nuclear@1: /* nuclear@1: * jidctint.c nuclear@1: * nuclear@1: * Copyright (C) 1991-1998, 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: * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine nuclear@1: * must also perform dequantization of the input coefficients. nuclear@1: * nuclear@1: * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT nuclear@1: * on each row (or vice versa, but it's more convenient to emit a row at nuclear@1: * a time). Direct algorithms are also available, but they are much more nuclear@1: * 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 IDCT step produces outputs which are a factor of sqrt(N) nuclear@1: * larger than the true IDCT 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 IDCT, nuclear@1: * because the y0 and y4 inputs need not be divided by sqrt(N). 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. (To scale up 12-bit sample data further, an nuclear@1: * intermediate INT32 array would be needed.) 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: /* Dequantize a coefficient by multiplying it by the multiplier-table nuclear@1: * entry; produce an int result. In this module, both inputs and result nuclear@1: * are 16 bits or less, so either int or short multiply will work. nuclear@1: */ nuclear@1: nuclear@1: #define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval)) nuclear@1: nuclear@1: nuclear@1: /* nuclear@1: * Perform dequantization and inverse DCT on one block of coefficients. nuclear@1: */ nuclear@1: nuclear@1: GLOBAL(void) nuclear@1: jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr, nuclear@1: JCOEFPTR coef_block, nuclear@1: JSAMPARRAY output_buf, JDIMENSION output_col) nuclear@1: { nuclear@1: INT32 tmp0, tmp1, tmp2, tmp3; nuclear@1: INT32 tmp10, tmp11, tmp12, tmp13; nuclear@1: INT32 z1, z2, z3, z4, z5; nuclear@1: JCOEFPTR inptr; nuclear@1: ISLOW_MULT_TYPE * quantptr; nuclear@1: int * wsptr; nuclear@1: JSAMPROW outptr; nuclear@1: JSAMPLE *range_limit = IDCT_range_limit(cinfo); nuclear@1: int ctr; nuclear@1: int workspace[DCTSIZE2]; /* buffers data between passes */ nuclear@1: SHIFT_TEMPS nuclear@1: nuclear@1: /* Pass 1: process columns from input, store into work array. */ nuclear@1: /* Note results are scaled up by sqrt(8) compared to a true IDCT; */ nuclear@1: /* furthermore, we scale the results by 2**PASS1_BITS. */ nuclear@1: nuclear@1: inptr = coef_block; nuclear@1: quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table; nuclear@1: wsptr = workspace; nuclear@1: for (ctr = DCTSIZE; ctr > 0; ctr--) { nuclear@1: /* Due to quantization, we will usually find that many of the input nuclear@1: * coefficients are zero, especially the AC terms. We can exploit this nuclear@1: * by short-circuiting the IDCT calculation for any column in which all nuclear@1: * the AC terms are zero. In that case each output is equal to the nuclear@1: * DC coefficient (with scale factor as needed). nuclear@1: * With typical images and quantization tables, half or more of the nuclear@1: * column DCT calculations can be simplified this way. nuclear@1: */ nuclear@1: nuclear@1: if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && nuclear@1: inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && nuclear@1: inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && nuclear@1: inptr[DCTSIZE*7] == 0) { nuclear@1: /* AC terms all zero */ nuclear@1: int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS; nuclear@1: nuclear@1: wsptr[DCTSIZE*0] = dcval; nuclear@1: wsptr[DCTSIZE*1] = dcval; nuclear@1: wsptr[DCTSIZE*2] = dcval; nuclear@1: wsptr[DCTSIZE*3] = dcval; nuclear@1: wsptr[DCTSIZE*4] = dcval; nuclear@1: wsptr[DCTSIZE*5] = dcval; nuclear@1: wsptr[DCTSIZE*6] = dcval; nuclear@1: wsptr[DCTSIZE*7] = dcval; nuclear@1: nuclear@1: inptr++; /* advance pointers to next column */ nuclear@1: quantptr++; nuclear@1: wsptr++; nuclear@1: continue; nuclear@1: } nuclear@1: nuclear@1: /* Even part: reverse the even part of the forward DCT. */ nuclear@1: /* The rotator is sqrt(2)*c(-6). */ nuclear@1: nuclear@1: z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); nuclear@1: z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); nuclear@1: nuclear@1: z1 = MULTIPLY(z2 + z3, FIX_0_541196100); nuclear@1: tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); nuclear@1: tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); nuclear@1: nuclear@1: z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); nuclear@1: z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); nuclear@1: nuclear@1: tmp0 = (z2 + z3) << CONST_BITS; nuclear@1: tmp1 = (z2 - z3) << CONST_BITS; 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: /* Odd part per figure 8; the matrix is unitary and hence its nuclear@1: * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. nuclear@1: */ nuclear@1: nuclear@1: tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); nuclear@1: tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); nuclear@1: tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); nuclear@1: tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); nuclear@1: nuclear@1: z1 = tmp0 + tmp3; nuclear@1: z2 = tmp1 + tmp2; nuclear@1: z3 = tmp0 + tmp2; nuclear@1: z4 = tmp1 + tmp3; nuclear@1: z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ nuclear@1: nuclear@1: tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ nuclear@1: tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ nuclear@1: tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ nuclear@1: tmp3 = MULTIPLY(tmp3, 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: tmp0 += z1 + z3; nuclear@1: tmp1 += z2 + z4; nuclear@1: tmp2 += z2 + z3; nuclear@1: tmp3 += z1 + z4; nuclear@1: nuclear@1: /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ nuclear@1: nuclear@1: wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS); nuclear@1: wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS); nuclear@1: wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS); nuclear@1: wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS); nuclear@1: wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS); nuclear@1: wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS); nuclear@1: wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS); nuclear@1: wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS); nuclear@1: nuclear@1: inptr++; /* advance pointers to next column */ nuclear@1: quantptr++; nuclear@1: wsptr++; nuclear@1: } nuclear@1: nuclear@1: /* Pass 2: process rows from work array, store into output array. */ nuclear@1: /* Note that we must descale the results by a factor of 8 == 2**3, */ nuclear@1: /* and also undo the PASS1_BITS scaling. */ nuclear@1: nuclear@1: wsptr = workspace; nuclear@1: for (ctr = 0; ctr < DCTSIZE; ctr++) { nuclear@1: outptr = output_buf[ctr] + output_col; nuclear@1: /* Rows of zeroes can be exploited in the same way as we did with columns. nuclear@1: * However, the column calculation has created many nonzero AC terms, so nuclear@1: * the simplification applies less often (typically 5% to 10% of the time). nuclear@1: * On machines with very fast multiplication, it's possible that the nuclear@1: * test takes more time than it's worth. In that case this section nuclear@1: * may be commented out. nuclear@1: */ nuclear@1: nuclear@1: #ifndef NO_ZERO_ROW_TEST nuclear@1: if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 && nuclear@1: wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) { nuclear@1: /* AC terms all zero */ nuclear@1: JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: nuclear@1: outptr[0] = dcval; nuclear@1: outptr[1] = dcval; nuclear@1: outptr[2] = dcval; nuclear@1: outptr[3] = dcval; nuclear@1: outptr[4] = dcval; nuclear@1: outptr[5] = dcval; nuclear@1: outptr[6] = dcval; nuclear@1: outptr[7] = dcval; nuclear@1: nuclear@1: wsptr += DCTSIZE; /* advance pointer to next row */ nuclear@1: continue; nuclear@1: } nuclear@1: #endif nuclear@1: nuclear@1: /* Even part: reverse the even part of the forward DCT. */ nuclear@1: /* The rotator is sqrt(2)*c(-6). */ nuclear@1: nuclear@1: z2 = (INT32) wsptr[2]; nuclear@1: z3 = (INT32) wsptr[6]; nuclear@1: nuclear@1: z1 = MULTIPLY(z2 + z3, FIX_0_541196100); nuclear@1: tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065); nuclear@1: tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865); nuclear@1: nuclear@1: tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS; nuclear@1: tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS; 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: /* Odd part per figure 8; the matrix is unitary and hence its nuclear@1: * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. nuclear@1: */ nuclear@1: nuclear@1: tmp0 = (INT32) wsptr[7]; nuclear@1: tmp1 = (INT32) wsptr[5]; nuclear@1: tmp2 = (INT32) wsptr[3]; nuclear@1: tmp3 = (INT32) wsptr[1]; nuclear@1: nuclear@1: z1 = tmp0 + tmp3; nuclear@1: z2 = tmp1 + tmp2; nuclear@1: z3 = tmp0 + tmp2; nuclear@1: z4 = tmp1 + tmp3; nuclear@1: z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ nuclear@1: nuclear@1: tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ nuclear@1: tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ nuclear@1: tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ nuclear@1: tmp3 = MULTIPLY(tmp3, 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: tmp0 += z1 + z3; nuclear@1: tmp1 += z2 + z4; nuclear@1: tmp2 += z2 + z3; nuclear@1: tmp3 += z1 + z4; nuclear@1: nuclear@1: /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ nuclear@1: nuclear@1: outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0, nuclear@1: CONST_BITS+PASS1_BITS+3) nuclear@1: & RANGE_MASK]; nuclear@1: nuclear@1: wsptr += DCTSIZE; /* advance pointer to next row */ nuclear@1: } nuclear@1: } nuclear@1: nuclear@1: #endif /* DCT_ISLOW_SUPPORTED */