/* | |

* jfdctfst.c | |

* | |

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

* Copyright (C) 1994-1996, Thomas G. Lane. | |

* libjpeg-turbo Modifications: | |

* Copyright (C) 2015, 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 | |

* forward DCT (Discrete Cosine Transform). | |

* | |

* A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT | |

* on each column. 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 jfdctint.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. | |

* | |

* Again to save a few shifts, the intermediate results between pass 1 and | |

* pass 2 are not upscaled, but are represented only to integral precision. | |

* | |

* 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). | |

*/ | |

#define CONST_BITS 8 | |

/* 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_0_382683433 ((JLONG) 98) /* FIX(0.382683433) */ | |

#define FIX_0_541196100 ((JLONG) 139) /* FIX(0.541196100) */ | |

#define FIX_0_707106781 ((JLONG) 181) /* FIX(0.707106781) */ | |

#define FIX_1_306562965 ((JLONG) 334) /* FIX(1.306562965) */ | |

#else | |

#define FIX_0_382683433 FIX(0.382683433) | |

#define FIX_0_541196100 FIX(0.541196100) | |

#define FIX_0_707106781 FIX(0.707106781) | |

#define FIX_1_306562965 FIX(1.306562965) | |

#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)) | |

/* | |

* Perform the forward DCT on one block of samples. | |

*/ | |

GLOBAL(void) | |

jpeg_fdct_ifast (DCTELEM *data) | |

{ | |

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

DCTELEM tmp10, tmp11, tmp12, tmp13; | |

DCTELEM z1, z2, z3, z4, z5, z11, z13; | |

DCTELEM *dataptr; | |

int ctr; | |

SHIFT_TEMPS | |

/* Pass 1: process rows. */ | |

dataptr = data; | |

for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |

tmp0 = dataptr[0] + dataptr[7]; | |

tmp7 = dataptr[0] - dataptr[7]; | |

tmp1 = dataptr[1] + dataptr[6]; | |

tmp6 = dataptr[1] - dataptr[6]; | |

tmp2 = dataptr[2] + dataptr[5]; | |

tmp5 = dataptr[2] - dataptr[5]; | |

tmp3 = dataptr[3] + dataptr[4]; | |

tmp4 = dataptr[3] - dataptr[4]; | |

/* Even part */ | |

tmp10 = tmp0 + tmp3; /* phase 2 */ | |

tmp13 = tmp0 - tmp3; | |

tmp11 = tmp1 + tmp2; | |

tmp12 = tmp1 - tmp2; | |

dataptr[0] = tmp10 + tmp11; /* phase 3 */ | |

dataptr[4] = tmp10 - tmp11; | |

z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ | |

dataptr[2] = tmp13 + z1; /* phase 5 */ | |

dataptr[6] = tmp13 - z1; | |

/* Odd part */ | |

tmp10 = tmp4 + tmp5; /* phase 2 */ | |

tmp11 = tmp5 + tmp6; | |

tmp12 = tmp6 + tmp7; | |

/* The rotator is modified from fig 4-8 to avoid extra negations. */ | |

z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ | |

z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ | |

z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ | |

z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ | |

z11 = tmp7 + z3; /* phase 5 */ | |

z13 = tmp7 - z3; | |

dataptr[5] = z13 + z2; /* phase 6 */ | |

dataptr[3] = z13 - z2; | |

dataptr[1] = z11 + z4; | |

dataptr[7] = z11 - z4; | |

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

} | |

/* Pass 2: process columns. */ | |

dataptr = data; | |

for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |

tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; | |

tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; | |

tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; | |

tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; | |

tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; | |

tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; | |

tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; | |

tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; | |

/* Even part */ | |

tmp10 = tmp0 + tmp3; /* phase 2 */ | |

tmp13 = tmp0 - tmp3; | |

tmp11 = tmp1 + tmp2; | |

tmp12 = tmp1 - tmp2; | |

dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ | |

dataptr[DCTSIZE*4] = tmp10 - tmp11; | |

z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ | |

dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ | |

dataptr[DCTSIZE*6] = tmp13 - z1; | |

/* Odd part */ | |

tmp10 = tmp4 + tmp5; /* phase 2 */ | |

tmp11 = tmp5 + tmp6; | |

tmp12 = tmp6 + tmp7; | |

/* The rotator is modified from fig 4-8 to avoid extra negations. */ | |

z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ | |

z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ | |

z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ | |

z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ | |

z11 = tmp7 + z3; /* phase 5 */ | |

z13 = tmp7 - z3; | |

dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ | |

dataptr[DCTSIZE*3] = z13 - z2; | |

dataptr[DCTSIZE*1] = z11 + z4; | |

dataptr[DCTSIZE*7] = z11 - z4; | |

dataptr++; /* advance pointer to next column */ | |

} | |

} | |

#endif /* DCT_IFAST_SUPPORTED */ |