Add new variadic integrate_1d_* signatures

docs/exposing_new_functions.mld

@@ -126,15 +126,27 @@ For example, the following line defines the signature [add(real, matrix) => matr
 Functions such as the ODE integrators or [reduce_sum], which take in user-functions and a variable-length
 list of arguments, are {b NOT} added to this list.
 
-"Nice" variadic functions are added to the hashtable [Stan_math_signatures.stan_math_variadic_signatures].
+"Nice" variadic functions are added to the hashtable [Generate.stan_math_variadic_signatures] using
+the function [add_variadic_fn name ~return_type ?control_args ~required_fn_rt ?required_fn_args ()].
 This is probably sufficient for most variadic functions, e.g. all the ODE solvers and DAE solvers are done
 via this method.
-[reduce_sum] is not "nice", since it is both variadic and {e polymorphic}, requiring certain arguments to have the same
-(but {e not predetermined}) type. Therefore, [reduce_sum] is treated as special case in the [Typechecker]
-module in the frontend folder.
 
-Note that higher-order functions also usually require changes to the C++ code generation to work properly.
-It is best to consult an existing example of how these are done before proceeding.
+The arguments are perhaps clearest to understand by example. [return_type] is
+the return type of the variadic function itself, e.g.
+[UArray UVector] for the variadic ODES. [control_args] is a list of arguments
+that come after the callback but before the arguments to the function. These
+tend to be initializations, or tolerances. [required_fn_rt] is what the user
+callback must return, e.g. [UVector] for the ODE system function. Finally,
+[required_fn_args] is the arguments that the callback must accept first, such as
+the time and state for ODE system functions.
+
+This final argument determines the C++ code generation of the function, as the
+`std::ostream*` argument will come immediately after the required_fn_args in the
+list. Ensure that the C++ for the function is calling it accordingly. It is best
+to consult an existing example of how these are done before proceeding.
+
+Other functions, such as [reduce_sum] or the laplace marginal functions, are not
+"nice". These are not added to this list, and are instead treated as special case in the [Typechecker] module in the frontend folder.
 
 {1 Testing}
 

src/stan_math_signatures/Generate.ml

@@ -2681,6 +2681,40 @@ let () =
         ; (DataOnly, UInt) ]
     ~required_fn_rt:UnsizedType.UVector
     ~required_fn_args:[UnsizedType.(AutoDiffable, UVector)]
+    ();
+  (* variadic versions of integrate_1d *)
+  add_variadic_fn "integrate_1d_gauss_kronrod" ~return_type:UnsizedType.UReal
+    ~control_args:
+      UnsizedType.
+        [(* interval a, b *) (AutoDiffable, UReal); (AutoDiffable, UReal)]
+    ~required_fn_rt:UnsizedType.UReal
+    ~required_fn_args:
+      UnsizedType.[(* x, xc *) (AutoDiffable, UReal); (AutoDiffable, UReal)]
+    ();
+  add_variadic_fn "integrate_1d_double_exponential"
+    ~return_type:UnsizedType.UReal
+    ~control_args:UnsizedType.[(AutoDiffable, UReal); (AutoDiffable, UReal)]
+    ~required_fn_rt:UnsizedType.UReal
+    ~required_fn_args:UnsizedType.[(AutoDiffable, UReal); (AutoDiffable, UReal)]
+    ();
+  (* _tol version accept rel_tol, abs_tol, and max_depth/max_refinements *)
+  add_variadic_fn "integrate_1d_double_exponential_tol"
+    ~return_type:UnsizedType.UReal
+    ~control_args:
+      UnsizedType.
+        [ (AutoDiffable, UReal); (AutoDiffable, UReal); (DataOnly, UReal)
+        ; (DataOnly, UReal); (DataOnly, UInt) ]
+    ~required_fn_rt:UnsizedType.UReal
+    ~required_fn_args:UnsizedType.[(AutoDiffable, UReal); (AutoDiffable, UReal)]
+    ();
+  add_variadic_fn "integrate_1d_gauss_kronrod_tol"
+    ~return_type:UnsizedType.UReal
+    ~control_args:
+      UnsizedType.
+        [ (AutoDiffable, UReal); (AutoDiffable, UReal); (DataOnly, UReal)
+        ; (DataOnly, UReal); (DataOnly, UInt) ]
+    ~required_fn_rt:UnsizedType.UReal
+    ~required_fn_args:UnsizedType.[(AutoDiffable, UReal); (AutoDiffable, UReal)]
     ()
 
 (** Print a module definition to [file] that contains the signatures computed

test/integration/good/function-signatures/math/functions/integrate_1d.stan

@@ -14,7 +14,6 @@ parameters {
 model {
   real y = integrate_1d(integrand, 0, 1, x, x_r, x_i);
   real z = integrate_1d(integrand, 0, 1, x, x_r, x_i, 1e-8);
-  
+
   x ~ normal(y + z, 1.0);
 }
-

test/integration/good/integrate_1d_double_exponential.stan

@@ -0,0 +1,16 @@
+functions {
+  real integrand(real x, real xc, vector theta, matrix alpha) {
+    return 0.0;
+  }
+}
+
+parameters {
+  vector[10] theta;
+  matrix[2,4] alpha;
+}
+model {
+  real y = integrate_1d_double_exponential(integrand, 0, 1, theta, alpha);
+  real z =  integrate_1d_double_exponential_tol(integrand, 0, 1, 1e-8, 0.0, 1, theta, alpha);
+
+  y + z ~ normal(0, 1.0);
+}

test/integration/good/integrate_1d_gauss_kronrod.stan

@@ -0,0 +1,16 @@
+functions {
+  real integrand(real x, real xc, vector theta, matrix alpha) {
+    return 0.0;
+  }
+}
+
+parameters {
+  vector[10] theta;
+  matrix[2,4] alpha;
+}
+model {
+  real y = integrate_1d_gauss_kronrod(integrand, 0, 1, theta, alpha);
+  real z =  integrate_1d_gauss_kronrod_tol(integrand, 0, 1, 1e-8, 0.0, 1, theta, alpha);
+
+  y+z ~ normal(0, 1.0);
+}

test/integration/good/pretty.expected

@@ -3758,6 +3758,76 @@ model {
   y_p ~ normal(0, 1);
 }
 
+[exit 0]
+  $ ../../../../install/default/bin/stanc --auto-format integrate_1d_double_exponential.stan
+functions {
+  real integrand(real x, real xc, vector theta, matrix alpha) {
+    return 0.0;
+  }
+}
+parameters {
+  vector[10] theta;
+  matrix[2, 4] alpha;
+}
+model {
+  real y = integrate_1d_double_exponential(integrand, 0, 1, theta, alpha);
+  real z = integrate_1d_double_exponential_tol(integrand, 0, 1, 1e-8, 0.0, 1,
+             theta, alpha);
+
+  y + z ~ normal(0, 1.0);
+}
+
+[exit 0]
+  $ ../../../../install/default/bin/stanc --auto-format integrate_1d_gauss_kronrod.stan
+functions {
+  real integrand(real x, real xc, vector theta, matrix alpha) {
+    return 0.0;
+  }
+}
+parameters {
+  vector[10] theta;
+  matrix[2, 4] alpha;
+}
+model {
+  real y = integrate_1d_gauss_kronrod(integrand, 0, 1, theta, alpha);
+  real z = integrate_1d_gauss_kronrod_tol(integrand, 0, 1, 1e-8, 0.0, 1,
+             theta, alpha);
+
+  y + z ~ normal(0, 1.0);
+}
+
+[exit 0]
+  $ ../../../../install/default/bin/stanc --auto-format integrate_1d_good.stan
+functions {
+  real foo(real x, real xc, array[] real theta, array[] real x_r,
+           array[] int x_i) {
+    return x ^ 2;
+  }
+}
+data {
+  array[2] real x_r;
+  array[10] int x_i;
+}
+transformed data {
+  array[3] real theta_d;
+  real int_foo1 = integrate_1d(foo, 0.2, 1.3, theta_d, x_r, x_i, 0.01);
+}
+parameters {
+  real lb;
+  real ub;
+  array[3] real theta;
+}
+model {
+  real int_foo2 = integrate_1d(foo, 0.2, 1.3, theta, x_r, x_i, 0.01);
+  real int_foo3 = integrate_1d(foo, lb, 1.3, theta, x_r, x_i, 0.01);
+  real int_foo4 = integrate_1d(foo, 0.2, ub, theta, x_r, x_i, 0.01);
+  real int_foo5 = integrate_1d(foo, lb, ub, theta, x_r, x_i, 0.01);
+  real int_foo6 = integrate_1d(foo, 0.2, 1.3, theta_d, x_r, x_i, 0.01);
+  real int_foo7 = integrate_1d(foo, lb, 1.3, theta_d, x_r, x_i, 0.01);
+  real int_foo8 = integrate_1d(foo, 0.2, ub, theta_d, x_r, x_i, 0.01);
+  real int_foo9 = integrate_1d(foo, lb, ub, theta_d, x_r, x_i, 0.01);
+}
+
 [exit 0]
   $ ../../../../install/default/bin/stanc --auto-format io_example.stan
 transformed data {

test/integration/good/warning/pretty.expected

@@ -119,38 +119,6 @@ Warning in 'int_div_user.stan', line 7, column 6 to column 10:
     write the division as
         a[1] * 1.0 / b[2]
     If rounding is intended please use the integer division operator %/%.
-[exit 0]
-  $ ../../../../../install/default/bin/stanc --auto-format integrate_1d_good.stan
-functions {
-  real foo(real x, real xc, array[] real theta, array[] real x_r,
-           array[] int x_i) {
-    return x ^ 2;
-  }
-}
-data {
-  array[2] real x_r;
-  array[10] int x_i;
-}
-transformed data {
-  array[3] real theta_d;
-  real int_foo1 = integrate_1d(foo, 0.2, 1.3, theta_d, x_r, x_i, 0.01);
-}
-parameters {
-  real lb;
-  real ub;
-  array[3] real theta;
-}
-model {
-  real int_foo2 = integrate_1d(foo, 0.2, 1.3, theta, x_r, x_i, 0.01);
-  real int_foo3 = integrate_1d(foo, lb, 1.3, theta, x_r, x_i, 0.01);
-  real int_foo4 = integrate_1d(foo, 0.2, ub, theta, x_r, x_i, 0.01);
-  real int_foo5 = integrate_1d(foo, lb, ub, theta, x_r, x_i, 0.01);
-  real int_foo6 = integrate_1d(foo, 0.2, 1.3, theta_d, x_r, x_i, 0.01);
-  real int_foo7 = integrate_1d(foo, lb, 1.3, theta_d, x_r, x_i, 0.01);
-  real int_foo8 = integrate_1d(foo, 0.2, ub, theta_d, x_r, x_i, 0.01);
-  real int_foo9 = integrate_1d(foo, lb, ub, theta_d, x_r, x_i, 0.01);
-}
-
 [exit 0]
   $ ../../../../../install/default/bin/stanc --auto-format integrate_ode_adams.stan
 functions {