/* | |

* 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 */ |