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1 | /* |

2 | * jfdctint.c |

3 | * |

4 | * Copyright (C) 1991-1996, Thomas G. Lane. |

5 | * This file is part of the Independent JPEG Group's software. |

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

7 | * |

8 | * This file contains a slow-but-accurate integer implementation of the |

9 | * forward DCT (Discrete Cosine Transform). |

10 | * |

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

12 | * on each column. Direct algorithms are also available, but they are |

13 | * much more complex and seem not to be any faster when reduced to code. |

14 | * |

15 | * This implementation is based on an algorithm described in |

16 | * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT |

17 | * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, |

18 | * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. |

19 | * The primary algorithm described there uses 11 multiplies and 29 adds. |

20 | * We use their alternate method with 12 multiplies and 32 adds. |

21 | * The advantage of this method is that no data path contains more than one |

22 | * multiplication; this allows a very simple and accurate implementation in |

23 | * scaled fixed-point arithmetic, with a minimal number of shifts. |

24 | */ |

25 | |

26 | #define JPEG_INTERNALS |

27 | #include "jinclude.h" |

28 | #include "jpeglib.h" |

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

30 | |

31 | #ifdef DCT_ISLOW_SUPPORTED |

32 | |

33 | |

34 | /* |

35 | * This module is specialized to the case DCTSIZE = 8. |

36 | */ |

37 | |

38 | #if DCTSIZE != 8 |

39 | Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ |

40 | #endif |

41 | |

42 | |

43 | /* |

44 | * The poop on this scaling stuff is as follows: |

45 | * |

46 | * Each 1-D DCT step produces outputs which are a factor of sqrt(N) |

47 | * larger than the true DCT outputs. The final outputs are therefore |

48 | * a factor of N larger than desired; since N=8 this can be cured by |

49 | * a simple right shift at the end of the algorithm. The advantage of |

50 | * this arrangement is that we save two multiplications per 1-D DCT, |

51 | * because the y0 and y4 outputs need not be divided by sqrt(N). |

52 | * In the IJG code, this factor of 8 is removed by the quantization step |

53 | * (in jcdctmgr.c), NOT in this module. |

54 | * |

55 | * We have to do addition and subtraction of the integer inputs, which |

56 | * is no problem, and multiplication by fractional constants, which is |

57 | * a problem to do in integer arithmetic. We multiply all the constants |

58 | * by CONST_SCALE and convert them to integer constants (thus retaining |

59 | * CONST_BITS bits of precision in the constants). After doing a |

60 | * multiplication we have to divide the product by CONST_SCALE, with proper |

61 | * rounding, to produce the correct output. This division can be done |

62 | * cheaply as a right shift of CONST_BITS bits. We postpone shifting |

63 | * as long as possible so that partial sums can be added together with |

64 | * full fractional precision. |

65 | * |

66 | * The outputs of the first pass are scaled up by PASS1_BITS bits so that |

67 | * they are represented to better-than-integral precision. These outputs |

68 | * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word |

69 | * with the recommended scaling. (For 12-bit sample data, the intermediate |

70 | * array is INT32 anyway.) |

71 | * |

72 | * To avoid overflow of the 32-bit intermediate results in pass 2, we must |

73 | * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis |

74 | * shows that the values given below are the most effective. |

75 | */ |

76 | |

77 | #if BITS_IN_JSAMPLE == 8 |

78 | #define CONST_BITS 13 |

79 | #define PASS1_BITS 2 |

80 | #else |

81 | #define CONST_BITS 13 |

82 | #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ |

83 | #endif |

84 | |

85 | /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus |

86 | * causing a lot of useless floating-point operations at run time. |

87 | * To get around this we use the following pre-calculated constants. |

88 | * If you change CONST_BITS you may want to add appropriate values. |

89 | * (With a reasonable C compiler, you can just rely on the FIX() macro...) |

90 | */ |

91 | |

92 | #if CONST_BITS == 13 |

93 | #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */ |

94 | #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ |

95 | #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ |

96 | #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ |

97 | #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ |

98 | #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ |

99 | #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ |

100 | #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ |

101 | #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ |

102 | #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ |

103 | #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ |

104 | #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */ |

105 | #else |

106 | #define FIX_0_298631336 FIX(0.298631336) |

107 | #define FIX_0_390180644 FIX(0.390180644) |

108 | #define FIX_0_541196100 FIX(0.541196100) |

109 | #define FIX_0_765366865 FIX(0.765366865) |

110 | #define FIX_0_899976223 FIX(0.899976223) |

111 | #define FIX_1_175875602 FIX(1.175875602) |

112 | #define FIX_1_501321110 FIX(1.501321110) |

113 | #define FIX_1_847759065 FIX(1.847759065) |

114 | #define FIX_1_961570560 FIX(1.961570560) |

115 | #define FIX_2_053119869 FIX(2.053119869) |

116 | #define FIX_2_562915447 FIX(2.562915447) |

117 | #define FIX_3_072711026 FIX(3.072711026) |

118 | #endif |

119 | |

120 | |

121 | /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. |

122 | * For 8-bit samples with the recommended scaling, all the variable |

123 | * and constant values involved are no more than 16 bits wide, so a |

124 | * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. |

125 | * For 12-bit samples, a full 32-bit multiplication will be needed. |

126 | */ |

127 | |

128 | #if BITS_IN_JSAMPLE == 8 |

129 | #define MULTIPLY(var,const) MULTIPLY16C16(var,const) |

130 | #else |

131 | #define MULTIPLY(var,const) ((var) * (const)) |

132 | #endif |

133 | |

134 | |

135 | /* |

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

137 | */ |

138 | |

139 | GLOBAL(void) |

140 | jpeg_fdct_islow (DCTELEM * data) |

141 | { |

142 | INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; |

143 | INT32 tmp10, tmp11, tmp12, tmp13; |

144 | INT32 z1, z2, z3, z4, z5; |

145 | DCTELEM *dataptr; |

146 | int ctr; |

147 | SHIFT_TEMPS |

148 | |

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

150 | /* Note results are scaled up by sqrt(8) compared to a true DCT; */ |

151 | /* furthermore, we scale the results by 2**PASS1_BITS. */ |

152 | |

153 | dataptr = data; |

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

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

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

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

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

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

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

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

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

163 | |

164 | /* Even part per LL&M figure 1 --- note that published figure is faulty; |

165 | * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". |

166 | */ |

167 | |

168 | tmp10 = tmp0 + tmp3; |

169 | tmp13 = tmp0 - tmp3; |

170 | tmp11 = tmp1 + tmp2; |

171 | tmp12 = tmp1 - tmp2; |

172 | |

173 | dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); |

174 | dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); |

175 | |

176 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); |

177 | dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), |

178 | CONST_BITS-PASS1_BITS); |

179 | dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), |

180 | CONST_BITS-PASS1_BITS); |

181 | |

182 | /* Odd part per figure 8 --- note paper omits factor of sqrt(2). |

183 | * cK represents cos(K*pi/16). |

184 | * i0..i3 in the paper are tmp4..tmp7 here. |

185 | */ |

186 | |

187 | z1 = tmp4 + tmp7; |

188 | z2 = tmp5 + tmp6; |

189 | z3 = tmp4 + tmp6; |

190 | z4 = tmp5 + tmp7; |

191 | z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ |

192 | |

193 | tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ |

194 | tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ |

195 | tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ |

196 | tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ |

197 | z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ |

198 | z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ |

199 | z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ |

200 | z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ |

201 | |

202 | z3 += z5; |

203 | z4 += z5; |

204 | |

205 | dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); |

206 | dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); |

207 | dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); |

208 | dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); |

209 | |

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

211 | } |

212 | |

213 | /* Pass 2: process columns. |

214 | * We remove the PASS1_BITS scaling, but leave the results scaled up |

215 | * by an overall factor of 8. |

216 | */ |

217 | |

218 | dataptr = data; |

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

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

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

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

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

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

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

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

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

228 | |

229 | /* Even part per LL&M figure 1 --- note that published figure is faulty; |

230 | * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". |

231 | */ |

232 | |

233 | tmp10 = tmp0 + tmp3; |

234 | tmp13 = tmp0 - tmp3; |

235 | tmp11 = tmp1 + tmp2; |

236 | tmp12 = tmp1 - tmp2; |

237 | |

238 | dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); |

239 | dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); |

240 | |

241 | z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); |

242 | dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), |

243 | CONST_BITS+PASS1_BITS); |

244 | dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), |

245 | CONST_BITS+PASS1_BITS); |

246 | |

247 | /* Odd part per figure 8 --- note paper omits factor of sqrt(2). |

248 | * cK represents cos(K*pi/16). |

249 | * i0..i3 in the paper are tmp4..tmp7 here. |

250 | */ |

251 | |

252 | z1 = tmp4 + tmp7; |

253 | z2 = tmp5 + tmp6; |

254 | z3 = tmp4 + tmp6; |

255 | z4 = tmp5 + tmp7; |

256 | z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ |

257 | |

258 | tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ |

259 | tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ |

260 | tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ |

261 | tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ |

262 | z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ |

263 | z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ |

264 | z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ |

265 | z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ |

266 | |

267 | z3 += z5; |

268 | z4 += z5; |

269 | |

270 | dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, |

271 | CONST_BITS+PASS1_BITS); |

272 | dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, |

273 | CONST_BITS+PASS1_BITS); |

274 | dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, |

275 | CONST_BITS+PASS1_BITS); |

276 | dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, |

277 | CONST_BITS+PASS1_BITS); |

278 | |

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

280 | } |

281 | } |

282 | |

283 | #endif /* DCT_ISLOW_SUPPORTED */ |

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