blob: 5d5e02efd0e4a39e511b7acf51125a6dbc4ae8e8 [file] [log] [blame]
 ; RUN: opt -analyze -scalar-evolution -S -debug-only=scalar-evolution,apint < %s 2>&1 | FileCheck %s ; REQUIRES: asserts ; Use the following template to get a chrec {L,+,M,+,N}. ; ; define signext i32 @func() { ; entry: ; br label %loop ; ; loop: ; %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] ; %inc = phi i32 [ X, %entry ], [ %inc1, %loop ] ; %acc = phi i32 [ Y, %entry ], [ %acc1, %loop ] ; %ivr1 = add i32 %ivr, %inc ; %inc1 = add i32 %inc, Z ; M = inc1 = inc + N = X + N ; %acc1 = add i32 %acc, %inc ; L = acc1 = X + Y ; %and = and i32 %acc1, 2^W-1 ; iW ; %cond = icmp eq i32 %and, 0 ; br i1 %cond, label %exit, label %loop ; ; exit: ; %rv = phi i32 [ %acc1, %loop ] ; ret i32 %rv ; } ; ; From ; X + Y = L ; X + Z = M ; Z = N ; get ; X = M - N ; Y = N - M + L ; Z = N ; The connection between the chrec coefficients {L,+,M,+,N} and the quadratic ; coefficients is that the quadratic equation is N x^2 + (2M-N) x + 2L = 0, ; where the equation was multiplied by 2 to make the coefficient at x^2 an ; integer (the actual equation is N/2 x^2 + (M-N/2) x + L = 0). ; Quadratic equation: 2x^2 + 2x + 4 in i4, solution (wrap): 4 ; {14,+,14,+,14} -> X=0, Y=14, Z=14 ; ; CHECK-LABEL: Printing analysis 'Scalar Evolution Analysis' for function 'test01' ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {-2,+,-2,+,-2}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 4 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation -2x^2 + -2x + -4, coeff bw: 5, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecExact{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving -2x^2 + -2x + -4, rw:5 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 2x^2 + 2x + -28, rw:5 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 4 ; CHECK: Loop %loop: Unpredictable backedge-taken count define signext i32 @test01() { entry: br label %loop loop: %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] %inc = phi i32 [ 0, %entry ], [ %inc1, %loop ] %acc = phi i32 [ 14, %entry ], [ %acc1, %loop ] %ivr1 = add i32 %ivr, %inc %inc1 = add i32 %inc, 14 %acc1 = add i32 %acc, %inc %and = and i32 %acc1, 15 %cond = icmp eq i32 %and, 0 br i1 %cond, label %exit, label %loop exit: %rv = phi i32 [ %acc1, %loop ] ret i32 %rv } ; Quadratic equation: 1x^2 + -73x + -146 in i32, solution (wrap): 75 ; {-72,+,-36,+,1} -> X=-37, Y=-35, Z=1 ; ; CHECK-LABEL: Printing analysis 'Scalar Evolution Analysis' for function 'test02': ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {0,+,-36,+,1}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 32 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation 1x^2 + -73x + 0, coeff bw: 33, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -73x + 4294967154, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -73x + -142, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 75 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -73x + 4294967154, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -73x + -4294967438, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 65573 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -73x + -146, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -73x + -146, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 75 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -73x + -146, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -73x + -146, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 75 ; CHECK: Loop %loop: backedge-taken count is 75 define signext i32 @test02() { entry: br label %loop loop: %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] %inc = phi i32 [ -37, %entry ], [ %inc1, %loop ] %acc = phi i32 [ -35, %entry ], [ %acc1, %loop ] %ivr1 = add i32 %ivr, %inc %inc1 = add i32 %inc, 1 %acc1 = add i32 %acc, %inc %and = and i32 %acc1, -1 %cond = icmp sgt i32 %and, 0 br i1 %cond, label %exit, label %loop exit: %rv = phi i32 [ %acc1, %loop ] ret i32 %rv } ; Quadratic equation: 2x^2 - 4x + 34 in i4, solution (exact): 1. ; {17,+,-1,+,2} -> X=-3, Y=20, Z=2 ; ; CHECK-LABEL: Printing analysis 'Scalar Evolution Analysis' for function 'test03': ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {1,+,-1,+,2}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 4 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation 2x^2 + -4x + 2, coeff bw: 5, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecExact{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 2x^2 + -4x + 2, rw:5 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 2x^2 + -4x + 2, rw:5 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (root): 1 ; CHECK: Loop %loop: backedge-taken count is 1 define signext i32 @test03() { entry: br label %loop loop: %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] %inc = phi i32 [ -3, %entry ], [ %inc1, %loop ] %acc = phi i32 [ 20, %entry ], [ %acc1, %loop ] %ivr1 = add i32 %ivr, %inc %inc1 = add i32 %inc, 2 %acc1 = add i32 %acc, %inc %and = and i32 %acc1, 15 %cond = icmp eq i32 %and, 0 br i1 %cond, label %exit, label %loop exit: %rv = phi i32 [ %acc1, %loop ] ret i32 %rv } ; Quadratic equation 4x^2 + 2x + 2 in i16, solution (wrap): 181 ; {1,+,3,+,4} -> X=-1, Y=2, Z=4 (i16) ; ; This is an example where the returned solution is the first time an ; unsigned wrap occurs, whereas the actual exit condition occurs much ; later. The number of iterations returned by SolveQuadraticEquation ; is 181, but the loop will iterate 37174 times. ; ; Here is a C code that corresponds to this case that calculates the number ; of iterations: ; ; int test04() { ; int c = 0; ; int ivr = 0; ; int inc = -1; ; int acc = 2; ; ; while (acc & 0xffff) { ; c++; ; ivr += inc; ; inc += 4; ; acc += inc; ; } ; ; return c; ; } ; ; CHECK-LABEL: Printing analysis 'Scalar Evolution Analysis' for function 'test04': ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {0,+,3,+,4}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 16 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation 4x^2 + 2x + 0, coeff bw: 17, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 4x^2 + 2x + 2, rw:16 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 4x^2 + 2x + -65534, rw:16 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 128 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 4x^2 + 2x + 2, rw:17 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 4x^2 + 2x + -131070, rw:17 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 181 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 4x^2 + 2x + 2, rw:16 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 4x^2 + 2x + -65534, rw:16 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 128 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 4x^2 + 2x + 2, rw:17 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 4x^2 + 2x + -131070, rw:17 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 181 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {1,+,3,+,4}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 16 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation 4x^2 + 2x + 2, coeff bw: 17, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecExact{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 4x^2 + 2x + 2, rw:17 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 4x^2 + 2x + -131070, rw:17 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 181 ; CHECK: Loop %loop: Unpredictable backedge-taken count. define signext i32 @test04() { entry: br label %loop loop: %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] %inc = phi i32 [ -1, %entry ], [ %inc1, %loop ] %acc = phi i32 [ 2, %entry ], [ %acc1, %loop ] %ivr1 = add i32 %ivr, %inc %inc1 = add i32 %inc, 4 %acc1 = add i32 %acc, %inc %and = trunc i32 %acc1 to i16 %cond = icmp eq i16 %and, 0 br i1 %cond, label %exit, label %loop exit: %rv = phi i32 [ %acc1, %loop ] ret i32 %rv } ; A case with signed arithmetic, but unsigned comparison. ; CHECK-LABEL: Printing analysis 'Scalar Evolution Analysis' for function 'test05': ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {0,+,-1,+,-1}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 32 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation -1x^2 + -1x + 0, coeff bw: 33, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving -1x^2 + -1x + 4, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + 1x + -4, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 2 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving -1x^2 + -1x + 4, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + 1x + -4, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 2 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving -1x^2 + -1x + -2, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + 1x + -4294967294, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 65536 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving -1x^2 + -1x + -2, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + 1x + -8589934590, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 92682 ; CHECK: Loop %loop: backedge-taken count is 2 define signext i32 @test05() { entry: br label %loop loop: %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] %inc = phi i32 [ 0, %entry ], [ %inc1, %loop ] %acc = phi i32 [ -1, %entry ], [ %acc1, %loop ] %ivr1 = add i32 %ivr, %inc %inc1 = add i32 %inc, -1 %acc1 = add i32 %acc, %inc %and = and i32 %acc1, -1 %cond = icmp ule i32 %and, -3 br i1 %cond, label %exit, label %loop exit: %rv = phi i32 [ %acc1, %loop ] ret i32 %rv } ; A test that used to crash with one of the earlier versions of the code. ; CHECK-LABEL: Printing analysis 'Scalar Evolution Analysis' for function 'test06': ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {0,+,-99999,+,1}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 32 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation 1x^2 + -199999x + 0, coeff bw: 33, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -199999x + -4294967294, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -199999x + 2, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 1 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -199999x + -4294967294, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -199999x + 4294967298, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 24469 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -199999x + -12, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -199999x + 4294967284, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 24469 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 1x^2 + -199999x + -12, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 1x^2 + -199999x + 8589934580, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solution (wrap): 62450 ; CHECK: Loop %loop: backedge-taken count is 24469 define signext i32 @test06() { entry: br label %loop loop: %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] %inc = phi i32 [ -100000, %entry ], [ %inc1, %loop ] %acc = phi i32 [ 100000, %entry ], [ %acc1, %loop ] %ivr1 = add i32 %ivr, %inc %inc1 = add i32 %inc, 1 %acc1 = add i32 %acc, %inc %and = and i32 %acc1, -1 %cond = icmp sgt i32 %and, 5 br i1 %cond, label %exit, label %loop exit: %rv = phi i32 [ %acc1, %loop ] ret i32 %rv } ; The equation ; 532052752x^2 + -450429774x + 71188414 = 0 ; has two exact solutions (up to two decimal digits): 0.21 and 0.64. ; Since there is no integer between them, there is no integer n that either ; solves the equation exactly, or changes the sign of it between n and n+1. ; CHECK-LABEL: Printing analysis 'Scalar Evolution Analysis' for function 'test07': ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {0,+,40811489,+,532052752}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 32 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation 532052752x^2 + -450429774x + 0, coeff bw: 33, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 532052752x^2 + -450429774x + 71188414, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 532052752x^2 + -450429774x + 71188414, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: no valid solution ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 532052752x^2 + -450429774x + 71188414, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 532052752x^2 + -450429774x + 71188414, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: no valid solution ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for signed overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 532052752x^2 + -450429774x + 71188414, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 532052752x^2 + -450429774x + 71188414, rw:32 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: no valid solution ; CHECK: {{.*}}SolveQuadraticAddRecRange{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 532052752x^2 + -450429774x + 71188414, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 532052752x^2 + -450429774x + 71188414, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: no valid solution ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: analyzing quadratic addrec: {35594207,+,40811489,+,532052752}<%loop> ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: addrec coeff bw: 32 ; CHECK: {{.*}}GetQuadraticEquation{{.*}}: equation 532052752x^2 + -450429774x + 71188414, coeff bw: 33, multiplied by 2 ; CHECK: {{.*}}SolveQuadraticAddRecExact{{.*}}: solving for unsigned overflow ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: solving 532052752x^2 + -450429774x + 71188414, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: updated coefficients 532052752x^2 + -450429774x + 71188414, rw:33 ; CHECK: {{.*}}SolveQuadraticEquationWrap{{.*}}: no valid solution ; CHECK: Loop %loop: Unpredictable backedge-taken count. define signext i32 @test07() { entry: br label %loop loop: %ivr = phi i32 [ 0, %entry ], [ %ivr1, %loop ] %inc = phi i32 [ -491241263, %entry ], [ %inc1, %loop ] %acc = phi i32 [ 526835470, %entry ], [ %acc1, %loop ] %ivr1 = add i32 %ivr, %inc %inc1 = add i32 %inc, 532052752 %acc1 = add i32 %acc, %inc %and = and i32 %acc1, -1 %cond = icmp eq i32 %and, 0 br i1 %cond, label %exit, label %loop exit: %rv = phi i32 [ %acc1, %loop ] ret i32 %rv }