c7) tmp6 = MULTIPLY(tmp6, FIX_3_072711026); // sqrt(2) * ( c1+c3+c5-c7) tmp7 = MULTIPLY(tmp7, FIX_1_501321110); // sqrt(2) * ( c1+c3-c5-c7) z1 = MULTIPLY(z1, - FIX_0_899976223); // sqrt(2) * (c7-c3) z2 = MULTIPLY(z2, - FIX_2_562915447); // sqrt(2) * (-c1-c3) z3 = MULTIPLY(z3, - FIX_1_961570560); // sqrt(2) * (-c3-c5) z4 = MULTIPLY(z4, - FIX_0_390180644); // sqrt(2) * (c5-c3) z3 += z5; z4 += z5; dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); dataptr += DCTSIZE; // advance pointer to next row } // 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 (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 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[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), CONST_BITS+PASS1_BITS); dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(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 = MULTIPLY(z3 + z4, FIX_1_175875602); // sqrt(2) * c3 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); // sqrt(2) * (-c1+c3+c5-c7) tmp5 = MULTIPLY(tmp5, FIX_2_053119869); // sqrt(2) * ( c1+c3-c5+c7) tmp6 = MULTIPLY(tmp6, FIX_3_072711026); // sqrt(2) * ( c1+c3+c5-c7) tmp7 = MULTIPLY(tmp7, FIX_1_501321110); // sqrt(2) * ( c1+c3-c5-c7) z1 = MULTIPLY(z1, - FIX_0_899976223); // sqrt(2) * (c7-c3) z2 = MULTIPLY(z2, - FIX_2_562915447); // sqrt(2) * (-c1-c3) z3 = MULTIPLY(z3, - FIX_1_961570560); // sqrt(2) * (-c3-c5) z4 = MULTIPLY(z4, - FIX_0_390180644); // sqrt(2) * (c5-c3) z3 += z5; z4 += z5; dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS+PASS1_BITS); dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS+PASS1_BITS); dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS+PASS1_BITS); dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS+PASS1_BITS); dataptr++; // advance pointer to next column } } #endif // DCT_ISLOW_SUPPORTED