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| -rw-r--r-- | libjpegtwrp/jfdctint.c | 283 |
1 files changed, 283 insertions, 0 deletions
diff --git a/libjpegtwrp/jfdctint.c b/libjpegtwrp/jfdctint.c new file mode 100644 index 000000000..0a78b64ae --- /dev/null +++ b/libjpegtwrp/jfdctint.c @@ -0,0 +1,283 @@ +/* + * jfdctint.c + * + * Copyright (C) 1991-1996, 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 */ |