/* * jidctint.c * * Copyright (C) 1991-1998, 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 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine * must also perform dequantization of the input coefficients. * * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT * on each row (or vice versa, but it's more convenient to emit a row at * a time). 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 IDCT step produces outputs which are a factor of sqrt(N) * larger than the true IDCT 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 IDCT, * because the y0 and y4 inputs need not be divided by sqrt(N). * * 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. (To scale up 12-bit sample data further, an * intermediate long array would be needed.) * * 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 ((long) 2446) /* FIX(0.298631336) */ #define FIX_0_390180644 ((long) 3196) /* FIX(0.390180644) */ #define FIX_0_541196100 ((long) 4433) /* FIX(0.541196100) */ #define FIX_0_765366865 ((long) 6270) /* FIX(0.765366865) */ #define FIX_0_899976223 ((long) 7373) /* FIX(0.899976223) */ #define FIX_1_175875602 ((long) 9633) /* FIX(1.175875602) */ #define FIX_1_501321110 ((long) 12299) /* FIX(1.501321110) */ #define FIX_1_847759065 ((long) 15137) /* FIX(1.847759065) */ #define FIX_1_961570560 ((long) 16069) /* FIX(1.961570560) */ #define FIX_2_053119869 ((long) 16819) /* FIX(2.053119869) */ #define FIX_2_562915447 ((long) 20995) /* FIX(2.562915447) */ #define FIX_3_072711026 ((long) 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 long variable by an long constant to yield an long 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 /* Dequantize a coefficient by multiplying it by the multiplier-table * entry; produce an int result. In this module, both inputs and result * are 16 bits or less, so either int or short multiply will work. */ #define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval)) /* * Perform dequantization and inverse DCT on one block of coefficients. */GLOBAL(void)jpeg_idct_islow(j_decompress_ptr cinfo, jpeg_component_info * compptr, JCOEFPTR coef_block, JSAMPARRAY output_buf, JDIMENSION output_col){longtmp0, tmp1, tmp2, tmp3;longtmp10, tmp11, tmp12, tmp13;longz1, z2, z3, z4, z5; JCOEFPTR inptr; ISLOW_MULT_TYPE * quantptr;int* wsptr; JSAMPROW outptr; JSAMPLE *range_limit = IDCT_range_limit(cinfo);intctr;intworkspace[DCTSIZE2]; /* buffers data between passes */ SHIFT_TEMPS /* Pass 1: process columns from input, store into work array. */ /* Note results are scaled up by sqrt(8) compared to a true IDCT; */ /* furthermore, we scale the results by 2**PASS1_BITS. */ inptr = coef_block; quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table; wsptr = workspace; for (ctr = DCTSIZE; ctr > 0; ctr--){/* Due to quantization, we will usually find that many of the input * coefficients are zero, especially the AC terms. We can exploit this * by short-circuiting the IDCT calculation for any column in which all * the AC terms are zero. In that case each output is equal to the * DC coefficient (with scale factor as needed). * With typical images and quantization tables, half or more of the * column DCT calculations can be simplified this way. */ if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && inptr[DCTSIZE*7] == 0){/* AC terms all zero */intdcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS; wsptr[DCTSIZE*0] = dcval; wsptr[DCTSIZE*1] = dcval; wsptr[DCTSIZE*2] = dcval; wsptr[DCTSIZE*3] = dcval; wsptr[DCTSIZE*4] = dcval; wsptr[DCTSIZE*5] = dcval; wsptr[DCTSIZE*6] = dcval; wsptr[DCTSIZE*7] = dcval; inptr++; /* advance pointers to next column */ quantptr++; wsptr++; continue;}/* Even part: reverse the even part of the forward DCT. */ /* The rotator is sqrt(2)*c(-6). */ z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); z1 = MULTIPLY(z2 + z3, FIX_0_541196100); tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); tmp0 = (z2 + z3) << CONST_BITS; tmp1 = (z2 - z3) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; /* Odd part per figure 8; the matrix is unitary and hence its * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. */ tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); z1 = tmp0 + tmp3; z2 = tmp1 + tmp2; z3 = tmp0 + tmp2; z4 = tmp1 + tmp3; z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ tmp3 = MULTIPLY(tmp3, 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; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS); wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS); wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS); wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS); wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS); wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS); wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS); wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS); inptr++; /* advance pointers to next column */ quantptr++; wsptr++;}/* Pass 2: process rows from work array, store into output array. */ /* Note that we must descale the results by a factor of 8 == 2**3, */ /* and also undo the PASS1_BITS scaling. */ wsptr = workspace; for (ctr = 0; ctr < DCTSIZE; ctr++){outptr = output_buf[ctr] + output_col; /* Rows of zeroes can be exploited in the same way as we did with columns. * However, the column calculation has created many nonzero AC terms, so * the simplification applies less often (typically 5% to 10% of the time). * On machines with very fast multiplication, it's possible that the * test takes more time than it's worth. In that case this section * may be commented out. */ #ifndef NO_ZERO_ROW_TEST if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0){/* AC terms all zero */ JSAMPLE dcval = range_limit[(int) DESCALE((long) wsptr[0], PASS1_BITS+3) & RANGE_MASK]; outptr[0] = dcval; outptr[1] = dcval; outptr[2] = dcval; outptr[3] = dcval; outptr[4] = dcval; outptr[5] = dcval; outptr[6] = dcval; outptr[7] = dcval; wsptr += DCTSIZE; /* advance pointer to next row */ continue;}#endif /* Even part: reverse the even part of the forward DCT. */ /* The rotator is sqrt(2)*c(-6). */ z2 = (long) wsptr[2]; z3 = (long) wsptr[6]; z1 = MULTIPLY(z2 + z3, FIX_0_541196100); tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); tmp0 = ((long) wsptr[0] + (long) wsptr[4]) << CONST_BITS; tmp1 = ((long) wsptr[0] - (long) wsptr[4]) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; /* Odd part per figure 8; the matrix is unitary and hence its * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. */ tmp0 = (long) wsptr[7]; tmp1 = (long) wsptr[5]; tmp2 = (long) wsptr[3]; tmp3 = (long) wsptr[1]; z1 = tmp0 + tmp3; z2 = tmp1 + tmp2; z3 = tmp0 + tmp2; z4 = tmp1 + tmp3; z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ tmp3 = MULTIPLY(tmp3, 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; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0, CONST_BITS+PASS1_BITS+3) & RANGE_MASK]; wsptr += DCTSIZE; /* advance pointer to next row */}}#endif /* DCT_ISLOW_SUPPORTED */