| /* |
| * jfdctint.c |
| * |
| * This file was part of the Independent JPEG Group's software: |
| * Copyright (C) 1991-1996, Thomas G. Lane. |
| * libjpeg-turbo Modifications: |
| * Copyright (C) 2015, 2020, D. R. Commander. |
| * For conditions of distribution and use, see the accompanying README.ijg |
| * file. |
| * |
| * This file contains a slower but more 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 JLONG 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 ((JLONG)2446) /* FIX(0.298631336) */ |
| #define FIX_0_390180644 ((JLONG)3196) /* FIX(0.390180644) */ |
| #define FIX_0_541196100 ((JLONG)4433) /* FIX(0.541196100) */ |
| #define FIX_0_765366865 ((JLONG)6270) /* FIX(0.765366865) */ |
| #define FIX_0_899976223 ((JLONG)7373) /* FIX(0.899976223) */ |
| #define FIX_1_175875602 ((JLONG)9633) /* FIX(1.175875602) */ |
| #define FIX_1_501321110 ((JLONG)12299) /* FIX(1.501321110) */ |
| #define FIX_1_847759065 ((JLONG)15137) /* FIX(1.847759065) */ |
| #define FIX_1_961570560 ((JLONG)16069) /* FIX(1.961570560) */ |
| #define FIX_2_053119869 ((JLONG)16819) /* FIX(2.053119869) */ |
| #define FIX_2_562915447 ((JLONG)20995) /* FIX(2.562915447) */ |
| #define FIX_3_072711026 ((JLONG)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 JLONG variable by an JLONG constant to yield an JLONG 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) |
| { |
| JLONG tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |
| JLONG tmp10, tmp11, tmp12, tmp13; |
| JLONG 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)LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS); |
| dataptr[4] = (DCTELEM)LEFT_SHIFT(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 */ |
