[13] | 1 | /* BDD size and profile routines */ |
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| 2 | |
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| 3 | |
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| 4 | #include "bddint.h" |
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| 5 | |
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| 6 | |
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| 7 | static |
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| 8 | void |
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| 9 | bdd_mark_bdd(bdd f) |
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| 10 | { |
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| 11 | int curr_marking, this_marking; |
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| 12 | |
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| 13 | BDD_SETUP(f); |
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| 14 | curr_marking=BDD_MARK(f); |
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| 15 | this_marking=(1 << TAG(f)); |
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| 16 | if (curr_marking & this_marking) |
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| 17 | return; |
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| 18 | BDD_MARK(f)=curr_marking | this_marking; |
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| 19 | if (BDD_IS_CONST(f)) |
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| 20 | return; |
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| 21 | bdd_mark_bdd(BDD_THEN(f)); |
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| 22 | bdd_mark_bdd(BDD_ELSE(f)); |
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| 23 | } |
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| 24 | |
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| 25 | |
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| 26 | static |
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| 27 | int |
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| 28 | bdd_count_no_nodes(bdd f) |
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| 29 | { |
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| 30 | BDD_SETUP(f); |
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| 31 | return (BDD_MARK(f) > 0); |
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| 32 | } |
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| 33 | |
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| 34 | |
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| 35 | static |
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| 36 | int |
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| 37 | bdd_count_nodes(bdd f) |
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| 38 | { |
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| 39 | int mark; |
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| 40 | |
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| 41 | BDD_SETUP(f); |
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| 42 | mark=BDD_MARK(f); |
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| 43 | return (((mark & 0x1) != 0)+((mark & 0x2) != 0)); |
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| 44 | } |
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| 45 | |
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| 46 | |
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| 47 | static |
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| 48 | int (*(counting_fns[]))(bdd)= |
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| 49 | { |
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| 50 | bdd_count_no_nodes, |
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| 51 | bdd_count_nodes, |
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| 52 | }; |
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| 53 | |
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| 54 | |
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| 55 | static |
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| 56 | long |
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| 57 | cmu_bdd_size_step(bdd f, int (*count_fn)(bdd)) |
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| 58 | { |
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| 59 | long result; |
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| 60 | |
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| 61 | BDD_SETUP(f); |
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| 62 | if (!BDD_MARK(f)) |
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| 63 | return (0l); |
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| 64 | result=(*count_fn)(f); |
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| 65 | if (!BDD_IS_CONST(f)) |
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| 66 | result+=cmu_bdd_size_step(BDD_THEN(f), count_fn)+cmu_bdd_size_step(BDD_ELSE(f), count_fn); |
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| 67 | BDD_MARK(f)=0; |
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| 68 | return (result); |
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| 69 | } |
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| 70 | |
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| 71 | |
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| 72 | /* cmu_bdd_size(bddm, f, negout) returns the number of nodes in f when */ |
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| 73 | /* negout is nonzero. If negout is zero, we pretend that the BDDs */ |
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| 74 | /* don't have negative-output pointers. */ |
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| 75 | |
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| 76 | long |
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| 77 | cmu_bdd_size(cmu_bdd_manager bddm, bdd f, int negout) |
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| 78 | { |
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| 79 | bdd g; |
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| 80 | |
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| 81 | if (bdd_check_arguments(1, f)) |
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| 82 | { |
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| 83 | g=BDD_ONE(bddm); |
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| 84 | { |
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| 85 | BDD_SETUP(g); |
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| 86 | BDD_MARK(g)=0; |
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| 87 | } |
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| 88 | bdd_mark_bdd(f); |
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| 89 | return (cmu_bdd_size_step(f, counting_fns[!negout])); |
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| 90 | } |
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| 91 | return (0l); |
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| 92 | } |
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| 93 | |
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| 94 | |
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| 95 | /* cmu_bdd_size_multiple is like cmu_bdd_size, but takes a null-terminated */ |
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| 96 | /* array of BDDs and accounts for sharing of nodes. */ |
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| 97 | |
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| 98 | long |
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| 99 | cmu_bdd_size_multiple(cmu_bdd_manager bddm, bdd* fs, int negout) |
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| 100 | { |
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| 101 | long size; |
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| 102 | bdd *f; |
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| 103 | bdd g; |
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| 104 | |
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| 105 | bdd_check_array(fs); |
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| 106 | g=BDD_ONE(bddm); |
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| 107 | { |
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| 108 | BDD_SETUP(g); |
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| 109 | BDD_MARK(g)=0; |
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| 110 | } |
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| 111 | for (f=fs; *f; ++f) |
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| 112 | bdd_mark_bdd(*f); |
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| 113 | size=0l; |
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| 114 | for (f=fs; *f; ++f) |
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| 115 | size+=cmu_bdd_size_step(*f, counting_fns[!negout]); |
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| 116 | return (size); |
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| 117 | } |
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| 118 | |
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| 119 | |
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| 120 | static |
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| 121 | void |
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| 122 | cmu_bdd_profile_step(cmu_bdd_manager bddm, bdd f, long *level_counts, int (*count_fn)(bdd)) |
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| 123 | { |
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| 124 | BDD_SETUP(f); |
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| 125 | if (!BDD_MARK(f)) |
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| 126 | return; |
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| 127 | if (BDD_IS_CONST(f)) |
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| 128 | level_counts[bddm->vars]+=(*count_fn)(f); |
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| 129 | else |
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| 130 | { |
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| 131 | level_counts[BDD_INDEX(bddm, f)]+=(*count_fn)(f); |
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| 132 | cmu_bdd_profile_step(bddm, BDD_THEN(f), level_counts, count_fn); |
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| 133 | cmu_bdd_profile_step(bddm, BDD_ELSE(f), level_counts, count_fn); |
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| 134 | } |
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| 135 | BDD_MARK(f)=0; |
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| 136 | } |
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| 137 | |
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| 138 | |
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| 139 | /* cmu_bdd_profile(bddm, f, level_counts, negout) returns a "node profile" */ |
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| 140 | /* of f, i.e., the number of nodes at each level in f. negout is as in */ |
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| 141 | /* cmu_bdd_size. level_counts should be an array of size cmu_bdd_vars(bddm)+1 */ |
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| 142 | /* to hold the profile. */ |
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| 143 | |
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| 144 | void |
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| 145 | cmu_bdd_profile(cmu_bdd_manager bddm, bdd f, long *level_counts, int negout) |
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| 146 | { |
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| 147 | bdd_index_type i; |
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| 148 | bdd g; |
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| 149 | |
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| 150 | for (i=0; i <= bddm->vars; ++i) |
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| 151 | level_counts[i]=0l; |
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| 152 | if (bdd_check_arguments(1, f)) |
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| 153 | { |
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| 154 | g=BDD_ONE(bddm); |
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| 155 | { |
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| 156 | BDD_SETUP(g); |
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| 157 | BDD_MARK(g)=0; |
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| 158 | } |
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| 159 | bdd_mark_bdd(f); |
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| 160 | cmu_bdd_profile_step(bddm, f, level_counts, counting_fns[!negout]); |
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| 161 | } |
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| 162 | } |
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| 163 | |
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| 164 | |
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| 165 | /* cmu_bdd_profile_multiple is to cmu_bdd_profile as cmu_bdd_size_multiple is to */ |
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| 166 | /* cmu_bdd_size. */ |
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| 167 | |
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| 168 | void |
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| 169 | cmu_bdd_profile_multiple(cmu_bdd_manager bddm, bdd *fs, long *level_counts, int negout) |
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| 170 | { |
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| 171 | bdd_index_type i; |
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| 172 | bdd *f; |
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| 173 | bdd g; |
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| 174 | |
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| 175 | bdd_check_array(fs); |
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| 176 | for (i=0; i <= bddm->vars; ++i) |
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| 177 | level_counts[i]=0l; |
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| 178 | g=BDD_ONE(bddm); |
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| 179 | { |
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| 180 | BDD_SETUP(g); |
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| 181 | BDD_MARK(g)=0; |
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| 182 | } |
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| 183 | for (f=fs; *f; ++f) |
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| 184 | bdd_mark_bdd(*f); |
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| 185 | for (f=fs; *f; ++f) |
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| 186 | cmu_bdd_profile_step(bddm, *f, level_counts, counting_fns[!negout]); |
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| 187 | } |
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| 188 | |
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| 189 | |
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| 190 | static |
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| 191 | void |
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| 192 | bdd_highest_ref_step(cmu_bdd_manager bddm, bdd f, hash_table h) |
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| 193 | { |
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| 194 | long *hash_result; |
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| 195 | long f_index; |
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| 196 | |
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| 197 | BDD_SETUP(f); |
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| 198 | if (BDD_IS_CONST(f)) |
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| 199 | return; |
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| 200 | f_index=BDD_INDEX(bddm, f); |
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| 201 | if ((hash_result=(long *)bdd_lookup_in_hash_table(h, BDD_THEN(f)))) |
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| 202 | { |
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| 203 | if (*hash_result > f_index) |
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| 204 | *hash_result=f_index; |
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| 205 | } |
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| 206 | else |
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| 207 | { |
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| 208 | bdd_insert_in_hash_table(h, BDD_THEN(f), (pointer)&f_index); |
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| 209 | bdd_highest_ref_step(bddm, BDD_THEN(f), h); |
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| 210 | } |
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| 211 | if ((hash_result=(long *)bdd_lookup_in_hash_table(h, BDD_ELSE(f)))) |
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| 212 | { |
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| 213 | if (*hash_result > f_index) |
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| 214 | *hash_result=f_index; |
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| 215 | } |
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| 216 | else |
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| 217 | { |
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| 218 | bdd_insert_in_hash_table(h, BDD_ELSE(f), (pointer)&f_index); |
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| 219 | bdd_highest_ref_step(bddm, BDD_ELSE(f), h); |
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| 220 | } |
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| 221 | } |
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| 222 | |
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| 223 | |
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| 224 | static |
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| 225 | void |
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| 226 | bdd_dominated_step(cmu_bdd_manager bddm, bdd f, long *func_counts, hash_table h) |
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| 227 | { |
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| 228 | long *hash_result; |
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| 229 | |
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| 230 | hash_result=(long *)bdd_lookup_in_hash_table(h, f); |
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| 231 | if (*hash_result >= 0) |
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| 232 | func_counts[*hash_result]-=2; |
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| 233 | if (*hash_result > -2) |
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| 234 | { |
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| 235 | BDD_SETUP(f); |
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| 236 | *hash_result= -2; |
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| 237 | if (!BDD_IS_CONST(f)) |
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| 238 | { |
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| 239 | bdd_dominated_step(bddm, BDD_THEN(f), func_counts, h); |
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| 240 | bdd_dominated_step(bddm, BDD_ELSE(f), func_counts, h); |
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| 241 | } |
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| 242 | } |
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| 243 | } |
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| 244 | |
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| 245 | |
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| 246 | /* cmu_bdd_function_profile(bddm, f, func_counts) returns a "function */ |
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| 247 | /* profile" for f. The nth entry of the function profile array is the */ |
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| 248 | /* number of subfunctions of f which may be obtained by restricting */ |
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| 249 | /* the variables whose index is less than n. An entry of zero */ |
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| 250 | /* indicates that f is independent of the variable with the */ |
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| 251 | /* corresponding index. */ |
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| 252 | |
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| 253 | void |
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| 254 | cmu_bdd_function_profile(cmu_bdd_manager bddm, bdd f, long *func_counts) |
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| 255 | { |
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| 256 | long i; |
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| 257 | bdd_index_type j; |
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| 258 | hash_table h; |
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| 259 | |
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| 260 | /* The number of subfunctions obtainable by restricting the */ |
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| 261 | /* variables of index < n is the number of subfunctions whose top */ |
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| 262 | /* variable has index n plus the number of subfunctions obtainable */ |
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| 263 | /* by restricting the variables of index < n+1 minus the number of */ |
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| 264 | /* these latter subfunctions whose highest reference is by a node at */ |
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| 265 | /* level n. */ |
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| 266 | /* The strategy will be to start with the number of subfunctions */ |
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| 267 | /* whose top variable has index n. We compute the highest level at */ |
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| 268 | /* which each subfunction is referenced. Then we work bottom up; at */ |
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| 269 | /* level n we add in the result from level n+1 and subtract the */ |
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| 270 | /* number of subfunctions whose highest reference is at level n. */ |
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| 271 | cmu_bdd_profile(bddm, f, func_counts, 0); |
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| 272 | if (bdd_check_arguments(1, f)) |
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| 273 | { |
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| 274 | /* Encode the profile. The low bit of a count will be zero for */ |
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| 275 | /* those levels where f actually has a node. */ |
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| 276 | for (j=0; j < bddm->vars; ++j) |
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| 277 | if (!func_counts[j]) |
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| 278 | func_counts[j]=1; |
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| 279 | else |
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| 280 | func_counts[j]<<=1; |
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| 281 | h=bdd_new_hash_table(bddm, sizeof(long)); |
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| 282 | /* For each subfunction in f, compute the highest level where it is */ |
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| 283 | /* referenced. f itself is conceptually referenced at the highest */ |
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| 284 | /* possible level, which we represent by -1. */ |
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| 285 | i= -1; |
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| 286 | bdd_insert_in_hash_table(h, f, (pointer)&i); |
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| 287 | bdd_highest_ref_step(bddm, f, h); |
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| 288 | /* Walk through these results. For each subfunction, decrement the */ |
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| 289 | /* count at the highest level where it is referenced. */ |
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| 290 | bdd_dominated_step(bddm, f, func_counts, h); |
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| 291 | cmu_bdd_free_hash_table(h); |
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| 292 | /* Now add each level n+1 result to that of level n. */ |
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| 293 | for (i=bddm->vars-1, j=i+1; i>= 0; --i) |
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| 294 | if (func_counts[i] != 1) |
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| 295 | { |
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| 296 | func_counts[i]=(func_counts[i] >> 1)+func_counts[j]; |
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| 297 | j=i; |
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| 298 | } |
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| 299 | else |
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| 300 | func_counts[i]=0; |
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| 301 | } |
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| 302 | } |
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| 303 | |
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| 304 | |
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| 305 | /* cmu_bdd_function_profile_multiple is to cmu_bdd_function_profile as */ |
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| 306 | /* cmu_bdd_size_multiple is to cmu_bdd_size. */ |
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| 307 | |
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| 308 | void |
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| 309 | cmu_bdd_function_profile_multiple(cmu_bdd_manager bddm, bdd *fs, long *func_counts) |
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| 310 | { |
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| 311 | long i; |
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| 312 | bdd_index_type j; |
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| 313 | bdd *f; |
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| 314 | long *hash_result; |
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| 315 | hash_table h; |
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| 316 | |
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| 317 | bdd_check_array(fs); |
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| 318 | /* See cmu_bdd_function_profile for the strategy involved here. */ |
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| 319 | cmu_bdd_profile_multiple(bddm, fs, func_counts, 0); |
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| 320 | for (j=0; j < bddm->vars; ++j) |
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| 321 | if (!func_counts[j]) |
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| 322 | func_counts[j]=1; |
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| 323 | else |
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| 324 | func_counts[j]<<=1; |
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| 325 | h=bdd_new_hash_table(bddm, sizeof(long)); |
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| 326 | for (f=fs; *f; ++f) |
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| 327 | bdd_highest_ref_step(bddm, *f, h); |
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| 328 | i= -1; |
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| 329 | for (f=fs; *f; ++f) |
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| 330 | if ((hash_result=(long *)bdd_lookup_in_hash_table(h, *f))) |
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| 331 | *hash_result= -1; |
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| 332 | else |
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| 333 | bdd_insert_in_hash_table(h, *f, (pointer)&i); |
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| 334 | for (f=fs; *f; ++f) |
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| 335 | bdd_dominated_step(bddm, *f, func_counts, h); |
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| 336 | cmu_bdd_free_hash_table(h); |
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| 337 | for (i=bddm->vars-1, j=i+1; i>= 0; --i) |
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| 338 | if (func_counts[i] != 1) |
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| 339 | { |
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| 340 | func_counts[i]=(func_counts[i] >> 1)+func_counts[j]; |
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| 341 | j=i; |
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| 342 | } |
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| 343 | else |
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| 344 | func_counts[i]=0; |
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| 345 | } |
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