/* | |

* jidctflt.c | |

* | |

* Copyright (C) 1994-1998, 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 floating-point implementation of the | |

* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine | |

* must also perform dequantization of the input coefficients. | |

* | |

* This implementation should be more accurate than either of the integer | |

* IDCT implementations. However, it may not give the same results on all | |

* machines because of differences in roundoff behavior. Speed will depend | |

* on the hardware's floating point capacity. | |

* | |

* 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). 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 a fixed-point | |

* implementation, accuracy is lost due to imprecise representation of the | |

* scaled quantization values. However, that problem does not arise if | |

* we use floating point arithmetic. | |

*/ | |

#define JPEG_INTERNALS | |

#include "jinclude.h" | |

#include "jpeglib.h" | |

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

#ifdef DCT_FLOAT_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 | |

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

* entry; produce a float result. | |

*/ | |

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

/* | |

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

*/ | |

GLOBAL(void) | |

jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr, | |

JCOEFPTR coef_block, | |

JSAMPARRAY output_buf, JDIMENSION output_col) | |

{ | |

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

FAST_FLOAT tmp10, tmp11, tmp12, tmp13; | |

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

JCOEFPTR inptr; | |

FLOAT_MULT_TYPE * quantptr; | |

FAST_FLOAT * wsptr; | |

JSAMPROW outptr; | |

JSAMPLE *range_limit = IDCT_range_limit(cinfo); | |

int ctr; | |

FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */ | |

SHIFT_TEMPS | |

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

inptr = coef_block; | |

quantptr = (FLOAT_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 */ | |

FAST_FLOAT dcval = 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 = (tmp1 - tmp3) * ((FAST_FLOAT) 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 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ | |

z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ | |

tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ | |

tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ | |

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

tmp5 = tmp11 - tmp6; | |

tmp4 = tmp10 + tmp5; | |

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

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

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

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

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

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

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

wsptr[DCTSIZE*3] = 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. */ | |

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). | |

* And testing floats for zero is relatively expensive, so we don't bother. | |

*/ | |

/* Even part */ | |

tmp10 = wsptr[0] + wsptr[4]; | |

tmp11 = wsptr[0] - wsptr[4]; | |

tmp13 = wsptr[2] + wsptr[6]; | |

tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13; | |

tmp0 = tmp10 + tmp13; | |

tmp3 = tmp10 - tmp13; | |

tmp1 = tmp11 + tmp12; | |

tmp2 = tmp11 - tmp12; | |

/* Odd part */ | |

z13 = wsptr[5] + wsptr[3]; | |

z10 = wsptr[5] - wsptr[3]; | |

z11 = wsptr[1] + wsptr[7]; | |

z12 = wsptr[1] - wsptr[7]; | |

tmp7 = z11 + z13; | |

tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); | |

z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ | |

tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ | |

tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ | |

tmp6 = tmp12 - tmp7; | |

tmp5 = tmp11 - tmp6; | |

tmp4 = tmp10 + tmp5; | |

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

outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3) | |

& RANGE_MASK]; | |

outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3) | |

& RANGE_MASK]; | |

outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3) | |

& RANGE_MASK]; | |

outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3) | |

& RANGE_MASK]; | |

outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3) | |

& RANGE_MASK]; | |

outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3) | |

& RANGE_MASK]; | |

outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3) | |

& RANGE_MASK]; | |

outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3) | |

& RANGE_MASK]; | |

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

} | |

} | |

#endif /* DCT_FLOAT_SUPPORTED */ |