loopbce.go

     1  // Copyright 2018 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package ssa
     6  
     7  import (
     8  	"cmd/compile/internal/base"
     9  	"cmd/compile/internal/types"
    10  	"fmt"
    11  )
    12  
    13  type indVarFlags uint8
    14  
    15  const (
    16  	indVarMinExc    indVarFlags = 1 << iota // minimum value is exclusive (default: inclusive)
    17  	indVarMaxInc                            // maximum value is inclusive (default: exclusive)
    18  	indVarCountDown                         // if set the iteration starts at max and count towards min (default: min towards max)
    19  )
    20  
    21  type indVar struct {
    22  	ind   *Value // induction variable
    23  	nxt   *Value // the incremented variable
    24  	min   *Value // minimum value, inclusive/exclusive depends on flags
    25  	max   *Value // maximum value, inclusive/exclusive depends on flags
    26  	entry *Block // entry block in the loop.
    27  	flags indVarFlags
    28  	// Invariant: for all blocks strictly dominated by entry:
    29  	//	min <= ind <  max    [if flags == 0]
    30  	//	min <  ind <  max    [if flags == indVarMinExc]
    31  	//	min <= ind <= max    [if flags == indVarMaxInc]
    32  	//	min <  ind <= max    [if flags == indVarMinExc|indVarMaxInc]
    33  }
    34  
    35  // parseIndVar checks whether the SSA value passed as argument is a valid induction
    36  // variable, and, if so, extracts:
    37  //   - the minimum bound
    38  //   - the increment value
    39  //   - the "next" value (SSA value that is Phi'd into the induction variable every loop)
    40  //
    41  // Currently, we detect induction variables that match (Phi min nxt),
    42  // with nxt being (Add inc ind).
    43  // If it can't parse the induction variable correctly, it returns (nil, nil, nil).
    44  func parseIndVar(ind *Value) (min, inc, nxt *Value) {
    45  	if ind.Op != OpPhi {
    46  		return
    47  	}
    48  
    49  	if n := ind.Args[0]; (n.Op == OpAdd64 || n.Op == OpAdd32 || n.Op == OpAdd16 || n.Op == OpAdd8) && (n.Args[0] == ind || n.Args[1] == ind) {
    50  		min, nxt = ind.Args[1], n
    51  	} else if n := ind.Args[1]; (n.Op == OpAdd64 || n.Op == OpAdd32 || n.Op == OpAdd16 || n.Op == OpAdd8) && (n.Args[0] == ind || n.Args[1] == ind) {
    52  		min, nxt = ind.Args[0], n
    53  	} else {
    54  		// Not a recognized induction variable.
    55  		return
    56  	}
    57  
    58  	if nxt.Args[0] == ind { // nxt = ind + inc
    59  		inc = nxt.Args[1]
    60  	} else if nxt.Args[1] == ind { // nxt = inc + ind
    61  		inc = nxt.Args[0]
    62  	} else {
    63  		panic("unreachable") // one of the cases must be true from the above.
    64  	}
    65  
    66  	return
    67  }
    68  
    69  // findIndVar finds induction variables in a function.
    70  //
    71  // Look for variables and blocks that satisfy the following
    72  //
    73  //	 loop:
    74  //	   ind = (Phi min nxt),
    75  //	   if ind < max
    76  //	     then goto enter_loop
    77  //	     else goto exit_loop
    78  //
    79  //	   enter_loop:
    80  //		do something
    81  //	      nxt = inc + ind
    82  //		goto loop
    83  //
    84  //	 exit_loop:
    85  func findIndVar(f *Func) []indVar {
    86  	var iv []indVar
    87  	sdom := f.Sdom()
    88  
    89  	for _, b := range f.Blocks {
    90  		if b.Kind != BlockIf || len(b.Preds) != 2 {
    91  			continue
    92  		}
    93  
    94  		var ind *Value   // induction variable
    95  		var init *Value  // starting value
    96  		var limit *Value // ending value
    97  
    98  		// Check that the control if it either ind </<= limit or limit </<= ind.
    99  		// TODO: Handle unsigned comparisons?
   100  		c := b.Controls[0]
   101  		inclusive := false
   102  		switch c.Op {
   103  		case OpLeq64, OpLeq32, OpLeq16, OpLeq8:
   104  			inclusive = true
   105  			fallthrough
   106  		case OpLess64, OpLess32, OpLess16, OpLess8:
   107  			ind, limit = c.Args[0], c.Args[1]
   108  		default:
   109  			continue
   110  		}
   111  
   112  		// See if this is really an induction variable
   113  		less := true
   114  		init, inc, nxt := parseIndVar(ind)
   115  		if init == nil {
   116  			// We failed to parse the induction variable. Before punting, we want to check
   117  			// whether the control op was written with the induction variable on the RHS
   118  			// instead of the LHS. This happens for the downwards case, like:
   119  			//     for i := len(n)-1; i >= 0; i--
   120  			init, inc, nxt = parseIndVar(limit)
   121  			if init == nil {
   122  				// No recognized induction variable on either operand
   123  				continue
   124  			}
   125  
   126  			// Ok, the arguments were reversed. Swap them, and remember that we're
   127  			// looking at an ind >/>= loop (so the induction must be decrementing).
   128  			ind, limit = limit, ind
   129  			less = false
   130  		}
   131  
   132  		if ind.Block != b {
   133  			// TODO: Could be extended to include disjointed loop headers.
   134  			// I don't think this is causing missed optimizations in real world code often.
   135  			// See https://go.dev/issue/63955
   136  			continue
   137  		}
   138  
   139  		// Expect the increment to be a nonzero constant.
   140  		if !inc.isGenericIntConst() {
   141  			continue
   142  		}
   143  		step := inc.AuxInt
   144  		if step == 0 {
   145  			continue
   146  		}
   147  
   148  		// Increment sign must match comparison direction.
   149  		// When incrementing, the termination comparison must be ind </<= limit.
   150  		// When decrementing, the termination comparison must be ind >/>= limit.
   151  		// See issue 26116.
   152  		if step > 0 && !less {
   153  			continue
   154  		}
   155  		if step < 0 && less {
   156  			continue
   157  		}
   158  
   159  		// Up to now we extracted the induction variable (ind),
   160  		// the increment delta (inc), the temporary sum (nxt),
   161  		// the initial value (init) and the limiting value (limit).
   162  		//
   163  		// We also know that ind has the form (Phi init nxt) where
   164  		// nxt is (Add inc nxt) which means: 1) inc dominates nxt
   165  		// and 2) there is a loop starting at inc and containing nxt.
   166  		//
   167  		// We need to prove that the induction variable is incremented
   168  		// only when it's smaller than the limiting value.
   169  		// Two conditions must happen listed below to accept ind
   170  		// as an induction variable.
   171  
   172  		// First condition: loop entry has a single predecessor, which
   173  		// is the header block.  This implies that b.Succs[0] is
   174  		// reached iff ind < limit.
   175  		if len(b.Succs[0].b.Preds) != 1 {
   176  			// b.Succs[1] must exit the loop.
   177  			continue
   178  		}
   179  
   180  		// Second condition: b.Succs[0] dominates nxt so that
   181  		// nxt is computed when inc < limit.
   182  		if !sdom.IsAncestorEq(b.Succs[0].b, nxt.Block) {
   183  			// inc+ind can only be reached through the branch that enters the loop.
   184  			continue
   185  		}
   186  
   187  		// Check for overflow/underflow. We need to make sure that inc never causes
   188  		// the induction variable to wrap around.
   189  		// We use a function wrapper here for easy return true / return false / keep going logic.
   190  		// This function returns true if the increment will never overflow/underflow.
   191  		ok := func() bool {
   192  			if step > 0 {
   193  				if limit.isGenericIntConst() {
   194  					// Figure out the actual largest value.
   195  					v := limit.AuxInt
   196  					if !inclusive {
   197  						if v == minSignedValue(limit.Type) {
   198  							return false // < minint is never satisfiable.
   199  						}
   200  						v--
   201  					}
   202  					if init.isGenericIntConst() {
   203  						// Use stride to compute a better lower limit.
   204  						if init.AuxInt > v {
   205  							return false
   206  						}
   207  						v = addU(init.AuxInt, diff(v, init.AuxInt)/uint64(step)*uint64(step))
   208  					}
   209  					if addWillOverflow(v, step) {
   210  						return false
   211  					}
   212  					if inclusive && v != limit.AuxInt || !inclusive && v+1 != limit.AuxInt {
   213  						// We know a better limit than the programmer did. Use our limit instead.
   214  						limit = f.constVal(limit.Op, limit.Type, v, true)
   215  						inclusive = true
   216  					}
   217  					return true
   218  				}
   219  				if step == 1 && !inclusive {
   220  					// Can't overflow because maxint is never a possible value.
   221  					return true
   222  				}
   223  				// If the limit is not a constant, check to see if it is a
   224  				// negative offset from a known non-negative value.
   225  				knn, k := findKNN(limit)
   226  				if knn == nil || k < 0 {
   227  					return false
   228  				}
   229  				// limit == (something nonnegative) - k. That subtraction can't underflow, so
   230  				// we can trust it.
   231  				if inclusive {
   232  					// ind <= knn - k cannot overflow if step is at most k
   233  					return step <= k
   234  				}
   235  				// ind < knn - k cannot overflow if step is at most k+1
   236  				return step <= k+1 && k != maxSignedValue(limit.Type)
   237  			} else { // step < 0
   238  				if limit.Op == OpConst64 {
   239  					// Figure out the actual smallest value.
   240  					v := limit.AuxInt
   241  					if !inclusive {
   242  						if v == maxSignedValue(limit.Type) {
   243  							return false // > maxint is never satisfiable.
   244  						}
   245  						v++
   246  					}
   247  					if init.isGenericIntConst() {
   248  						// Use stride to compute a better lower limit.
   249  						if init.AuxInt < v {
   250  							return false
   251  						}
   252  						v = subU(init.AuxInt, diff(init.AuxInt, v)/uint64(-step)*uint64(-step))
   253  					}
   254  					if subWillUnderflow(v, -step) {
   255  						return false
   256  					}
   257  					if inclusive && v != limit.AuxInt || !inclusive && v-1 != limit.AuxInt {
   258  						// We know a better limit than the programmer did. Use our limit instead.
   259  						limit = f.constVal(limit.Op, limit.Type, v, true)
   260  						inclusive = true
   261  					}
   262  					return true
   263  				}
   264  				if step == -1 && !inclusive {
   265  					// Can't underflow because minint is never a possible value.
   266  					return true
   267  				}
   268  			}
   269  			return false
   270  
   271  		}
   272  
   273  		if ok() {
   274  			flags := indVarFlags(0)
   275  			var min, max *Value
   276  			if step > 0 {
   277  				min = init
   278  				max = limit
   279  				if inclusive {
   280  					flags |= indVarMaxInc
   281  				}
   282  			} else {
   283  				min = limit
   284  				max = init
   285  				flags |= indVarMaxInc
   286  				if !inclusive {
   287  					flags |= indVarMinExc
   288  				}
   289  				flags |= indVarCountDown
   290  				step = -step
   291  			}
   292  			if f.pass.debug >= 1 {
   293  				printIndVar(b, ind, min, max, step, flags)
   294  			}
   295  
   296  			iv = append(iv, indVar{
   297  				ind:   ind,
   298  				nxt:   nxt,
   299  				min:   min,
   300  				max:   max,
   301  				entry: b.Succs[0].b,
   302  				flags: flags,
   303  			})
   304  			b.Logf("found induction variable %v (inc = %v, min = %v, max = %v)\n", ind, inc, min, max)
   305  		}
   306  
   307  		// TODO: other unrolling idioms
   308  		// for i := 0; i < KNN - KNN % k ; i += k
   309  		// for i := 0; i < KNN&^(k-1) ; i += k // k a power of 2
   310  		// for i := 0; i < KNN&(-k) ; i += k // k a power of 2
   311  	}
   312  
   313  	return iv
   314  }
   315  
   316  // addWillOverflow reports whether x+y would result in a value more than maxint.
   317  func addWillOverflow(x, y int64) bool {
   318  	return x+y < x
   319  }
   320  
   321  // subWillUnderflow reports whether x-y would result in a value less than minint.
   322  func subWillUnderflow(x, y int64) bool {
   323  	return x-y > x
   324  }
   325  
   326  // diff returns x-y as a uint64. Requires x>=y.
   327  func diff(x, y int64) uint64 {
   328  	if x < y {
   329  		base.Fatalf("diff %d - %d underflowed", x, y)
   330  	}
   331  	return uint64(x - y)
   332  }
   333  
   334  // addU returns x+y. Requires that x+y does not overflow an int64.
   335  func addU(x int64, y uint64) int64 {
   336  	if y >= 1<<63 {
   337  		if x >= 0 {
   338  			base.Fatalf("addU overflowed %d + %d", x, y)
   339  		}
   340  		x += 1<<63 - 1
   341  		x += 1
   342  		y -= 1 << 63
   343  	}
   344  	if addWillOverflow(x, int64(y)) {
   345  		base.Fatalf("addU overflowed %d + %d", x, y)
   346  	}
   347  	return x + int64(y)
   348  }
   349  
   350  // subU returns x-y. Requires that x-y does not underflow an int64.
   351  func subU(x int64, y uint64) int64 {
   352  	if y >= 1<<63 {
   353  		if x < 0 {
   354  			base.Fatalf("subU underflowed %d - %d", x, y)
   355  		}
   356  		x -= 1<<63 - 1
   357  		x -= 1
   358  		y -= 1 << 63
   359  	}
   360  	if subWillUnderflow(x, int64(y)) {
   361  		base.Fatalf("subU underflowed %d - %d", x, y)
   362  	}
   363  	return x - int64(y)
   364  }
   365  
   366  // if v is known to be x - c, where x is known to be nonnegative and c is a
   367  // constant, return x, c. Otherwise return nil, 0.
   368  func findKNN(v *Value) (*Value, int64) {
   369  	var x, y *Value
   370  	x = v
   371  	switch v.Op {
   372  	case OpSub64, OpSub32, OpSub16, OpSub8:
   373  		x = v.Args[0]
   374  		y = v.Args[1]
   375  
   376  	case OpAdd64, OpAdd32, OpAdd16, OpAdd8:
   377  		x = v.Args[0]
   378  		y = v.Args[1]
   379  		if x.isGenericIntConst() {
   380  			x, y = y, x
   381  		}
   382  	}
   383  	switch x.Op {
   384  	case OpSliceLen, OpStringLen, OpSliceCap:
   385  	default:
   386  		return nil, 0
   387  	}
   388  	if y == nil {
   389  		return x, 0
   390  	}
   391  	if !y.isGenericIntConst() {
   392  		return nil, 0
   393  	}
   394  	if v.Op == OpAdd64 || v.Op == OpAdd32 || v.Op == OpAdd16 || v.Op == OpAdd8 {
   395  		return x, -y.AuxInt
   396  	}
   397  	return x, y.AuxInt
   398  }
   399  
   400  func printIndVar(b *Block, i, min, max *Value, inc int64, flags indVarFlags) {
   401  	mb1, mb2 := "[", "]"
   402  	if flags&indVarMinExc != 0 {
   403  		mb1 = "("
   404  	}
   405  	if flags&indVarMaxInc == 0 {
   406  		mb2 = ")"
   407  	}
   408  
   409  	mlim1, mlim2 := fmt.Sprint(min.AuxInt), fmt.Sprint(max.AuxInt)
   410  	if !min.isGenericIntConst() {
   411  		if b.Func.pass.debug >= 2 {
   412  			mlim1 = fmt.Sprint(min)
   413  		} else {
   414  			mlim1 = "?"
   415  		}
   416  	}
   417  	if !max.isGenericIntConst() {
   418  		if b.Func.pass.debug >= 2 {
   419  			mlim2 = fmt.Sprint(max)
   420  		} else {
   421  			mlim2 = "?"
   422  		}
   423  	}
   424  	extra := ""
   425  	if b.Func.pass.debug >= 2 {
   426  		extra = fmt.Sprintf(" (%s)", i)
   427  	}
   428  	b.Func.Warnl(b.Pos, "Induction variable: limits %v%v,%v%v, increment %d%s", mb1, mlim1, mlim2, mb2, inc, extra)
   429  }
   430  
   431  func minSignedValue(t *types.Type) int64 {
   432  	return -1 << (t.Size()*8 - 1)
   433  }
   434  
   435  func maxSignedValue(t *types.Type) int64 {
   436  	return 1<<((t.Size()*8)-1) - 1
   437  }
   438
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