diff --git a/runTests.py b/runTests.py
index 4bce225109b..e6adc86b84f 100755
--- a/runTests.py
+++ b/runTests.py
@@ -23,9 +23,12 @@
 
 allowed_paths_with_jumbo = [
     "test/unit/math/prim/",
+    "test/unit/math/prim/constraint",
     "test/unit/math/",
     "test/unit/math/rev/",
+     "test/unit/math/rev/constraint",
     "test/unit/math/fwd/",
+    "test/unit/math/fwd/constraint",
     "test/unit/math/mix/",
     "test/unit/math/mix/fun/",
     "test/unit/math/opencl/",
@@ -33,18 +36,21 @@
 ]
 
 jumbo_folders = [
+    "test/unit/math/prim/constraint",
     "test/unit/math/prim/core",
     "test/unit/math/prim/err",
     "test/unit/math/prim/fun",
     "test/unit/math/prim/functor",
     "test/unit/math/prim/meta",
     "test/unit/math/prim/prob",
+     "test/unit/math/rev/constraint",
     "test/unit/math/rev/core",
     "test/unit/math/rev/err",
     "test/unit/math/rev/fun",
     "test/unit/math/rev/functor",
     "test/unit/math/rev/meta",
     "test/unit/math/rev/prob",
+    "test/unit/math/fwd/constraint",
     "test/unit/math/fwd/core",
     "test/unit/math/fwd/fun",
     "test/unit/math/fwd/functor",
@@ -58,7 +64,9 @@
     "test/unit/math/opencl/device_functions",
     "test/unit/math/opencl/kernel_generator",
     "test/unit/math/opencl/prim",
+    "test/unit/math/opencl/prim/constraint",
     "test/unit/math/opencl/rev",
+    "test/unit/math/opencl/rev/constraint",
 ]
 
 
diff --git a/stan/math/fwd.hpp b/stan/math/fwd.hpp
index 3bab5be267f..2ff806f5d34 100644
--- a/stan/math/fwd.hpp
+++ b/stan/math/fwd.hpp
@@ -5,8 +5,10 @@
 
 #ifdef STAN_OPENCL
 #include <stan/math/opencl/prim.hpp>
+#include <stan/math/opencl/prim_constraint.hpp>
 #endif
 
+#include <stan/math/fwd/constraint.hpp>
 #include <stan/math/fwd/core.hpp>
 #include <stan/math/fwd/meta.hpp>
 #include <stan/math/fwd/fun.hpp>
diff --git a/stan/math/fwd/constraint.hpp b/stan/math/fwd/constraint.hpp
new file mode 100644
index 00000000000..c0d7912cc83
--- /dev/null
+++ b/stan/math/fwd/constraint.hpp
@@ -0,0 +1,9 @@
+#ifndef STAN_MATH_FWD_CONSTRAINT_HPP
+#define STAN_MATH_FWD_CONSTRAINT_HPP
+
+#include <stan/math/prim/fun/Eigen.hpp>
+#include <stan/math/fwd/fun/Eigen_NumTraits.hpp>
+
+#include <stan/math/fwd/constraint/unit_vector_constrain.hpp>
+
+#endif
diff --git a/stan/math/fwd/fun/unit_vector_constrain.hpp b/stan/math/fwd/constraint/unit_vector_constrain.hpp
similarity index 90%
rename from stan/math/fwd/fun/unit_vector_constrain.hpp
rename to stan/math/fwd/constraint/unit_vector_constrain.hpp
index 1cd708174cb..1b1b258e5a8 100644
--- a/stan/math/fwd/fun/unit_vector_constrain.hpp
+++ b/stan/math/fwd/constraint/unit_vector_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_FWD_FUN_UNIT_VECTOR_CONSTRAIN_HPP
-#define STAN_MATH_FWD_FUN_UNIT_VECTOR_CONSTRAIN_HPP
+#ifndef STAN_MATH_FWD_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
+#define STAN_MATH_FWD_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
 
 #include <stan/math/fwd/core.hpp>
 #include <stan/math/fwd/fun/tcrossprod.hpp>
@@ -8,7 +8,7 @@
 #include <stan/math/prim/fun/dot_self.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
 #include <stan/math/prim/fun/inv.hpp>
-#include <stan/math/prim/fun/unit_vector_constrain.hpp>
+#include <stan/math/prim/constraint/unit_vector_constrain.hpp>
 #include <stan/math/prim/fun/tcrossprod.hpp>
 #include <cmath>
 
diff --git a/stan/math/fwd/fun.hpp b/stan/math/fwd/fun.hpp
index 37dbc449038..b56232a0121 100644
--- a/stan/math/fwd/fun.hpp
+++ b/stan/math/fwd/fun.hpp
@@ -121,7 +121,7 @@
 #include <stan/math/fwd/fun/trigamma.hpp>
 #include <stan/math/fwd/fun/trunc.hpp>
 #include <stan/math/fwd/fun/typedefs.hpp>
-#include <stan/math/fwd/fun/unit_vector_constrain.hpp>
+#include <stan/math/fwd/constraint/unit_vector_constrain.hpp>
 #include <stan/math/fwd/fun/value_of.hpp>
 #include <stan/math/fwd/fun/value_of_rec.hpp>
 
diff --git a/stan/math/mix.hpp b/stan/math/mix.hpp
index deb3cbba522..bb7ff7c0b1f 100644
--- a/stan/math/mix.hpp
+++ b/stan/math/mix.hpp
@@ -5,6 +5,7 @@
 #include <stan/math/mix/fun.hpp>
 #include <stan/math/mix/functor.hpp>
 
+#include <stan/math/fwd/constraint.hpp>
 #include <stan/math/fwd/core.hpp>
 #include <stan/math/fwd/meta.hpp>
 #include <stan/math/fwd/fun.hpp>
@@ -13,8 +14,10 @@
 
 #ifdef STAN_OPENCL
 #include <stan/math/opencl/rev.hpp>
+#include <stan/math/opencl/rev_constraint.hpp>
 #endif
 
+#include <stan/math/rev/constraint.hpp>
 #include <stan/math/rev/core.hpp>
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/fun.hpp>
diff --git a/stan/math/opencl/prim.hpp b/stan/math/opencl/prim.hpp
index f0875a4268c..4c5b193a7da 100644
--- a/stan/math/opencl/prim.hpp
+++ b/stan/math/opencl/prim.hpp
@@ -99,6 +99,8 @@
 #include <stan/math/opencl/zeros_strict_tri.hpp>
 #include <stan/math/opencl/qr_decomposition.hpp>
 
+#include <stan/math/opencl/prim_constraint.hpp>
+
 #include <stan/math/opencl/prim/add_diag.hpp>
 #include <stan/math/opencl/prim/append_array.hpp>
 #include <stan/math/opencl/prim/bernoulli_cdf.hpp>
@@ -172,7 +174,6 @@
 #include <stan/math/opencl/prim/inv_cloglog.hpp>
 #include <stan/math/opencl/prim/inv_gamma_lpdf.hpp>
 #include <stan/math/opencl/prim/inv_sqrt.hpp>
-#include <stan/math/opencl/prim/lb_constrain.hpp>
 #include <stan/math/opencl/prim/log_mix.hpp>
 #include <stan/math/opencl/prim/log_softmax.hpp>
 #include <stan/math/opencl/prim/logistic_cdf.hpp>
@@ -184,7 +185,6 @@
 #include <stan/math/opencl/prim/lognormal_lccdf.hpp>
 #include <stan/math/opencl/prim/lognormal_lcdf.hpp>
 #include <stan/math/opencl/prim/lognormal_lpdf.hpp>
-#include <stan/math/opencl/prim/lub_constrain.hpp>
 #include <stan/math/opencl/prim/matrix_power.hpp>
 #include <stan/math/opencl/prim/mdivide_left_tri_low.hpp>
 #include <stan/math/opencl/prim/mdivide_right_tri_low.hpp>
@@ -201,7 +201,6 @@
 #include <stan/math/opencl/prim/normal_lcdf.hpp>
 #include <stan/math/opencl/prim/normal_lpdf.hpp>
 #include <stan/math/opencl/prim/num_elements.hpp>
-#include <stan/math/opencl/prim/offset_multiplier_constrain.hpp>
 #include <stan/math/opencl/prim/ordered_logistic_glm_lpmf.hpp>
 #include <stan/math/opencl/prim/ordered_logistic_lpmf.hpp>
 #include <stan/math/opencl/prim/pareto_cdf.hpp>
@@ -266,12 +265,10 @@
 #include <stan/math/opencl/prim/to_row_vector.hpp>
 #include <stan/math/opencl/prim/to_vector.hpp>
 #include <stan/math/opencl/prim/trace.hpp>
-#include <stan/math/opencl/prim/ub_constrain.hpp>
 #include <stan/math/opencl/prim/uniform_cdf.hpp>
 #include <stan/math/opencl/prim/uniform_lccdf.hpp>
 #include <stan/math/opencl/prim/uniform_lcdf.hpp>
 #include <stan/math/opencl/prim/uniform_lpdf.hpp>
-#include <stan/math/opencl/prim/unit_vector_constrain.hpp>
 #include <stan/math/opencl/prim/variance.hpp>
 #include <stan/math/opencl/prim/weibull_cdf.hpp>
 #include <stan/math/opencl/prim/weibull_lccdf.hpp>
diff --git a/stan/math/opencl/prim/lb_constrain.hpp b/stan/math/opencl/prim/constraint/lb_constrain.hpp
similarity index 94%
rename from stan/math/opencl/prim/lb_constrain.hpp
rename to stan/math/opencl/prim/constraint/lb_constrain.hpp
index 0ef7e77b16d..e94f6ead13f 100644
--- a/stan/math/opencl/prim/lb_constrain.hpp
+++ b/stan/math/opencl/prim/constraint/lb_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_PRIM_LB_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_PRIM_LB_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_PRIM_CONSTRAINT_LB_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_PRIM_CONSTRAINT_LB_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/prim/sum.hpp>
diff --git a/stan/math/opencl/prim/lub_constrain.hpp b/stan/math/opencl/prim/constraint/lub_constrain.hpp
similarity index 96%
rename from stan/math/opencl/prim/lub_constrain.hpp
rename to stan/math/opencl/prim/constraint/lub_constrain.hpp
index 212e89537fe..a5fa4c6e2ea 100644
--- a/stan/math/opencl/prim/lub_constrain.hpp
+++ b/stan/math/opencl/prim/constraint/lub_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_PRIM_LUB_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_PRIM_LUB_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_PRIM_CONSTRAINT_LUB_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_PRIM_CONSTRAINT_LUB_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/prim/sum.hpp>
diff --git a/stan/math/opencl/prim/offset_multiplier_constrain.hpp b/stan/math/opencl/prim/constraint/offset_multiplier_constrain.hpp
similarity index 96%
rename from stan/math/opencl/prim/offset_multiplier_constrain.hpp
rename to stan/math/opencl/prim/constraint/offset_multiplier_constrain.hpp
index 67c4b6457bc..481287f6457 100644
--- a/stan/math/opencl/prim/offset_multiplier_constrain.hpp
+++ b/stan/math/opencl/prim/constraint/offset_multiplier_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_PRIM_OFFSET_MULTIPLIER_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_PRIM_OFFSET_MULTIPLIER_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_PRIM_CONSTRAINT_OFFSET_MULTIPLIER_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_PRIM_CONSTRAINT_OFFSET_MULTIPLIER_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/prim/sum.hpp>
diff --git a/stan/math/opencl/prim/ub_constrain.hpp b/stan/math/opencl/prim/constraint/ub_constrain.hpp
similarity index 94%
rename from stan/math/opencl/prim/ub_constrain.hpp
rename to stan/math/opencl/prim/constraint/ub_constrain.hpp
index eebb3e927c2..fd158ee93c8 100644
--- a/stan/math/opencl/prim/ub_constrain.hpp
+++ b/stan/math/opencl/prim/constraint/ub_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_PRIM_UB_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_PRIM_UB_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_PRIM_CONSTRAINT_UB_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_PRIM_CONSTRAINT_UB_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/prim/sum.hpp>
diff --git a/stan/math/opencl/prim/unit_vector_constrain.hpp b/stan/math/opencl/prim/constraint/unit_vector_constrain.hpp
similarity index 92%
rename from stan/math/opencl/prim/unit_vector_constrain.hpp
rename to stan/math/opencl/prim/constraint/unit_vector_constrain.hpp
index e1f0b283061..a5a4c8c10bc 100644
--- a/stan/math/opencl/prim/unit_vector_constrain.hpp
+++ b/stan/math/opencl/prim/constraint/unit_vector_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_UNIT_VECTOR_CONSTRAIN_BLOCK_HPP
-#define STAN_MATH_OPENCL_UNIT_VECTOR_CONSTRAIN_BLOCK_HPP
+#ifndef STAN_MATH_OPENCL_PRIM_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_BLOCK_HPP
+#define STAN_MATH_OPENCL_PRIM_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_BLOCK_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/matrix_cl.hpp>
diff --git a/stan/math/opencl/prim_constraint.hpp b/stan/math/opencl/prim_constraint.hpp
new file mode 100644
index 00000000000..b092eafc275
--- /dev/null
+++ b/stan/math/opencl/prim_constraint.hpp
@@ -0,0 +1,12 @@
+#ifndef STAN_MATH_OPENCL_PRIM_CONSTRAINT_HPP
+#define STAN_MATH_OPENCL_PRIM_CONSTRAINT_HPP
+#ifdef STAN_OPENCL
+
+#include <stan/math/opencl/prim/constraint/lb_constrain.hpp>
+#include <stan/math/opencl/prim/constraint/lub_constrain.hpp>
+#include <stan/math/opencl/prim/constraint/offset_multiplier_constrain.hpp>
+#include <stan/math/opencl/prim/constraint/ub_constrain.hpp>
+#include <stan/math/opencl/prim/constraint/unit_vector_constrain.hpp>
+
+#endif
+#endif
diff --git a/stan/math/opencl/rev.hpp b/stan/math/opencl/rev.hpp
index f48de0b806f..37c5b716230 100644
--- a/stan/math/opencl/rev.hpp
+++ b/stan/math/opencl/rev.hpp
@@ -3,6 +3,8 @@
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/prim.hpp>
+#include <stan/math/opencl/rev_constraint.hpp>
+
 #include <stan/math/opencl/rev/append_col.hpp>
 #include <stan/math/opencl/rev/append_row.hpp>
 #include <stan/math/opencl/rev/as_column_vector_or_scalar.hpp>
@@ -58,7 +60,6 @@
 #include <stan/math/opencl/rev/inv_Phi.hpp>
 #include <stan/math/opencl/rev/inv_sqrt.hpp>
 #include <stan/math/opencl/rev/inv_square.hpp>
-#include <stan/math/opencl/rev/lb_constrain.hpp>
 #include <stan/math/opencl/rev/lbeta.hpp>
 #include <stan/math/opencl/rev/ldexp.hpp>
 #include <stan/math/opencl/rev/lgamma.hpp>
@@ -77,14 +78,12 @@
 #include <stan/math/opencl/rev/log_diff_exp.hpp>
 #include <stan/math/opencl/rev/log_softmax.hpp>
 #include <stan/math/opencl/rev/log_sum_exp.hpp>
-#include <stan/math/opencl/rev/lub_constrain.hpp>
 #include <stan/math/opencl/rev/matrix_power.hpp>
 #include <stan/math/opencl/rev/mdivide_left_tri_low.hpp>
 #include <stan/math/opencl/rev/mdivide_right_tri_low.hpp>
 #include <stan/math/opencl/rev/multiply.hpp>
 #include <stan/math/opencl/rev/multiply_log.hpp>
 #include <stan/math/opencl/rev/multiply_lower_tri_self_transpose.hpp>
-#include <stan/math/opencl/rev/offset_multiplier_constrain.hpp>
 #include <stan/math/opencl/rev/operands_and_partials.hpp>
 #include <stan/math/opencl/rev/operator_unary_minus.hpp>
 #include <stan/math/opencl/rev/operator_unary_plus.hpp>
@@ -117,8 +116,6 @@
 #include <stan/math/opencl/rev/trace.hpp>
 #include <stan/math/opencl/rev/transpose.hpp>
 #include <stan/math/opencl/rev/trunc.hpp>
-#include <stan/math/opencl/rev/ub_constrain.hpp>
-#include <stan/math/opencl/rev/unit_vector_constrain.hpp>
 #include <stan/math/opencl/rev/variance.hpp>
 #include <stan/math/rev.hpp>
 
diff --git a/stan/math/opencl/rev/lb_constrain.hpp b/stan/math/opencl/rev/constraint/lb_constrain.hpp
similarity index 96%
rename from stan/math/opencl/rev/lb_constrain.hpp
rename to stan/math/opencl/rev/constraint/lb_constrain.hpp
index e796073586c..012d81a8bde 100644
--- a/stan/math/opencl/rev/lb_constrain.hpp
+++ b/stan/math/opencl/rev/constraint/lb_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_REV_LB_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_REV_LB_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_REV_CONSTRAINT_LB_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_REV_CONSTRAINT_LB_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/rev/adjoint_results.hpp>
diff --git a/stan/math/opencl/rev/lub_constrain.hpp b/stan/math/opencl/rev/constraint/lub_constrain.hpp
similarity index 97%
rename from stan/math/opencl/rev/lub_constrain.hpp
rename to stan/math/opencl/rev/constraint/lub_constrain.hpp
index 21ded0b24e2..9fae858693d 100644
--- a/stan/math/opencl/rev/lub_constrain.hpp
+++ b/stan/math/opencl/rev/constraint/lub_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_REV_LUB_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_REV_LUB_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_REV_CONSTRAINT_LUB_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_REV_CONSTRAINT_LUB_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/rev/adjoint_results.hpp>
diff --git a/stan/math/opencl/rev/offset_multiplier_constrain.hpp b/stan/math/opencl/rev/constraint/offset_multiplier_constrain.hpp
similarity index 96%
rename from stan/math/opencl/rev/offset_multiplier_constrain.hpp
rename to stan/math/opencl/rev/constraint/offset_multiplier_constrain.hpp
index ca6f6fe3ecc..c75eecc0571 100644
--- a/stan/math/opencl/rev/offset_multiplier_constrain.hpp
+++ b/stan/math/opencl/rev/constraint/offset_multiplier_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_REV_OFFSET_MULTIPLIER_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_REV_OFFSET_MULTIPLIER_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_REV_CONSTRAINT_OFFSET_MULTIPLIER_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_REV_CONSTRAINT_OFFSET_MULTIPLIER_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/kernel_generator.hpp>
diff --git a/stan/math/opencl/rev/ub_constrain.hpp b/stan/math/opencl/rev/constraint/ub_constrain.hpp
similarity index 96%
rename from stan/math/opencl/rev/ub_constrain.hpp
rename to stan/math/opencl/rev/constraint/ub_constrain.hpp
index ef87c2ba07e..c8748447593 100644
--- a/stan/math/opencl/rev/ub_constrain.hpp
+++ b/stan/math/opencl/rev/constraint/ub_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_REV_UB_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_REV_UB_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_REV_CONSTRAINT_UB_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_REV_CONSTRAINT_UB_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/rev/adjoint_results.hpp>
diff --git a/stan/math/opencl/rev/unit_vector_constrain.hpp b/stan/math/opencl/rev/constraint/unit_vector_constrain.hpp
similarity index 93%
rename from stan/math/opencl/rev/unit_vector_constrain.hpp
rename to stan/math/opencl/rev/constraint/unit_vector_constrain.hpp
index e2fa6a63462..968005880fa 100644
--- a/stan/math/opencl/rev/unit_vector_constrain.hpp
+++ b/stan/math/opencl/rev/constraint/unit_vector_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_OPENCL_REV_UNIT_VECTOR_CONSTRAIN_HPP
-#define STAN_MATH_OPENCL_REV_UNIT_VECTOR_CONSTRAIN_HPP
+#ifndef STAN_MATH_OPENCL_REV_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
+#define STAN_MATH_OPENCL_REV_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
 #ifdef STAN_OPENCL
 
 #include <stan/math/opencl/kernel_generator.hpp>
diff --git a/stan/math/opencl/rev_constraint.hpp b/stan/math/opencl/rev_constraint.hpp
new file mode 100644
index 00000000000..2b42eee74cb
--- /dev/null
+++ b/stan/math/opencl/rev_constraint.hpp
@@ -0,0 +1,12 @@
+#ifndef STAN_MATH_OPENCL_REV_CONSTRAINT_HPP
+#define STAN_MATH_OPENCL_REV_CONSTRAINT_HPP
+#ifdef STAN_OPENCL
+
+#include <stan/math/opencl/rev/constraint/lb_constrain.hpp>
+#include <stan/math/opencl/rev/constraint/lub_constrain.hpp>
+#include <stan/math/opencl/rev/constraint/offset_multiplier_constrain.hpp>
+#include <stan/math/opencl/rev/constraint/ub_constrain.hpp>
+#include <stan/math/opencl/rev/constraint/unit_vector_constrain.hpp>
+
+#endif
+#endif
diff --git a/stan/math/prim.hpp b/stan/math/prim.hpp
index 30b66815356..208818ae116 100644
--- a/stan/math/prim.hpp
+++ b/stan/math/prim.hpp
@@ -5,8 +5,10 @@
 
 #ifdef STAN_OPENCL
 #include <stan/math/opencl/prim.hpp>
+#include <stan/math/opencl/prim_constraint.hpp>
 #endif
 
+#include <stan/math/prim/constraint.hpp>
 #include <stan/math/prim/core.hpp>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/constraint.hpp b/stan/math/prim/constraint.hpp
new file mode 100644
index 00000000000..169fd8f2e31
--- /dev/null
+++ b/stan/math/prim/constraint.hpp
@@ -0,0 +1,45 @@
+#ifndef STAN_MATH_PRIM_CONSTRAINT_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_HPP
+
+#include <stan/math/prim/fun.hpp>
+
+#include <stan/math/prim/constraint/cholesky_corr_constrain.hpp>
+#include <stan/math/prim/constraint/cholesky_corr_free.hpp>
+#include <stan/math/prim/constraint/cholesky_factor_constrain.hpp>
+#include <stan/math/prim/constraint/cholesky_factor_free.hpp>
+#include <stan/math/prim/constraint/corr_constrain.hpp>
+#include <stan/math/prim/constraint/corr_free.hpp>
+#include <stan/math/prim/constraint/corr_matrix_constrain.hpp>
+#include <stan/math/prim/constraint/corr_matrix_free.hpp>
+#include <stan/math/prim/constraint/cov_matrix_constrain.hpp>
+#include <stan/math/prim/constraint/cov_matrix_constrain_lkj.hpp>
+#include <stan/math/prim/constraint/cov_matrix_free.hpp>
+#include <stan/math/prim/constraint/cov_matrix_free_lkj.hpp>
+#include <stan/math/prim/constraint/identity_constrain.hpp>
+#include <stan/math/prim/constraint/identity_free.hpp>
+#include <stan/math/prim/constraint/lb_constrain.hpp>
+#include <stan/math/prim/constraint/lb_free.hpp>
+#include <stan/math/prim/constraint/lub_constrain.hpp>
+#include <stan/math/prim/constraint/lub_free.hpp>
+#include <stan/math/prim/constraint/offset_multiplier_constrain.hpp>
+#include <stan/math/prim/constraint/offset_multiplier_free.hpp>
+#include <stan/math/prim/constraint/ordered_constrain.hpp>
+#include <stan/math/prim/constraint/ordered_free.hpp>
+#include <stan/math/prim/constraint/positive_constrain.hpp>
+#include <stan/math/prim/constraint/positive_free.hpp>
+#include <stan/math/prim/constraint/positive_ordered_constrain.hpp>
+#include <stan/math/prim/constraint/positive_ordered_free.hpp>
+#include <stan/math/prim/constraint/prob_constrain.hpp>
+#include <stan/math/prim/constraint/prob_free.hpp>
+#include <stan/math/prim/constraint/simplex_constrain.hpp>
+#include <stan/math/prim/constraint/simplex_free.hpp>
+#include <stan/math/prim/constraint/stochastic_column_constrain.hpp>
+#include <stan/math/prim/constraint/stochastic_column_free.hpp>
+#include <stan/math/prim/constraint/stochastic_row_constrain.hpp>
+#include <stan/math/prim/constraint/stochastic_row_free.hpp>
+#include <stan/math/prim/constraint/ub_constrain.hpp>
+#include <stan/math/prim/constraint/ub_free.hpp>
+#include <stan/math/prim/constraint/unit_vector_constrain.hpp>
+#include <stan/math/prim/constraint/unit_vector_free.hpp>
+
+#endif
diff --git a/stan/math/prim/fun/cholesky_corr_constrain.hpp b/stan/math/prim/constraint/cholesky_corr_constrain.hpp
similarity index 96%
rename from stan/math/prim/fun/cholesky_corr_constrain.hpp
rename to stan/math/prim/constraint/cholesky_corr_constrain.hpp
index c949b85554d..b7909de4d0f 100644
--- a/stan/math/prim/fun/cholesky_corr_constrain.hpp
+++ b/stan/math/prim/constraint/cholesky_corr_constrain.hpp
@@ -1,12 +1,12 @@
-#ifndef STAN_MATH_PRIM_FUN_CHOLESKY_CORR_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_CHOLESKY_CORR_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_CORR_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_CORR_CONSTRAIN_HPP
 
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
 #include <stan/math/prim/fun/log1m.hpp>
 #include <stan/math/prim/fun/sqrt.hpp>
 #include <stan/math/prim/fun/square.hpp>
-#include <stan/math/prim/fun/corr_constrain.hpp>
+#include <stan/math/prim/constraint/corr_constrain.hpp>
 #include <cmath>
 
 namespace stan {
diff --git a/stan/math/prim/fun/cholesky_corr_free.hpp b/stan/math/prim/constraint/cholesky_corr_free.hpp
similarity index 89%
rename from stan/math/prim/fun/cholesky_corr_free.hpp
rename to stan/math/prim/constraint/cholesky_corr_free.hpp
index f5746eaceeb..4245e495bdc 100644
--- a/stan/math/prim/fun/cholesky_corr_free.hpp
+++ b/stan/math/prim/constraint/cholesky_corr_free.hpp
@@ -1,9 +1,9 @@
-#ifndef STAN_MATH_PRIM_FUN_CHOLESKY_CORR_FREE_HPP
-#define STAN_MATH_PRIM_FUN_CHOLESKY_CORR_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_CORR_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_CORR_FREE_HPP
 
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <stan/math/prim/fun/corr_free.hpp>
+#include <stan/math/prim/constraint/corr_free.hpp>
 #include <stan/math/prim/fun/square.hpp>
 #include <cmath>
 
diff --git a/stan/math/prim/fun/cholesky_factor_constrain.hpp b/stan/math/prim/constraint/cholesky_factor_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/cholesky_factor_constrain.hpp
rename to stan/math/prim/constraint/cholesky_factor_constrain.hpp
index ef8addb9ae1..31ef9731079 100644
--- a/stan/math/prim/fun/cholesky_factor_constrain.hpp
+++ b/stan/math/prim/constraint/cholesky_factor_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_CHOLESKY_FACTOR_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_CHOLESKY_FACTOR_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_FACTOR_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_FACTOR_CONSTRAIN_HPP
 
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
diff --git a/stan/math/prim/fun/cholesky_factor_free.hpp b/stan/math/prim/constraint/cholesky_factor_free.hpp
similarity index 94%
rename from stan/math/prim/fun/cholesky_factor_free.hpp
rename to stan/math/prim/constraint/cholesky_factor_free.hpp
index 0cc4185a3fc..9077f7b8829 100644
--- a/stan/math/prim/fun/cholesky_factor_free.hpp
+++ b/stan/math/prim/constraint/cholesky_factor_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_CHOLESKY_FACTOR_FREE_HPP
-#define STAN_MATH_PRIM_FUN_CHOLESKY_FACTOR_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_FACTOR_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CHOLESKY_FACTOR_FREE_HPP
 
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
diff --git a/stan/math/prim/fun/corr_constrain.hpp b/stan/math/prim/constraint/corr_constrain.hpp
similarity index 95%
rename from stan/math/prim/fun/corr_constrain.hpp
rename to stan/math/prim/constraint/corr_constrain.hpp
index 277846b6ffc..fcbad5125ce 100644
--- a/stan/math/prim/fun/corr_constrain.hpp
+++ b/stan/math/prim/constraint/corr_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_CORR_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_CORR_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CORR_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CORR_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/log1m.hpp>
diff --git a/stan/math/prim/fun/corr_free.hpp b/stan/math/prim/constraint/corr_free.hpp
similarity index 89%
rename from stan/math/prim/fun/corr_free.hpp
rename to stan/math/prim/constraint/corr_free.hpp
index a5b4065d0e3..b76d7f96a2b 100644
--- a/stan/math/prim/fun/corr_free.hpp
+++ b/stan/math/prim/constraint/corr_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_CORR_FREE_HPP
-#define STAN_MATH_PRIM_FUN_CORR_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CORR_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CORR_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/corr_matrix_constrain.hpp b/stan/math/prim/constraint/corr_matrix_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/corr_matrix_constrain.hpp
rename to stan/math/prim/constraint/corr_matrix_constrain.hpp
index cbe8fc6cc25..b556adcb988 100644
--- a/stan/math/prim/fun/corr_matrix_constrain.hpp
+++ b/stan/math/prim/constraint/corr_matrix_constrain.hpp
@@ -1,10 +1,10 @@
-#ifndef STAN_MATH_PRIM_FUN_CORR_MATRIX_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_CORR_MATRIX_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CORR_MATRIX_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CORR_MATRIX_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <stan/math/prim/fun/corr_constrain.hpp>
+#include <stan/math/prim/constraint/corr_constrain.hpp>
 #include <stan/math/prim/fun/read_corr_matrix.hpp>
 #include <stdexcept>
 
diff --git a/stan/math/prim/fun/corr_matrix_free.hpp b/stan/math/prim/constraint/corr_matrix_free.hpp
similarity index 95%
rename from stan/math/prim/fun/corr_matrix_free.hpp
rename to stan/math/prim/constraint/corr_matrix_free.hpp
index 3a0242ab257..81c0630dd50 100644
--- a/stan/math/prim/fun/corr_matrix_free.hpp
+++ b/stan/math/prim/constraint/corr_matrix_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_CORR_MATRIX_FREE_HPP
-#define STAN_MATH_PRIM_FUN_CORR_MATRIX_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_CORR_MATRIX_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_CORR_MATRIX_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/cov_matrix_constrain.hpp b/stan/math/prim/constraint/cov_matrix_constrain.hpp
similarity index 98%
rename from stan/math/prim/fun/cov_matrix_constrain.hpp
rename to stan/math/prim/constraint/cov_matrix_constrain.hpp
index 6b761b10000..46083c3aeb2 100644
--- a/stan/math/prim/fun/cov_matrix_constrain.hpp
+++ b/stan/math/prim/constraint/cov_matrix_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_COV_MATRIX_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_COV_MATRIX_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/cov_matrix_constrain_lkj.hpp b/stan/math/prim/constraint/cov_matrix_constrain_lkj.hpp
similarity index 95%
rename from stan/math/prim/fun/cov_matrix_constrain_lkj.hpp
rename to stan/math/prim/constraint/cov_matrix_constrain_lkj.hpp
index a74bbc0844d..c5605cdd43d 100644
--- a/stan/math/prim/fun/cov_matrix_constrain_lkj.hpp
+++ b/stan/math/prim/constraint/cov_matrix_constrain_lkj.hpp
@@ -1,9 +1,9 @@
-#ifndef STAN_MATH_PRIM_FUN_COV_MATRIX_CONSTRAIN_LKJ_HPP
-#define STAN_MATH_PRIM_FUN_COV_MATRIX_CONSTRAIN_LKJ_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_CONSTRAIN_LKJ_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_CONSTRAIN_LKJ_HPP
 
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <stan/math/prim/fun/corr_constrain.hpp>
-#include <stan/math/prim/fun/positive_constrain.hpp>
+#include <stan/math/prim/constraint/corr_constrain.hpp>
+#include <stan/math/prim/constraint/positive_constrain.hpp>
 #include <stan/math/prim/fun/read_cov_matrix.hpp>
 #include <stan/math/prim/fun/to_ref.hpp>
 
diff --git a/stan/math/prim/fun/cov_matrix_free.hpp b/stan/math/prim/constraint/cov_matrix_free.hpp
similarity index 95%
rename from stan/math/prim/fun/cov_matrix_free.hpp
rename to stan/math/prim/constraint/cov_matrix_free.hpp
index a507655bf28..1a5ad30c4e5 100644
--- a/stan/math/prim/fun/cov_matrix_free.hpp
+++ b/stan/math/prim/constraint/cov_matrix_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_COV_MATRIX_FREE_HPP
-#define STAN_MATH_PRIM_FUN_COV_MATRIX_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/cov_matrix_free_lkj.hpp b/stan/math/prim/constraint/cov_matrix_free_lkj.hpp
similarity index 95%
rename from stan/math/prim/fun/cov_matrix_free_lkj.hpp
rename to stan/math/prim/constraint/cov_matrix_free_lkj.hpp
index 81c16068813..b0d6c94f7a8 100644
--- a/stan/math/prim/fun/cov_matrix_free_lkj.hpp
+++ b/stan/math/prim/constraint/cov_matrix_free_lkj.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_COV_MATRIX_FREE_LKJ_HPP
-#define STAN_MATH_PRIM_FUN_COV_MATRIX_FREE_LKJ_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_FREE_LKJ_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_COV_MATRIX_FREE_LKJ_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/identity_constrain.hpp b/stan/math/prim/constraint/identity_constrain.hpp
similarity index 87%
rename from stan/math/prim/fun/identity_constrain.hpp
rename to stan/math/prim/constraint/identity_constrain.hpp
index 86b1e294388..00590438700 100644
--- a/stan/math/prim/fun/identity_constrain.hpp
+++ b/stan/math/prim/constraint/identity_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_IDENTITY_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_IDENTITY_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_IDENTITY_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_IDENTITY_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 
diff --git a/stan/math/prim/fun/identity_free.hpp b/stan/math/prim/constraint/identity_free.hpp
similarity index 86%
rename from stan/math/prim/fun/identity_free.hpp
rename to stan/math/prim/constraint/identity_free.hpp
index 0652ac11e24..ef5925c2355 100644
--- a/stan/math/prim/fun/identity_free.hpp
+++ b/stan/math/prim/constraint/identity_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_IDENTITY_FREE_HPP
-#define STAN_MATH_PRIM_FUN_IDENTITY_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_IDENTITY_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_IDENTITY_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 
diff --git a/stan/math/prim/fun/lb_constrain.hpp b/stan/math/prim/constraint/lb_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/lb_constrain.hpp
rename to stan/math/prim/constraint/lb_constrain.hpp
index f31da80cfbf..3df5ce62107 100644
--- a/stan/math/prim/fun/lb_constrain.hpp
+++ b/stan/math/prim/constraint/lb_constrain.hpp
@@ -1,11 +1,11 @@
-#ifndef STAN_MATH_PRIM_FUN_LB_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_LB_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_LB_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_LB_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/constants.hpp>
-#include <stan/math/prim/fun/identity_constrain.hpp>
-#include <stan/math/prim/fun/identity_free.hpp>
+#include <stan/math/prim/constraint/identity_constrain.hpp>
+#include <stan/math/prim/constraint/identity_free.hpp>
 #include <stan/math/prim/fun/add.hpp>
 #include <stan/math/prim/fun/exp.hpp>
 #include <stan/math/prim/fun/eval.hpp>
diff --git a/stan/math/prim/fun/lb_free.hpp b/stan/math/prim/constraint/lb_free.hpp
similarity index 96%
rename from stan/math/prim/fun/lb_free.hpp
rename to stan/math/prim/constraint/lb_free.hpp
index 9e1ee605ebf..f5e80d700e6 100644
--- a/stan/math/prim/fun/lb_free.hpp
+++ b/stan/math/prim/constraint/lb_free.hpp
@@ -1,10 +1,10 @@
-#ifndef STAN_MATH_PRIM_FUN_LB_FREE_HPP
-#define STAN_MATH_PRIM_FUN_LB_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_LB_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_LB_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/constants.hpp>
-#include <stan/math/prim/fun/identity_free.hpp>
+#include <stan/math/prim/constraint/identity_free.hpp>
 #include <stan/math/prim/fun/log.hpp>
 #include <stan/math/prim/fun/subtract.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
diff --git a/stan/math/prim/fun/lub_constrain.hpp b/stan/math/prim/constraint/lub_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/lub_constrain.hpp
rename to stan/math/prim/constraint/lub_constrain.hpp
index a3e91883f51..23b3369a5e7 100644
--- a/stan/math/prim/fun/lub_constrain.hpp
+++ b/stan/math/prim/constraint/lub_constrain.hpp
@@ -1,21 +1,22 @@
-#ifndef STAN_MATH_PRIM_FUN_LUB_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_LUB_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_LUB_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_LUB_CONSTRAIN_HPP
 
+#include <stan/math/prim/constraint/identity_constrain.hpp>
+#include <stan/math/prim/constraint/lb_constrain.hpp>
+#include <stan/math/prim/constraint/ub_constrain.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/add.hpp>
 #include <stan/math/prim/fun/exp.hpp>
 #include <stan/math/prim/fun/elt_multiply.hpp>
-#include <stan/math/prim/fun/identity_constrain.hpp>
 #include <stan/math/prim/fun/inv_logit.hpp>
 #include <stan/math/prim/fun/log.hpp>
 #include <stan/math/prim/fun/log1p.hpp>
-#include <stan/math/prim/fun/lb_constrain.hpp>
+#include <stan/math/prim/fun/log1p_exp.hpp>
 #include <stan/math/prim/fun/multiply.hpp>
 #include <stan/math/prim/fun/subtract.hpp>
 #include <stan/math/prim/fun/sum.hpp>
-#include <stan/math/prim/fun/ub_constrain.hpp>
 #include <cmath>
 
 namespace stan {
diff --git a/stan/math/prim/fun/lub_free.hpp b/stan/math/prim/constraint/lub_free.hpp
similarity index 96%
rename from stan/math/prim/fun/lub_free.hpp
rename to stan/math/prim/constraint/lub_free.hpp
index c4876cbcd6d..23afee1c60d 100644
--- a/stan/math/prim/fun/lub_free.hpp
+++ b/stan/math/prim/constraint/lub_free.hpp
@@ -1,13 +1,13 @@
-#ifndef STAN_MATH_PRIM_FUN_LUB_FREE_HPP
-#define STAN_MATH_PRIM_FUN_LUB_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_LUB_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_LUB_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/divide.hpp>
 #include <stan/math/prim/fun/eval.hpp>
 #include <stan/math/prim/fun/logit.hpp>
-#include <stan/math/prim/fun/lb_free.hpp>
-#include <stan/math/prim/fun/ub_free.hpp>
+#include <stan/math/prim/constraint/lb_free.hpp>
+#include <stan/math/prim/constraint/ub_free.hpp>
 #include <stan/math/prim/fun/subtract.hpp>
 
 namespace stan {
diff --git a/stan/math/prim/fun/offset_multiplier_constrain.hpp b/stan/math/prim/constraint/offset_multiplier_constrain.hpp
similarity index 98%
rename from stan/math/prim/fun/offset_multiplier_constrain.hpp
rename to stan/math/prim/constraint/offset_multiplier_constrain.hpp
index 85a58ce4771..a226ae2e15f 100644
--- a/stan/math/prim/fun/offset_multiplier_constrain.hpp
+++ b/stan/math/prim/constraint/offset_multiplier_constrain.hpp
@@ -1,10 +1,10 @@
-#ifndef STAN_MATH_PRIM_FUN_OFFSET_MULTIPLIER_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_OFFSET_MULTIPLIER_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_OFFSET_MULTIPLIER_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_OFFSET_MULTIPLIER_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/fma.hpp>
-#include <stan/math/prim/fun/identity_constrain.hpp>
+#include <stan/math/prim/constraint/identity_constrain.hpp>
 #include <stan/math/prim/fun/multiply_log.hpp>
 #include <stan/math/prim/fun/size.hpp>
 #include <stan/math/prim/fun/sum.hpp>
diff --git a/stan/math/prim/fun/offset_multiplier_free.hpp b/stan/math/prim/constraint/offset_multiplier_free.hpp
similarity index 96%
rename from stan/math/prim/fun/offset_multiplier_free.hpp
rename to stan/math/prim/constraint/offset_multiplier_free.hpp
index e0fe927330e..becf0e0d6b5 100644
--- a/stan/math/prim/fun/offset_multiplier_free.hpp
+++ b/stan/math/prim/constraint/offset_multiplier_free.hpp
@@ -1,9 +1,9 @@
-#ifndef STAN_MATH_PRIM_FUN_OFFSET_MULTIPLIER_FREE_HPP
-#define STAN_MATH_PRIM_FUN_OFFSET_MULTIPLIER_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_OFFSET_MULTIPLIER_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_OFFSET_MULTIPLIER_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
-#include <stan/math/prim/fun/identity_free.hpp>
+#include <stan/math/prim/constraint/identity_free.hpp>
 #include <stan/math/prim/fun/to_ref.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
 #include <cmath>
diff --git a/stan/math/prim/fun/ordered_constrain.hpp b/stan/math/prim/constraint/ordered_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/ordered_constrain.hpp
rename to stan/math/prim/constraint/ordered_constrain.hpp
index ac0c18ca74d..91a75c2f1fd 100644
--- a/stan/math/prim/fun/ordered_constrain.hpp
+++ b/stan/math/prim/constraint/ordered_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_ORDERED_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_ORDERED_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_ORDERED_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_ORDERED_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
diff --git a/stan/math/prim/fun/ordered_free.hpp b/stan/math/prim/constraint/ordered_free.hpp
similarity index 94%
rename from stan/math/prim/fun/ordered_free.hpp
rename to stan/math/prim/constraint/ordered_free.hpp
index 4764bceb6a8..b8fbc46624c 100644
--- a/stan/math/prim/fun/ordered_free.hpp
+++ b/stan/math/prim/constraint/ordered_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_ORDERED_FREE_HPP
-#define STAN_MATH_PRIM_FUN_ORDERED_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_ORDERED_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_ORDERED_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/positive_constrain.hpp b/stan/math/prim/constraint/positive_constrain.hpp
similarity index 96%
rename from stan/math/prim/fun/positive_constrain.hpp
rename to stan/math/prim/constraint/positive_constrain.hpp
index b6d46129c42..dc52cfb57f0 100644
--- a/stan/math/prim/fun/positive_constrain.hpp
+++ b/stan/math/prim/constraint/positive_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_POSITIVE_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_POSITIVE_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_POSITIVE_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_POSITIVE_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/exp.hpp>
diff --git a/stan/math/prim/fun/positive_free.hpp b/stan/math/prim/constraint/positive_free.hpp
similarity index 89%
rename from stan/math/prim/fun/positive_free.hpp
rename to stan/math/prim/constraint/positive_free.hpp
index af18b5e0119..4317fdfa70c 100644
--- a/stan/math/prim/fun/positive_free.hpp
+++ b/stan/math/prim/constraint/positive_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_POSITIVE_FREE_HPP
-#define STAN_MATH_PRIM_FUN_POSITIVE_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_POSITIVE_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_POSITIVE_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/positive_ordered_constrain.hpp b/stan/math/prim/constraint/positive_ordered_constrain.hpp
similarity index 96%
rename from stan/math/prim/fun/positive_ordered_constrain.hpp
rename to stan/math/prim/constraint/positive_ordered_constrain.hpp
index f3f0adf1fcf..30ab958209f 100644
--- a/stan/math/prim/fun/positive_ordered_constrain.hpp
+++ b/stan/math/prim/constraint/positive_ordered_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_POSITIVE_ORDERED_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_POSITIVE_ORDERED_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_POSITIVE_ORDERED_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_POSITIVE_ORDERED_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
diff --git a/stan/math/prim/fun/positive_ordered_free.hpp b/stan/math/prim/constraint/positive_ordered_free.hpp
similarity index 93%
rename from stan/math/prim/fun/positive_ordered_free.hpp
rename to stan/math/prim/constraint/positive_ordered_free.hpp
index c627f03ec5c..408b0922650 100644
--- a/stan/math/prim/fun/positive_ordered_free.hpp
+++ b/stan/math/prim/constraint/positive_ordered_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_POSITIVE_ORDERED_FREE_HPP
-#define STAN_MATH_PRIM_FUN_POSITIVE_ORDERED_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_POSITIVE_ORDERED_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_POSITIVE_ORDERED_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/prob_constrain.hpp b/stan/math/prim/constraint/prob_constrain.hpp
similarity index 95%
rename from stan/math/prim/fun/prob_constrain.hpp
rename to stan/math/prim/constraint/prob_constrain.hpp
index 0ed4ee605aa..d05193c8648 100644
--- a/stan/math/prim/fun/prob_constrain.hpp
+++ b/stan/math/prim/constraint/prob_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_PROB_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_PROB_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_PROB_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_PROB_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/log_inv_logit.hpp>
diff --git a/stan/math/prim/fun/prob_free.hpp b/stan/math/prim/constraint/prob_free.hpp
similarity index 89%
rename from stan/math/prim/fun/prob_free.hpp
rename to stan/math/prim/constraint/prob_free.hpp
index debefb5efb5..0f980ab87cd 100644
--- a/stan/math/prim/fun/prob_free.hpp
+++ b/stan/math/prim/constraint/prob_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_PROB_FREE_HPP
-#define STAN_MATH_PRIM_FUN_PROB_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_PROB_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_PROB_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/simplex_constrain.hpp b/stan/math/prim/constraint/simplex_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/simplex_constrain.hpp
rename to stan/math/prim/constraint/simplex_constrain.hpp
index cd10e93d587..b92c65779ee 100644
--- a/stan/math/prim/fun/simplex_constrain.hpp
+++ b/stan/math/prim/constraint/simplex_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_SIMPLEX_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_SIMPLEX_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
diff --git a/stan/math/prim/fun/simplex_free.hpp b/stan/math/prim/constraint/simplex_free.hpp
similarity index 95%
rename from stan/math/prim/fun/simplex_free.hpp
rename to stan/math/prim/constraint/simplex_free.hpp
index 39487a0cae0..f3bb6195b7c 100644
--- a/stan/math/prim/fun/simplex_free.hpp
+++ b/stan/math/prim/constraint/simplex_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_SIMPLEX_FREE_HPP
-#define STAN_MATH_PRIM_FUN_SIMPLEX_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun/stochastic_column_constrain.hpp b/stan/math/prim/constraint/stochastic_column_constrain.hpp
similarity index 95%
rename from stan/math/prim/fun/stochastic_column_constrain.hpp
rename to stan/math/prim/constraint/stochastic_column_constrain.hpp
index 8ed66883579..42c4f87d3b8 100644
--- a/stan/math/prim/fun/stochastic_column_constrain.hpp
+++ b/stan/math/prim/constraint/stochastic_column_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_SIMPLEX_COLUMN_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_SIMPLEX_COLUMN_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_COLUMN_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_SIMPLEX_COLUMN_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
@@ -7,7 +7,7 @@
 #include <stan/math/prim/fun/log.hpp>
 #include <stan/math/prim/fun/log1p_exp.hpp>
 #include <stan/math/prim/fun/logit.hpp>
-#include <stan/math/prim/fun/simplex_constrain.hpp>
+#include <stan/math/prim/constraint/simplex_constrain.hpp>
 #include <cmath>
 
 namespace stan {
diff --git a/stan/math/prim/fun/stochastic_column_free.hpp b/stan/math/prim/constraint/stochastic_column_free.hpp
similarity index 88%
rename from stan/math/prim/fun/stochastic_column_free.hpp
rename to stan/math/prim/constraint/stochastic_column_free.hpp
index b7a69fced25..fa4d2a43449 100644
--- a/stan/math/prim/fun/stochastic_column_free.hpp
+++ b/stan/math/prim/constraint/stochastic_column_free.hpp
@@ -1,9 +1,9 @@
-#ifndef STAN_MATH_PRIM_FUN_STOCHASTIC_COLUMN_FREE_HPP
-#define STAN_MATH_PRIM_FUN_STOCHASTIC_COLUMN_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_STOCHASTIC_COLUMN_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_STOCHASTIC_COLUMN_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <stan/math/prim/fun/simplex_free.hpp>
+#include <stan/math/prim/constraint/simplex_free.hpp>
 
 namespace stan {
 namespace math {
diff --git a/stan/math/prim/fun/stochastic_row_constrain.hpp b/stan/math/prim/constraint/stochastic_row_constrain.hpp
similarity index 96%
rename from stan/math/prim/fun/stochastic_row_constrain.hpp
rename to stan/math/prim/constraint/stochastic_row_constrain.hpp
index 7ea9306a933..d0f183f273a 100644
--- a/stan/math/prim/fun/stochastic_row_constrain.hpp
+++ b/stan/math/prim/constraint/stochastic_row_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_STOCHASTIC_ROW_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_STOCHASTIC_ROW_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_STOCHASTIC_ROW_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_STOCHASTIC_ROW_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
@@ -7,7 +7,7 @@
 #include <stan/math/prim/fun/log.hpp>
 #include <stan/math/prim/fun/log1p_exp.hpp>
 #include <stan/math/prim/fun/logit.hpp>
-#include <stan/math/prim/fun/simplex_constrain.hpp>
+#include <stan/math/prim/constraint/simplex_constrain.hpp>
 #include <cmath>
 
 namespace stan {
diff --git a/stan/math/prim/fun/stochastic_row_free.hpp b/stan/math/prim/constraint/stochastic_row_free.hpp
similarity index 89%
rename from stan/math/prim/fun/stochastic_row_free.hpp
rename to stan/math/prim/constraint/stochastic_row_free.hpp
index 7fa255b9949..82ad3e3ea92 100644
--- a/stan/math/prim/fun/stochastic_row_free.hpp
+++ b/stan/math/prim/constraint/stochastic_row_free.hpp
@@ -1,9 +1,9 @@
-#ifndef STAN_MATH_PRIM_FUN_STOCHASTIC_ROW_FREE_HPP
-#define STAN_MATH_PRIM_FUN_STOCHASTIC_ROW_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_STOCHASTIC_ROW_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_STOCHASTIC_ROW_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <stan/math/prim/fun/simplex_free.hpp>
+#include <stan/math/prim/constraint/simplex_free.hpp>
 
 namespace stan {
 namespace math {
diff --git a/stan/math/prim/fun/ub_constrain.hpp b/stan/math/prim/constraint/ub_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/ub_constrain.hpp
rename to stan/math/prim/constraint/ub_constrain.hpp
index f753f744b52..2c523e9ff47 100644
--- a/stan/math/prim/fun/ub_constrain.hpp
+++ b/stan/math/prim/constraint/ub_constrain.hpp
@@ -1,12 +1,12 @@
-#ifndef STAN_MATH_PRIM_FUN_UB_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_UB_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_UB_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_UB_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/constants.hpp>
 #include <stan/math/prim/fun/exp.hpp>
-#include <stan/math/prim/fun/identity_constrain.hpp>
-#include <stan/math/prim/fun/identity_free.hpp>
+#include <stan/math/prim/constraint/identity_constrain.hpp>
+#include <stan/math/prim/constraint/identity_free.hpp>
 #include <stan/math/prim/fun/subtract.hpp>
 #include <stan/math/prim/fun/sum.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
diff --git a/stan/math/prim/fun/ub_free.hpp b/stan/math/prim/constraint/ub_free.hpp
similarity index 96%
rename from stan/math/prim/fun/ub_free.hpp
rename to stan/math/prim/constraint/ub_free.hpp
index 4c58f475a7d..05a3acce775 100644
--- a/stan/math/prim/fun/ub_free.hpp
+++ b/stan/math/prim/constraint/ub_free.hpp
@@ -1,10 +1,10 @@
-#ifndef STAN_MATH_PRIM_FUN_UB_FREE_HPP
-#define STAN_MATH_PRIM_FUN_UB_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_UB_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_UB_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/constants.hpp>
-#include <stan/math/prim/fun/identity_free.hpp>
+#include <stan/math/prim/constraint/identity_free.hpp>
 #include <stan/math/prim/fun/log.hpp>
 #include <cmath>
 
diff --git a/stan/math/prim/fun/unit_vector_constrain.hpp b/stan/math/prim/constraint/unit_vector_constrain.hpp
similarity index 97%
rename from stan/math/prim/fun/unit_vector_constrain.hpp
rename to stan/math/prim/constraint/unit_vector_constrain.hpp
index 7239c765f56..19ccfae39a3 100644
--- a/stan/math/prim/fun/unit_vector_constrain.hpp
+++ b/stan/math/prim/constraint/unit_vector_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_UNIT_VECTOR_CONSTRAIN_HPP
-#define STAN_MATH_PRIM_FUN_UNIT_VECTOR_CONSTRAIN_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
 
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
diff --git a/stan/math/prim/fun/unit_vector_free.hpp b/stan/math/prim/constraint/unit_vector_free.hpp
similarity index 92%
rename from stan/math/prim/fun/unit_vector_free.hpp
rename to stan/math/prim/constraint/unit_vector_free.hpp
index 870e30e6b35..9f7d39e61ac 100644
--- a/stan/math/prim/fun/unit_vector_free.hpp
+++ b/stan/math/prim/constraint/unit_vector_free.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_FUN_UNIT_VECTOR_FREE_HPP
-#define STAN_MATH_PRIM_FUN_UNIT_VECTOR_FREE_HPP
+#ifndef STAN_MATH_PRIM_CONSTRAINT_UNIT_VECTOR_FREE_HPP
+#define STAN_MATH_PRIM_CONSTRAINT_UNIT_VECTOR_FREE_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/prim/fun.hpp b/stan/math/prim/fun.hpp
index 66dba1f3bdd..21403200b41 100644
--- a/stan/math/prim/fun.hpp
+++ b/stan/math/prim/fun.hpp
@@ -38,11 +38,7 @@
 #include <stan/math/prim/fun/cbrt.hpp>
 #include <stan/math/prim/fun/ceil.hpp>
 #include <stan/math/prim/fun/chol2inv.hpp>
-#include <stan/math/prim/fun/cholesky_corr_constrain.hpp>
-#include <stan/math/prim/fun/cholesky_corr_free.hpp>
 #include <stan/math/prim/fun/cholesky_decompose.hpp>
-#include <stan/math/prim/fun/cholesky_factor_constrain.hpp>
-#include <stan/math/prim/fun/cholesky_factor_free.hpp>
 #include <stan/math/prim/fun/choose.hpp>
 #include <stan/math/prim/fun/col.hpp>
 #include <stan/math/prim/fun/cols.hpp>
@@ -52,17 +48,9 @@
 #include <stan/math/prim/fun/conj.hpp>
 #include <stan/math/prim/fun/constants.hpp>
 #include <stan/math/prim/fun/copysign.hpp>
-#include <stan/math/prim/fun/corr_constrain.hpp>
-#include <stan/math/prim/fun/corr_free.hpp>
-#include <stan/math/prim/fun/corr_matrix_constrain.hpp>
-#include <stan/math/prim/fun/corr_matrix_free.hpp>
 #include <stan/math/prim/fun/cos.hpp>
 #include <stan/math/prim/fun/cosh.hpp>
 #include <stan/math/prim/fun/cov_exp_quad.hpp>
-#include <stan/math/prim/fun/cov_matrix_constrain.hpp>
-#include <stan/math/prim/fun/cov_matrix_constrain_lkj.hpp>
-#include <stan/math/prim/fun/cov_matrix_free.hpp>
-#include <stan/math/prim/fun/cov_matrix_free_lkj.hpp>
 #include <stan/math/prim/fun/crossprod.hpp>
 #include <stan/math/prim/fun/csr_extract.hpp>
 #include <stan/math/prim/fun/csr_extract_u.hpp>
@@ -140,8 +128,6 @@
 #include <stan/math/prim/fun/hypergeometric_3F2.hpp>
 #include <stan/math/prim/fun/hypergeometric_pFq.hpp>
 #include <stan/math/prim/fun/hypot.hpp>
-#include <stan/math/prim/fun/identity_constrain.hpp>
-#include <stan/math/prim/fun/identity_free.hpp>
 #include <stan/math/prim/fun/identity_matrix.hpp>
 #include <stan/math/prim/fun/i_times.hpp>
 #include <stan/math/prim/fun/if_else.hpp>
@@ -170,8 +156,6 @@
 #include <stan/math/prim/fun/is_nan.hpp>
 #include <stan/math/prim/fun/is_uninitialized.hpp>
 #include <stan/math/prim/fun/lambert_w.hpp>
-#include <stan/math/prim/fun/lb_constrain.hpp>
-#include <stan/math/prim/fun/lb_free.hpp>
 #include <stan/math/prim/fun/lbeta.hpp>
 #include <stan/math/prim/fun/ldexp.hpp>
 #include <stan/math/prim/fun/LDLT_factor.hpp>
@@ -214,8 +198,6 @@
 #include <stan/math/prim/fun/logical_neq.hpp>
 #include <stan/math/prim/fun/logical_or.hpp>
 #include <stan/math/prim/fun/logit.hpp>
-#include <stan/math/prim/fun/lub_constrain.hpp>
-#include <stan/math/prim/fun/lub_free.hpp>
 #include <stan/math/prim/fun/make_nu.hpp>
 #include <stan/math/prim/fun/matrix_exp.hpp>
 #include <stan/math/prim/fun/matrix_exp_multiply.hpp>
@@ -246,8 +228,6 @@
 #include <stan/math/prim/fun/norm1.hpp>
 #include <stan/math/prim/fun/norm2.hpp>
 #include <stan/math/prim/fun/num_elements.hpp>
-#include <stan/math/prim/fun/offset_multiplier_constrain.hpp>
-#include <stan/math/prim/fun/offset_multiplier_free.hpp>
 #include <stan/math/prim/fun/one_hot_array.hpp>
 #include <stan/math/prim/fun/one_hot_int_array.hpp>
 #include <stan/math/prim/fun/one_hot_row_vector.hpp>
@@ -256,22 +236,14 @@
 #include <stan/math/prim/fun/ones_int_array.hpp>
 #include <stan/math/prim/fun/ones_row_vector.hpp>
 #include <stan/math/prim/fun/ones_vector.hpp>
-#include <stan/math/prim/fun/ordered_constrain.hpp>
-#include <stan/math/prim/fun/ordered_free.hpp>
 #include <stan/math/prim/fun/owens_t.hpp>
 #include <stan/math/prim/fun/Phi.hpp>
 #include <stan/math/prim/fun/Phi_approx.hpp>
 #include <stan/math/prim/fun/plus.hpp>
 #include <stan/math/prim/fun/poisson_binomial_log_probs.hpp>
 #include <stan/math/prim/fun/polar.hpp>
-#include <stan/math/prim/fun/positive_constrain.hpp>
-#include <stan/math/prim/fun/positive_free.hpp>
-#include <stan/math/prim/fun/positive_ordered_constrain.hpp>
-#include <stan/math/prim/fun/positive_ordered_free.hpp>
 #include <stan/math/prim/fun/pow.hpp>
 #include <stan/math/prim/fun/primitive_value.hpp>
-#include <stan/math/prim/fun/prob_constrain.hpp>
-#include <stan/math/prim/fun/prob_free.hpp>
 #include <stan/math/prim/fun/prod.hpp>
 #include <stan/math/prim/fun/proj.hpp>
 #include <stan/math/prim/fun/promote_elements.hpp>
@@ -316,8 +288,6 @@
 #include <stan/math/prim/fun/select.hpp>
 #include <stan/math/prim/fun/sign.hpp>
 #include <stan/math/prim/fun/signbit.hpp>
-#include <stan/math/prim/fun/simplex_constrain.hpp>
-#include <stan/math/prim/fun/simplex_free.hpp>
 #include <stan/math/prim/fun/sin.hpp>
 #include <stan/math/prim/fun/singular_values.hpp>
 #include <stan/math/prim/fun/sinh.hpp>
@@ -335,10 +305,6 @@
 #include <stan/math/prim/fun/squared_distance.hpp>
 #include <stan/math/prim/fun/stan_print.hpp>
 #include <stan/math/prim/fun/step.hpp>
-#include <stan/math/prim/fun/stochastic_column_constrain.hpp>
-#include <stan/math/prim/fun/stochastic_column_free.hpp>
-#include <stan/math/prim/fun/stochastic_row_constrain.hpp>
-#include <stan/math/prim/fun/stochastic_row_free.hpp>
 #include <stan/math/prim/fun/sub_col.hpp>
 #include <stan/math/prim/fun/sub_row.hpp>
 #include <stan/math/prim/fun/subtract.hpp>
@@ -370,12 +336,8 @@
 #include <stan/math/prim/fun/trigamma.hpp>
 #include <stan/math/prim/fun/trunc.hpp>
 #include <stan/math/prim/fun/typedefs.hpp>
-#include <stan/math/prim/fun/ub_constrain.hpp>
-#include <stan/math/prim/fun/ub_free.hpp>
 #include <stan/math/prim/fun/uniform_simplex.hpp>
 #include <stan/math/prim/fun/unitspaced_array.hpp>
-#include <stan/math/prim/fun/unit_vector_constrain.hpp>
-#include <stan/math/prim/fun/unit_vector_free.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
 #include <stan/math/prim/fun/value_of_rec.hpp>
 #include <stan/math/prim/fun/vec_concat.hpp>
diff --git a/stan/math/prim/prob/wiener5_lpdf.hpp b/stan/math/prim/prob/wiener5_lpdf.hpp
index 0414b59f60c..9a1081006c7 100644
--- a/stan/math/prim/prob/wiener5_lpdf.hpp
+++ b/stan/math/prim/prob/wiener5_lpdf.hpp
@@ -2,6 +2,7 @@
 #define STAN_MATH_PRIM_PROB_WIENER5_LPDF_HPP
 
 #include <stan/math/prim/fun.hpp>
+#include <stan/math/prim/functor/apply.hpp>
 
 namespace stan {
 namespace math {
diff --git a/stan/math/rev.hpp b/stan/math/rev.hpp
index 91d374eb12d..e89df411728 100644
--- a/stan/math/rev.hpp
+++ b/stan/math/rev.hpp
@@ -5,8 +5,10 @@
 
 #ifdef STAN_OPENCL
 #include <stan/math/opencl/rev.hpp>
+#include <stan/math/opencl/rev_constraint.hpp>
 #endif
 
+#include <stan/math/rev/constraint.hpp>
 #include <stan/math/rev/core.hpp>
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/fun.hpp>
diff --git a/stan/math/rev/constraint.hpp b/stan/math/rev/constraint.hpp
new file mode 100644
index 00000000000..3ab4a6f72c7
--- /dev/null
+++ b/stan/math/rev/constraint.hpp
@@ -0,0 +1,28 @@
+#ifndef STAN_MATH_REV_CONSTRAINT_HPP
+#define STAN_MATH_REV_CONSTRAINT_HPP
+
+#include <stan/math/prim/fun/Eigen.hpp>
+
+#include <stan/math/rev/constraint/cholesky_corr_constrain.hpp>
+#include <stan/math/rev/constraint/cholesky_factor_constrain.hpp>
+#include <stan/math/rev/constraint/corr_matrix_constrain.hpp>
+#include <stan/math/rev/constraint/cov_matrix_constrain.hpp>
+#include <stan/math/rev/constraint/cov_matrix_constrain_lkj.hpp>
+#include <stan/math/rev/constraint/identity_constrain.hpp>
+#include <stan/math/rev/constraint/identity_free.hpp>
+#include <stan/math/rev/constraint/lb_constrain.hpp>
+#include <stan/math/rev/constraint/lub_constrain.hpp>
+#include <stan/math/rev/constraint/ordered_constrain.hpp>
+#include <stan/math/rev/constraint/positive_ordered_constrain.hpp>
+#include <stan/math/rev/constraint/simplex_constrain.hpp>
+#include <stan/math/rev/constraint/stochastic_column_constrain.hpp>
+#include <stan/math/rev/constraint/stochastic_row_constrain.hpp>
+#include <stan/math/rev/constraint/unit_vector_constrain.hpp>
+#include <stan/math/rev/constraint/ub_constrain.hpp>
+
+#include <stan/math/prim/constraint.hpp>
+#include <stan/math/prim/err.hpp>
+#include <stan/math/prim/fun.hpp>
+#include <stan/math/prim/meta.hpp>
+
+#endif
diff --git a/stan/math/rev/fun/cholesky_corr_constrain.hpp b/stan/math/rev/constraint/cholesky_corr_constrain.hpp
similarity index 96%
rename from stan/math/rev/fun/cholesky_corr_constrain.hpp
rename to stan/math/rev/constraint/cholesky_corr_constrain.hpp
index f65c32c4770..e61fcbc5cbd 100644
--- a/stan/math/rev/fun/cholesky_corr_constrain.hpp
+++ b/stan/math/rev/constraint/cholesky_corr_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_CHOLESKY_CORR_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_CHOLESKY_CORR_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_CHOLESKY_CORR_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_CHOLESKY_CORR_CONSTRAIN_HPP
 
 #include <stan/math/rev/core.hpp>
 #include <stan/math/prim/err.hpp>
@@ -7,7 +7,7 @@
 #include <stan/math/prim/fun/log1m.hpp>
 #include <stan/math/prim/fun/sqrt.hpp>
 #include <stan/math/prim/fun/square.hpp>
-#include <stan/math/prim/fun/corr_constrain.hpp>
+#include <stan/math/prim/constraint/corr_constrain.hpp>
 #include <cmath>
 
 namespace stan {
diff --git a/stan/math/rev/fun/cholesky_factor_constrain.hpp b/stan/math/rev/constraint/cholesky_factor_constrain.hpp
similarity index 96%
rename from stan/math/rev/fun/cholesky_factor_constrain.hpp
rename to stan/math/rev/constraint/cholesky_factor_constrain.hpp
index 3cc96382180..17d18d7ee0e 100644
--- a/stan/math/rev/fun/cholesky_factor_constrain.hpp
+++ b/stan/math/rev/constraint/cholesky_factor_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_CHOLESKY_FACTOR_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_CHOLESKY_FACTOR_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_CHOLESKY_FACTOR_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_CHOLESKY_FACTOR_CONSTRAIN_HPP
 
 #include <stan/math/rev/core.hpp>
 #include <stan/math/prim/err.hpp>
diff --git a/stan/math/rev/fun/corr_matrix_constrain.hpp b/stan/math/rev/constraint/corr_matrix_constrain.hpp
similarity index 94%
rename from stan/math/rev/fun/corr_matrix_constrain.hpp
rename to stan/math/rev/constraint/corr_matrix_constrain.hpp
index f28d7ed5e01..c3d1b8d2f7d 100644
--- a/stan/math/rev/fun/corr_matrix_constrain.hpp
+++ b/stan/math/rev/constraint/corr_matrix_constrain.hpp
@@ -1,11 +1,11 @@
-#ifndef STAN_MATH_REV_FUN_CORR_MATRIX_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_CORR_MATRIX_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_CORR_MATRIX_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_CORR_MATRIX_CONSTRAIN_HPP
 
 #include <stan/math/rev/core.hpp>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <stan/math/prim/fun/corr_constrain.hpp>
+#include <stan/math/prim/constraint/corr_constrain.hpp>
 #include <stan/math/prim/fun/read_corr_matrix.hpp>
 #include <stdexcept>
 
diff --git a/stan/math/rev/fun/cov_matrix_constrain.hpp b/stan/math/rev/constraint/cov_matrix_constrain.hpp
similarity index 97%
rename from stan/math/rev/fun/cov_matrix_constrain.hpp
rename to stan/math/rev/constraint/cov_matrix_constrain.hpp
index f0e6eca08f5..ccf4ac496ba 100644
--- a/stan/math/rev/fun/cov_matrix_constrain.hpp
+++ b/stan/math/rev/constraint/cov_matrix_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_COV_MATRIX_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_COV_MATRIX_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_COV_MATRIX_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_COV_MATRIX_CONSTRAIN_HPP
 
 #include <stan/math/rev/core.hpp>
 #include <stan/math/prim/meta.hpp>
diff --git a/stan/math/rev/fun/cov_matrix_constrain_lkj.hpp b/stan/math/rev/constraint/cov_matrix_constrain_lkj.hpp
similarity index 92%
rename from stan/math/rev/fun/cov_matrix_constrain_lkj.hpp
rename to stan/math/rev/constraint/cov_matrix_constrain_lkj.hpp
index 29ef3a2b0fe..1e8d8ea3e8c 100644
--- a/stan/math/rev/fun/cov_matrix_constrain_lkj.hpp
+++ b/stan/math/rev/constraint/cov_matrix_constrain_lkj.hpp
@@ -1,10 +1,10 @@
-#ifndef STAN_MATH_REV_FUN_COV_MATRIX_CONSTRAIN_LKJ_HPP
-#define STAN_MATH_REV_FUN_COV_MATRIX_CONSTRAIN_LKJ_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_COV_MATRIX_CONSTRAIN_LKJ_HPP
+#define STAN_MATH_REV_CONSTRAINT_COV_MATRIX_CONSTRAIN_LKJ_HPP
 
 #include <stan/math/prim/fun/Eigen.hpp>
 #include <stan/math/rev/core.hpp>
-#include <stan/math/prim/fun/corr_constrain.hpp>
-#include <stan/math/prim/fun/positive_constrain.hpp>
+#include <stan/math/prim/constraint/corr_constrain.hpp>
+#include <stan/math/prim/constraint/positive_constrain.hpp>
 #include <stan/math/prim/fun/read_cov_matrix.hpp>
 #include <stan/math/prim/fun/to_ref.hpp>
 
diff --git a/stan/math/rev/fun/identity_constrain.hpp b/stan/math/rev/constraint/identity_constrain.hpp
similarity index 87%
rename from stan/math/rev/fun/identity_constrain.hpp
rename to stan/math/rev/constraint/identity_constrain.hpp
index 821aa441996..6d6bbff205c 100644
--- a/stan/math/rev/fun/identity_constrain.hpp
+++ b/stan/math/rev/constraint/identity_constrain.hpp
@@ -1,9 +1,9 @@
-#ifndef STAN_MATH_REV_FUN_IDENTITY_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_IDENTITY_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_IDENTITY_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_IDENTITY_CONSTRAIN_HPP
 
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/core.hpp>
-#include <stan/math/prim/fun/identity_constrain.hpp>
+#include <stan/math/prim/constraint/identity_constrain.hpp>
 #include <stan/math/rev/fun/to_var_value.hpp>
 namespace stan {
 namespace math {
diff --git a/stan/math/rev/fun/identity_free.hpp b/stan/math/rev/constraint/identity_free.hpp
similarity index 80%
rename from stan/math/rev/fun/identity_free.hpp
rename to stan/math/rev/constraint/identity_free.hpp
index 09fa323466c..596d52e6cdf 100644
--- a/stan/math/rev/fun/identity_free.hpp
+++ b/stan/math/rev/constraint/identity_free.hpp
@@ -1,8 +1,8 @@
-#ifndef STAN_MATH_REV_FUN_IDENTITY_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_IDENTITY_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_IDENTITY_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_IDENTITY_CONSTRAIN_HPP
 
 #include <stan/math/prim/meta.hpp>
-#include <stan/math/prim/fun/identity_free.hpp>
+#include <stan/math/prim/constraint/identity_free.hpp>
 #include <stan/math/rev/fun/to_var_value.hpp>
 
 namespace stan {
diff --git a/stan/math/rev/fun/lb_constrain.hpp b/stan/math/rev/constraint/lb_constrain.hpp
similarity index 98%
rename from stan/math/rev/fun/lb_constrain.hpp
rename to stan/math/rev/constraint/lb_constrain.hpp
index 0bdad75a716..8f8da96afce 100644
--- a/stan/math/rev/fun/lb_constrain.hpp
+++ b/stan/math/rev/constraint/lb_constrain.hpp
@@ -1,15 +1,15 @@
-#ifndef STAN_MATH_REV_FUN_LB_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_LB_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_LB_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_LB_CONSTRAIN_HPP
 
 #include <stan/math/rev/core.hpp>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/constants.hpp>
-#include <stan/math/prim/fun/lb_constrain.hpp>
+#include <stan/math/prim/constraint/lb_constrain.hpp>
 #include <stan/math/prim/fun/sum.hpp>
 #include <stan/math/prim/fun/to_ref.hpp>
-#include <stan/math/rev/fun/identity_constrain.hpp>
-#include <stan/math/rev/fun/identity_free.hpp>
+#include <stan/math/rev/constraint/identity_constrain.hpp>
+#include <stan/math/rev/constraint/identity_free.hpp>
 #include <stan/math/rev/fun/sum.hpp>
 #include <stan/math/rev/fun/to_arena.hpp>
 #include <stan/math/rev/fun/value_of.hpp>
diff --git a/stan/math/rev/fun/lub_constrain.hpp b/stan/math/rev/constraint/lub_constrain.hpp
similarity index 99%
rename from stan/math/rev/fun/lub_constrain.hpp
rename to stan/math/rev/constraint/lub_constrain.hpp
index ac54a675b8b..36715e4de95 100644
--- a/stan/math/rev/fun/lub_constrain.hpp
+++ b/stan/math/rev/constraint/lub_constrain.hpp
@@ -1,11 +1,11 @@
-#ifndef STAN_MATH_REV_FUN_LUB_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_LUB_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_LUB_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_LUB_CONSTRAIN_HPP
 
 #include <stan/math/rev/core.hpp>
 #include <stan/math/prim/meta.hpp>
-#include <stan/math/rev/fun/lb_constrain.hpp>
-#include <stan/math/prim/fun/lub_constrain.hpp>
-#include <stan/math/rev/fun/ub_constrain.hpp>
+#include <stan/math/rev/constraint/lb_constrain.hpp>
+#include <stan/math/prim/constraint/lub_constrain.hpp>
+#include <stan/math/rev/constraint/ub_constrain.hpp>
 #include <cmath>
 
 namespace stan {
diff --git a/stan/math/rev/fun/ordered_constrain.hpp b/stan/math/rev/constraint/ordered_constrain.hpp
similarity index 95%
rename from stan/math/rev/fun/ordered_constrain.hpp
rename to stan/math/rev/constraint/ordered_constrain.hpp
index 3f10ab70e75..98b10919875 100644
--- a/stan/math/rev/fun/ordered_constrain.hpp
+++ b/stan/math/rev/constraint/ordered_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_ORDERED_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_ORDERED_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_ORDERED_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_ORDERED_CONSTRAIN_HPP
 
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/core/reverse_pass_callback.hpp>
diff --git a/stan/math/rev/fun/positive_ordered_constrain.hpp b/stan/math/rev/constraint/positive_ordered_constrain.hpp
similarity index 92%
rename from stan/math/rev/fun/positive_ordered_constrain.hpp
rename to stan/math/rev/constraint/positive_ordered_constrain.hpp
index 7c39d83a667..d5c6b02f9e9 100644
--- a/stan/math/rev/fun/positive_ordered_constrain.hpp
+++ b/stan/math/rev/constraint/positive_ordered_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_POSITIVE_ORDERED_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_POSITIVE_ORDERED_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_POSITIVE_ORDERED_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_POSITIVE_ORDERED_CONSTRAIN_HPP
 
 #include <stan/math/prim/fun/Eigen.hpp>
 #include <stan/math/rev/meta.hpp>
diff --git a/stan/math/rev/fun/simplex_constrain.hpp b/stan/math/rev/constraint/simplex_constrain.hpp
similarity index 97%
rename from stan/math/rev/fun/simplex_constrain.hpp
rename to stan/math/rev/constraint/simplex_constrain.hpp
index c7dd57788b8..e81cc53557d 100644
--- a/stan/math/rev/fun/simplex_constrain.hpp
+++ b/stan/math/rev/constraint/simplex_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_SIMPLEX_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_SIMPLEX_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_SIMPLEX_CONSTRAIN_HPP
 
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/core/reverse_pass_callback.hpp>
diff --git a/stan/math/rev/fun/stochastic_column_constrain.hpp b/stan/math/rev/constraint/stochastic_column_constrain.hpp
similarity index 97%
rename from stan/math/rev/fun/stochastic_column_constrain.hpp
rename to stan/math/rev/constraint/stochastic_column_constrain.hpp
index 3838e0d0f77..02970513ff2 100644
--- a/stan/math/rev/fun/stochastic_column_constrain.hpp
+++ b/stan/math/rev/constraint/stochastic_column_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_STOCHASTIC_COLUMN_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_STOCHASTIC_COLUMN_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_STOCHASTIC_COLUMN_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_STOCHASTIC_COLUMN_CONSTRAIN_HPP
 
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/core/reverse_pass_callback.hpp>
diff --git a/stan/math/rev/fun/stochastic_row_constrain.hpp b/stan/math/rev/constraint/stochastic_row_constrain.hpp
similarity index 97%
rename from stan/math/rev/fun/stochastic_row_constrain.hpp
rename to stan/math/rev/constraint/stochastic_row_constrain.hpp
index 98f6781a1c3..654681107a7 100644
--- a/stan/math/rev/fun/stochastic_row_constrain.hpp
+++ b/stan/math/rev/constraint/stochastic_row_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_STOCHASTIC_ROW_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_STOCHASTIC_ROW_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_STOCHASTIC_ROW_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_STOCHASTIC_ROW_CONSTRAIN_HPP
 
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/core/reverse_pass_callback.hpp>
diff --git a/stan/math/rev/fun/ub_constrain.hpp b/stan/math/rev/constraint/ub_constrain.hpp
similarity index 98%
rename from stan/math/rev/fun/ub_constrain.hpp
rename to stan/math/rev/constraint/ub_constrain.hpp
index 9057330c691..f31f9bc21f3 100644
--- a/stan/math/rev/fun/ub_constrain.hpp
+++ b/stan/math/rev/constraint/ub_constrain.hpp
@@ -1,10 +1,10 @@
-#ifndef STAN_MATH_REV_FUN_UB_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_UB_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_UB_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_UB_CONSTRAIN_HPP
 
 #include <stan/math/rev/core.hpp>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/constants.hpp>
-#include <stan/math/prim/fun/ub_constrain.hpp>
+#include <stan/math/prim/constraint/ub_constrain.hpp>
 #include <cmath>
 
 namespace stan {
diff --git a/stan/math/rev/fun/unit_vector_constrain.hpp b/stan/math/rev/constraint/unit_vector_constrain.hpp
similarity index 95%
rename from stan/math/rev/fun/unit_vector_constrain.hpp
rename to stan/math/rev/constraint/unit_vector_constrain.hpp
index 6bc7536d326..86193c28e7e 100644
--- a/stan/math/rev/fun/unit_vector_constrain.hpp
+++ b/stan/math/rev/constraint/unit_vector_constrain.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_REV_FUN_UNIT_VECTOR_CONSTRAIN_HPP
-#define STAN_MATH_REV_FUN_UNIT_VECTOR_CONSTRAIN_HPP
+#ifndef STAN_MATH_REV_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
+#define STAN_MATH_REV_CONSTRAINT_UNIT_VECTOR_CONSTRAIN_HPP
 
 #include <stan/math/rev/meta.hpp>
 #include <stan/math/rev/core.hpp>
diff --git a/stan/math/rev/fun.hpp b/stan/math/rev/fun.hpp
index 9324df2edcc..4893ddc0540 100644
--- a/stan/math/rev/fun.hpp
+++ b/stan/math/rev/fun.hpp
@@ -28,18 +28,13 @@
 #include <stan/math/rev/fun/cbrt.hpp>
 #include <stan/math/rev/fun/ceil.hpp>
 #include <stan/math/rev/fun/cholesky_decompose.hpp>
-#include <stan/math/rev/fun/cholesky_corr_constrain.hpp>
-#include <stan/math/rev/fun/cholesky_factor_constrain.hpp>
 #include <stan/math/rev/fun/cumulative_sum.hpp>
 #include <stan/math/rev/fun/columns_dot_product.hpp>
 #include <stan/math/rev/fun/columns_dot_self.hpp>
 #include <stan/math/rev/fun/conj.hpp>
 #include <stan/math/rev/fun/cos.hpp>
 #include <stan/math/rev/fun/cosh.hpp>
-#include <stan/math/rev/fun/corr_matrix_constrain.hpp>
-#include <stan/math/rev/fun/cov_matrix_constrain.hpp>
 #include <stan/math/rev/fun/cov_exp_quad.hpp>
-#include <stan/math/rev/fun/cov_matrix_constrain_lkj.hpp>
 #include <stan/math/rev/fun/csr_matrix_times_vector.hpp>
 #include <stan/math/rev/fun/determinant.hpp>
 #include <stan/math/rev/fun/diag_pre_multiply.hpp>
@@ -80,8 +75,6 @@
 #include <stan/math/rev/fun/hypergeometric_2F1.hpp>
 #include <stan/math/rev/fun/hypergeometric_pFq.hpp>
 #include <stan/math/rev/fun/hypot.hpp>
-#include <stan/math/rev/fun/identity_constrain.hpp>
-#include <stan/math/rev/fun/identity_free.hpp>
 #include <stan/math/rev/fun/if_else.hpp>
 #include <stan/math/rev/fun/inc_beta.hpp>
 #include <stan/math/rev/fun/inv_inc_beta.hpp>
@@ -99,7 +92,6 @@
 #include <stan/math/rev/fun/is_nan.hpp>
 #include <stan/math/rev/fun/is_uninitialized.hpp>
 #include <stan/math/rev/fun/lambert_w.hpp>
-#include <stan/math/rev/fun/lb_constrain.hpp>
 #include <stan/math/rev/fun/lbeta.hpp>
 #include <stan/math/rev/fun/ldexp.hpp>
 #include <stan/math/rev/fun/lgamma.hpp>
@@ -125,7 +117,6 @@
 #include <stan/math/rev/fun/log_softmax.hpp>
 #include <stan/math/rev/fun/log_sum_exp.hpp>
 #include <stan/math/rev/fun/logit.hpp>
-#include <stan/math/rev/fun/lub_constrain.hpp>
 #include <stan/math/rev/fun/matrix_exp_multiply.hpp>
 #include <stan/math/rev/fun/matrix_power.hpp>
 #include <stan/math/rev/fun/mdivide_left.hpp>
@@ -140,10 +131,8 @@
 #include <stan/math/rev/fun/norm.hpp>
 #include <stan/math/rev/fun/norm1.hpp>
 #include <stan/math/rev/fun/norm2.hpp>
-#include <stan/math/rev/fun/ordered_constrain.hpp>
 #include <stan/math/rev/fun/owens_t.hpp>
 #include <stan/math/rev/fun/polar.hpp>
-#include <stan/math/rev/fun/positive_ordered_constrain.hpp>
 #include <stan/math/rev/fun/pow.hpp>
 #include <stan/math/rev/fun/primitive_value.hpp>
 #include <stan/math/rev/fun/proj.hpp>
@@ -161,11 +150,8 @@
 #include <stan/math/rev/fun/rows_dot_product.hpp>
 #include <stan/math/rev/fun/rows_dot_self.hpp>
 #include <stan/math/rev/fun/sd.hpp>
-#include <stan/math/rev/fun/simplex_constrain.hpp>
 #include <stan/math/rev/fun/sin.hpp>
 #include <stan/math/rev/fun/singular_values.hpp>
-#include <stan/math/rev/fun/stochastic_column_constrain.hpp>
-#include <stan/math/rev/fun/stochastic_row_constrain.hpp>
 #include <stan/math/rev/fun/svd.hpp>
 #include <stan/math/rev/fun/svd_U.hpp>
 #include <stan/math/rev/fun/svd_V.hpp>
@@ -192,12 +178,11 @@
 #include <stan/math/rev/fun/trace_quad_form.hpp>
 #include <stan/math/rev/fun/trigamma.hpp>
 #include <stan/math/rev/fun/trunc.hpp>
-#include <stan/math/rev/fun/unit_vector_constrain.hpp>
-#include <stan/math/rev/fun/ub_constrain.hpp>
 #include <stan/math/rev/fun/value_of.hpp>
 #include <stan/math/rev/fun/value_of_rec.hpp>
 #include <stan/math/rev/fun/variance.hpp>
 
+#include <stan/math/prim/constraint.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun.hpp>
 #include <stan/math/prim/functor.hpp>
diff --git a/test/unit/math/mix/fun/cholesky_corr_constrain_test.cpp b/test/unit/math/mix/constraint/cholesky_corr_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/cholesky_corr_constrain_test.cpp
rename to test/unit/math/mix/constraint/cholesky_corr_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/cholesky_factor_constrain_test.cpp b/test/unit/math/mix/constraint/cholesky_factor_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/cholesky_factor_constrain_test.cpp
rename to test/unit/math/mix/constraint/cholesky_factor_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/corr_constrain_test.cpp b/test/unit/math/mix/constraint/corr_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/corr_constrain_test.cpp
rename to test/unit/math/mix/constraint/corr_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/corr_matrix_constrain_test.cpp b/test/unit/math/mix/constraint/corr_matrix_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/corr_matrix_constrain_test.cpp
rename to test/unit/math/mix/constraint/corr_matrix_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/cov_matrix_constrain_lkj_test.cpp b/test/unit/math/mix/constraint/cov_matrix_constrain_lkj_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/cov_matrix_constrain_lkj_test.cpp
rename to test/unit/math/mix/constraint/cov_matrix_constrain_lkj_test.cpp
diff --git a/test/unit/math/mix/fun/cov_matrix_constrain_test.cpp b/test/unit/math/mix/constraint/cov_matrix_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/cov_matrix_constrain_test.cpp
rename to test/unit/math/mix/constraint/cov_matrix_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/identity_constrain_test.cpp b/test/unit/math/mix/constraint/identity_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/identity_constrain_test.cpp
rename to test/unit/math/mix/constraint/identity_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/lb_constrain_matvar_test.cpp b/test/unit/math/mix/constraint/lb_constrain_matvar_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/lb_constrain_matvar_test.cpp
rename to test/unit/math/mix/constraint/lb_constrain_matvar_test.cpp
diff --git a/test/unit/math/mix/fun/lb_constrain_test.cpp b/test/unit/math/mix/constraint/lb_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/lb_constrain_test.cpp
rename to test/unit/math/mix/constraint/lb_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/lub_constrain_1_test.cpp b/test/unit/math/mix/constraint/lub_constrain_1_test.cpp
similarity index 91%
rename from test/unit/math/mix/fun/lub_constrain_1_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_1_test.cpp
index 04c7466dd87..d76175a441c 100644
--- a/test/unit/math/mix/fun/lub_constrain_1_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_1_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 TEST(mathMixMatFun, lub_constrain_scalars) {
   double x1 = 0.7;
diff --git a/test/unit/math/mix/fun/lub_constrain_2_test.cpp b/test/unit/math/mix/constraint/lub_constrain_2_test.cpp
similarity index 95%
rename from test/unit/math/mix/fun/lub_constrain_2_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_2_test.cpp
index 22fa33e28d1..bdd88ef0a6c 100644
--- a/test/unit/math/mix/fun/lub_constrain_2_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_2_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 TEST(mathMixMatFun, lub_constrain_vector_scalar_scalar) {
   Eigen::MatrixXd x1(1, 1);
diff --git a/test/unit/math/mix/fun/lub_constrain_3_test.cpp b/test/unit/math/mix/constraint/lub_constrain_3_test.cpp
similarity index 96%
rename from test/unit/math/mix/fun/lub_constrain_3_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_3_test.cpp
index e2fca238fde..d3dd04ed10f 100644
--- a/test/unit/math/mix/fun/lub_constrain_3_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_3_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 TEST(mathMixMatFun, lub_constrain_vector_scalar_vector) {
   Eigen::MatrixXd x1(2, 2);
diff --git a/test/unit/math/mix/fun/lub_constrain_4_test.cpp b/test/unit/math/mix/constraint/lub_constrain_4_test.cpp
similarity index 94%
rename from test/unit/math/mix/fun/lub_constrain_4_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_4_test.cpp
index 077e6bfda98..30b9322aab7 100644
--- a/test/unit/math/mix/fun/lub_constrain_4_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_4_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 // real[], real[], real[]
 // real[], real, real[]
diff --git a/test/unit/math/mix/fun/lub_constrain_5_test.cpp b/test/unit/math/mix/constraint/lub_constrain_5_test.cpp
similarity index 96%
rename from test/unit/math/mix/fun/lub_constrain_5_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_5_test.cpp
index b1934ddbf04..f8fcf301904 100644
--- a/test/unit/math/mix/fun/lub_constrain_5_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_5_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 // array matrix[], array matrix[], array matrix[]
 // array matrix[], array matrix[], matrix[]
diff --git a/test/unit/math/mix/fun/lub_constrain_6_test.cpp b/test/unit/math/mix/constraint/lub_constrain_6_test.cpp
similarity index 96%
rename from test/unit/math/mix/fun/lub_constrain_6_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_6_test.cpp
index 504bb67095b..00d91f7bceb 100644
--- a/test/unit/math/mix/fun/lub_constrain_6_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_6_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 // array matrix[], array matrix[], array matrix[]
 // array matrix[], array matrix[], matrix[]
diff --git a/test/unit/math/mix/fun/lub_constrain_7_test.cpp b/test/unit/math/mix/constraint/lub_constrain_7_test.cpp
similarity index 96%
rename from test/unit/math/mix/fun/lub_constrain_7_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_7_test.cpp
index 8c097445b3d..e75009d2dee 100644
--- a/test/unit/math/mix/fun/lub_constrain_7_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_7_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 // array matrix[], array matrix[], array matrix[]
 // array matrix[], array matrix[], matrix[]
diff --git a/test/unit/math/mix/fun/lub_constrain_8_test.cpp b/test/unit/math/mix/constraint/lub_constrain_8_test.cpp
similarity index 96%
rename from test/unit/math/mix/fun/lub_constrain_8_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_8_test.cpp
index 3e18bfa2602..4811f56d4a0 100644
--- a/test/unit/math/mix/fun/lub_constrain_8_test.cpp
+++ b/test/unit/math/mix/constraint/lub_constrain_8_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/lub_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/lub_constrain_helpers.hpp>
 
 // array matrix[], array matrix[], array matrix[]
 // array matrix[], array matrix[], matrix[]
diff --git a/test/unit/math/mix/fun/lub_constrain_helpers.hpp b/test/unit/math/mix/constraint/lub_constrain_helpers.hpp
similarity index 94%
rename from test/unit/math/mix/fun/lub_constrain_helpers.hpp
rename to test/unit/math/mix/constraint/lub_constrain_helpers.hpp
index c12c99fcc9e..52c2c7a85dc 100644
--- a/test/unit/math/mix/fun/lub_constrain_helpers.hpp
+++ b/test/unit/math/mix/constraint/lub_constrain_helpers.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_TEST_UNIT_MATH_MIX_FUN_LUB_CONSTRAIN_HELPERS_HPP
-#define STAN_TEST_UNIT_MATH_MIX_FUN_LUB_CONSTRAIN_HELPERS_HPP
+#ifndef STAN_TEST_UNIT_MATH_MIX_CONSTRAINT_LUB_CONSTRAIN_HELPERS_HPP
+#define STAN_TEST_UNIT_MATH_MIX_CONSTRAINT_LUB_CONSTRAIN_HELPERS_HPP
 
 namespace lub_constrain_tests {
 template <typename T1, typename T2, typename T3>
diff --git a/test/unit/math/mix/fun/lub_constrain_matvar_test.cpp b/test/unit/math/mix/constraint/lub_constrain_matvar_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/lub_constrain_matvar_test.cpp
rename to test/unit/math/mix/constraint/lub_constrain_matvar_test.cpp
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_1_matvar_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_1_matvar_test.cpp
similarity index 92%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_1_matvar_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_1_matvar_test.cpp
index c3e123c5de5..ebb66b4e3b1 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_1_matvar_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_1_matvar_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp>
 
 TEST(mathMixMatFun, offset_multiplier_constrain_matvar_scalars) {
   double x1 = 0.7;
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_1_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_1_test.cpp
similarity index 92%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_1_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_1_test.cpp
index 5a22a26ca6f..c0aca029305 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_1_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_1_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp>
 
 TEST(mathMixMatFun, offset_multiplier_constrain_scalars) {
   double x1 = 0.7;
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_2_matvar_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_2_matvar_test.cpp
similarity index 91%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_2_matvar_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_2_matvar_test.cpp
index 7f0232eef66..38d0712c69c 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_2_matvar_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_2_matvar_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp>
 
 TEST(mathMixMatFun, offset_multiplier_constrain_matvar_vector_scalar_vector) {
   Eigen::MatrixXd x1(2, 2);
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_2_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_2_test.cpp
similarity index 91%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_2_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_2_test.cpp
index c62a0747501..5a47fa2b6d0 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_2_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_2_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp>
 
 TEST(mathMixMatFun, offset_multiplier_constrain_vector_scalar_vector) {
   Eigen::MatrixXd x1(2, 2);
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_3_matvar_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_3_matvar_test.cpp
similarity index 94%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_3_matvar_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_3_matvar_test.cpp
index 764c84c0a1b..a48cc636521 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_3_matvar_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_3_matvar_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp>
 
 // array[] matrix, matrix, array[] matrix
 // array[] matrix, matrix, matrix
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_3_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_3_test.cpp
similarity index 94%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_3_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_3_test.cpp
index 28089aacc8a..0bbb27ebee9 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_3_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_3_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp>
 
 // array[] matrix, matrix, array[] matrix
 // array[] matrix, matrix, matrix
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_4_matvar_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_4_matvar_test.cpp
similarity index 88%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_4_matvar_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_4_matvar_test.cpp
index 79c0c36867e..0b2d6506959 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_4_matvar_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_4_matvar_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp>
 
 // real[], real[], real[]
 // real[], real, real[]
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_4_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_4_test.cpp
similarity index 88%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_4_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_4_test.cpp
index fb37442f6f0..ec20c584407 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_4_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_4_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp>
 
 // real[], real[], real[]
 // real[], real, real[]
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_5_matvar_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_5_matvar_test.cpp
similarity index 90%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_5_matvar_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_5_matvar_test.cpp
index e47b579f2ed..f9191a79757 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_5_matvar_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_5_matvar_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp>
 
 // array[] matrix, array[] matrix, real
 // array[] matrix, real, array[] matrix
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_5_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_5_test.cpp
similarity index 90%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_5_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_5_test.cpp
index 610a2f9de11..6663ec2e3cf 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_5_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_5_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp>
 
 // array[] matrix, array[] matrix, real
 // array[] matrix, real, array[] matrix
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_6_matvar_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_6_matvar_test.cpp
similarity index 91%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_6_matvar_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_6_matvar_test.cpp
index b65f76bb0c7..a4d86a774dd 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_6_matvar_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_6_matvar_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp>
 
 // array[] matrix, matrix, real
 // array[] matrix, real, matrix
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_6_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_6_test.cpp
similarity index 91%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_6_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_6_test.cpp
index 190d01f0c81..3dd21630ce9 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_6_test.cpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_6_test.cpp
@@ -1,5 +1,5 @@
 #include <test/unit/math/test_ad.hpp>
-#include <test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp>
+#include <test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp>
 
 // array[] matrix, matrix, real
 // array[] matrix, real, matrix
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_7_test.cpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_7_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_7_test.cpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_7_test.cpp
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp
similarity index 94%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp
index 7d28a595dda..92f063e207c 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_helpers.hpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_helpers.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_TEST_UNIT_MATH_MIX_FUN_offset_multiplier_CONSTRAIN_HELPERS_HPP
-#define STAN_TEST_UNIT_MATH_MIX_FUN_offset_multiplier_CONSTRAIN_HELPERS_HPP
+#ifndef STAN_TEST_UNIT_MATH_MIX_OFFSET_MULTIPLIER_CONSTRAIN_HELPERS_HPP
+#define STAN_TEST_UNIT_MATH_MIX_OFFSET_MULTIPLIER_CONSTRAIN_HELPERS_HPP
 
 namespace offset_multiplier_constrain_tests {
 template <typename T1, typename T2, typename T3>
diff --git a/test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp b/test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp
similarity index 94%
rename from test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp
rename to test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp
index ecb5a50da82..fc299d5dfb5 100644
--- a/test/unit/math/mix/fun/offset_multiplier_constrain_matvar_helpers.hpp
+++ b/test/unit/math/mix/constraint/offset_multiplier_constrain_matvar_helpers.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_TEST_UNIT_MATH_MIX_FUN_OFFSET_MULTIPLIER_MAT_CONSTRAIN_HELPERS_HPP
-#define STAN_TEST_UNIT_MATH_MIX_FUN_OFFSET_MULTIPLIER_MAT_CONSTRAIN_HELPERS_HPP
+#ifndef STAN_TEST_UNIT_MATH_MIX_OFFSET_MULTIPLIER_MAT_CONSTRAIN_HELPERS_HPP
+#define STAN_TEST_UNIT_MATH_MIX_OFFSET_MULTIPLIER_MAT_CONSTRAIN_HELPERS_HPP
 
 namespace offset_multiplier_constrain_tests {
 template <typename T1, typename T2, typename T3>
diff --git a/test/unit/math/mix/fun/ordered_constrain_test.cpp b/test/unit/math/mix/constraint/ordered_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/ordered_constrain_test.cpp
rename to test/unit/math/mix/constraint/ordered_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/positive_ordered_constrain_test.cpp b/test/unit/math/mix/constraint/positive_ordered_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/positive_ordered_constrain_test.cpp
rename to test/unit/math/mix/constraint/positive_ordered_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/simplex_constrain_test.cpp b/test/unit/math/mix/constraint/simplex_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/simplex_constrain_test.cpp
rename to test/unit/math/mix/constraint/simplex_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/stochastic_column_constrain_test.cpp b/test/unit/math/mix/constraint/stochastic_column_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/stochastic_column_constrain_test.cpp
rename to test/unit/math/mix/constraint/stochastic_column_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/stochastic_row_constrain_test.cpp b/test/unit/math/mix/constraint/stochastic_row_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/stochastic_row_constrain_test.cpp
rename to test/unit/math/mix/constraint/stochastic_row_constrain_test.cpp
diff --git a/test/unit/math/mix/fun/unit_vector_constrain_test.cpp b/test/unit/math/mix/constraint/unit_vector_constrain_test.cpp
similarity index 100%
rename from test/unit/math/mix/fun/unit_vector_constrain_test.cpp
rename to test/unit/math/mix/constraint/unit_vector_constrain_test.cpp
diff --git a/test/unit/math/opencl/rev/lb_constrain_test.cpp b/test/unit/math/opencl/rev/constraint/lb_constrain_test.cpp
similarity index 100%
rename from test/unit/math/opencl/rev/lb_constrain_test.cpp
rename to test/unit/math/opencl/rev/constraint/lb_constrain_test.cpp
diff --git a/test/unit/math/opencl/rev/lub_constrain_test.cpp b/test/unit/math/opencl/rev/constraint/lub_constrain_test.cpp
similarity index 100%
rename from test/unit/math/opencl/rev/lub_constrain_test.cpp
rename to test/unit/math/opencl/rev/constraint/lub_constrain_test.cpp
diff --git a/test/unit/math/opencl/rev/offset_multiplier_constrain_test.cpp b/test/unit/math/opencl/rev/constraint/offset_multiplier_constrain_test.cpp
similarity index 100%
rename from test/unit/math/opencl/rev/offset_multiplier_constrain_test.cpp
rename to test/unit/math/opencl/rev/constraint/offset_multiplier_constrain_test.cpp
diff --git a/test/unit/math/opencl/rev/ub_constrain_test.cpp b/test/unit/math/opencl/rev/constraint/ub_constrain_test.cpp
similarity index 100%
rename from test/unit/math/opencl/rev/ub_constrain_test.cpp
rename to test/unit/math/opencl/rev/constraint/ub_constrain_test.cpp
diff --git a/test/unit/math/opencl/rev/unit_vector_constrain_test.cpp b/test/unit/math/opencl/rev/constraint/unit_vector_constrain_test.cpp
similarity index 100%
rename from test/unit/math/opencl/rev/unit_vector_constrain_test.cpp
rename to test/unit/math/opencl/rev/constraint/unit_vector_constrain_test.cpp
diff --git a/test/unit/math/prim/fun/cholesky_corr_transform_test.cpp b/test/unit/math/prim/constraint/cholesky_corr_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/cholesky_corr_transform_test.cpp
rename to test/unit/math/prim/constraint/cholesky_corr_transform_test.cpp
diff --git a/test/unit/math/prim/fun/cholesky_factor_transform_test.cpp b/test/unit/math/prim/constraint/cholesky_factor_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/cholesky_factor_transform_test.cpp
rename to test/unit/math/prim/constraint/cholesky_factor_transform_test.cpp
diff --git a/test/unit/math/prim/fun/corr_transform_test.cpp b/test/unit/math/prim/constraint/corr_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/corr_transform_test.cpp
rename to test/unit/math/prim/constraint/corr_transform_test.cpp
diff --git a/test/unit/math/prim/fun/cov_matrix_transform_test.cpp b/test/unit/math/prim/constraint/cov_matrix_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/cov_matrix_transform_test.cpp
rename to test/unit/math/prim/constraint/cov_matrix_transform_test.cpp
diff --git a/test/unit/math/prim/fun/identity_transform_test.cpp b/test/unit/math/prim/constraint/identity_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/identity_transform_test.cpp
rename to test/unit/math/prim/constraint/identity_transform_test.cpp
diff --git a/test/unit/math/prim/fun/lb_transform_test.cpp b/test/unit/math/prim/constraint/lb_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/lb_transform_test.cpp
rename to test/unit/math/prim/constraint/lb_transform_test.cpp
diff --git a/test/unit/math/prim/fun/lub_transform_test.cpp b/test/unit/math/prim/constraint/lub_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/lub_transform_test.cpp
rename to test/unit/math/prim/constraint/lub_transform_test.cpp
diff --git a/test/unit/math/prim/fun/offset_multiplier_matrix_transform_test.cpp b/test/unit/math/prim/constraint/offset_multiplier_matrix_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/offset_multiplier_matrix_transform_test.cpp
rename to test/unit/math/prim/constraint/offset_multiplier_matrix_transform_test.cpp
diff --git a/test/unit/math/prim/fun/offset_multiplier_transform_test.cpp b/test/unit/math/prim/constraint/offset_multiplier_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/offset_multiplier_transform_test.cpp
rename to test/unit/math/prim/constraint/offset_multiplier_transform_test.cpp
diff --git a/test/unit/math/prim/fun/ordered_transform_test.cpp b/test/unit/math/prim/constraint/ordered_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/ordered_transform_test.cpp
rename to test/unit/math/prim/constraint/ordered_transform_test.cpp
diff --git a/test/unit/math/prim/fun/prob_transform_test.cpp b/test/unit/math/prim/constraint/prob_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/prob_transform_test.cpp
rename to test/unit/math/prim/constraint/prob_transform_test.cpp
diff --git a/test/unit/math/prim/fun/simplex_transform_test.cpp b/test/unit/math/prim/constraint/simplex_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/simplex_transform_test.cpp
rename to test/unit/math/prim/constraint/simplex_transform_test.cpp
diff --git a/test/unit/math/prim/fun/stochastic_column_constrain_test.cpp b/test/unit/math/prim/constraint/stochastic_column_constrain_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/stochastic_column_constrain_test.cpp
rename to test/unit/math/prim/constraint/stochastic_column_constrain_test.cpp
diff --git a/test/unit/math/prim/fun/stochastic_row_constrain_test.cpp b/test/unit/math/prim/constraint/stochastic_row_constrain_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/stochastic_row_constrain_test.cpp
rename to test/unit/math/prim/constraint/stochastic_row_constrain_test.cpp
diff --git a/test/unit/math/prim/fun/ub_transform_test.cpp b/test/unit/math/prim/constraint/ub_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/ub_transform_test.cpp
rename to test/unit/math/prim/constraint/ub_transform_test.cpp
diff --git a/test/unit/math/prim/fun/unit_vector_transform_test.cpp b/test/unit/math/prim/constraint/unit_vector_transform_test.cpp
similarity index 100%
rename from test/unit/math/prim/fun/unit_vector_transform_test.cpp
rename to test/unit/math/prim/constraint/unit_vector_transform_test.cpp