/* | |

* jidctfst.c | |

* | |

* This file was part of the Independent JPEG Group's software: | |

* Copyright (C) 1994-1998, Thomas G. Lane. | |

* libjpeg-turbo Modifications: | |

* Copyright (C) 2015, 2022, D. R. Commander. | |

* For conditions of distribution and use, see the accompanying README.ijg | |

* file. | |

* | |

* This file contains a fast, not so 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 Arai, Agui, and Nakajima's algorithm for | |

* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in | |

* Japanese, but the algorithm is described in the Pennebaker & Mitchell | |

* JPEG textbook (see REFERENCES section in file README.ijg). The following | |

* code is based directly on figure 4-8 in P&M. | |

* While an 8-point DCT cannot be done in less than 11 multiplies, it is | |

* possible to arrange the computation so that many of the multiplies are | |

* simple scalings of the final outputs. These multiplies can then be | |

* folded into the multiplications or divisions by the JPEG quantization | |

* table entries. The AA&N method leaves only 5 multiplies and 29 adds | |

* to be done in the DCT itself. | |

* The primary disadvantage of this method is that with fixed-point math, | |

* accuracy is lost due to imprecise representation of the scaled | |

* quantization values. The smaller the quantization table entry, the less | |

* precise the scaled value, so this implementation does worse with high- | |

* quality-setting files than with low-quality ones. | |

*/ | |

#define JPEG_INTERNALS | |

#include "jinclude.h" | |

#include "jpeglib.h" | |

#include "jdct.h" /* Private declarations for DCT subsystem */ | |

#ifdef DCT_IFAST_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 | |

/* Scaling decisions are generally the same as in the LL&M algorithm; | |

* see jidctint.c for more details. However, we choose to descale | |

* (right shift) multiplication products as soon as they are formed, | |

* rather than carrying additional fractional bits into subsequent additions. | |

* This compromises accuracy slightly, but it lets us save a few shifts. | |

* More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) | |

* everywhere except in the multiplications proper; this saves a good deal | |

* of work on 16-bit-int machines. | |

* | |

* The dequantized coefficients are not integers because the AA&N scaling | |

* factors have been incorporated. We represent them scaled up by PASS1_BITS, | |

* so that the first and second IDCT rounds have the same input scaling. | |

* For 8-bit samples, we choose IFAST_SCALE_BITS = PASS1_BITS so as to | |

* avoid a descaling shift; this compromises accuracy rather drastically | |

* for small quantization table entries, but it saves a lot of shifts. | |

* For 12-bit samples, there's no hope of using 16x16 multiplies anyway, | |

* so we use a much larger scaling factor to preserve accuracy. | |

* | |

* A final compromise is to represent the multiplicative constants to only | |

* 8 fractional bits, rather than 13. This saves some shifting work on some | |

* machines, and may also reduce the cost of multiplication (since there | |

* are fewer one-bits in the constants). | |

*/ | |

#if BITS_IN_JSAMPLE == 8 | |

#define CONST_BITS 8 | |

#define PASS1_BITS 2 | |

#else | |

#define CONST_BITS 8 | |

#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 == 8 | |

#define FIX_1_082392200 ((JLONG)277) /* FIX(1.082392200) */ | |

#define FIX_1_414213562 ((JLONG)362) /* FIX(1.414213562) */ | |

#define FIX_1_847759065 ((JLONG)473) /* FIX(1.847759065) */ | |

#define FIX_2_613125930 ((JLONG)669) /* FIX(2.613125930) */ | |

#else | |

#define FIX_1_082392200 FIX(1.082392200) | |

#define FIX_1_414213562 FIX(1.414213562) | |

#define FIX_1_847759065 FIX(1.847759065) | |

#define FIX_2_613125930 FIX(2.613125930) | |

#endif | |

/* We can gain a little more speed, with a further compromise in accuracy, | |

* by omitting the addition in a descaling shift. This yields an incorrectly | |

* rounded result half the time... | |

*/ | |

#ifndef USE_ACCURATE_ROUNDING | |

#undef DESCALE | |

#define DESCALE(x, n) RIGHT_SHIFT(x, n) | |

#endif | |

/* Multiply a DCTELEM variable by an JLONG constant, and immediately | |

* descale to yield a DCTELEM result. | |

*/ | |

#define MULTIPLY(var, const) ((DCTELEM)DESCALE((var) * (const), CONST_BITS)) | |

/* Dequantize a coefficient by multiplying it by the multiplier-table | |

* entry; produce a DCTELEM result. For 8-bit data a 16x16->16 | |

* multiplication will do. For 12-bit data, the multiplier table is | |

* declared JLONG, so a 32-bit multiply will be used. | |

*/ | |

#if BITS_IN_JSAMPLE == 8 | |

#define DEQUANTIZE(coef, quantval) (((IFAST_MULT_TYPE)(coef)) * (quantval)) | |

#else | |

#define DEQUANTIZE(coef, quantval) \ | |

DESCALE((coef) * (quantval), IFAST_SCALE_BITS - PASS1_BITS) | |

#endif | |

/* Like DESCALE, but applies to a DCTELEM and produces an int. | |

* We assume that int right shift is unsigned if JLONG right shift is. | |

*/ | |

#ifdef RIGHT_SHIFT_IS_UNSIGNED | |

#define ISHIFT_TEMPS DCTELEM ishift_temp; | |

#if BITS_IN_JSAMPLE == 8 | |

#define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ | |

#else | |

#define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ | |

#endif | |

#define IRIGHT_SHIFT(x, shft) \ | |

((ishift_temp = (x)) < 0 ? \ | |

(ishift_temp >> (shft)) | ((~((DCTELEM)0)) << (DCTELEMBITS - (shft))) : \ | |

(ishift_temp >> (shft))) | |

#else | |

#define ISHIFT_TEMPS | |

#define IRIGHT_SHIFT(x, shft) ((x) >> (shft)) | |

#endif | |

#ifdef USE_ACCURATE_ROUNDING | |

#define IDESCALE(x, n) ((int)IRIGHT_SHIFT((x) + (1 << ((n) - 1)), n)) | |

#else | |

#define IDESCALE(x, n) ((int)IRIGHT_SHIFT(x, n)) | |

#endif | |

/* | |

* Perform dequantization and inverse DCT on one block of coefficients. | |

*/ | |

GLOBAL(void) | |

_jpeg_idct_ifast(j_decompress_ptr cinfo, jpeg_component_info *compptr, | |

JCOEFPTR coef_block, _JSAMPARRAY output_buf, | |

JDIMENSION output_col) | |

{ | |

DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; | |

DCTELEM tmp10, tmp11, tmp12, tmp13; | |

DCTELEM z5, z10, z11, z12, z13; | |

JCOEFPTR inptr; | |

IFAST_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 /* for DESCALE */ | |

ISHIFT_TEMPS /* for IDESCALE */ | |

/* Pass 1: process columns from input, store into work array. */ | |

inptr = coef_block; | |

quantptr = (IFAST_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 = (int)DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0]); | |

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 */ | |

tmp0 = DEQUANTIZE(inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0]); | |

tmp1 = DEQUANTIZE(inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2]); | |

tmp2 = DEQUANTIZE(inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4]); | |

tmp3 = DEQUANTIZE(inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6]); | |

tmp10 = tmp0 + tmp2; /* phase 3 */ | |

tmp11 = tmp0 - tmp2; | |

tmp13 = tmp1 + tmp3; /* phases 5-3 */ | |

tmp12 = MULTIPLY(tmp1 - tmp3, FIX_1_414213562) - tmp13; /* 2*c4 */ | |

tmp0 = tmp10 + tmp13; /* phase 2 */ | |

tmp3 = tmp10 - tmp13; | |

tmp1 = tmp11 + tmp12; | |

tmp2 = tmp11 - tmp12; | |

/* Odd part */ | |

tmp4 = DEQUANTIZE(inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1]); | |

tmp5 = DEQUANTIZE(inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3]); | |

tmp6 = DEQUANTIZE(inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5]); | |

tmp7 = DEQUANTIZE(inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7]); | |

z13 = tmp6 + tmp5; /* phase 6 */ | |

z10 = tmp6 - tmp5; | |

z11 = tmp4 + tmp7; | |

z12 = tmp4 - tmp7; | |

tmp7 = z11 + z13; /* phase 5 */ | |

tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ | |

z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ | |

tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ | |

tmp12 = MULTIPLY(z10, -FIX_2_613125930) + z5; /* -2*(c2+c6) */ | |

tmp6 = tmp12 - tmp7; /* phase 2 */ | |

tmp5 = tmp11 - tmp6; | |

tmp4 = tmp10 + tmp5; | |

wsptr[DCTSIZE * 0] = (int)(tmp0 + tmp7); | |

wsptr[DCTSIZE * 7] = (int)(tmp0 - tmp7); | |

wsptr[DCTSIZE * 1] = (int)(tmp1 + tmp6); | |

wsptr[DCTSIZE * 6] = (int)(tmp1 - tmp6); | |

wsptr[DCTSIZE * 2] = (int)(tmp2 + tmp5); | |

wsptr[DCTSIZE * 5] = (int)(tmp2 - tmp5); | |

wsptr[DCTSIZE * 4] = (int)(tmp3 + tmp4); | |

wsptr[DCTSIZE * 3] = (int)(tmp3 - tmp4); | |

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[IDESCALE(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 */ | |

tmp10 = ((DCTELEM)wsptr[0] + (DCTELEM)wsptr[4]); | |

tmp11 = ((DCTELEM)wsptr[0] - (DCTELEM)wsptr[4]); | |

tmp13 = ((DCTELEM)wsptr[2] + (DCTELEM)wsptr[6]); | |

tmp12 = | |

MULTIPLY((DCTELEM)wsptr[2] - (DCTELEM)wsptr[6], FIX_1_414213562) - tmp13; | |

tmp0 = tmp10 + tmp13; | |

tmp3 = tmp10 - tmp13; | |

tmp1 = tmp11 + tmp12; | |

tmp2 = tmp11 - tmp12; | |

/* Odd part */ | |

z13 = (DCTELEM)wsptr[5] + (DCTELEM)wsptr[3]; | |

z10 = (DCTELEM)wsptr[5] - (DCTELEM)wsptr[3]; | |

z11 = (DCTELEM)wsptr[1] + (DCTELEM)wsptr[7]; | |

z12 = (DCTELEM)wsptr[1] - (DCTELEM)wsptr[7]; | |

tmp7 = z11 + z13; /* phase 5 */ | |

tmp11 = MULTIPLY(z11 - z13, FIX_1_414213562); /* 2*c4 */ | |

z5 = MULTIPLY(z10 + z12, FIX_1_847759065); /* 2*c2 */ | |

tmp10 = MULTIPLY(z12, FIX_1_082392200) - z5; /* 2*(c2-c6) */ | |

tmp12 = MULTIPLY(z10, -FIX_2_613125930) + z5; /* -2*(c2+c6) */ | |

tmp6 = tmp12 - tmp7; /* phase 2 */ | |

tmp5 = tmp11 - tmp6; | |

tmp4 = tmp10 + tmp5; | |

/* Final output stage: scale down by a factor of 8 and range-limit */ | |

outptr[0] = | |

range_limit[IDESCALE(tmp0 + tmp7, PASS1_BITS + 3) & RANGE_MASK]; | |

outptr[7] = | |

range_limit[IDESCALE(tmp0 - tmp7, PASS1_BITS + 3) & RANGE_MASK]; | |

outptr[1] = | |

range_limit[IDESCALE(tmp1 + tmp6, PASS1_BITS + 3) & RANGE_MASK]; | |

outptr[6] = | |

range_limit[IDESCALE(tmp1 - tmp6, PASS1_BITS + 3) & RANGE_MASK]; | |

outptr[2] = | |

range_limit[IDESCALE(tmp2 + tmp5, PASS1_BITS + 3) & RANGE_MASK]; | |

outptr[5] = | |

range_limit[IDESCALE(tmp2 - tmp5, PASS1_BITS + 3) & RANGE_MASK]; | |

outptr[4] = | |

range_limit[IDESCALE(tmp3 + tmp4, PASS1_BITS + 3) & RANGE_MASK]; | |

outptr[3] = | |

range_limit[IDESCALE(tmp3 - tmp4, PASS1_BITS + 3) & RANGE_MASK]; | |

wsptr += DCTSIZE; /* advance pointer to next row */ | |

} | |

} | |

#endif /* DCT_IFAST_SUPPORTED */ |