Optimized computing powers in CompiledExpression (#3520)

* Optimized computing powers in CompiledExpression

* Fixed compilation error

* Attempt at fixing compilation error

devtools/ci/gh-actions/conda-envs/build-ubuntu-latest.yml

@@ -7,6 +7,7 @@ dependencies:
 - cmake
 - make
 - ccache
+- sysroot_linux-64 2.17
 # host
 - python
 - cython

libraries/lepton/include/lepton/CompiledExpression.h

@@ -105,6 +105,7 @@ private:
     std::map<std::string, double> dummyVariables;
     double (*jitCode)();
 #ifdef LEPTON_USE_JIT
+    void findPowerGroups(std::vector<std::vector<int> >& groups, std::vector<std::vector<int> >& groupPowers, std::vector<int>& stepGroup);
     void generateJitCode();
 #if defined(__ARM__) || defined(__ARM64__)
     void generateSingleArgCall(asmjit::a64::Compiler& c, asmjit::arm::Vec& dest, asmjit::arm::Vec& arg, double (*function)(double));

libraries/lepton/src/CompiledExpression.cpp

@@ -192,6 +192,48 @@ static double evaluateOperation(Operation* op, double* args) {
     return op->evaluate(args, dummyVariables);
 }
 
+void CompiledExpression::findPowerGroups(vector<vector<int> >& groups, vector<vector<int> >& groupPowers, vector<int>& stepGroup) {
+    // Identify every step that raises an argument to an integer power.
+
+    vector<int> stepPower(operation.size(), 0);
+    vector<int> stepArg(operation.size(), -1);
+    for (int step = 0; step < operation.size(); step++) {
+        Operation& op = *operation[step];
+        int power = 0;
+        if (op.getId() == Operation::SQUARE)
+            power = 2;
+        else if (op.getId() == Operation::CUBE)
+            power = 3;
+        else if (op.getId() == Operation::POWER_CONSTANT) {
+            double realPower = dynamic_cast<const Operation::PowerConstant*>(&op)->getValue();
+            if (realPower == (int) realPower)
+                power = (int) realPower;
+        }
+        if (power != 0) {
+            stepPower[step] = power;
+            stepArg[step] = arguments[step][0];
+        }
+    }
+
+    // Find groups that operate on the same argument and whose powers have the same sign.
+
+    stepGroup.resize(operation.size(), -1);
+    for (int i = 0; i < operation.size(); i++) {
+        if (stepGroup[i] != -1)
+            continue;
+        vector<int> group, power;
+        for (int j = i; j < operation.size(); j++) {
+            if (stepArg[i] == stepArg[j] && stepPower[i]*stepPower[j] > 0) {
+                stepGroup[j] = groups.size();
+                group.push_back(j);
+                power.push_back(stepPower[j]);
+            }
+        }
+        groups.push_back(group);
+        groupPowers.push_back(power);
+    }
+}
+
 #if defined(__ARM__) || defined(__ARM64__)
 void CompiledExpression::generateJitCode() {
     CodeHolder code;
@@ -203,6 +245,9 @@ void CompiledExpression::generateJitCode() {
         workspaceVar[i] = c.newVecD();
     arm::Gp argsPointer = c.newIntPtr();
     c.mov(argsPointer, imm(&argValues[0]));
+    vector<vector<int> > groups, groupPowers;
+    vector<int> stepGroup;
+    findPowerGroups(groups, groupPowers, stepGroup);
     
     // Load the arguments into variables.
     
@@ -233,6 +278,12 @@ void CompiledExpression::generateJitCode() {
             value = 1.0;
         else if (op.getId() == Operation::DELTA)
             value = 1.0;
+        else if (op.getId() == Operation::POWER_CONSTANT) {
+            if (stepGroup[step] == -1)
+                value = dynamic_cast<Operation::PowerConstant&>(op).getValue();
+            else
+                value = 1.0;
+        }
         else
             continue;
         
@@ -260,10 +311,54 @@ void CompiledExpression::generateJitCode() {
             c.ldr(constantVar[i], arm::ptr(constantsPointer, 8*i));
         }
     }
-    
+
     // Evaluate the operations.
-    
+
+    vector<bool> hasComputedPower(operation.size(), false);
     for (int step = 0; step < (int) operation.size(); step++) {
+        if (hasComputedPower[step])
+            continue;
+
+        // When one or more steps involve raising the same argument to multiple integer
+        // powers, we can compute them all together for efficiency.
+
+        if (stepGroup[step] != -1) {
+            vector<int>& group = groups[stepGroup[step]];
+            vector<int>& powers = groupPowers[stepGroup[step]];
+            arm::Vec multiplier = c.newVecD();
+            if (powers[0] > 0)
+                c.fmov(multiplier, workspaceVar[arguments[step][0]]);
+            else {
+                c.fdiv(multiplier, constantVar[operationConstantIndex[step]], workspaceVar[arguments[step][0]]);
+                for (int i = 0; i < powers.size(); i++)
+                    powers[i] = -powers[i];
+            }
+            vector<bool> hasAssigned(group.size(), false);
+            bool done = false;
+            while (!done) {
+                done = true;
+                for (int i = 0; i < group.size(); i++) {
+                    if (powers[i]%2 == 1) {
+                        if (!hasAssigned[i])
+                            c.fmov(workspaceVar[target[group[i]]], multiplier);
+                        else
+                            c.fmul(workspaceVar[target[group[i]]], workspaceVar[target[group[i]]], multiplier);
+                        hasAssigned[i] = true;
+                    }
+                    powers[i] >>= 1;
+                    if (powers[i] != 0)
+                        done = false;
+                }
+                if (!done)
+                    c.fmul(multiplier, multiplier, multiplier);
+            }
+            for (int step : group)
+                hasComputedPower[step] = true;
+            continue;
+        }
+
+        // Evaluate the step.
+
         Operation& op = *operation[step];
         vector<int> args = arguments[step];
         if (args.size() == 1) {
@@ -360,6 +455,9 @@ void CompiledExpression::generateJitCode() {
             case Operation::MULTIPLY_CONSTANT:
                 c.fmul(workspaceVar[target[step]], workspaceVar[args[0]], constantVar[operationConstantIndex[step]]);
                 break;
+            case Operation::POWER_CONSTANT:
+                generateTwoArgCall(c, workspaceVar[target[step]], workspaceVar[args[0]], constantVar[operationConstantIndex[step]], pow);
+                break;
             case Operation::ABS:
                 c.fabs(workspaceVar[target[step]], workspaceVar[args[0]]);
                 break;
@@ -418,7 +516,10 @@ void CompiledExpression::generateJitCode() {
         workspaceVar[i] = c.newXmmSd();
     x86::Gp argsPointer = c.newIntPtr();
     c.mov(argsPointer, imm(&argValues[0]));
-    
+    vector<vector<int> > groups, groupPowers;
+    vector<int> stepGroup;
+    findPowerGroups(groups, groupPowers, stepGroup);
+
     // Load the arguments into variables.
     
     for (set<string>::const_iterator iter = variableNames.begin(); iter != variableNames.end(); ++iter) {
@@ -448,6 +549,12 @@ void CompiledExpression::generateJitCode() {
             value = 1.0;
         else if (op.getId() == Operation::DELTA)
             value = 1.0;
+        else if (op.getId() == Operation::POWER_CONSTANT) {
+            if (stepGroup[step] == -1)
+                value = dynamic_cast<Operation::PowerConstant&>(op).getValue();
+            else
+                value = 1.0;
+        }
         else
             continue;
         
@@ -478,7 +585,52 @@ void CompiledExpression::generateJitCode() {
     
     // Evaluate the operations.
     
+    vector<bool> hasComputedPower(operation.size(), false);
     for (int step = 0; step < (int) operation.size(); step++) {
+        if (hasComputedPower[step])
+            continue;
+
+        // When one or more steps involve raising the same argument to multiple integer
+        // powers, we can compute them all together for efficiency.
+
+        if (stepGroup[step] != -1) {
+            vector<int>& group = groups[stepGroup[step]];
+            vector<int>& powers = groupPowers[stepGroup[step]];
+            x86::Xmm multiplier = c.newXmmSd();
+            if (powers[0] > 0)
+                c.movsd(multiplier, workspaceVar[arguments[step][0]]);
+            else {
+                c.movsd(multiplier, constantVar[operationConstantIndex[step]]);
+                c.divsd(multiplier, workspaceVar[arguments[step][0]]);
+                for (int i = 0; i < powers.size(); i++)
+                    powers[i] = -powers[i];
+            }
+            vector<bool> hasAssigned(group.size(), false);
+            bool done = false;
+            while (!done) {
+                done = true;
+                for (int i = 0; i < group.size(); i++) {
+                    if (powers[i]%2 == 1) {
+                        if (!hasAssigned[i])
+                            c.movsd(workspaceVar[target[group[i]]], multiplier);
+                        else
+                            c.mulsd(workspaceVar[target[group[i]]], multiplier);
+                        hasAssigned[i] = true;
+                    }
+                    powers[i] >>= 1;
+                    if (powers[i] != 0)
+                        done = false;
+                }
+                if (!done)
+                    c.mulsd(multiplier, multiplier);
+            }
+            for (int step : group)
+                hasComputedPower[step] = true;
+            continue;
+        }
+
+        // Evaluate the step.
+
         Operation& op = *operation[step];
         vector<int> args = arguments[step];
         if (args.size() == 1) {
@@ -587,6 +739,9 @@ void CompiledExpression::generateJitCode() {
                 c.movsd(workspaceVar[target[step]], workspaceVar[args[0]]);
                 c.mulsd(workspaceVar[target[step]], constantVar[operationConstantIndex[step]]);
                 break;
+            case Operation::POWER_CONSTANT:
+                generateTwoArgCall(c, workspaceVar[target[step]], workspaceVar[args[0]], constantVar[operationConstantIndex[step]], pow);
+                break;
             case Operation::ABS:
                 generateSingleArgCall(c, workspaceVar[target[step]], workspaceVar[args[0]], fabs);
                 break;