| /* |
| * 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 INT32 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 ((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 |
| |
| |
| /* 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) |
| { |
| INT32 tmp0, tmp1, tmp2, tmp3; |
| INT32 tmp10, tmp11, tmp12, tmp13; |
| INT32 z1, z2, z3, z4, z5; |
| JCOEFPTR inptr; |
| ISLOW_MULT_TYPE * quantptr; |
| int * wsptr; |
| JSAMPROW outptr; |
| JSAMPLE *range_limit = IDCT_range_limit(cinfo); |
| int ctr; |
| int workspace[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 */ |
| int dcval = 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((INT32) 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 = (INT32) wsptr[2]; |
| z3 = (INT32) wsptr[6]; |
| |
| z1 = MULTIPLY(z2 + z3, FIX_0_541196100); |
| tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); |
| tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); |
| |
| tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS; |
| tmp1 = ((INT32) wsptr[0] - (INT32) 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 = (INT32) wsptr[7]; |
| tmp1 = (INT32) wsptr[5]; |
| tmp2 = (INT32) wsptr[3]; |
| tmp3 = (INT32) 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 */ |
