Separate the "configuration" and "evaluation" phases of chart functions

Summary:
Depends on D20446. Currently, chart functions are both configured through arguments and evaluated through arguments. This sort of conflates things and makes some logic more difficult than it should be.

Instead:

  - Function arguments are used to configure function behavior. For example, `scale(2)` configures a function which does `f(x) => 2 * x`.
  - Evaluation is now separate, after configuration.

We can get rid of "sourceFunction" (which was basically marking one argument as "this is the thing that gets piped in" in a weird magical way) and "canEvaluate()" and "impulse".

Sequences of functions are achieved with `compose(u, v, w)`, which configures a function `f(x) => w(v(u(x)))` (note order is left-to right, like piping `x | u | v | w` to produce `y`).

The new flow is:

  - Every chartable function is `compose(...)` at top level, and composes one or more functions. `compose(x)` is longhand for `id(x)`. This just gives us a root/anchor node.
  - Figure out a domain, through various means.
  - Ask the function for a list of good input X values in that domain. This lets function chains which include a "fact" with distinct datapoints tell us that we should evaluate those datapoints.
  - Pipe those X values through the function.
  - We get Y values out.
  - Draw those points.

Also:

  - Adds `accumluate()`.
  - Adds `sum()`, which is now easy to implement.
  - Adds `compose()`.
  - All functions can now always evaluate everywhere, they just return `null` if they are not defined at a given X.
  - Adds repeatable arguments for `compose(f, g, ...)` and `sum(f, g, ...)`.

Test Plan: {F6409890}

Reviewers: amckinley

Reviewed By: amckinley

Subscribers: yelirekim

Differential Revision: https://secure.phabricator.com/D20454

src/__phutil_library_map__.php

@@ -2107,6 +2107,7 @@ phutil_register_library_map(array(
     'PhabricatorAccessLog' => 'infrastructure/log/PhabricatorAccessLog.php',
     'PhabricatorAccessLogConfigOptions' => 'applications/config/option/PhabricatorAccessLogConfigOptions.php',
     'PhabricatorAccessibilitySetting' => 'applications/settings/setting/PhabricatorAccessibilitySetting.php',
+    'PhabricatorAccumulateChartFunction' => 'applications/fact/chart/PhabricatorAccumulateChartFunction.php',
     'PhabricatorActionListView' => 'view/layout/PhabricatorActionListView.php',
     'PhabricatorActionView' => 'view/layout/PhabricatorActionView.php',
     'PhabricatorActivitySettingsPanel' => 'applications/settings/panel/PhabricatorActivitySettingsPanel.php',
@@ -2695,6 +2696,7 @@ phutil_register_library_map(array(
     'PhabricatorCommitSearchEngine' => 'applications/audit/query/PhabricatorCommitSearchEngine.php',
     'PhabricatorCommitTagsField' => 'applications/repository/customfield/PhabricatorCommitTagsField.php',
     'PhabricatorCommonPasswords' => 'applications/auth/constants/PhabricatorCommonPasswords.php',
+    'PhabricatorComposeChartFunction' => 'applications/fact/chart/PhabricatorComposeChartFunction.php',
     'PhabricatorConduitAPIController' => 'applications/conduit/controller/PhabricatorConduitAPIController.php',
     'PhabricatorConduitApplication' => 'applications/conduit/application/PhabricatorConduitApplication.php',
     'PhabricatorConduitCallManagementWorkflow' => 'applications/conduit/management/PhabricatorConduitCallManagementWorkflow.php',
@@ -3425,6 +3427,7 @@ phutil_register_library_map(array(
     'PhabricatorHeraldContentSource' => 'applications/herald/contentsource/PhabricatorHeraldContentSource.php',
     'PhabricatorHexdumpDocumentEngine' => 'applications/files/document/PhabricatorHexdumpDocumentEngine.php',
     'PhabricatorHighSecurityRequestExceptionHandler' => 'aphront/handler/PhabricatorHighSecurityRequestExceptionHandler.php',
+    'PhabricatorHigherOrderChartFunction' => 'applications/fact/chart/PhabricatorHigherOrderChartFunction.php',
     'PhabricatorHomeApplication' => 'applications/home/application/PhabricatorHomeApplication.php',
     'PhabricatorHomeConstants' => 'applications/home/constants/PhabricatorHomeConstants.php',
     'PhabricatorHomeController' => 'applications/home/controller/PhabricatorHomeController.php',
@@ -4725,6 +4728,7 @@ phutil_register_library_map(array(
     'PhabricatorSubscriptionsUIEventListener' => 'applications/subscriptions/events/PhabricatorSubscriptionsUIEventListener.php',
     'PhabricatorSubscriptionsUnsubscribeEmailCommand' => 'applications/subscriptions/command/PhabricatorSubscriptionsUnsubscribeEmailCommand.php',
     'PhabricatorSubtypeEditEngineExtension' => 'applications/transactions/engineextension/PhabricatorSubtypeEditEngineExtension.php',
+    'PhabricatorSumChartFunction' => 'applications/fact/chart/PhabricatorSumChartFunction.php',
     'PhabricatorSupportApplication' => 'applications/support/application/PhabricatorSupportApplication.php',
     'PhabricatorSyntaxHighlighter' => 'infrastructure/markup/PhabricatorSyntaxHighlighter.php',
     'PhabricatorSyntaxHighlightingConfigOptions' => 'applications/config/option/PhabricatorSyntaxHighlightingConfigOptions.php',
@@ -4952,7 +4956,6 @@ phutil_register_library_map(array(
     'PhabricatorWorkingCopyDiscoveryTestCase' => 'applications/repository/engine/__tests__/PhabricatorWorkingCopyDiscoveryTestCase.php',
     'PhabricatorWorkingCopyPullTestCase' => 'applications/repository/engine/__tests__/PhabricatorWorkingCopyPullTestCase.php',
     'PhabricatorWorkingCopyTestCase' => 'applications/repository/engine/__tests__/PhabricatorWorkingCopyTestCase.php',
-    'PhabricatorXChartFunction' => 'applications/fact/chart/PhabricatorXChartFunction.php',
     'PhabricatorXHPASTDAO' => 'applications/phpast/storage/PhabricatorXHPASTDAO.php',
     'PhabricatorXHPASTParseTree' => 'applications/phpast/storage/PhabricatorXHPASTParseTree.php',
     'PhabricatorXHPASTViewController' => 'applications/phpast/controller/PhabricatorXHPASTViewController.php',
@@ -7987,6 +7990,7 @@ phutil_register_library_map(array(
     'PhabricatorAccessLog' => 'Phobject',
     'PhabricatorAccessLogConfigOptions' => 'PhabricatorApplicationConfigOptions',
     'PhabricatorAccessibilitySetting' => 'PhabricatorSelectSetting',
+    'PhabricatorAccumulateChartFunction' => 'PhabricatorChartFunction',
     'PhabricatorActionListView' => 'AphrontTagView',
     'PhabricatorActionView' => 'AphrontView',
     'PhabricatorActivitySettingsPanel' => 'PhabricatorSettingsPanel',
@@ -8691,6 +8695,7 @@ phutil_register_library_map(array(
     'PhabricatorCommitSearchEngine' => 'PhabricatorApplicationSearchEngine',
     'PhabricatorCommitTagsField' => 'PhabricatorCommitCustomField',
     'PhabricatorCommonPasswords' => 'Phobject',
+    'PhabricatorComposeChartFunction' => 'PhabricatorHigherOrderChartFunction',
     'PhabricatorConduitAPIController' => 'PhabricatorConduitController',
     'PhabricatorConduitApplication' => 'PhabricatorApplication',
     'PhabricatorConduitCallManagementWorkflow' => 'PhabricatorConduitManagementWorkflow',
@@ -9520,6 +9525,7 @@ phutil_register_library_map(array(
     'PhabricatorHeraldContentSource' => 'PhabricatorContentSource',
     'PhabricatorHexdumpDocumentEngine' => 'PhabricatorDocumentEngine',
     'PhabricatorHighSecurityRequestExceptionHandler' => 'PhabricatorRequestExceptionHandler',
+    'PhabricatorHigherOrderChartFunction' => 'PhabricatorChartFunction',
     'PhabricatorHomeApplication' => 'PhabricatorApplication',
     'PhabricatorHomeConstants' => 'PhabricatorHomeController',
     'PhabricatorHomeController' => 'PhabricatorController',
@@ -11053,6 +11059,7 @@ phutil_register_library_map(array(
     'PhabricatorSubscriptionsUIEventListener' => 'PhabricatorEventListener',
     'PhabricatorSubscriptionsUnsubscribeEmailCommand' => 'MetaMTAEmailTransactionCommand',
     'PhabricatorSubtypeEditEngineExtension' => 'PhabricatorEditEngineExtension',
+    'PhabricatorSumChartFunction' => 'PhabricatorHigherOrderChartFunction',
     'PhabricatorSupportApplication' => 'PhabricatorApplication',
     'PhabricatorSyntaxHighlighter' => 'Phobject',
     'PhabricatorSyntaxHighlightingConfigOptions' => 'PhabricatorApplicationConfigOptions',
@@ -11323,7 +11330,6 @@ phutil_register_library_map(array(
     'PhabricatorWorkingCopyDiscoveryTestCase' => 'PhabricatorWorkingCopyTestCase',
     'PhabricatorWorkingCopyPullTestCase' => 'PhabricatorWorkingCopyTestCase',
     'PhabricatorWorkingCopyTestCase' => 'PhabricatorTestCase',
-    'PhabricatorXChartFunction' => 'PhabricatorChartFunction',
     'PhabricatorXHPASTDAO' => 'PhabricatorLiskDAO',
     'PhabricatorXHPASTParseTree' => 'PhabricatorXHPASTDAO',
     'PhabricatorXHPASTViewController' => 'PhabricatorController',

src/applications/fact/chart/PhabricatorAccumulateChartFunction.php

@@ -0,0 +1,81 @@
+<?php
+
+final class PhabricatorAccumulateChartFunction
+  extends PhabricatorChartFunction {
+
+  const FUNCTIONKEY = 'accumulate';
+
+  protected function newArguments() {
+    return array(
+      $this->newArgument()
+        ->setName('x')
+        ->setType('function'),
+    );
+  }
+
+  public function getDomain() {
+    return $this->getArgument('x')->getDomain();
+  }
+
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    return $this->getArgument('x')->newInputValues($query);
+  }
+
+  public function evaluateFunction(array $xv) {
+    // First, we're going to accumulate the underlying function. Then
+    // we'll map the inputs through the accumulation.
+
+    $datasource = $this->getArgument('x');
+
+    // Use an unconstrained query to pull all the data from the underlying
+    // source. We need to accumulate data since the beginning of time to
+    // figure out the right Y-intercept -- otherwise, we'll always start at
+    // "0" wherever our domain begins.
+    $empty_query = new PhabricatorChartDataQuery();
+
+    $datasource_xv = $datasource->newInputValues($empty_query);
+    if (!$datasource_xv) {
+      // TODO: Maybe this should just be an error?
+      $datasource_xv = $xv;
+    }
+
+    $yv = $datasource->evaluateFunction($datasource_xv);
+
+    $map = array_combine($datasource_xv, $yv);
+
+    $accumulator = 0;
+    foreach ($map as $x => $y) {
+      $accumulator += $y;
+      $map[$x] = $accumulator;
+    }
+
+    // The value of "accumulate(x)" is the largest datapoint in the map which
+    // is no larger than "x".
+
+    $map_x = array_keys($map);
+    $idx = -1;
+    $max = count($map_x) - 1;
+
+    $yv = array();
+
+    $value = 0;
+    foreach ($xv as $x) {
+      // While the next "x" we need to evaluate the function at lies to the
+      // right of the next datapoint, move the current datapoint forward until
+      // we're at the rightmost datapoint which is not larger than "x".
+      while ($idx < $max) {
+        if ($map_x[$idx + 1] > $x) {
+          break;
+        }
+
+        $idx++;
+        $value = $map[$map_x[$idx]];
+      }
+
+      $yv[] = $value;
+    }
+
+    return $yv;
+  }
+
+}

src/applications/fact/chart/PhabricatorChartDataQuery.php

@@ -34,4 +34,48 @@ final class PhabricatorChartDataQuery
     return $this->limit;
   }
 
+  public function selectInputValues(array $xv) {
+    $result = array();
+
+    $x_min = $this->getMinimumValue();
+    $x_max = $this->getMaximumValue();
+    $limit = $this->getLimit();
+
+    if ($x_min !== null) {
+      foreach ($xv as $key => $x) {
+        if ($x < $x_min) {
+          unset($xv[$key]);
+        }
+      }
+    }
+
+    if ($x_max !== null) {
+      foreach ($xv as $key => $x) {
+        if ($x > $x_max) {
+          unset($xv[$key]);
+        }
+      }
+    }
+
+    // If we have too many data points, throw away some of the data.
+
+    // TODO: This doesn't work especially well right now.
+
+    if ($limit !== null) {
+      $count = count($xv);
+      if ($count > $limit) {
+        $ii = 0;
+        $every = ceil($count / $limit);
+        foreach ($xv as $key => $x) {
+          $ii++;
+          if (($ii % $every) && ($ii != $count)) {
+            unset($xv[$key]);
+          }
+        }
+      }
+    }
+
+    return array_values($xv);
+  }
+
 }

src/applications/fact/chart/PhabricatorChartFunction.php

@@ -3,11 +3,7 @@
 abstract class PhabricatorChartFunction
   extends Phobject {
 
-  private $xAxis;
-  private $yAxis;
-
   private $argumentParser;
-  private $sourceFunction;
 
   final public function getFunctionKey() {
     return $this->getPhobjectClassConstant('FUNCTIONKEY', 32);
@@ -44,13 +40,73 @@ abstract class PhabricatorChartFunction
     $parser->setHaveAllArguments(true);
     $parser->parseArguments();
 
-    $source_argument = $parser->getSourceFunctionArgument();
-    if ($source_argument) {
-      $source_function = $this->getArgument($source_argument->getName());
-      $this->setSourceFunction($source_function);
+    return $this;
+  }
+
+  public function getSubfunctions() {
+    $result = array();
+    $result[] = $this;
+
+    foreach ($this->getFunctionArguments() as $argument) {
+      foreach ($argument->getSubfunctions() as $subfunction) {
+        $result[] = $subfunction;
+      }
     }
 
-    return $this;
+    return $result;
+  }
+
+  public function getFunctionArguments() {
+    $results = array();
+
+    $parser = $this->getArgumentParser();
+    foreach ($parser->getAllArguments() as $argument) {
+      if ($argument->getType() !== 'function') {
+        continue;
+      }
+
+      $name = $argument->getName();
+      $value = $this->getArgument($name);
+
+      if (!is_array($value)) {
+        $results[] = $value;
+      } else {
+        foreach ($value as $arg_value) {
+          $results[] = $arg_value;
+        }
+      }
+    }
+
+    return $results;
+  }
+
+  public function newDatapoints(PhabricatorChartDataQuery $query) {
+    $xv = $this->newInputValues($query);
+
+    if ($xv === null) {
+      $xv = $this->newDefaultInputValues($query);
+    }
+
+    $xv = $query->selectInputValues($xv);
+
+    $n = count($xv);
+    $yv = $this->evaluateFunction($xv);
+
+    $points = array();
+    for ($ii = 0; $ii < $n; $ii++) {
+      $y = $yv[$ii];
+
+      if ($y === null) {
+        continue;
+      }
+
+      $points[] = array(
+        'x' => $xv[$ii],
+        'y' => $y,
+      );
+    }
+
+    return $points;
   }
 
   abstract protected function newArguments();
@@ -73,96 +129,26 @@ abstract class PhabricatorChartFunction
     return $this->argumentParser;
   }
 
+  abstract public function evaluateFunction(array $xv);
+
+  public function getDomain() {
+    return null;
+  }
+
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    return null;
+  }
+
   public function loadData() {
     return;
   }
 
-  protected function setSourceFunction(PhabricatorChartFunction $source) {
-    $this->sourceFunction = $source;
-    return $this;
-  }
-
-  protected function getSourceFunction() {
-    return $this->sourceFunction;
-  }
-
-  final public function setXAxis(PhabricatorChartAxis $x_axis) {
-    $this->xAxis = $x_axis;
-    return $this;
-  }
-
-  final public function getXAxis() {
-    return $this->xAxis;
-  }
-
-  final public function setYAxis(PhabricatorChartAxis $y_axis) {
-    $this->yAxis = $y_axis;
-    return $this;
-  }
-
-  final public function getYAxis() {
-    return $this->yAxis;
-  }
-
-  protected function canEvaluateFunction() {
-    return false;
-  }
-
-  protected function evaluateFunction($x) {
-    throw new PhutilMethodNotImplementedException();
-  }
-
-  public function hasDomain() {
-    if ($this->canEvaluateFunction()) {
-      return false;
-    }
-
-    throw new PhutilMethodNotImplementedException();
-  }
-
-  public function getDatapoints(PhabricatorChartDataQuery $query) {
-    if ($this->canEvaluateFunction()) {
-      $points = $this->newSourceDatapoints($query);
-      foreach ($points as $key => $point) {
-        $y = $point['y'];
-        $y = $this->evaluateFunction($y);
-        $points[$key]['y'] = $y;
-      }
-
-      return $points;
-    }
-
-    return $this->newDatapoints($query);
-  }
-
-  protected function newDatapoints(PhabricatorChartDataQuery $query) {
-    throw new PhutilMethodNotImplementedException();
-  }
-
-  protected function newSourceDatapoints(PhabricatorChartDataQuery $query) {
-    $source = $this->getSourceFunction();
-    if ($source) {
-      return $source->getDatapoints($query);
-    }
-
-    return $this->newDefaultDatapoints($query);
-  }
-
-  protected function newDefaultDatapoints(PhabricatorChartDataQuery $query) {
+  protected function newDefaultInputValues(PhabricatorChartDataQuery $query) {
     $x_min = $query->getMinimumValue();
     $x_max = $query->getMaximumValue();
     $limit = $query->getLimit();
 
-    $points = array();
-    $steps = $this->newLinearSteps($x_min, $x_max, $limit);
-    foreach ($steps as $step) {
-      $points[] = array(
-        'x' => $step,
-        'y' => $step,
-      );
-    }
-
-    return $points;
+    return $this->newLinearSteps($x_min, $x_max, $limit);
   }
 
   protected function newLinearSteps($src, $dst, $count) {
@@ -213,5 +199,4 @@ abstract class PhabricatorChartFunction
 
     return $steps;
   }
-
 }

src/applications/fact/chart/PhabricatorChartFunctionArgument.php

@@ -5,7 +5,7 @@ final class PhabricatorChartFunctionArgument
 
   private $name;
   private $type;
-  private $isSourceFunction;
+  private $repeatable;
 
   public function setName($name) {
     $this->name = $name;
@@ -16,6 +16,15 @@ final class PhabricatorChartFunctionArgument
     return $this->name;
   }
 
+  public function setRepeatable($repeatable) {
+    $this->repeatable = $repeatable;
+    return $this;
+  }
+
+  public function getRepeatable() {
+    return $this->repeatable;
+  }
+
   public function setType($type) {
     $types = array(
       'fact-key' => true,
@@ -40,15 +49,6 @@ final class PhabricatorChartFunctionArgument
     return $this->type;
   }
 
-  public function setIsSourceFunction($is_source_function) {
-    $this->isSourceFunction = $is_source_function;
-    return $this;
-  }
-
-  public function getIsSourceFunction() {
-    return $this->isSourceFunction;
-  }
-
   public function newValue($value) {
     switch ($this->getType()) {
       case 'fact-key':

src/applications/fact/chart/PhabricatorChartFunctionArgumentParser.php

@@ -11,6 +11,7 @@ final class PhabricatorChartFunctionArgumentParser
   private $argumentMap = array();
   private $argumentPosition = 0;
   private $argumentValues = array();
+  private $repeatableArgument = null;
 
   public function setFunction(PhabricatorChartFunction $function) {
     $this->function = $function;
@@ -55,6 +56,32 @@ final class PhabricatorChartFunctionArgumentParser
           $name));
     }
 
+    if ($this->repeatableArgument) {
+      if ($spec->getRepeatable()) {
+        throw new Exception(
+          pht(
+            'Chart function "%s" emitted multiple repeatable argument '.
+            'specifications ("%s" and "%s"). Only one argument may be '.
+            'repeatable and it must be the last argument.',
+            $this->getFunctionArgumentSignature(),
+            $name,
+            $this->repeatableArgument->getName()));
+      } else {
+        throw new Exception(
+          pht(
+            'Chart function "%s" emitted a repeatable argument ("%s"), then '.
+            'another argument ("%s"). No arguments are permitted after a '.
+            'repeatable argument.',
+            $this->getFunctionArgumentSignature(),
+            $this->repeatableArgument->getName(),
+            $name));
+      }
+    }
+
+    if ($spec->getRepeatable()) {
+      $this->repeatableArgument = $spec;
+    }
+
     $this->argumentMap[$name] = $spec;
     $this->unparsedArguments[] = $spec;
 
@@ -72,12 +99,26 @@ final class PhabricatorChartFunctionArgumentParser
     return $this;
   }
 
+  public function getAllArguments() {
+    return array_values($this->argumentMap);
+  }
+
   public function parseArguments() {
     $have_count = count($this->rawArguments);
     $want_count = count($this->argumentMap);
 
     if ($this->haveAllArguments) {
-      if ($want_count !== $have_count) {
+      if ($this->repeatableArgument) {
+        if ($want_count > $have_count) {
+          throw new Exception(
+            pht(
+              'Function "%s" expects %s or more argument(s), but only %s '.
+              'argument(s) were provided.',
+              $this->getFunctionArgumentSignature(),
+              $want_count,
+              $have_count));
+        }
+      } else if ($want_count !== $have_count) {
         throw new Exception(
           pht(
             'Function "%s" expects %s argument(s), but %s argument(s) were '.
@@ -105,6 +146,14 @@ final class PhabricatorChartFunctionArgumentParser
       $raw_argument = array_shift($this->unconsumedArguments);
       $this->argumentPosition++;
 
+      $is_repeatable = $argument->getRepeatable();
+
+      // If this argument is repeatable and we have more arguments, add it
+      // back to the end of the list so we can continue parsing.
+      if ($is_repeatable && $this->unconsumedArguments) {
+        $this->unparsedArguments[] = $argument;
+      }
+
       try {
         $value = $argument->newValue($raw_argument);
       } catch (Exception $ex) {
@@ -118,7 +167,14 @@ final class PhabricatorChartFunctionArgumentParser
             $ex->getMessage()));
       }
 
-      $this->argumentValues[$name] = $value;
+      if ($is_repeatable) {
+        if (!isset($this->argumentValues[$name])) {
+          $this->argumentValues[$name] = array();
+        }
+        $this->argumentValues[$name][] = $value;
+      } else {
+        $this->argumentValues[$name] = $value;
+      }
     }
   }
 
@@ -141,7 +197,7 @@ final class PhabricatorChartFunctionArgumentParser
       $argument_list[] = $key;
     }
 
-    if (!$this->haveAllArguments) {
+    if (!$this->haveAllArguments || $this->repeatableArgument) {
       $argument_list[] = '...';
     }
 
@@ -151,43 +207,4 @@ final class PhabricatorChartFunctionArgumentParser
       implode(', ', $argument_list));
   }
 
-  public function getSourceFunctionArgument() {
-    $required_type = 'function';
-
-    $sources = array();
-    foreach ($this->argumentMap as $key => $argument) {
-      if (!$argument->getIsSourceFunction()) {
-        continue;
-      }
-
-      if ($argument->getType() !== $required_type) {
-        throw new Exception(
-          pht(
-            'Function "%s" defines an argument "%s" which is marked as a '.
-            'source function, but the type of this argument is not "%s".',
-            $this->getFunctionArgumentSignature(),
-            $argument->getName(),
-            $required_type));
-      }
-
-      $sources[$key] = $argument;
-    }
-
-    if (!$sources) {
-      return null;
-    }
-
-    if (count($sources) > 1) {
-      throw new Exception(
-        pht(
-          'Function "%s" defines more than one argument as a source '.
-          'function (arguments: %s). Functions must have zero or one '.
-          'source function.',
-          $this->getFunctionArgumentSignature(),
-          implode(', ', array_keys($sources))));
-    }
-
-    return head($sources);
-  }
-
 }

src/applications/fact/chart/PhabricatorComposeChartFunction.php

@@ -0,0 +1,73 @@
+<?php
+
+final class PhabricatorComposeChartFunction
+  extends PhabricatorHigherOrderChartFunction {
+
+  const FUNCTIONKEY = 'compose';
+
+  protected function newArguments() {
+    return array(
+      $this->newArgument()
+        ->setName('f')
+        ->setType('function')
+        ->setRepeatable(true),
+    );
+  }
+
+  public function evaluateFunction(array $xv) {
+    $original_positions = array_keys($xv);
+    $remaining_positions = $original_positions;
+    foreach ($this->getFunctionArguments() as $function) {
+      $xv = $function->evaluateFunction($xv);
+
+      // If a function evaluates to "null" at some positions, we want to return
+      // "null" at those positions and stop evaluating the function.
+
+      // We also want to pass "evaluateFunction()" a natural list containing
+      // only values it should evaluate: keys should not be important and we
+      // should not pass "null". This simplifies implementation of functions.
+
+      // To do this, first create a map from original input positions to
+      // function return values.
+      $xv = array_combine($remaining_positions, $xv);
+
+      // If a function evaluated to "null" at any position where we evaluated
+      // it, the result will be "null". We remove the position from the
+      // vector so we stop evaluating it.
+      foreach ($xv as $x => $y) {
+        if ($y !== null) {
+          continue;
+        }
+
+        unset($xv[$x]);
+      }
+
+      // Store the remaining original input positions for the next round, then
+      // throw away the array keys so we're passing the next function a natural
+      // list with only non-"null" values.
+      $remaining_positions = array_keys($xv);
+      $xv = array_values($xv);
+
+      // If we have no more inputs to evaluate, we can bail out early rather
+      // than passing empty vectors to functions for evaluation.
+      if (!$xv) {
+        break;
+      }
+    }
+
+
+    $yv = array();
+    $xv = array_combine($remaining_positions, $xv);
+    foreach ($original_positions as $position) {
+      if (isset($xv[$position])) {
+        $y = $xv[$position];
+      } else {
+        $y = null;
+      }
+      $yv[$position] = $y;
+    }
+
+    return $yv;
+  }
+
+}

src/applications/fact/chart/PhabricatorConstantChartFunction.php

@@ -13,12 +13,16 @@ final class PhabricatorConstantChartFunction
     );
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $n = $this->getArgument('n');
 
-  protected function evaluateFunction($x) {
-    return $this->getArgument('n');
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = $n;
+    }
+
+    return $yv;
   }
 
 }

src/applications/fact/chart/PhabricatorCosChartFunction.php

@@ -6,20 +6,17 @@ final class PhabricatorCosChartFunction
   const FUNCTIONKEY = 'cos';
 
   protected function newArguments() {
-    return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
-    );
+    return array();
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $yv = array();
 
-  protected function evaluateFunction($x) {
-    return cos(deg2rad($x));
+    foreach ($xv as $x) {
+      $yv[] = cos(deg2rad($x));
+    }
+
+    return $yv;
   }
 
 }

src/applications/fact/chart/PhabricatorFactChartFunction.php

@@ -6,7 +6,7 @@ final class PhabricatorFactChartFunction
   const FUNCTIONKEY = 'fact';
 
   private $fact;
-  private $datapoints;
+  private $map;
 
   protected function newArguments() {
     $key_argument = $this->newArgument()
@@ -44,73 +44,46 @@ final class PhabricatorFactChartFunction
       return;
     }
 
-    $points = array();
+    $map = array();
+    foreach ($data as $row) {
+      $value = (int)$row['value'];
+      $epoch = (int)$row['epoch'];
 
-    $sum = 0;
-    foreach ($data as $key => $row) {
-      $sum += (int)$row['value'];
-      $points[] = array(
-        'x' => (int)$row['epoch'],
-        'y' => $sum,
-      );
-    }
-
-    $this->datapoints = $points;
-  }
-
-  public function getDatapoints(PhabricatorChartDataQuery $query) {
-    $points = $this->datapoints;
-    if (!$points) {
-      return array();
-    }
-
-    $x_min = $query->getMinimumValue();
-    $x_max = $query->getMaximumValue();
-    $limit = $query->getLimit();
-
-    if ($x_min !== null) {
-      foreach ($points as $key => $point) {
-        if ($point['x'] < $x_min) {
-          unset($points[$key]);
-        }
+      if (!isset($map[$epoch])) {
+        $map[$epoch] = 0;
       }
+
+      $map[$epoch] += $value;
     }
 
-    if ($x_max !== null) {
-      foreach ($points as $key => $point) {
-        if ($point['x'] > $x_max) {
-          unset($points[$key]);
-        }
-      }
-    }
-
-    // If we have too many data points, throw away some of the data.
-    if ($limit !== null) {
-      $count = count($points);
-      if ($count > $limit) {
-        $ii = 0;
-        $every = ceil($count / $limit);
-        foreach ($points as $key => $point) {
-          $ii++;
-          if (($ii % $every) && ($ii != $count)) {
-            unset($points[$key]);
-          }
-        }
-      }
-    }
-
-    return $points;
-  }
-
-  public function hasDomain() {
-    return true;
+    $this->map = $map;
   }
 
   public function getDomain() {
-    // TODO: We can examine the data to fit a better domain.
+    return array(
+      head_key($this->map),
+      last_key($this->map),
+    );
+  }
 
-    $now = PhabricatorTime::getNow();
-    return array($now - phutil_units('90 days in seconds'), $now);
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    return array_keys($this->map);
+  }
+
+  public function evaluateFunction(array $xv) {
+    $map = $this->map;
+
+    $yv = array();
+
+    foreach ($xv as $x) {
+      if (isset($map[$x])) {
+        $yv[] = $map[$x];
+      } else {
+        $yv[] = null;
+      }
+    }
+
+    return $yv;
   }
 
 }

src/applications/fact/chart/PhabricatorHigherOrderChartFunction.php

@@ -0,0 +1,56 @@
+<?php
+
+abstract class PhabricatorHigherOrderChartFunction
+  extends PhabricatorChartFunction {
+
+  public function getDomain() {
+    $minv = array();
+    $maxv = array();
+    foreach ($this->getFunctionArguments() as $function) {
+      $domain = $function->getDomain();
+      if ($domain !== null) {
+        list($min, $max) = $domain;
+        $minv[] = $min;
+        $maxv[] = $max;
+      }
+    }
+
+    if (!$minv && !$maxv) {
+      return null;
+    }
+
+    $min = null;
+    $max = null;
+
+    if ($minv) {
+      $min = min($minv);
+    }
+
+    if ($maxv) {
+      $max = max($maxv);
+    }
+
+    return array($min, $max);
+  }
+
+  public function newInputValues(PhabricatorChartDataQuery $query) {
+    $map = array();
+    foreach ($this->getFunctionArguments() as $function) {
+      $xv = $function->newInputValues($query);
+      if ($xv !== null) {
+        foreach ($xv as $x) {
+          $map[$x] = true;
+        }
+      }
+    }
+
+    if (!$map) {
+      return null;
+    }
+
+    ksort($map);
+
+    return array_keys($map);
+  }
+
+}

src/applications/fact/chart/PhabricatorScaleChartFunction.php

@@ -7,22 +7,22 @@ final class PhabricatorScaleChartFunction
 
   protected function newArguments() {
     return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
       $this->newArgument()
         ->setName('scale')
         ->setType('number'),
     );
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $scale = $this->getArgument('scale');
 
-  protected function evaluateFunction($x) {
-    return $x * $this->getArgument('scale');
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = $x * $scale;
+    }
+
+    return $yv;
   }
 
 }

src/applications/fact/chart/PhabricatorShiftChartFunction.php

@@ -7,22 +7,22 @@ final class PhabricatorShiftChartFunction
 
   protected function newArguments() {
     return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
       $this->newArgument()
         ->setName('shift')
         ->setType('number'),
     );
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $shift = $this->getArgument('shift');
 
-  protected function evaluateFunction($x) {
-    return $x * $this->getArgument('shift');
+    $yv = array();
+
+    foreach ($xv as $x) {
+      $yv[] = $x + $shift;
+    }
+
+    return $yv;
   }
 
 }

src/applications/fact/chart/PhabricatorSinChartFunction.php

@@ -6,20 +6,17 @@ final class PhabricatorSinChartFunction
   const FUNCTIONKEY = 'sin';
 
   protected function newArguments() {
-    return array(
-      $this->newArgument()
-        ->setName('x')
-        ->setType('function')
-        ->setIsSourceFunction(true),
-    );
+    return array();
   }
 
-  protected function canEvaluateFunction() {
-    return true;
-  }
+  public function evaluateFunction(array $xv) {
+    $yv = array();
 
-  protected function evaluateFunction($x) {
-    return sin(deg2rad($x));
+    foreach ($xv as $x) {
+      $yv[] = sin(deg2rad($x));
+    }
+
+    return $yv;
   }
 
 }

src/applications/fact/chart/PhabricatorSumChartFunction.php

@@ -0,0 +1,40 @@
+<?php
+
+final class PhabricatorSumChartFunction
+  extends PhabricatorHigherOrderChartFunction {
+
+  const FUNCTIONKEY = 'sum';
+
+  protected function newArguments() {
+    return array(
+      $this->newArgument()
+        ->setName('f')
+        ->setType('function')
+        ->setRepeatable(true),
+    );
+  }
+
+  public function evaluateFunction(array $xv) {
+    $fv = array();
+    foreach ($this->getFunctionArguments() as $function) {
+      $fv[] = $function->evaluateFunction($xv);
+    }
+
+    $n = count($xv);
+    $yv = array_fill(0, $n, null);
+
+    foreach ($fv as $f) {
+      for ($ii = 0; $ii < $n; $ii++) {
+        if ($f[$ii] !== null) {
+          if (!isset($yv[$ii])) {
+            $yv[$ii] = 0;
+          }
+          $yv[$ii] += $f[$ii];
+        }
+      }
+    }
+
+    return $yv;
+  }
+
+}

src/applications/fact/chart/PhabricatorXChartFunction.php

@@ -1,20 +0,0 @@
-<?php
-
-final class PhabricatorXChartFunction
-  extends PhabricatorChartFunction {
-
-  const FUNCTIONKEY = 'x';
-
-  protected function newArguments() {
-    return array();
-  }
-
-  protected function canEvaluateFunction() {
-    return true;
-  }
-
-  protected function evaluateFunction($x) {
-    return $x;
-  }
-
-}

src/applications/fact/controller/PhabricatorFactChartController.php

@@ -12,43 +12,50 @@ final class PhabricatorFactChartController extends PhabricatorFactController {
     $is_chart_mode = ($mode === 'chart');
     $is_draw_mode = ($mode === 'draw');
 
+    $argvs = array();
+
+    $argvs[] = array('fact', 'tasks.count.create');
+
+    $argvs[] = array('constant', 360);
+
+    $argvs[] = array('fact', 'tasks.open-count.create');
+
+    $argvs[] = array(
+      'sum',
+      array(
+        'accumulate',
+        array('fact', 'tasks.count.create'),
+      ),
+      array(
+        'accumulate',
+        array('fact', 'tasks.open-count.create'),
+      ),
+    );
+
+    $argvs[] = array(
+      'compose',
+      array('scale', 0.001),
+      array('cos'),
+      array('scale', 100),
+      array('shift', 800),
+    );
+
     $functions = array();
+    foreach ($argvs as $argv) {
+      $functions[] = id(new PhabricatorComposeChartFunction())
+        ->setArguments(array($argv));
+    }
 
-    $functions[] = id(new PhabricatorFactChartFunction())
-      ->setArguments(array('tasks.count.create'));
+    $subfunctions = array();
+    foreach ($functions as $function) {
+      foreach ($function->getSubfunctions() as $subfunction) {
+        $subfunctions[] = $subfunction;
+      }
+    }
 
-    $functions[] = id(new PhabricatorFactChartFunction())
-      ->setArguments(array('tasks.open-count.create'));
-
-    $x_function = id(new PhabricatorXChartFunction())
-      ->setArguments(array());
-
-    $functions[] = id(new PhabricatorConstantChartFunction())
-      ->setArguments(array(360));
-
-    $functions[] = id(new PhabricatorSinChartFunction())
-      ->setArguments(array($x_function));
-
-    $cos_function = id(new PhabricatorCosChartFunction())
-      ->setArguments(array($x_function));
-
-    $functions[] = id(new PhabricatorShiftChartFunction())
-      ->setArguments(
-        array(
-          array(
-            'scale',
-            array(
-              'cos',
-              array(
-                'scale',
-                array('x'),
-                0.001,
-              ),
-            ),
-            10,
-          ),
-          200,
-        ));
+    foreach ($subfunctions as $subfunction) {
+      $subfunction->loadData();
+    }
 
     list($domain_min, $domain_max) = $this->getDomain($functions);
 
@@ -63,11 +70,7 @@ final class PhabricatorFactChartController extends PhabricatorFactController {
 
     $datasets = array();
     foreach ($functions as $function) {
-      $function->setXAxis($axis);
-
-      $function->loadData();
-
-      $points = $function->getDatapoints($data_query);
+      $points = $function->newDatapoints($data_query);
 
       $x = array();
       $y = array();
@@ -157,19 +160,18 @@ final class PhabricatorFactChartController extends PhabricatorFactController {
   private function getDomain(array $functions) {
     $domain_min_list = null;
     $domain_max_list = null;
+
     foreach ($functions as $function) {
-      if ($function->hasDomain()) {
-        $domain = $function->getDomain();
+      $domain = $function->getDomain();
 
-        list($domain_min, $domain_max) = $domain;
+      list($function_min, $function_max) = $domain;
 
-        if ($domain_min !== null) {
-          $domain_min_list[] = $domain_min;
-        }
+      if ($function_min !== null) {
+        $domain_min_list[] = $function_min;
+      }
 
-        if ($domain_max !== null) {
-          $domain_max_list[] = $domain_max;
-        }
+      if ($function_max !== null) {
+        $domain_max_list[] = $function_max;
       }
     }