Mercurial > hg > CbC > CbC_gcc
annotate gcc/tree-chrec.c @ 88:f214c1d5b862
merge 89
| author | Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp> |
|---|---|
| date | Tue, 20 Dec 2011 18:53:46 +0900 |
| parents | f6334be47118 |
| children | 04ced10e8804 |
| rev | line source |
|---|---|
| 0 | 1 /* Chains of recurrences. |
|
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2 Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 |
| 0 | 3 Free Software Foundation, Inc. |
| 4 Contributed by Sebastian Pop <pop@cri.ensmp.fr> | |
| 5 | |
| 6 This file is part of GCC. | |
| 7 | |
| 8 GCC is free software; you can redistribute it and/or modify it under | |
| 9 the terms of the GNU General Public License as published by the Free | |
| 10 Software Foundation; either version 3, or (at your option) any later | |
| 11 version. | |
| 12 | |
| 13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY | |
| 14 WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 16 for more details. | |
| 17 | |
| 18 You should have received a copy of the GNU General Public License | |
| 19 along with GCC; see the file COPYING3. If not see | |
| 20 <http://www.gnu.org/licenses/>. */ | |
| 21 | |
| 22 /* This file implements operations on chains of recurrences. Chains | |
| 23 of recurrences are used for modeling evolution functions of scalar | |
| 24 variables. | |
| 25 */ | |
| 26 | |
| 27 #include "config.h" | |
| 28 #include "system.h" | |
| 29 #include "coretypes.h" | |
|
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30 #include "tree-pretty-print.h" |
| 0 | 31 #include "cfgloop.h" |
| 32 #include "tree-flow.h" | |
| 33 #include "tree-chrec.h" | |
| 34 #include "tree-pass.h" | |
| 35 #include "params.h" | |
| 36 #include "tree-scalar-evolution.h" | |
| 37 | |
| 38 /* Extended folder for chrecs. */ | |
| 39 | |
| 40 /* Determines whether CST is not a constant evolution. */ | |
| 41 | |
| 42 static inline bool | |
| 43 is_not_constant_evolution (const_tree cst) | |
| 44 { | |
| 45 return (TREE_CODE (cst) == POLYNOMIAL_CHREC); | |
| 46 } | |
| 47 | |
| 48 /* Fold CODE for a polynomial function and a constant. */ | |
| 49 | |
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50 static inline tree |
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51 chrec_fold_poly_cst (enum tree_code code, |
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52 tree type, |
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53 tree poly, |
| 0 | 54 tree cst) |
| 55 { | |
| 56 gcc_assert (poly); | |
| 57 gcc_assert (cst); | |
| 58 gcc_assert (TREE_CODE (poly) == POLYNOMIAL_CHREC); | |
| 59 gcc_assert (!is_not_constant_evolution (cst)); | |
| 60 gcc_assert (type == chrec_type (poly)); | |
| 61 | |
| 62 switch (code) | |
| 63 { | |
| 64 case PLUS_EXPR: | |
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65 return build_polynomial_chrec |
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66 (CHREC_VARIABLE (poly), |
| 0 | 67 chrec_fold_plus (type, CHREC_LEFT (poly), cst), |
| 68 CHREC_RIGHT (poly)); | |
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69 |
| 0 | 70 case MINUS_EXPR: |
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71 return build_polynomial_chrec |
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72 (CHREC_VARIABLE (poly), |
| 0 | 73 chrec_fold_minus (type, CHREC_LEFT (poly), cst), |
| 74 CHREC_RIGHT (poly)); | |
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75 |
| 0 | 76 case MULT_EXPR: |
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77 return build_polynomial_chrec |
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78 (CHREC_VARIABLE (poly), |
| 0 | 79 chrec_fold_multiply (type, CHREC_LEFT (poly), cst), |
| 80 chrec_fold_multiply (type, CHREC_RIGHT (poly), cst)); | |
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81 |
| 0 | 82 default: |
| 83 return chrec_dont_know; | |
| 84 } | |
| 85 } | |
| 86 | |
| 87 /* Fold the addition of two polynomial functions. */ | |
| 88 | |
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89 static inline tree |
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90 chrec_fold_plus_poly_poly (enum tree_code code, |
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91 tree type, |
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92 tree poly0, |
| 0 | 93 tree poly1) |
| 94 { | |
| 95 tree left, right; | |
| 96 struct loop *loop0 = get_chrec_loop (poly0); | |
| 97 struct loop *loop1 = get_chrec_loop (poly1); | |
| 98 tree rtype = code == POINTER_PLUS_EXPR ? sizetype : type; | |
| 99 | |
| 100 gcc_assert (poly0); | |
| 101 gcc_assert (poly1); | |
| 102 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); | |
| 103 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); | |
| 104 if (POINTER_TYPE_P (chrec_type (poly0))) | |
| 105 gcc_assert (chrec_type (poly1) == sizetype); | |
| 106 else | |
| 107 gcc_assert (chrec_type (poly0) == chrec_type (poly1)); | |
| 108 gcc_assert (type == chrec_type (poly0)); | |
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109 |
| 0 | 110 /* |
| 111 {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2, | |
| 112 {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2, | |
| 113 {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */ | |
| 114 if (flow_loop_nested_p (loop0, loop1)) | |
| 115 { | |
| 116 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
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117 return build_polynomial_chrec |
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118 (CHREC_VARIABLE (poly1), |
| 0 | 119 chrec_fold_plus (type, poly0, CHREC_LEFT (poly1)), |
| 120 CHREC_RIGHT (poly1)); | |
| 121 else | |
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122 return build_polynomial_chrec |
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123 (CHREC_VARIABLE (poly1), |
| 0 | 124 chrec_fold_minus (type, poly0, CHREC_LEFT (poly1)), |
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125 chrec_fold_multiply (type, CHREC_RIGHT (poly1), |
| 0 | 126 SCALAR_FLOAT_TYPE_P (type) |
| 127 ? build_real (type, dconstm1) | |
| 128 : build_int_cst_type (type, -1))); | |
| 129 } | |
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130 |
| 0 | 131 if (flow_loop_nested_p (loop1, loop0)) |
| 132 { | |
| 133 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
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134 return build_polynomial_chrec |
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135 (CHREC_VARIABLE (poly0), |
| 0 | 136 chrec_fold_plus (type, CHREC_LEFT (poly0), poly1), |
| 137 CHREC_RIGHT (poly0)); | |
| 138 else | |
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139 return build_polynomial_chrec |
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140 (CHREC_VARIABLE (poly0), |
| 0 | 141 chrec_fold_minus (type, CHREC_LEFT (poly0), poly1), |
| 142 CHREC_RIGHT (poly0)); | |
| 143 } | |
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144 |
| 0 | 145 /* This function should never be called for chrecs of loops that |
| 146 do not belong to the same loop nest. */ | |
| 147 gcc_assert (loop0 == loop1); | |
| 148 | |
| 149 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
| 150 { | |
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151 left = chrec_fold_plus |
| 0 | 152 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); |
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153 right = chrec_fold_plus |
| 0 | 154 (rtype, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); |
| 155 } | |
| 156 else | |
| 157 { | |
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158 left = chrec_fold_minus |
| 0 | 159 (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); |
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160 right = chrec_fold_minus |
| 0 | 161 (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); |
| 162 } | |
| 163 | |
| 164 if (chrec_zerop (right)) | |
| 165 return left; | |
| 166 else | |
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167 return build_polynomial_chrec |
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168 (CHREC_VARIABLE (poly0), left, right); |
| 0 | 169 } |
| 170 | |
| 171 | |
| 172 | |
| 173 /* Fold the multiplication of two polynomial functions. */ | |
| 174 | |
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175 static inline tree |
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176 chrec_fold_multiply_poly_poly (tree type, |
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177 tree poly0, |
| 0 | 178 tree poly1) |
| 179 { | |
| 180 tree t0, t1, t2; | |
| 181 int var; | |
| 182 struct loop *loop0 = get_chrec_loop (poly0); | |
| 183 struct loop *loop1 = get_chrec_loop (poly1); | |
| 184 | |
| 185 gcc_assert (poly0); | |
| 186 gcc_assert (poly1); | |
| 187 gcc_assert (TREE_CODE (poly0) == POLYNOMIAL_CHREC); | |
| 188 gcc_assert (TREE_CODE (poly1) == POLYNOMIAL_CHREC); | |
| 189 gcc_assert (chrec_type (poly0) == chrec_type (poly1)); | |
| 190 gcc_assert (type == chrec_type (poly0)); | |
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191 |
| 0 | 192 /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2, |
| 193 {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2, | |
| 194 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
| 195 if (flow_loop_nested_p (loop0, loop1)) | |
| 196 /* poly0 is a constant wrt. poly1. */ | |
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197 return build_polynomial_chrec |
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198 (CHREC_VARIABLE (poly1), |
| 0 | 199 chrec_fold_multiply (type, CHREC_LEFT (poly1), poly0), |
| 200 CHREC_RIGHT (poly1)); | |
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201 |
| 0 | 202 if (flow_loop_nested_p (loop1, loop0)) |
| 203 /* poly1 is a constant wrt. poly0. */ | |
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204 return build_polynomial_chrec |
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205 (CHREC_VARIABLE (poly0), |
| 0 | 206 chrec_fold_multiply (type, CHREC_LEFT (poly0), poly1), |
| 207 CHREC_RIGHT (poly0)); | |
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208 |
| 0 | 209 gcc_assert (loop0 == loop1); |
| 210 | |
| 211 /* poly0 and poly1 are two polynomials in the same variable, | |
| 212 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */ | |
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213 |
| 0 | 214 /* "a*c". */ |
| 215 t0 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_LEFT (poly1)); | |
| 216 | |
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217 /* "a*d + b*c". */ |
| 0 | 218 t1 = chrec_fold_multiply (type, CHREC_LEFT (poly0), CHREC_RIGHT (poly1)); |
| 219 t1 = chrec_fold_plus (type, t1, chrec_fold_multiply (type, | |
| 220 CHREC_RIGHT (poly0), | |
| 221 CHREC_LEFT (poly1))); | |
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222 /* "b*d". */ |
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223 t2 = chrec_fold_multiply (type, CHREC_RIGHT (poly0), CHREC_RIGHT (poly1)); |
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224 /* "a*d + b*c + b*d". */ |
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225 t1 = chrec_fold_plus (type, t1, t2); |
| 0 | 226 /* "2*b*d". */ |
| 227 t2 = chrec_fold_multiply (type, SCALAR_FLOAT_TYPE_P (type) | |
| 228 ? build_real (type, dconst2) | |
| 229 : build_int_cst (type, 2), t2); | |
| 230 | |
| 231 var = CHREC_VARIABLE (poly0); | |
| 232 return build_polynomial_chrec (var, t0, | |
| 233 build_polynomial_chrec (var, t1, t2)); | |
| 234 } | |
| 235 | |
| 236 /* When the operands are automatically_generated_chrec_p, the fold has | |
| 237 to respect the semantics of the operands. */ | |
| 238 | |
|
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239 static inline tree |
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240 chrec_fold_automatically_generated_operands (tree op0, |
| 0 | 241 tree op1) |
| 242 { | |
| 243 if (op0 == chrec_dont_know | |
| 244 || op1 == chrec_dont_know) | |
| 245 return chrec_dont_know; | |
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246 |
| 0 | 247 if (op0 == chrec_known |
| 248 || op1 == chrec_known) | |
| 249 return chrec_known; | |
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250 |
| 0 | 251 if (op0 == chrec_not_analyzed_yet |
| 252 || op1 == chrec_not_analyzed_yet) | |
| 253 return chrec_not_analyzed_yet; | |
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254 |
| 0 | 255 /* The default case produces a safe result. */ |
| 256 return chrec_dont_know; | |
| 257 } | |
| 258 | |
| 259 /* Fold the addition of two chrecs. */ | |
| 260 | |
| 261 static tree | |
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262 chrec_fold_plus_1 (enum tree_code code, tree type, |
| 0 | 263 tree op0, tree op1) |
| 264 { | |
| 265 tree op1_type = code == POINTER_PLUS_EXPR ? sizetype : type; | |
| 266 | |
| 267 if (automatically_generated_chrec_p (op0) | |
| 268 || automatically_generated_chrec_p (op1)) | |
| 269 return chrec_fold_automatically_generated_operands (op0, op1); | |
|
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270 |
| 0 | 271 switch (TREE_CODE (op0)) |
| 272 { | |
| 273 case POLYNOMIAL_CHREC: | |
| 274 switch (TREE_CODE (op1)) | |
| 275 { | |
| 276 case POLYNOMIAL_CHREC: | |
| 277 return chrec_fold_plus_poly_poly (code, type, op0, op1); | |
| 278 | |
|
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279 CASE_CONVERT: |
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280 if (tree_contains_chrecs (op1, NULL)) |
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281 return chrec_dont_know; |
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282 |
| 0 | 283 default: |
| 284 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
|
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285 return build_polynomial_chrec |
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286 (CHREC_VARIABLE (op0), |
| 0 | 287 chrec_fold_plus (type, CHREC_LEFT (op0), op1), |
| 288 CHREC_RIGHT (op0)); | |
| 289 else | |
|
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290 return build_polynomial_chrec |
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291 (CHREC_VARIABLE (op0), |
| 0 | 292 chrec_fold_minus (type, CHREC_LEFT (op0), op1), |
| 293 CHREC_RIGHT (op0)); | |
| 294 } | |
| 295 | |
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296 CASE_CONVERT: |
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297 if (tree_contains_chrecs (op0, NULL)) |
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298 return chrec_dont_know; |
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299 |
| 0 | 300 default: |
| 301 switch (TREE_CODE (op1)) | |
| 302 { | |
| 303 case POLYNOMIAL_CHREC: | |
| 304 if (code == PLUS_EXPR || code == POINTER_PLUS_EXPR) | |
|
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305 return build_polynomial_chrec |
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306 (CHREC_VARIABLE (op1), |
| 0 | 307 chrec_fold_plus (type, op0, CHREC_LEFT (op1)), |
| 308 CHREC_RIGHT (op1)); | |
| 309 else | |
|
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310 return build_polynomial_chrec |
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311 (CHREC_VARIABLE (op1), |
| 0 | 312 chrec_fold_minus (type, op0, CHREC_LEFT (op1)), |
|
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313 chrec_fold_multiply (type, CHREC_RIGHT (op1), |
| 0 | 314 SCALAR_FLOAT_TYPE_P (type) |
| 315 ? build_real (type, dconstm1) | |
| 316 : build_int_cst_type (type, -1))); | |
| 317 | |
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318 CASE_CONVERT: |
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319 if (tree_contains_chrecs (op1, NULL)) |
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320 return chrec_dont_know; |
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321 |
| 0 | 322 default: |
| 323 { | |
| 324 int size = 0; | |
| 325 if ((tree_contains_chrecs (op0, &size) | |
| 326 || tree_contains_chrecs (op1, &size)) | |
| 327 && size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) | |
| 328 return build2 (code, type, op0, op1); | |
| 329 else if (size < PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE)) | |
| 330 return fold_build2 (code, type, | |
| 331 fold_convert (type, op0), | |
| 332 fold_convert (op1_type, op1)); | |
| 333 else | |
| 334 return chrec_dont_know; | |
| 335 } | |
| 336 } | |
| 337 } | |
| 338 } | |
| 339 | |
| 340 /* Fold the addition of two chrecs. */ | |
| 341 | |
| 342 tree | |
|
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343 chrec_fold_plus (tree type, |
| 0 | 344 tree op0, |
| 345 tree op1) | |
| 346 { | |
| 347 enum tree_code code; | |
| 348 if (automatically_generated_chrec_p (op0) | |
| 349 || automatically_generated_chrec_p (op1)) | |
| 350 return chrec_fold_automatically_generated_operands (op0, op1); | |
| 351 | |
| 352 if (integer_zerop (op0)) | |
| 353 return chrec_convert (type, op1, NULL); | |
| 354 if (integer_zerop (op1)) | |
| 355 return chrec_convert (type, op0, NULL); | |
| 356 | |
| 357 if (POINTER_TYPE_P (type)) | |
| 358 code = POINTER_PLUS_EXPR; | |
| 359 else | |
| 360 code = PLUS_EXPR; | |
|
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361 |
| 0 | 362 return chrec_fold_plus_1 (code, type, op0, op1); |
| 363 } | |
| 364 | |
| 365 /* Fold the subtraction of two chrecs. */ | |
| 366 | |
|
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367 tree |
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368 chrec_fold_minus (tree type, |
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369 tree op0, |
| 0 | 370 tree op1) |
| 371 { | |
| 372 if (automatically_generated_chrec_p (op0) | |
| 373 || automatically_generated_chrec_p (op1)) | |
| 374 return chrec_fold_automatically_generated_operands (op0, op1); | |
| 375 | |
| 376 if (integer_zerop (op1)) | |
| 377 return op0; | |
|
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378 |
| 0 | 379 return chrec_fold_plus_1 (MINUS_EXPR, type, op0, op1); |
| 380 } | |
| 381 | |
| 382 /* Fold the multiplication of two chrecs. */ | |
| 383 | |
| 384 tree | |
|
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385 chrec_fold_multiply (tree type, |
| 0 | 386 tree op0, |
| 387 tree op1) | |
| 388 { | |
| 389 if (automatically_generated_chrec_p (op0) | |
| 390 || automatically_generated_chrec_p (op1)) | |
| 391 return chrec_fold_automatically_generated_operands (op0, op1); | |
|
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392 |
| 0 | 393 switch (TREE_CODE (op0)) |
| 394 { | |
| 395 case POLYNOMIAL_CHREC: | |
| 396 switch (TREE_CODE (op1)) | |
| 397 { | |
| 398 case POLYNOMIAL_CHREC: | |
| 399 return chrec_fold_multiply_poly_poly (type, op0, op1); | |
|
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400 |
|
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401 CASE_CONVERT: |
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402 if (tree_contains_chrecs (op1, NULL)) |
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403 return chrec_dont_know; |
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404 |
| 0 | 405 default: |
| 406 if (integer_onep (op1)) | |
| 407 return op0; | |
| 408 if (integer_zerop (op1)) | |
| 409 return build_int_cst (type, 0); | |
|
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410 |
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411 return build_polynomial_chrec |
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412 (CHREC_VARIABLE (op0), |
| 0 | 413 chrec_fold_multiply (type, CHREC_LEFT (op0), op1), |
| 414 chrec_fold_multiply (type, CHREC_RIGHT (op0), op1)); | |
| 415 } | |
|
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416 |
|
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417 CASE_CONVERT: |
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418 if (tree_contains_chrecs (op0, NULL)) |
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419 return chrec_dont_know; |
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420 |
| 0 | 421 default: |
| 422 if (integer_onep (op0)) | |
| 423 return op1; | |
|
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424 |
| 0 | 425 if (integer_zerop (op0)) |
| 426 return build_int_cst (type, 0); | |
|
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427 |
| 0 | 428 switch (TREE_CODE (op1)) |
| 429 { | |
| 430 case POLYNOMIAL_CHREC: | |
|
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431 return build_polynomial_chrec |
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432 (CHREC_VARIABLE (op1), |
| 0 | 433 chrec_fold_multiply (type, CHREC_LEFT (op1), op0), |
| 434 chrec_fold_multiply (type, CHREC_RIGHT (op1), op0)); | |
|
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435 |
|
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436 CASE_CONVERT: |
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437 if (tree_contains_chrecs (op1, NULL)) |
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438 return chrec_dont_know; |
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439 |
| 0 | 440 default: |
| 441 if (integer_onep (op1)) | |
| 442 return op0; | |
| 443 if (integer_zerop (op1)) | |
| 444 return build_int_cst (type, 0); | |
| 445 return fold_build2 (MULT_EXPR, type, op0, op1); | |
| 446 } | |
| 447 } | |
| 448 } | |
| 449 | |
| 450 | |
| 451 | |
| 452 /* Operations. */ | |
| 453 | |
| 454 /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate | |
| 455 calculation overflows, otherwise return C(n,k) with type TYPE. */ | |
| 456 | |
|
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457 static tree |
| 0 | 458 tree_fold_binomial (tree type, tree n, unsigned int k) |
| 459 { | |
| 460 unsigned HOST_WIDE_INT lidx, lnum, ldenom, lres, ldum; | |
| 461 HOST_WIDE_INT hidx, hnum, hdenom, hres, hdum; | |
| 462 unsigned int i; | |
| 463 tree res; | |
| 464 | |
| 465 /* Handle the most frequent cases. */ | |
| 466 if (k == 0) | |
| 467 return build_int_cst (type, 1); | |
| 468 if (k == 1) | |
| 469 return fold_convert (type, n); | |
| 470 | |
| 471 /* Check that k <= n. */ | |
| 472 if (TREE_INT_CST_HIGH (n) == 0 | |
| 473 && TREE_INT_CST_LOW (n) < k) | |
| 474 return NULL_TREE; | |
| 475 | |
| 476 /* Numerator = n. */ | |
| 477 lnum = TREE_INT_CST_LOW (n); | |
| 478 hnum = TREE_INT_CST_HIGH (n); | |
| 479 | |
| 480 /* Denominator = 2. */ | |
| 481 ldenom = 2; | |
| 482 hdenom = 0; | |
| 483 | |
| 484 /* Index = Numerator-1. */ | |
| 485 if (lnum == 0) | |
| 486 { | |
| 487 hidx = hnum - 1; | |
| 488 lidx = ~ (unsigned HOST_WIDE_INT) 0; | |
| 489 } | |
| 490 else | |
| 491 { | |
| 492 hidx = hnum; | |
| 493 lidx = lnum - 1; | |
| 494 } | |
| 495 | |
| 496 /* Numerator = Numerator*Index = n*(n-1). */ | |
| 497 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) | |
| 498 return NULL_TREE; | |
| 499 | |
| 500 for (i = 3; i <= k; i++) | |
| 501 { | |
| 502 /* Index--. */ | |
| 503 if (lidx == 0) | |
| 504 { | |
| 505 hidx--; | |
| 506 lidx = ~ (unsigned HOST_WIDE_INT) 0; | |
| 507 } | |
| 508 else | |
| 509 lidx--; | |
| 510 | |
| 511 /* Numerator *= Index. */ | |
| 512 if (mul_double (lnum, hnum, lidx, hidx, &lnum, &hnum)) | |
| 513 return NULL_TREE; | |
| 514 | |
| 515 /* Denominator *= i. */ | |
| 516 mul_double (ldenom, hdenom, i, 0, &ldenom, &hdenom); | |
| 517 } | |
| 518 | |
| 519 /* Result = Numerator / Denominator. */ | |
| 520 div_and_round_double (EXACT_DIV_EXPR, 1, lnum, hnum, ldenom, hdenom, | |
| 521 &lres, &hres, &ldum, &hdum); | |
| 522 | |
| 523 res = build_int_cst_wide (type, lres, hres); | |
| 524 return int_fits_type_p (res, type) ? res : NULL_TREE; | |
| 525 } | |
| 526 | |
| 527 /* Helper function. Use the Newton's interpolating formula for | |
| 528 evaluating the value of the evolution function. */ | |
| 529 | |
|
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530 static tree |
| 0 | 531 chrec_evaluate (unsigned var, tree chrec, tree n, unsigned int k) |
| 532 { | |
| 533 tree arg0, arg1, binomial_n_k; | |
| 534 tree type = TREE_TYPE (chrec); | |
| 535 struct loop *var_loop = get_loop (var); | |
| 536 | |
| 537 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 538 && flow_loop_nested_p (var_loop, get_chrec_loop (chrec))) | |
| 539 chrec = CHREC_LEFT (chrec); | |
| 540 | |
| 541 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 542 && CHREC_VARIABLE (chrec) == var) | |
| 543 { | |
| 544 arg1 = chrec_evaluate (var, CHREC_RIGHT (chrec), n, k + 1); | |
| 545 if (arg1 == chrec_dont_know) | |
| 546 return chrec_dont_know; | |
| 547 binomial_n_k = tree_fold_binomial (type, n, k); | |
| 548 if (!binomial_n_k) | |
| 549 return chrec_dont_know; | |
| 550 arg0 = fold_build2 (MULT_EXPR, type, | |
| 551 CHREC_LEFT (chrec), binomial_n_k); | |
| 552 return chrec_fold_plus (type, arg0, arg1); | |
| 553 } | |
| 554 | |
| 555 binomial_n_k = tree_fold_binomial (type, n, k); | |
| 556 if (!binomial_n_k) | |
| 557 return chrec_dont_know; | |
|
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558 |
| 0 | 559 return fold_build2 (MULT_EXPR, type, chrec, binomial_n_k); |
| 560 } | |
| 561 | |
|
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562 /* Evaluates "CHREC (X)" when the varying variable is VAR. |
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563 Example: Given the following parameters, |
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564 |
| 0 | 565 var = 1 |
| 566 chrec = {3, +, 4}_1 | |
| 567 x = 10 | |
|
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568 |
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569 The result is given by the Newton's interpolating formula: |
| 0 | 570 3 * \binom{10}{0} + 4 * \binom{10}{1}. |
| 571 */ | |
| 572 | |
|
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573 tree |
| 0 | 574 chrec_apply (unsigned var, |
|
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575 tree chrec, |
| 0 | 576 tree x) |
| 577 { | |
| 578 tree type = chrec_type (chrec); | |
| 579 tree res = chrec_dont_know; | |
| 580 | |
| 581 if (automatically_generated_chrec_p (chrec) | |
| 582 || automatically_generated_chrec_p (x) | |
| 583 | |
| 584 /* When the symbols are defined in an outer loop, it is possible | |
| 585 to symbolically compute the apply, since the symbols are | |
| 586 constants with respect to the varying loop. */ | |
| 587 || chrec_contains_symbols_defined_in_loop (chrec, var)) | |
| 588 return chrec_dont_know; | |
|
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589 |
| 0 | 590 if (dump_file && (dump_flags & TDF_DETAILS)) |
| 591 fprintf (dump_file, "(chrec_apply \n"); | |
| 592 | |
| 593 if (TREE_CODE (x) == INTEGER_CST && SCALAR_FLOAT_TYPE_P (type)) | |
| 594 x = build_real_from_int_cst (type, x); | |
| 595 | |
|
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596 switch (TREE_CODE (chrec)) |
| 0 | 597 { |
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598 case POLYNOMIAL_CHREC: |
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599 if (evolution_function_is_affine_p (chrec)) |
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600 { |
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601 if (CHREC_VARIABLE (chrec) != var) |
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602 return build_polynomial_chrec |
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603 (CHREC_VARIABLE (chrec), |
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604 chrec_apply (var, CHREC_LEFT (chrec), x), |
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605 chrec_apply (var, CHREC_RIGHT (chrec), x)); |
|
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606 |
|
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607 /* "{a, +, b} (x)" -> "a + b*x". */ |
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608 x = chrec_convert_rhs (type, x, NULL); |
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609 res = chrec_fold_multiply (TREE_TYPE (x), CHREC_RIGHT (chrec), x); |
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610 res = chrec_fold_plus (type, CHREC_LEFT (chrec), res); |
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611 } |
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612 else if (TREE_CODE (x) == INTEGER_CST |
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613 && tree_int_cst_sgn (x) == 1) |
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614 /* testsuite/.../ssa-chrec-38.c. */ |
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615 res = chrec_evaluate (var, chrec, x, 0); |
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616 else |
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617 res = chrec_dont_know; |
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618 break; |
|
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619 |
|
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620 CASE_CONVERT: |
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621 res = chrec_convert (TREE_TYPE (chrec), |
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622 chrec_apply (var, TREE_OPERAND (chrec, 0), x), |
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623 NULL); |
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624 break; |
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625 |
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626 default: |
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627 res = chrec; |
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628 break; |
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629 } |
|
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630 |
| 0 | 631 if (dump_file && (dump_flags & TDF_DETAILS)) |
| 632 { | |
| 633 fprintf (dump_file, " (varying_loop = %d\n", var); | |
| 634 fprintf (dump_file, ")\n (chrec = "); | |
| 635 print_generic_expr (dump_file, chrec, 0); | |
| 636 fprintf (dump_file, ")\n (x = "); | |
| 637 print_generic_expr (dump_file, x, 0); | |
| 638 fprintf (dump_file, ")\n (res = "); | |
| 639 print_generic_expr (dump_file, res, 0); | |
| 640 fprintf (dump_file, "))\n"); | |
| 641 } | |
|
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642 |
| 0 | 643 return res; |
| 644 } | |
| 645 | |
|
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646 /* For a given CHREC and an induction variable map IV_MAP that maps |
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647 (loop->num, expr) for every loop number of the current_loops an |
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648 expression, calls chrec_apply when the expression is not NULL. */ |
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649 |
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650 tree |
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651 chrec_apply_map (tree chrec, VEC (tree, heap) *iv_map) |
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652 { |
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653 int i; |
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654 tree expr; |
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655 |
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656 FOR_EACH_VEC_ELT (tree, iv_map, i, expr) |
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657 if (expr) |
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658 chrec = chrec_apply (i, chrec, expr); |
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659 |
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660 return chrec; |
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661 } |
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662 |
| 0 | 663 /* Replaces the initial condition in CHREC with INIT_COND. */ |
| 664 | |
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665 tree |
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666 chrec_replace_initial_condition (tree chrec, |
| 0 | 667 tree init_cond) |
| 668 { | |
| 669 if (automatically_generated_chrec_p (chrec)) | |
| 670 return chrec; | |
| 671 | |
| 672 gcc_assert (chrec_type (chrec) == chrec_type (init_cond)); | |
| 673 | |
| 674 switch (TREE_CODE (chrec)) | |
| 675 { | |
| 676 case POLYNOMIAL_CHREC: | |
|
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677 return build_polynomial_chrec |
| 0 | 678 (CHREC_VARIABLE (chrec), |
| 679 chrec_replace_initial_condition (CHREC_LEFT (chrec), init_cond), | |
| 680 CHREC_RIGHT (chrec)); | |
|
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681 |
| 0 | 682 default: |
| 683 return init_cond; | |
| 684 } | |
| 685 } | |
| 686 | |
| 687 /* Returns the initial condition of a given CHREC. */ | |
| 688 | |
|
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689 tree |
| 0 | 690 initial_condition (tree chrec) |
| 691 { | |
| 692 if (automatically_generated_chrec_p (chrec)) | |
| 693 return chrec; | |
|
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694 |
| 0 | 695 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |
| 696 return initial_condition (CHREC_LEFT (chrec)); | |
| 697 else | |
| 698 return chrec; | |
| 699 } | |
| 700 | |
| 701 /* Returns a univariate function that represents the evolution in | |
| 702 LOOP_NUM. Mask the evolution of any other loop. */ | |
| 703 | |
|
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704 tree |
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705 hide_evolution_in_other_loops_than_loop (tree chrec, |
| 0 | 706 unsigned loop_num) |
| 707 { | |
| 708 struct loop *loop = get_loop (loop_num), *chloop; | |
| 709 if (automatically_generated_chrec_p (chrec)) | |
| 710 return chrec; | |
|
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711 |
| 0 | 712 switch (TREE_CODE (chrec)) |
| 713 { | |
| 714 case POLYNOMIAL_CHREC: | |
| 715 chloop = get_chrec_loop (chrec); | |
| 716 | |
| 717 if (chloop == loop) | |
|
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718 return build_polynomial_chrec |
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719 (loop_num, |
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720 hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), |
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721 loop_num), |
| 0 | 722 CHREC_RIGHT (chrec)); |
|
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723 |
| 0 | 724 else if (flow_loop_nested_p (chloop, loop)) |
| 725 /* There is no evolution in this loop. */ | |
| 726 return initial_condition (chrec); | |
|
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727 |
| 0 | 728 else |
| 729 { | |
| 730 gcc_assert (flow_loop_nested_p (loop, chloop)); | |
|
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731 return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec), |
| 0 | 732 loop_num); |
| 733 } | |
|
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734 |
| 0 | 735 default: |
| 736 return chrec; | |
| 737 } | |
| 738 } | |
| 739 | |
| 740 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is | |
| 741 true, otherwise returns the initial condition in LOOP_NUM. */ | |
| 742 | |
|
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743 static tree |
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744 chrec_component_in_loop_num (tree chrec, |
| 0 | 745 unsigned loop_num, |
| 746 bool right) | |
| 747 { | |
| 748 tree component; | |
| 749 struct loop *loop = get_loop (loop_num), *chloop; | |
| 750 | |
| 751 if (automatically_generated_chrec_p (chrec)) | |
| 752 return chrec; | |
|
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753 |
| 0 | 754 switch (TREE_CODE (chrec)) |
| 755 { | |
| 756 case POLYNOMIAL_CHREC: | |
| 757 chloop = get_chrec_loop (chrec); | |
| 758 | |
| 759 if (chloop == loop) | |
| 760 { | |
| 761 if (right) | |
| 762 component = CHREC_RIGHT (chrec); | |
| 763 else | |
| 764 component = CHREC_LEFT (chrec); | |
| 765 | |
| 766 if (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC | |
| 767 || CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec)) | |
| 768 return component; | |
|
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769 |
| 0 | 770 else |
| 771 return build_polynomial_chrec | |
|
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|
772 (loop_num, |
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773 chrec_component_in_loop_num (CHREC_LEFT (chrec), |
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|
774 loop_num, |
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775 right), |
| 0 | 776 component); |
| 777 } | |
|
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778 |
| 0 | 779 else if (flow_loop_nested_p (chloop, loop)) |
| 780 /* There is no evolution part in this loop. */ | |
| 781 return NULL_TREE; | |
|
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782 |
| 0 | 783 else |
| 784 { | |
| 785 gcc_assert (flow_loop_nested_p (loop, chloop)); | |
|
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786 return chrec_component_in_loop_num (CHREC_LEFT (chrec), |
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787 loop_num, |
| 0 | 788 right); |
| 789 } | |
|
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790 |
| 0 | 791 default: |
| 792 if (right) | |
| 793 return NULL_TREE; | |
| 794 else | |
| 795 return chrec; | |
| 796 } | |
| 797 } | |
| 798 | |
| 799 /* Returns the evolution part in LOOP_NUM. Example: the call | |
|
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800 evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns |
| 0 | 801 {1, +, 2}_1 */ |
| 802 | |
|
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803 tree |
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804 evolution_part_in_loop_num (tree chrec, |
| 0 | 805 unsigned loop_num) |
| 806 { | |
| 807 return chrec_component_in_loop_num (chrec, loop_num, true); | |
| 808 } | |
| 809 | |
| 810 /* Returns the initial condition in LOOP_NUM. Example: the call | |
|
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811 initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns |
| 0 | 812 {0, +, 1}_1 */ |
| 813 | |
|
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814 tree |
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815 initial_condition_in_loop_num (tree chrec, |
| 0 | 816 unsigned loop_num) |
| 817 { | |
| 818 return chrec_component_in_loop_num (chrec, loop_num, false); | |
| 819 } | |
| 820 | |
| 821 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM. | |
| 822 This function is essentially used for setting the evolution to | |
| 823 chrec_dont_know, for example after having determined that it is | |
| 824 impossible to say how many times a loop will execute. */ | |
| 825 | |
|
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826 tree |
| 0 | 827 reset_evolution_in_loop (unsigned loop_num, |
|
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828 tree chrec, |
| 0 | 829 tree new_evol) |
| 830 { | |
| 831 struct loop *loop = get_loop (loop_num); | |
| 832 | |
| 833 if (POINTER_TYPE_P (chrec_type (chrec))) | |
| 834 gcc_assert (sizetype == chrec_type (new_evol)); | |
| 835 else | |
| 836 gcc_assert (chrec_type (chrec) == chrec_type (new_evol)); | |
| 837 | |
| 838 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 839 && flow_loop_nested_p (loop, get_chrec_loop (chrec))) | |
| 840 { | |
| 841 tree left = reset_evolution_in_loop (loop_num, CHREC_LEFT (chrec), | |
| 842 new_evol); | |
| 843 tree right = reset_evolution_in_loop (loop_num, CHREC_RIGHT (chrec), | |
| 844 new_evol); | |
| 845 return build3 (POLYNOMIAL_CHREC, TREE_TYPE (left), | |
| 846 build_int_cst (NULL_TREE, CHREC_VARIABLE (chrec)), | |
| 847 left, right); | |
| 848 } | |
| 849 | |
| 850 while (TREE_CODE (chrec) == POLYNOMIAL_CHREC | |
| 851 && CHREC_VARIABLE (chrec) == loop_num) | |
| 852 chrec = CHREC_LEFT (chrec); | |
|
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853 |
| 0 | 854 return build_polynomial_chrec (loop_num, chrec, new_evol); |
| 855 } | |
| 856 | |
| 857 /* Merges two evolution functions that were found by following two | |
| 858 alternate paths of a conditional expression. */ | |
| 859 | |
| 860 tree | |
|
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861 chrec_merge (tree chrec1, |
| 0 | 862 tree chrec2) |
| 863 { | |
| 864 if (chrec1 == chrec_dont_know | |
| 865 || chrec2 == chrec_dont_know) | |
| 866 return chrec_dont_know; | |
| 867 | |
|
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868 if (chrec1 == chrec_known |
| 0 | 869 || chrec2 == chrec_known) |
| 870 return chrec_known; | |
| 871 | |
| 872 if (chrec1 == chrec_not_analyzed_yet) | |
| 873 return chrec2; | |
| 874 if (chrec2 == chrec_not_analyzed_yet) | |
| 875 return chrec1; | |
| 876 | |
| 877 if (eq_evolutions_p (chrec1, chrec2)) | |
| 878 return chrec1; | |
| 879 | |
| 880 return chrec_dont_know; | |
| 881 } | |
| 882 | |
| 883 | |
| 884 | |
| 885 /* Observers. */ | |
| 886 | |
| 887 /* Helper function for is_multivariate_chrec. */ | |
| 888 | |
|
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|
889 static bool |
| 0 | 890 is_multivariate_chrec_rec (const_tree chrec, unsigned int rec_var) |
| 891 { | |
| 892 if (chrec == NULL_TREE) | |
| 893 return false; | |
|
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894 |
| 0 | 895 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |
| 896 { | |
| 897 if (CHREC_VARIABLE (chrec) != rec_var) | |
| 898 return true; | |
| 899 else | |
|
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|
900 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), rec_var) |
| 0 | 901 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), rec_var)); |
| 902 } | |
| 903 else | |
| 904 return false; | |
| 905 } | |
| 906 | |
| 907 /* Determine whether the given chrec is multivariate or not. */ | |
| 908 | |
|
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|
909 bool |
| 0 | 910 is_multivariate_chrec (const_tree chrec) |
| 911 { | |
| 912 if (chrec == NULL_TREE) | |
| 913 return false; | |
|
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914 |
| 0 | 915 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) |
|
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916 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec), |
| 0 | 917 CHREC_VARIABLE (chrec)) |
|
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918 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec), |
| 0 | 919 CHREC_VARIABLE (chrec))); |
| 920 else | |
| 921 return false; | |
| 922 } | |
| 923 | |
| 924 /* Determines whether the chrec contains symbolic names or not. */ | |
| 925 | |
|
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|
926 bool |
| 0 | 927 chrec_contains_symbols (const_tree chrec) |
| 928 { | |
| 929 int i, n; | |
| 930 | |
| 931 if (chrec == NULL_TREE) | |
| 932 return false; | |
|
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933 |
| 0 | 934 if (TREE_CODE (chrec) == SSA_NAME |
| 935 || TREE_CODE (chrec) == VAR_DECL | |
| 936 || TREE_CODE (chrec) == PARM_DECL | |
| 937 || TREE_CODE (chrec) == FUNCTION_DECL | |
| 938 || TREE_CODE (chrec) == LABEL_DECL | |
| 939 || TREE_CODE (chrec) == RESULT_DECL | |
| 940 || TREE_CODE (chrec) == FIELD_DECL) | |
| 941 return true; | |
| 942 | |
| 943 n = TREE_OPERAND_LENGTH (chrec); | |
| 944 for (i = 0; i < n; i++) | |
| 945 if (chrec_contains_symbols (TREE_OPERAND (chrec, i))) | |
| 946 return true; | |
| 947 return false; | |
| 948 } | |
| 949 | |
| 950 /* Determines whether the chrec contains undetermined coefficients. */ | |
| 951 | |
|
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|
952 bool |
| 0 | 953 chrec_contains_undetermined (const_tree chrec) |
| 954 { | |
| 955 int i, n; | |
| 956 | |
| 957 if (chrec == chrec_dont_know) | |
| 958 return true; | |
| 959 | |
| 960 if (chrec == NULL_TREE) | |
| 961 return false; | |
| 962 | |
| 963 n = TREE_OPERAND_LENGTH (chrec); | |
| 964 for (i = 0; i < n; i++) | |
| 965 if (chrec_contains_undetermined (TREE_OPERAND (chrec, i))) | |
| 966 return true; | |
| 967 return false; | |
| 968 } | |
| 969 | |
| 970 /* Determines whether the tree EXPR contains chrecs, and increment | |
| 971 SIZE if it is not a NULL pointer by an estimation of the depth of | |
| 972 the tree. */ | |
| 973 | |
| 974 bool | |
| 975 tree_contains_chrecs (const_tree expr, int *size) | |
| 976 { | |
| 977 int i, n; | |
| 978 | |
| 979 if (expr == NULL_TREE) | |
| 980 return false; | |
| 981 | |
| 982 if (size) | |
| 983 (*size)++; | |
|
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|
984 |
| 0 | 985 if (tree_is_chrec (expr)) |
| 986 return true; | |
| 987 | |
| 988 n = TREE_OPERAND_LENGTH (expr); | |
| 989 for (i = 0; i < n; i++) | |
| 990 if (tree_contains_chrecs (TREE_OPERAND (expr, i), size)) | |
| 991 return true; | |
| 992 return false; | |
| 993 } | |
| 994 | |
| 995 /* Recursive helper function. */ | |
| 996 | |
| 997 static bool | |
| 998 evolution_function_is_invariant_rec_p (tree chrec, int loopnum) | |
| 999 { | |
| 1000 if (evolution_function_is_constant_p (chrec)) | |
| 1001 return true; | |
| 1002 | |
| 1003 if (TREE_CODE (chrec) == SSA_NAME | |
| 1004 && (loopnum == 0 | |
| 1005 || expr_invariant_in_loop_p (get_loop (loopnum), chrec))) | |
| 1006 return true; | |
| 1007 | |
| 1008 if (TREE_CODE (chrec) == POLYNOMIAL_CHREC) | |
| 1009 { | |
| 1010 if (CHREC_VARIABLE (chrec) == (unsigned) loopnum | |
| 1011 || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), | |
| 1012 loopnum) | |
| 1013 || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), | |
| 1014 loopnum)) | |
| 1015 return false; | |
| 1016 return true; | |
| 1017 } | |
| 1018 | |
| 1019 switch (TREE_OPERAND_LENGTH (chrec)) | |
| 1020 { | |
| 1021 case 2: | |
| 1022 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 1), | |
| 1023 loopnum)) | |
| 1024 return false; | |
|
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|
1025 |
| 0 | 1026 case 1: |
| 1027 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec, 0), | |
| 1028 loopnum)) | |
| 1029 return false; | |
| 1030 return true; | |
| 1031 | |
| 1032 default: | |
| 1033 return false; | |
| 1034 } | |
| 1035 | |
| 1036 return false; | |
| 1037 } | |
| 1038 | |
| 1039 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */ | |
| 1040 | |
| 1041 bool | |
| 1042 evolution_function_is_invariant_p (tree chrec, int loopnum) | |
| 1043 { | |
| 1044 return evolution_function_is_invariant_rec_p (chrec, loopnum); | |
| 1045 } | |
| 1046 | |
| 1047 /* Determine whether the given tree is an affine multivariate | |
| 1048 evolution. */ | |
| 1049 | |
|
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1050 bool |
| 0 | 1051 evolution_function_is_affine_multivariate_p (const_tree chrec, int loopnum) |
| 1052 { | |
| 1053 if (chrec == NULL_TREE) | |
| 1054 return false; | |
|
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|
1055 |
| 0 | 1056 switch (TREE_CODE (chrec)) |
| 1057 { | |
| 1058 case POLYNOMIAL_CHREC: | |
| 1059 if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec), loopnum)) | |
| 1060 { | |
| 1061 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum)) | |
| 1062 return true; | |
| 1063 else | |
| 1064 { | |
| 1065 if (TREE_CODE (CHREC_RIGHT (chrec)) == POLYNOMIAL_CHREC | |
|
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1066 && CHREC_VARIABLE (CHREC_RIGHT (chrec)) |
| 0 | 1067 != CHREC_VARIABLE (chrec) |
|
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1068 && evolution_function_is_affine_multivariate_p |
| 0 | 1069 (CHREC_RIGHT (chrec), loopnum)) |
| 1070 return true; | |
| 1071 else | |
| 1072 return false; | |
| 1073 } | |
| 1074 } | |
| 1075 else | |
| 1076 { | |
| 1077 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec), loopnum) | |
| 1078 && TREE_CODE (CHREC_LEFT (chrec)) == POLYNOMIAL_CHREC | |
| 1079 && CHREC_VARIABLE (CHREC_LEFT (chrec)) != CHREC_VARIABLE (chrec) | |
|
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1080 && evolution_function_is_affine_multivariate_p |
| 0 | 1081 (CHREC_LEFT (chrec), loopnum)) |
| 1082 return true; | |
| 1083 else | |
| 1084 return false; | |
| 1085 } | |
|
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|
1086 |
| 0 | 1087 default: |
| 1088 return false; | |
| 1089 } | |
| 1090 } | |
| 1091 | |
|
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1092 /* Determine whether the given tree is a function in zero or one |
| 0 | 1093 variables. */ |
| 1094 | |
| 1095 bool | |
| 1096 evolution_function_is_univariate_p (const_tree chrec) | |
| 1097 { | |
| 1098 if (chrec == NULL_TREE) | |
| 1099 return true; | |
|
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|
1100 |
| 0 | 1101 switch (TREE_CODE (chrec)) |
| 1102 { | |
| 1103 case POLYNOMIAL_CHREC: | |
| 1104 switch (TREE_CODE (CHREC_LEFT (chrec))) | |
| 1105 { | |
| 1106 case POLYNOMIAL_CHREC: | |
| 1107 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_LEFT (chrec))) | |
| 1108 return false; | |
| 1109 if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec))) | |
| 1110 return false; | |
| 1111 break; | |
|
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1112 |
| 0 | 1113 default: |
| 1114 break; | |
| 1115 } | |
|
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1116 |
| 0 | 1117 switch (TREE_CODE (CHREC_RIGHT (chrec))) |
| 1118 { | |
| 1119 case POLYNOMIAL_CHREC: | |
| 1120 if (CHREC_VARIABLE (chrec) != CHREC_VARIABLE (CHREC_RIGHT (chrec))) | |
| 1121 return false; | |
| 1122 if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec))) | |
| 1123 return false; | |
| 1124 break; | |
|
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1125 |
| 0 | 1126 default: |
|
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1127 break; |
| 0 | 1128 } |
|
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1129 |
| 0 | 1130 default: |
| 1131 return true; | |
| 1132 } | |
| 1133 } | |
| 1134 | |
| 1135 /* Returns the number of variables of CHREC. Example: the call | |
| 1136 nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */ | |
| 1137 | |
|
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1138 unsigned |
| 0 | 1139 nb_vars_in_chrec (tree chrec) |
| 1140 { | |
| 1141 if (chrec == NULL_TREE) | |
| 1142 return 0; | |
| 1143 | |
| 1144 switch (TREE_CODE (chrec)) | |
| 1145 { | |
| 1146 case POLYNOMIAL_CHREC: | |
|
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1147 return 1 + nb_vars_in_chrec |
| 0 | 1148 (initial_condition_in_loop_num (chrec, CHREC_VARIABLE (chrec))); |
| 1149 | |
| 1150 default: | |
| 1151 return 0; | |
| 1152 } | |
| 1153 } | |
| 1154 | |
| 1155 static tree chrec_convert_1 (tree, tree, gimple, bool); | |
| 1156 | |
| 1157 /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv | |
| 1158 the scev corresponds to. AT_STMT is the statement at that the scev is | |
| 1159 evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume that | |
| 1160 the rules for overflow of the given language apply (e.g., that signed | |
| 1161 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary | |
| 1162 tests, but also to enforce that the result follows them. Returns true if the | |
| 1163 conversion succeeded, false otherwise. */ | |
| 1164 | |
| 1165 bool | |
| 1166 convert_affine_scev (struct loop *loop, tree type, | |
| 1167 tree *base, tree *step, gimple at_stmt, | |
| 1168 bool use_overflow_semantics) | |
| 1169 { | |
| 1170 tree ct = TREE_TYPE (*step); | |
| 1171 bool enforce_overflow_semantics; | |
| 1172 bool must_check_src_overflow, must_check_rslt_overflow; | |
| 1173 tree new_base, new_step; | |
| 1174 tree step_type = POINTER_TYPE_P (type) ? sizetype : type; | |
| 1175 | |
| 1176 /* In general, | |
| 1177 (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i, | |
| 1178 but we must check some assumptions. | |
|
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1179 |
| 0 | 1180 1) If [BASE, +, STEP] wraps, the equation is not valid when precision |
| 1181 of CT is smaller than the precision of TYPE. For example, when we | |
| 1182 cast unsigned char [254, +, 1] to unsigned, the values on left side | |
| 1183 are 254, 255, 0, 1, ..., but those on the right side are | |
| 1184 254, 255, 256, 257, ... | |
| 1185 2) In case that we must also preserve the fact that signed ivs do not | |
| 1186 overflow, we must additionally check that the new iv does not wrap. | |
| 1187 For example, unsigned char [125, +, 1] casted to signed char could | |
| 1188 become a wrapping variable with values 125, 126, 127, -128, -127, ..., | |
| 1189 which would confuse optimizers that assume that this does not | |
| 1190 happen. */ | |
| 1191 must_check_src_overflow = TYPE_PRECISION (ct) < TYPE_PRECISION (type); | |
| 1192 | |
| 1193 enforce_overflow_semantics = (use_overflow_semantics | |
| 1194 && nowrap_type_p (type)); | |
| 1195 if (enforce_overflow_semantics) | |
| 1196 { | |
| 1197 /* We can avoid checking whether the result overflows in the following | |
| 1198 cases: | |
| 1199 | |
| 1200 -- must_check_src_overflow is true, and the range of TYPE is superset | |
| 1201 of the range of CT -- i.e., in all cases except if CT signed and | |
| 1202 TYPE unsigned. | |
| 1203 -- both CT and TYPE have the same precision and signedness, and we | |
| 1204 verify instead that the source does not overflow (this may be | |
| 1205 easier than verifying it for the result, as we may use the | |
| 1206 information about the semantics of overflow in CT). */ | |
| 1207 if (must_check_src_overflow) | |
| 1208 { | |
| 1209 if (TYPE_UNSIGNED (type) && !TYPE_UNSIGNED (ct)) | |
| 1210 must_check_rslt_overflow = true; | |
| 1211 else | |
| 1212 must_check_rslt_overflow = false; | |
| 1213 } | |
| 1214 else if (TYPE_UNSIGNED (ct) == TYPE_UNSIGNED (type) | |
| 1215 && TYPE_PRECISION (ct) == TYPE_PRECISION (type)) | |
| 1216 { | |
| 1217 must_check_rslt_overflow = false; | |
| 1218 must_check_src_overflow = true; | |
| 1219 } | |
| 1220 else | |
| 1221 must_check_rslt_overflow = true; | |
| 1222 } | |
| 1223 else | |
| 1224 must_check_rslt_overflow = false; | |
| 1225 | |
| 1226 if (must_check_src_overflow | |
| 1227 && scev_probably_wraps_p (*base, *step, at_stmt, loop, | |
| 1228 use_overflow_semantics)) | |
| 1229 return false; | |
| 1230 | |
| 1231 new_base = chrec_convert_1 (type, *base, at_stmt, | |
| 1232 use_overflow_semantics); | |
| 1233 /* The step must be sign extended, regardless of the signedness | |
| 1234 of CT and TYPE. This only needs to be handled specially when | |
| 1235 CT is unsigned -- to avoid e.g. unsigned char [100, +, 255] | |
| 1236 (with values 100, 99, 98, ...) from becoming signed or unsigned | |
|
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1237 [100, +, 255] with values 100, 355, ...; the sign-extension is |
| 0 | 1238 performed by default when CT is signed. */ |
| 1239 new_step = *step; | |
| 1240 if (TYPE_PRECISION (step_type) > TYPE_PRECISION (ct) && TYPE_UNSIGNED (ct)) | |
|
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1241 { |
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|
1242 tree signed_ct = build_nonstandard_integer_type (TYPE_PRECISION (ct), 0); |
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|
1243 new_step = chrec_convert_1 (signed_ct, new_step, at_stmt, |
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1244 use_overflow_semantics); |
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|
1245 } |
| 0 | 1246 new_step = chrec_convert_1 (step_type, new_step, at_stmt, use_overflow_semantics); |
| 1247 | |
| 1248 if (automatically_generated_chrec_p (new_base) | |
| 1249 || automatically_generated_chrec_p (new_step)) | |
| 1250 return false; | |
| 1251 | |
| 1252 if (must_check_rslt_overflow | |
| 1253 /* Note that in this case we cannot use the fact that signed variables | |
| 1254 do not overflow, as this is what we are verifying for the new iv. */ | |
| 1255 && scev_probably_wraps_p (new_base, new_step, at_stmt, loop, false)) | |
| 1256 return false; | |
| 1257 | |
| 1258 *base = new_base; | |
| 1259 *step = new_step; | |
| 1260 return true; | |
| 1261 } | |
| 1262 | |
| 1263 | |
|
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1264 /* Convert CHREC for the right hand side of a CHREC. |
| 0 | 1265 The increment for a pointer type is always sizetype. */ |
|
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|
1266 |
|
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1267 tree |
| 0 | 1268 chrec_convert_rhs (tree type, tree chrec, gimple at_stmt) |
| 1269 { | |
| 1270 if (POINTER_TYPE_P (type)) | |
|
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|
1271 type = sizetype; |
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|
1272 |
| 0 | 1273 return chrec_convert (type, chrec, at_stmt); |
| 1274 } | |
| 1275 | |
| 1276 /* Convert CHREC to TYPE. When the analyzer knows the context in | |
| 1277 which the CHREC is built, it sets AT_STMT to the statement that | |
| 1278 contains the definition of the analyzed variable, otherwise the | |
| 1279 conversion is less accurate: the information is used for | |
| 1280 determining a more accurate estimation of the number of iterations. | |
| 1281 By default AT_STMT could be safely set to NULL_TREE. | |
| 1282 | |
| 1283 The following rule is always true: TREE_TYPE (chrec) == | |
| 1284 TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)). | |
| 1285 An example of what could happen when adding two chrecs and the type | |
| 1286 of the CHREC_RIGHT is different than CHREC_LEFT is: | |
|
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1287 |
| 0 | 1288 {(uint) 0, +, (uchar) 10} + |
| 1289 {(uint) 0, +, (uchar) 250} | |
|
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1290 |
| 0 | 1291 that would produce a wrong result if CHREC_RIGHT is not (uint): |
|
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1292 |
| 0 | 1293 {(uint) 0, +, (uchar) 4} |
| 1294 | |
| 1295 instead of | |
| 1296 | |
| 1297 {(uint) 0, +, (uint) 260} | |
| 1298 */ | |
| 1299 | |
|
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1300 tree |
| 0 | 1301 chrec_convert (tree type, tree chrec, gimple at_stmt) |
| 1302 { | |
| 1303 return chrec_convert_1 (type, chrec, at_stmt, true); | |
| 1304 } | |
| 1305 | |
| 1306 /* Convert CHREC to TYPE. When the analyzer knows the context in | |
| 1307 which the CHREC is built, it sets AT_STMT to the statement that | |
| 1308 contains the definition of the analyzed variable, otherwise the | |
| 1309 conversion is less accurate: the information is used for | |
| 1310 determining a more accurate estimation of the number of iterations. | |
| 1311 By default AT_STMT could be safely set to NULL_TREE. | |
|
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1312 |
| 0 | 1313 USE_OVERFLOW_SEMANTICS is true if this function should assume that |
| 1314 the rules for overflow of the given language apply (e.g., that signed | |
| 1315 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary | |
| 1316 tests, but also to enforce that the result follows them. */ | |
| 1317 | |
|
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1318 static tree |
| 0 | 1319 chrec_convert_1 (tree type, tree chrec, gimple at_stmt, |
| 1320 bool use_overflow_semantics) | |
| 1321 { | |
| 1322 tree ct, res; | |
| 1323 tree base, step; | |
| 1324 struct loop *loop; | |
| 1325 | |
| 1326 if (automatically_generated_chrec_p (chrec)) | |
| 1327 return chrec; | |
|
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1328 |
| 0 | 1329 ct = chrec_type (chrec); |
| 1330 if (ct == type) | |
| 1331 return chrec; | |
| 1332 | |
| 1333 if (!evolution_function_is_affine_p (chrec)) | |
| 1334 goto keep_cast; | |
| 1335 | |
| 1336 loop = get_chrec_loop (chrec); | |
| 1337 base = CHREC_LEFT (chrec); | |
| 1338 step = CHREC_RIGHT (chrec); | |
| 1339 | |
| 1340 if (convert_affine_scev (loop, type, &base, &step, at_stmt, | |
| 1341 use_overflow_semantics)) | |
| 1342 return build_polynomial_chrec (loop->num, base, step); | |
| 1343 | |
| 1344 /* If we cannot propagate the cast inside the chrec, just keep the cast. */ | |
| 1345 keep_cast: | |
|
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1346 /* Fold will not canonicalize (long)(i - 1) to (long)i - 1 because that |
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1347 may be more expensive. We do want to perform this optimization here |
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1348 though for canonicalization reasons. */ |
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1349 if (use_overflow_semantics |
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1350 && (TREE_CODE (chrec) == PLUS_EXPR |
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1351 || TREE_CODE (chrec) == MINUS_EXPR) |
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1352 && TREE_CODE (type) == INTEGER_TYPE |
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1353 && TREE_CODE (ct) == INTEGER_TYPE |
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1354 && TYPE_PRECISION (type) > TYPE_PRECISION (ct) |
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1355 && TYPE_OVERFLOW_UNDEFINED (ct)) |
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1356 res = fold_build2 (TREE_CODE (chrec), type, |
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1357 fold_convert (type, TREE_OPERAND (chrec, 0)), |
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1358 fold_convert (type, TREE_OPERAND (chrec, 1))); |
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1359 else |
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|
1360 res = fold_convert (type, chrec); |
| 0 | 1361 |
| 1362 /* Don't propagate overflows. */ | |
| 1363 if (CONSTANT_CLASS_P (res)) | |
| 1364 TREE_OVERFLOW (res) = 0; | |
| 1365 | |
| 1366 /* But reject constants that don't fit in their type after conversion. | |
| 1367 This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the | |
| 1368 natural values associated with TYPE_PRECISION and TYPE_UNSIGNED, | |
| 1369 and can cause problems later when computing niters of loops. Note | |
| 1370 that we don't do the check before converting because we don't want | |
| 1371 to reject conversions of negative chrecs to unsigned types. */ | |
| 1372 if (TREE_CODE (res) == INTEGER_CST | |
| 1373 && TREE_CODE (type) == INTEGER_TYPE | |
| 1374 && !int_fits_type_p (res, type)) | |
| 1375 res = chrec_dont_know; | |
| 1376 | |
| 1377 return res; | |
| 1378 } | |
| 1379 | |
| 1380 /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new | |
| 1381 chrec if something else than what chrec_convert would do happens, NULL_TREE | |
| 1382 otherwise. */ | |
| 1383 | |
| 1384 tree | |
| 1385 chrec_convert_aggressive (tree type, tree chrec) | |
| 1386 { | |
| 1387 tree inner_type, left, right, lc, rc, rtype; | |
| 1388 | |
| 1389 if (automatically_generated_chrec_p (chrec) | |
| 1390 || TREE_CODE (chrec) != POLYNOMIAL_CHREC) | |
| 1391 return NULL_TREE; | |
| 1392 | |
| 1393 inner_type = TREE_TYPE (chrec); | |
| 1394 if (TYPE_PRECISION (type) > TYPE_PRECISION (inner_type)) | |
| 1395 return NULL_TREE; | |
| 1396 | |
| 1397 rtype = POINTER_TYPE_P (type) ? sizetype : type; | |
| 1398 | |
| 1399 left = CHREC_LEFT (chrec); | |
| 1400 right = CHREC_RIGHT (chrec); | |
| 1401 lc = chrec_convert_aggressive (type, left); | |
| 1402 if (!lc) | |
| 1403 lc = chrec_convert (type, left, NULL); | |
| 1404 rc = chrec_convert_aggressive (rtype, right); | |
| 1405 if (!rc) | |
| 1406 rc = chrec_convert (rtype, right, NULL); | |
|
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1407 |
| 0 | 1408 return build_polynomial_chrec (CHREC_VARIABLE (chrec), lc, rc); |
| 1409 } | |
| 1410 | |
| 1411 /* Returns true when CHREC0 == CHREC1. */ | |
| 1412 | |
|
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1413 bool |
| 0 | 1414 eq_evolutions_p (const_tree chrec0, const_tree chrec1) |
| 1415 { | |
| 1416 if (chrec0 == NULL_TREE | |
| 1417 || chrec1 == NULL_TREE | |
| 1418 || TREE_CODE (chrec0) != TREE_CODE (chrec1)) | |
| 1419 return false; | |
| 1420 | |
| 1421 if (chrec0 == chrec1) | |
| 1422 return true; | |
| 1423 | |
| 1424 switch (TREE_CODE (chrec0)) | |
| 1425 { | |
| 1426 case INTEGER_CST: | |
| 1427 return operand_equal_p (chrec0, chrec1, 0); | |
| 1428 | |
| 1429 case POLYNOMIAL_CHREC: | |
| 1430 return (CHREC_VARIABLE (chrec0) == CHREC_VARIABLE (chrec1) | |
| 1431 && eq_evolutions_p (CHREC_LEFT (chrec0), CHREC_LEFT (chrec1)) | |
| 1432 && eq_evolutions_p (CHREC_RIGHT (chrec0), CHREC_RIGHT (chrec1))); | |
|
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1433 |
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1434 case PLUS_EXPR: |
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1435 case MULT_EXPR: |
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1436 case MINUS_EXPR: |
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1437 case POINTER_PLUS_EXPR: |
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1438 return eq_evolutions_p (TREE_OPERAND (chrec0, 0), |
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1439 TREE_OPERAND (chrec1, 0)) |
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1440 && eq_evolutions_p (TREE_OPERAND (chrec0, 1), |
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1441 TREE_OPERAND (chrec1, 1)); |
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1442 |
| 0 | 1443 default: |
| 1444 return false; | |
|
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1445 } |
| 0 | 1446 } |
| 1447 | |
| 1448 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow), | |
| 1449 EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine | |
| 1450 which of these cases happens. */ | |
| 1451 | |
| 1452 enum ev_direction | |
| 1453 scev_direction (const_tree chrec) | |
| 1454 { | |
| 1455 const_tree step; | |
| 1456 | |
| 1457 if (!evolution_function_is_affine_p (chrec)) | |
| 1458 return EV_DIR_UNKNOWN; | |
| 1459 | |
| 1460 step = CHREC_RIGHT (chrec); | |
| 1461 if (TREE_CODE (step) != INTEGER_CST) | |
| 1462 return EV_DIR_UNKNOWN; | |
| 1463 | |
| 1464 if (tree_int_cst_sign_bit (step)) | |
| 1465 return EV_DIR_DECREASES; | |
| 1466 else | |
| 1467 return EV_DIR_GROWS; | |
| 1468 } | |
| 1469 | |
| 1470 /* Iterates over all the components of SCEV, and calls CBCK. */ | |
| 1471 | |
| 1472 void | |
| 1473 for_each_scev_op (tree *scev, bool (*cbck) (tree *, void *), void *data) | |
| 1474 { | |
| 1475 switch (TREE_CODE_LENGTH (TREE_CODE (*scev))) | |
| 1476 { | |
| 1477 case 3: | |
| 1478 for_each_scev_op (&TREE_OPERAND (*scev, 2), cbck, data); | |
| 1479 | |
| 1480 case 2: | |
| 1481 for_each_scev_op (&TREE_OPERAND (*scev, 1), cbck, data); | |
|
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1482 |
| 0 | 1483 case 1: |
| 1484 for_each_scev_op (&TREE_OPERAND (*scev, 0), cbck, data); | |
| 1485 | |
| 1486 default: | |
| 1487 cbck (scev, data); | |
| 1488 break; | |
| 1489 } | |
| 1490 } | |
| 1491 | |
| 1492 /* Returns true when the operation can be part of a linear | |
| 1493 expression. */ | |
| 1494 | |
| 1495 static inline bool | |
| 1496 operator_is_linear (tree scev) | |
| 1497 { | |
| 1498 switch (TREE_CODE (scev)) | |
| 1499 { | |
| 1500 case INTEGER_CST: | |
| 1501 case POLYNOMIAL_CHREC: | |
| 1502 case PLUS_EXPR: | |
| 1503 case POINTER_PLUS_EXPR: | |
| 1504 case MULT_EXPR: | |
| 1505 case MINUS_EXPR: | |
| 1506 case NEGATE_EXPR: | |
| 1507 case SSA_NAME: | |
| 1508 case NON_LVALUE_EXPR: | |
|
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1509 case BIT_NOT_EXPR: |
| 0 | 1510 CASE_CONVERT: |
| 1511 return true; | |
| 1512 | |
| 1513 default: | |
| 1514 return false; | |
| 1515 } | |
| 1516 } | |
| 1517 | |
| 1518 /* Return true when SCEV is a linear expression. Linear expressions | |
| 1519 can contain additions, substractions and multiplications. | |
| 1520 Multiplications are restricted to constant scaling: "cst * x". */ | |
| 1521 | |
| 1522 bool | |
| 1523 scev_is_linear_expression (tree scev) | |
| 1524 { | |
| 1525 if (scev == NULL | |
| 1526 || !operator_is_linear (scev)) | |
| 1527 return false; | |
| 1528 | |
| 1529 if (TREE_CODE (scev) == MULT_EXPR) | |
| 1530 return !(tree_contains_chrecs (TREE_OPERAND (scev, 0), NULL) | |
| 1531 && tree_contains_chrecs (TREE_OPERAND (scev, 1), NULL)); | |
| 1532 | |
|
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1533 if (TREE_CODE (scev) == POLYNOMIAL_CHREC |
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1534 && !evolution_function_is_affine_multivariate_p (scev, CHREC_VARIABLE (scev))) |
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1535 return false; |
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1536 |
| 0 | 1537 switch (TREE_CODE_LENGTH (TREE_CODE (scev))) |
| 1538 { | |
| 1539 case 3: | |
| 1540 return scev_is_linear_expression (TREE_OPERAND (scev, 0)) | |
| 1541 && scev_is_linear_expression (TREE_OPERAND (scev, 1)) | |
| 1542 && scev_is_linear_expression (TREE_OPERAND (scev, 2)); | |
| 1543 | |
| 1544 case 2: | |
| 1545 return scev_is_linear_expression (TREE_OPERAND (scev, 0)) | |
| 1546 && scev_is_linear_expression (TREE_OPERAND (scev, 1)); | |
|
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1547 |
| 0 | 1548 case 1: |
| 1549 return scev_is_linear_expression (TREE_OPERAND (scev, 0)); | |
| 1550 | |
| 1551 case 0: | |
| 1552 return true; | |
| 1553 | |
| 1554 default: | |
| 1555 return false; | |
| 1556 } | |
| 1557 } | |
|
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1558 |
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1559 /* Determines whether the expression CHREC contains only interger consts |
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1560 in the right parts. */ |
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1561 |
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1562 bool |
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1563 evolution_function_right_is_integer_cst (const_tree chrec) |
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1564 { |
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1565 if (chrec == NULL_TREE) |
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1566 return false; |
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1567 |
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1568 switch (TREE_CODE (chrec)) |
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1569 { |
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1570 case INTEGER_CST: |
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1571 return true; |
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1572 |
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1573 case POLYNOMIAL_CHREC: |
|
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1574 return TREE_CODE (CHREC_RIGHT (chrec)) == INTEGER_CST |
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1575 && (TREE_CODE (CHREC_LEFT (chrec)) != POLYNOMIAL_CHREC |
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1576 || evolution_function_right_is_integer_cst (CHREC_LEFT (chrec))); |
|
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1577 |
|
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1578 CASE_CONVERT: |
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1579 return evolution_function_right_is_integer_cst (TREE_OPERAND (chrec, 0)); |
|
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1580 |
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1581 default: |
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1582 return false; |
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1583 } |
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1584 } |