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33 #ifndef _SCIP_DBLDBL_ARITH_
34 #define _SCIP_DBLDBL_ARITH_
39 #ifndef DISABLE_QUADPREC
42 #define QUAD_EPSILON 1e-12
45 #define QUAD_HI(x) x ## hi
46 #define QUAD_LO(x) x ## lo
47 #define QUAD(x) QUAD_HI(x), QUAD_LO(x)
48 #define QUAD_MEMBER(x) QUAD_HI(x); QUAD_LO(x)
49 #define QUAD_TO_DBL(x) ( QUAD_HI(x) + QUAD_LO(x) )
50 #define QUAD_SCALE(x, a) do { QUAD_HI(x) *= (a); QUAD_LO(x) *= (a); } while(0)
51 #define QUAD_ASSIGN(a, constant) do { QUAD_HI(a) = (constant); QUAD_LO(a) = 0.0; } while(0)
52 #define QUAD_ASSIGN_Q(a, b) do { QUAD_HI(a) = QUAD_HI(b); QUAD_LO(a) = QUAD_LO(b); } while(0)
53 #define QUAD_ARRAY_SIZE(size) ((size)*2)
54 #define QUAD_ARRAY_LOAD(r, a, idx) do { QUAD_HI(r) = (a)[2*(idx)]; QUAD_LO(r) = (a)[2*(idx) + 1]; } while(0)
55 #define QUAD_ARRAY_STORE(a, idx, x) do { (a)[2*(idx)] = QUAD_HI(x); (a)[2*(idx) + 1] = QUAD_LO(x); } while(0)
58 #define SCIPquadprecProdDD(r, a, b) SCIPdbldblProd(QUAD_HI(r), QUAD_LO(r), a, b)
59 #define SCIPquadprecSquareD(r, a) SCIPdbldblSquare(QUAD_HI(r), QUAD_LO(r), a)
60 #define SCIPquadprecSumDD(r, a, b) SCIPdbldblSum(QUAD_HI(r), QUAD_LO(r), a, b)
61 #define SCIPquadprecDivDD(r, a, b) SCIPdbldblDiv(QUAD_HI(r), QUAD_LO(r), a, b)
62 #define SCIPquadprecSumQD(r, a, b) SCIPdbldblSum21(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), b)
63 #define SCIPquadprecProdQD(r, a, b) SCIPdbldblProd21(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), b)
64 #define SCIPquadprecDivDQ(r, a, b) SCIPdbldblDiv12(QUAD_HI(r), QUAD_LO(r), a, QUAD_HI(b), QUAD_LO(b))
65 #define SCIPquadprecDivQD(r, a, b) SCIPdbldblDiv21(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), b)
66 #define SCIPquadprecProdQQ(r, a, b) SCIPdbldblProd22(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), QUAD_HI(b), QUAD_LO(b))
67 #define SCIPquadprecSumQQ(r, a, b) SCIPdbldblSum22(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), QUAD_HI(b), QUAD_LO(b))
68 #define SCIPquadprecSquareQ(r, a) SCIPdbldblSquare2(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a))
69 #define SCIPquadprecDivQQ(r, a, b) SCIPdbldblDiv22(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), QUAD_HI(b), QUAD_LO(b))
70 #define SCIPquadprecSqrtD(r, a) SCIPdbldblSqrt(QUAD_HI(r), QUAD_LO(r), a)
71 #define SCIPquadprecSqrtQ(r, a) SCIPdbldblSqrt2(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a))
72 #define SCIPquadprecAbsQ(r, a) SCIPdbldblAbs2(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a))
73 #define SCIPquadprecFloorQ(r, a) SCIPdbldblFloor2(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a))
74 #define SCIPquadprecCeilQ(r, a) SCIPdbldblCeil2(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a))
75 #define SCIPquadprecEpsFloorQ(r, a, eps) SCIPdbldblEpsFloor2(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), eps)
76 #define SCIPquadprecEpsCeilQ(r, a, eps) SCIPdbldblEpsCeil2(QUAD_HI(r), QUAD_LO(r), QUAD_HI(a), QUAD_LO(a), eps)
81 #define QUAD_EPSILON 1e-9
87 #define QUAD_MEMBER(x) x
88 #define QUAD_TO_DBL(x) (x)
89 #define QUAD_SCALE(x, a) do { (x) *= (a); } while(0)
90 #define QUAD_ASSIGN(a, constant) do { (a) = constant; } while(0)
91 #define QUAD_ASSIGN_Q(a, b) do { (a) = (b); } while(0)
92 #define QUAD_ARRAY_SIZE(size) (size)
93 #define QUAD_ARRAY_LOAD(r, a, idx) do { r = (a)[(idx)]; } while(0)
94 #define QUAD_ARRAY_STORE(a, idx, x) do { (a)[(idx)] = (x); } while(0)
96 #define SCIPquadprecProdDD(r, a, b) do { (r) = (a) * (b); } while(0)
97 #define SCIPquadprecSquareD(r, a) do { (r) = (a) * (a); } while(0)
98 #define SCIPquadprecSumDD(r, a, b) do { (r) = (a) + (b); } while(0)
99 #define SCIPquadprecDivDD(r, a, b) do { (r) = (a) / (b); } while(0)
100 #define SCIPquadprecSumQD(r, a, b) do { (r) = (a) + (b); } while(0)
101 #define SCIPquadprecProdQD(r, a, b) do { (r) = (a) * (b); } while(0)
102 #define SCIPquadprecDivDQ(r, a, b) do { (r) = (a) / (b); } while(0)
103 #define SCIPquadprecDivQD(r, a, b) do { (r) = (a) / (b); } while(0)
104 #define SCIPquadprecProdQQ(r, a, b) do { (r) = (a) * (b); } while(0)
105 #define SCIPquadprecSumQQ(r, a, b) do { (r) = (a) + (b); } while(0)
106 #define SCIPquadprecSquareQ(r, a) do { (r) = (a) * (a); } while(0)
107 #define SCIPquadprecDivQQ(r, a, b) do { (r) = (a) / (b); } while(0)
108 #define SCIPquadprecSqrtD(r, a) do { (r) = sqrt(a); } while(0)
109 #define SCIPquadprecSqrtQ(r, a) do { (r) = sqrt(a); } while(0)
110 #define SCIPquadprecAbsQ(r, a) do { (r) = fabs(a); } while(0)
111 #define SCIPquadprecFloorQ(r, a) do { (r) = floor(a); } while(0)
112 #define SCIPquadprecCeilQ(r, a) do { (r) = ceil(a); } while(0)
113 #define SCIPquadprecEpsFloorQ(r, a, eps) do { (r) = floor((a) + (eps)); } while(0)
114 #define SCIPquadprecEpsCeilQ(r, a, eps) do { (r) = ceil((a) - (eps)); } while(0)
118 #define __SCIPdbldblSplit(rhi, rlo, x) \
120 const double __tmp_split_dbl = 134217729.0 * (x); \
121 (rhi) = __tmp_split_dbl - (__tmp_split_dbl - (x)); \
122 (rlo) = (x) - (rhi);\
126 #define SCIPdbldblProd(rhi, rlo, a, b) \
128 double __tmp_dbldbl_prod_ahi; \
129 double __tmp_dbldbl_prod_alo; \
130 double __tmp_dbldbl_prod_bhi; \
131 double __tmp_dbldbl_prod_blo; \
132 __SCIPdbldblSplit(__tmp_dbldbl_prod_ahi, __tmp_dbldbl_prod_alo, a); \
133 __SCIPdbldblSplit(__tmp_dbldbl_prod_bhi, __tmp_dbldbl_prod_blo, b); \
135 (rlo) = __tmp_dbldbl_prod_alo * __tmp_dbldbl_prod_blo - \
136 ((((rhi) - __tmp_dbldbl_prod_ahi * __tmp_dbldbl_prod_bhi) \
137 - __tmp_dbldbl_prod_alo * __tmp_dbldbl_prod_bhi) \
138 - __tmp_dbldbl_prod_ahi * __tmp_dbldbl_prod_blo); \
142 #define SCIPdbldblSquare(rhi, rlo, a) \
144 double __tmp_dbldbl_square_ahi; \
145 double __tmp_dbldbl_square_alo; \
146 __SCIPdbldblSplit(__tmp_dbldbl_square_ahi, __tmp_dbldbl_square_alo, a); \
148 (rlo) = __tmp_dbldbl_square_alo * __tmp_dbldbl_square_alo - \
149 ((((rhi) - __tmp_dbldbl_square_ahi * __tmp_dbldbl_square_ahi) \
150 - 2.0 * __tmp_dbldbl_square_alo * __tmp_dbldbl_square_ahi)); \
154 #define SCIPdbldblSum(rhi, rlo, a, b) \
156 double __tmp1_dbldbl_sum; \
157 double __tmp2_dbldbl_sum; \
158 __tmp2_dbldbl_sum = (a) + (b); \
159 __tmp1_dbldbl_sum = __tmp2_dbldbl_sum - (a); \
160 (rlo) = ((a) - (__tmp2_dbldbl_sum - __tmp1_dbldbl_sum)) + ((b) - __tmp1_dbldbl_sum); \
161 (rhi) = __tmp2_dbldbl_sum; \
165 #define SCIPdbldblDiv(rhi, rlo, a, b) \
167 double __tmp_dbldbl_div_hi; \
168 double __tmp_dbldbl_div_lo; \
169 double __estim_dbldbl_div = (a)/(b); \
170 SCIPdbldblProd(__tmp_dbldbl_div_hi, __tmp_dbldbl_div_lo, b, __estim_dbldbl_div); \
171 SCIPdbldblSum21(__tmp_dbldbl_div_hi, __tmp_dbldbl_div_lo, __tmp_dbldbl_div_hi, __tmp_dbldbl_div_lo, -(a)); \
172 __tmp_dbldbl_div_hi /= (b); \
173 __tmp_dbldbl_div_lo /= (b); \
174 SCIPdbldblSum21(rhi, rlo, -__tmp_dbldbl_div_hi, -__tmp_dbldbl_div_lo, __estim_dbldbl_div); \
180 #define SCIPdbldblSum21(rhi, rlo, ahi, alo, b) \
182 double __tmp_dbldbl_sum21_hi; \
183 double __tmp_dbldbl_sum21_lo; \
184 SCIPdbldblSum(__tmp_dbldbl_sum21_hi, __tmp_dbldbl_sum21_lo, ahi, b); \
185 (rlo) = __tmp_dbldbl_sum21_lo + (alo); \
186 (rhi) = __tmp_dbldbl_sum21_hi; \
193 #define SCIPdbldblProd21(rhi, rlo, ahi, alo, b) \
195 double __tmp_dbldbl_prod21_hi; \
196 double __tmp_dbldbl_prod21_lo; \
197 SCIPdbldblProd(__tmp_dbldbl_prod21_hi, __tmp_dbldbl_prod21_lo, ahi, b); \
198 (rlo) = (alo) * (b) + __tmp_dbldbl_prod21_lo; \
199 (rhi) = __tmp_dbldbl_prod21_hi; \
205 #define SCIPdbldblDiv12(rhi, rlo, a, bhi, blo) \
207 double __tmp_dbldbl_div12_hi; \
208 double __tmp_dbldbl_div12_lo; \
209 double __estim_dbldbl_div12 = (a)/(bhi); \
210 SCIPdbldblProd21(__tmp_dbldbl_div12_hi, __tmp_dbldbl_div12_lo, bhi, blo, __estim_dbldbl_div12); \
211 SCIPdbldblSum21(__tmp_dbldbl_div12_hi, __tmp_dbldbl_div12_lo, __tmp_dbldbl_div12_hi, __tmp_dbldbl_div12_lo, -(a)); \
212 __tmp_dbldbl_div12_hi /= (bhi); \
213 __tmp_dbldbl_div12_lo /= (bhi); \
214 SCIPdbldblSum21(rhi, rlo, -__tmp_dbldbl_div12_hi, -__tmp_dbldbl_div12_lo, __estim_dbldbl_div12); \
221 #define SCIPdbldblDiv21(rhi, rlo, ahi, alo, b) \
223 double __tmp_dbldbl_div21_hi; \
224 double __tmp_dbldbl_div21_lo; \
225 double __estim_dbldbl_div21_hi; \
226 double __estim_dbldbl_div21_lo; \
227 __estim_dbldbl_div21_hi = (ahi)/(b); \
228 __estim_dbldbl_div21_lo = (alo)/(b); \
229 SCIPdbldblProd21(__tmp_dbldbl_div21_hi, __tmp_dbldbl_div21_lo, __estim_dbldbl_div21_hi, __estim_dbldbl_div21_lo, b); \
230 SCIPdbldblSum22(__tmp_dbldbl_div21_hi, __tmp_dbldbl_div21_lo, __tmp_dbldbl_div21_hi, __tmp_dbldbl_div21_lo, -(ahi), -(alo)); \
231 __tmp_dbldbl_div21_hi /= (b); \
232 __tmp_dbldbl_div21_lo /= (b); \
233 SCIPdbldblSum22(rhi, rlo, __estim_dbldbl_div21_hi, __estim_dbldbl_div21_lo, -__tmp_dbldbl_div21_hi, -__tmp_dbldbl_div21_lo); \
237 #define SCIPdbldblProd22(rhi, rlo, ahi, alo, bhi, blo) \
239 double __tmp_dbldbl_prod22_hi; \
240 double __tmp_dbldbl_prod22_lo; \
241 SCIPdbldblProd(__tmp_dbldbl_prod22_hi, __tmp_dbldbl_prod22_lo, ahi, bhi); \
242 SCIPdbldblSum21(__tmp_dbldbl_prod22_hi, __tmp_dbldbl_prod22_lo, \
243 __tmp_dbldbl_prod22_hi, __tmp_dbldbl_prod22_lo, (alo) * (bhi)); \
244 SCIPdbldblSum21(rhi, rlo, \
245 __tmp_dbldbl_prod22_hi, __tmp_dbldbl_prod22_lo, (ahi) * (blo)); \
249 #define SCIPdbldblSum22(rhi, rlo, ahi, alo, bhi, blo) \
251 double __tmp_dbldbl_sum22_hi; \
252 double __tmp_dbldbl_sum22_lo; \
253 SCIPdbldblSum21(__tmp_dbldbl_sum22_hi, __tmp_dbldbl_sum22_lo, ahi, alo, bhi); \
254 SCIPdbldblSum21(rhi, rlo, __tmp_dbldbl_sum22_hi, __tmp_dbldbl_sum22_lo, blo); \
258 #define SCIPdbldblSquare2(rhi, rlo, ahi, alo) \
260 double __tmp_dbldbl_square2_hi; \
261 double __tmp_dbldbl_square2_lo; \
262 SCIPdbldblSquare(__tmp_dbldbl_square2_hi, __tmp_dbldbl_square2_lo, (ahi)); \
263 SCIPdbldblSum21(rhi, rlo, __tmp_dbldbl_square2_hi, __tmp_dbldbl_square2_lo, 2 * (ahi) * (alo)); \
267 #define SCIPdbldblDiv22(rhi, rlo, ahi, alo, bhi, blo) \
269 double __tmp_dbldbl_div22_hi; \
270 double __tmp_dbldbl_div22_lo; \
271 double __estim_dbldbl_div22_hi = (ahi) / (bhi); \
272 double __estim_dbldbl_div22_lo = (alo) / (bhi); \
273 SCIPdbldblProd22(__tmp_dbldbl_div22_hi, __tmp_dbldbl_div22_lo, \
274 bhi, blo, __estim_dbldbl_div22_hi, __estim_dbldbl_div22_lo); \
275 SCIPdbldblSum22(__tmp_dbldbl_div22_hi, __tmp_dbldbl_div22_lo, \
276 __tmp_dbldbl_div22_hi, __tmp_dbldbl_div22_lo, -(ahi), -(alo)); \
277 __tmp_dbldbl_div22_hi /= (bhi); \
278 __tmp_dbldbl_div22_lo /= (bhi); \
279 SCIPdbldblSum22(rhi, rlo, __estim_dbldbl_div22_hi, __estim_dbldbl_div22_lo, \
280 -__tmp_dbldbl_div22_hi, -__tmp_dbldbl_div22_lo); \
285 #define SCIPdbldblSqrt(rhi, rlo, a) \
287 double __estim_dbldbl_sqrt = sqrt(a); \
288 if( __estim_dbldbl_sqrt != 0.0 ) \
290 SCIPdbldblDiv(rhi, rlo, a, __estim_dbldbl_sqrt); \
291 SCIPdbldblSum21(rhi, rlo, rhi, rlo, __estim_dbldbl_sqrt); \
304 #define SCIPdbldblSqrt2(rhi, rlo, ahi, alo) \
306 double __estim_dbldbl_sqrt2 = sqrt(ahi + alo); \
307 if( __estim_dbldbl_sqrt2 != 0.0 ) \
309 SCIPdbldblDiv21(rhi, rlo, ahi, alo, __estim_dbldbl_sqrt2); \
310 SCIPdbldblSum21(rhi, rlo, rhi, rlo, __estim_dbldbl_sqrt2); \
322 #define SCIPdbldblAbs2(rhi, rlo, ahi, alo) \
337 #define SCIPdbldblFloor2(rhi, rlo, ahi, alo) \
339 double __tmp_dbldbl_floor; \
340 __tmp_dbldbl_floor = floor((ahi) + (alo)); \
341 SCIPdbldblSum21(rhi, rlo, ahi, alo, -__tmp_dbldbl_floor); \
342 if( ((rhi) - 1.0) + (rlo) < 0.0 && (rhi) + (rlo) >= 0.0 ) \
345 (rhi) = __tmp_dbldbl_floor; \
351 double __tmp2_dbldbl_floor = floor((rhi) + (rlo)); \
352 SCIPdbldblSum(rhi, rlo, __tmp_dbldbl_floor, __tmp2_dbldbl_floor); \
357 #define SCIPdbldblCeil2(rhi, rlo, ahi, alo) \
359 double __tmp_dbldbl_ceil; \
360 __tmp_dbldbl_ceil = ceil((ahi) + (alo)); \
361 SCIPdbldblSum21(rhi, rlo, -(ahi), -(alo), __tmp_dbldbl_ceil); \
362 if( ((rhi) - 1.0) + (rlo) < 0.0 && (rhi) + (rlo) >= 0.0 ) \
365 (rhi) = __tmp_dbldbl_ceil; \
371 double __tmp2_dbldbl_ceil = floor((rhi) + (rlo)); \
372 SCIPdbldblSum(rhi, rlo, __tmp_dbldbl_ceil, -__tmp2_dbldbl_ceil); \
377 #define SCIPdbldblEpsFloor2(rhi, rlo, ahi, alo, eps) SCIPdbldblFloor2(rhi, rlo, ahi, (alo) + (eps))
380 #define SCIPdbldblEpsCeil2(rhi, rlo, ahi, alo, eps) SCIPdbldblCeil2(rhi, rlo, ahi, (alo) - (eps))