nuclear@1: /* nuclear@1: * jfdctint.c nuclear@1: * nuclear@1: * Copyright (C) 1991-1996, Thomas G. Lane. nuclear@1: * This file is part of the Independent JPEG Group's software. nuclear@1: * For conditions of distribution and use, see the accompanying README file. nuclear@1: * nuclear@1: * This file contains a slow-but-accurate integer implementation of the nuclear@1: * forward DCT (Discrete Cosine Transform). nuclear@1: * nuclear@1: * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT nuclear@1: * on each column. Direct algorithms are also available, but they are nuclear@1: * much more complex and seem not to be any faster when reduced to code. nuclear@1: * nuclear@1: * This implementation is based on an algorithm described in nuclear@1: * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT nuclear@1: * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, nuclear@1: * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. nuclear@1: * The primary algorithm described there uses 11 multiplies and 29 adds. nuclear@1: * We use their alternate method with 12 multiplies and 32 adds. nuclear@1: * The advantage of this method is that no data path contains more than one nuclear@1: * multiplication; this allows a very simple and accurate implementation in nuclear@1: * scaled fixed-point arithmetic, with a minimal number of shifts. nuclear@1: */ nuclear@1: nuclear@1: #define JPEG_INTERNALS nuclear@1: #include "jinclude.h" nuclear@1: #include "jpeglib.h" nuclear@1: #include "jdct.h" /* Private declarations for DCT subsystem */ nuclear@1: nuclear@1: #ifdef DCT_ISLOW_SUPPORTED nuclear@1: nuclear@1: nuclear@1: /* nuclear@1: * This module is specialized to the case DCTSIZE = 8. nuclear@1: */ nuclear@1: nuclear@1: #if DCTSIZE != 8 nuclear@1: Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* nuclear@1: * The poop on this scaling stuff is as follows: nuclear@1: * nuclear@1: * Each 1-D DCT step produces outputs which are a factor of sqrt(N) nuclear@1: * larger than the true DCT outputs. The final outputs are therefore nuclear@1: * a factor of N larger than desired; since N=8 this can be cured by nuclear@1: * a simple right shift at the end of the algorithm. The advantage of nuclear@1: * this arrangement is that we save two multiplications per 1-D DCT, nuclear@1: * because the y0 and y4 outputs need not be divided by sqrt(N). nuclear@1: * In the IJG code, this factor of 8 is removed by the quantization step nuclear@1: * (in jcdctmgr.c), NOT in this module. nuclear@1: * nuclear@1: * We have to do addition and subtraction of the integer inputs, which nuclear@1: * is no problem, and multiplication by fractional constants, which is nuclear@1: * a problem to do in integer arithmetic. We multiply all the constants nuclear@1: * by CONST_SCALE and convert them to integer constants (thus retaining nuclear@1: * CONST_BITS bits of precision in the constants). After doing a nuclear@1: * multiplication we have to divide the product by CONST_SCALE, with proper nuclear@1: * rounding, to produce the correct output. This division can be done nuclear@1: * cheaply as a right shift of CONST_BITS bits. We postpone shifting nuclear@1: * as long as possible so that partial sums can be added together with nuclear@1: * full fractional precision. nuclear@1: * nuclear@1: * The outputs of the first pass are scaled up by PASS1_BITS bits so that nuclear@1: * they are represented to better-than-integral precision. These outputs nuclear@1: * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word nuclear@1: * with the recommended scaling. (For 12-bit sample data, the intermediate nuclear@1: * array is INT32 anyway.) nuclear@1: * nuclear@1: * To avoid overflow of the 32-bit intermediate results in pass 2, we must nuclear@1: * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis nuclear@1: * shows that the values given below are the most effective. nuclear@1: */ nuclear@1: nuclear@1: #if BITS_IN_JSAMPLE == 8 nuclear@1: #define CONST_BITS 13 nuclear@1: #define PASS1_BITS 2 nuclear@1: #else nuclear@1: #define CONST_BITS 13 nuclear@1: #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ nuclear@1: #endif nuclear@1: nuclear@1: /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus nuclear@1: * causing a lot of useless floating-point operations at run time. nuclear@1: * To get around this we use the following pre-calculated constants. nuclear@1: * If you change CONST_BITS you may want to add appropriate values. nuclear@1: * (With a reasonable C compiler, you can just rely on the FIX() macro...) nuclear@1: */ nuclear@1: nuclear@1: #if CONST_BITS == 13 nuclear@1: #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */ nuclear@1: #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ nuclear@1: #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ nuclear@1: #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ nuclear@1: #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ nuclear@1: #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ nuclear@1: #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ nuclear@1: #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ nuclear@1: #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ nuclear@1: #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ nuclear@1: #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ nuclear@1: #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */ nuclear@1: #else nuclear@1: #define FIX_0_298631336 FIX(0.298631336) nuclear@1: #define FIX_0_390180644 FIX(0.390180644) nuclear@1: #define FIX_0_541196100 FIX(0.541196100) nuclear@1: #define FIX_0_765366865 FIX(0.765366865) nuclear@1: #define FIX_0_899976223 FIX(0.899976223) nuclear@1: #define FIX_1_175875602 FIX(1.175875602) nuclear@1: #define FIX_1_501321110 FIX(1.501321110) nuclear@1: #define FIX_1_847759065 FIX(1.847759065) nuclear@1: #define FIX_1_961570560 FIX(1.961570560) nuclear@1: #define FIX_2_053119869 FIX(2.053119869) nuclear@1: #define FIX_2_562915447 FIX(2.562915447) nuclear@1: #define FIX_3_072711026 FIX(3.072711026) nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. nuclear@1: * For 8-bit samples with the recommended scaling, all the variable nuclear@1: * and constant values involved are no more than 16 bits wide, so a nuclear@1: * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. nuclear@1: * For 12-bit samples, a full 32-bit multiplication will be needed. nuclear@1: */ nuclear@1: nuclear@1: #if BITS_IN_JSAMPLE == 8 nuclear@1: #define MULTIPLY(var,const) MULTIPLY16C16(var,const) nuclear@1: #else nuclear@1: #define MULTIPLY(var,const) ((var) * (const)) nuclear@1: #endif nuclear@1: nuclear@1: nuclear@1: /* nuclear@1: * Perform the forward DCT on one block of samples. nuclear@1: */ nuclear@1: nuclear@1: GLOBAL(void) nuclear@1: jpeg_fdct_islow (DCTELEM * data) nuclear@1: { nuclear@1: INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; nuclear@1: INT32 tmp10, tmp11, tmp12, tmp13; nuclear@1: INT32 z1, z2, z3, z4, z5; nuclear@1: DCTELEM *dataptr; nuclear@1: int ctr; nuclear@1: SHIFT_TEMPS nuclear@1: nuclear@1: /* Pass 1: process rows. */ nuclear@1: /* Note results are scaled up by sqrt(8) compared to a true DCT; */ nuclear@1: /* furthermore, we scale the results by 2**PASS1_BITS. */ nuclear@1: nuclear@1: dataptr = data; nuclear@1: for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { nuclear@1: tmp0 = dataptr[0] + dataptr[7]; nuclear@1: tmp7 = dataptr[0] - dataptr[7]; nuclear@1: tmp1 = dataptr[1] + dataptr[6]; nuclear@1: tmp6 = dataptr[1] - dataptr[6]; nuclear@1: tmp2 = dataptr[2] + dataptr[5]; nuclear@1: tmp5 = dataptr[2] - dataptr[5]; nuclear@1: tmp3 = dataptr[3] + dataptr[4]; nuclear@1: tmp4 = dataptr[3] - dataptr[4]; nuclear@1: nuclear@1: /* Even part per LL&M figure 1 --- note that published figure is faulty; nuclear@1: * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". nuclear@1: */ nuclear@1: nuclear@1: tmp10 = tmp0 + tmp3; nuclear@1: tmp13 = tmp0 - tmp3; nuclear@1: tmp11 = tmp1 + tmp2; nuclear@1: tmp12 = tmp1 - tmp2; nuclear@1: nuclear@1: dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); nuclear@1: dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); nuclear@1: nuclear@1: z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); nuclear@1: dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), nuclear@1: CONST_BITS-PASS1_BITS); nuclear@1: dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), nuclear@1: CONST_BITS-PASS1_BITS); nuclear@1: nuclear@1: /* Odd part per figure 8 --- note paper omits factor of sqrt(2). nuclear@1: * cK represents cos(K*pi/16). nuclear@1: * i0..i3 in the paper are tmp4..tmp7 here. nuclear@1: */ nuclear@1: nuclear@1: z1 = tmp4 + tmp7; nuclear@1: z2 = tmp5 + tmp6; nuclear@1: z3 = tmp4 + tmp6; nuclear@1: z4 = tmp5 + tmp7; nuclear@1: z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ nuclear@1: nuclear@1: tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ nuclear@1: tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ nuclear@1: tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ nuclear@1: tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ nuclear@1: z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ nuclear@1: z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ nuclear@1: z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ nuclear@1: z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ nuclear@1: nuclear@1: z3 += z5; nuclear@1: z4 += z5; nuclear@1: nuclear@1: dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); nuclear@1: dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); nuclear@1: dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); nuclear@1: dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); nuclear@1: nuclear@1: dataptr += DCTSIZE; /* advance pointer to next row */ nuclear@1: } nuclear@1: nuclear@1: /* Pass 2: process columns. nuclear@1: * We remove the PASS1_BITS scaling, but leave the results scaled up nuclear@1: * by an overall factor of 8. nuclear@1: */ nuclear@1: nuclear@1: dataptr = data; nuclear@1: for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { nuclear@1: tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; nuclear@1: tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; nuclear@1: tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; nuclear@1: tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; nuclear@1: tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; nuclear@1: tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; nuclear@1: tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; nuclear@1: tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; nuclear@1: nuclear@1: /* Even part per LL&M figure 1 --- note that published figure is faulty; nuclear@1: * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". nuclear@1: */ nuclear@1: nuclear@1: tmp10 = tmp0 + tmp3; nuclear@1: tmp13 = tmp0 - tmp3; nuclear@1: tmp11 = tmp1 + tmp2; nuclear@1: tmp12 = tmp1 - tmp2; nuclear@1: nuclear@1: dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); nuclear@1: dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); nuclear@1: nuclear@1: z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); nuclear@1: dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), nuclear@1: CONST_BITS+PASS1_BITS); nuclear@1: dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), nuclear@1: CONST_BITS+PASS1_BITS); nuclear@1: nuclear@1: /* Odd part per figure 8 --- note paper omits factor of sqrt(2). nuclear@1: * cK represents cos(K*pi/16). nuclear@1: * i0..i3 in the paper are tmp4..tmp7 here. nuclear@1: */ nuclear@1: nuclear@1: z1 = tmp4 + tmp7; nuclear@1: z2 = tmp5 + tmp6; nuclear@1: z3 = tmp4 + tmp6; nuclear@1: z4 = tmp5 + tmp7; nuclear@1: z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ nuclear@1: nuclear@1: tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ nuclear@1: tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ nuclear@1: tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ nuclear@1: tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ nuclear@1: z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ nuclear@1: z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ nuclear@1: z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ nuclear@1: z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ nuclear@1: nuclear@1: z3 += z5; nuclear@1: z4 += z5; nuclear@1: nuclear@1: dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, nuclear@1: CONST_BITS+PASS1_BITS); nuclear@1: dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, nuclear@1: CONST_BITS+PASS1_BITS); nuclear@1: dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, nuclear@1: CONST_BITS+PASS1_BITS); nuclear@1: dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, nuclear@1: CONST_BITS+PASS1_BITS); nuclear@1: nuclear@1: dataptr++; /* advance pointer to next column */ nuclear@1: } nuclear@1: } nuclear@1: nuclear@1: #endif /* DCT_ISLOW_SUPPORTED */