Harmonize softplus implementations

aesara/link/jax/dispatch/scalar.py

@@ -125,10 +125,18 @@ def psi(x):
 @jax_funcify.register(Softplus)
 def jax_funcify_Softplus(op, **kwargs):
     def softplus(x):
-        # This expression is numerically equivalent to the Aesara one
-        # It just contains one "speed" optimization less than the Aesara counterpart
         return jnp.where(
-            x < -37.0, jnp.exp(x), jnp.where(x > 33.3, x, jnp.log1p(jnp.exp(x)))
+            x < -37.0,
+            jnp.exp(x),
+            jnp.where(
+                x < 18.0,
+                jnp.log1p(jnp.exp(x)),
+                jnp.where(
+                    x < 33.3,
+                    x + jnp.exp(-x),
+                    x,
+                ),
+            ),
         )
 
     return softplus

aesara/scalar/math.py

@@ -6,6 +6,7 @@
 
 import os
 import warnings
+from textwrap import dedent
 
 import numpy as np
 import scipy.special
@@ -1134,7 +1135,8 @@ class Softplus(UnaryScalarOp):
     r"""
     Compute log(1 + exp(x)), also known as softplus or log1pexp
 
-    This function is numerically more stable than the naive approach.
+    This function is numerically faster than the naive approach, and does not overflow
+    for large values of x.
 
     For details, see
     https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf
@@ -1172,52 +1174,38 @@ def grad(self, inp, grads):
     def c_code(self, node, name, inp, out, sub):
         (x,) = inp
         (z,) = out
-        # The boundary constants were obtained by looking at the output of
-        # python commands like:
-        # import numpy, aesara
-        # dt='float32'  # or float64
-        #  for i in range(750):
-        #      print i, repr(numpy.log1p(numpy.exp(_asarray([i,-i], dtype=dt))))
-        # the upper boundary check prevents us from generating inf, whereas the
-        # the lower boundary check prevents using exp when the result will be 0 anyway.
-        # The intermediate constants are taken from Machler (2012).
-
-        # We use the float32 limits for float16 for now as the
-        # computation will happen in float32 anyway.
+        # We use the same limits for all precisions, which may be suboptimal. The reference
+        # paper only looked at double precision
         if node.inputs[0].type in float_types:
             if node.inputs[0].type == float64:
-                return (
-                    """
-                    %(z)s = (
-                        %(x)s < -745.0 ? 0.0 :
-                        %(x)s < -37.0 ? exp(%(x)s) :
-                        %(x)s < 18.0 ? log1p(exp(%(x)s)) :
-                        %(x)s < 33.3 ? %(x)s + exp(-%(x)s) :
-                        %(x)s
+                return dedent(
+                    f"""
+                    {z} = (
+                        {x} < -37.0 ? exp({x}) :
+                        {x} < 18.0 ? log1p(exp({x})) :
+                        {x} < 33.3 ? {x} + exp(-{x}) :
+                        {x}
                     );
                     """
-                    % locals()
                 )
             else:
-                return (
-                    """
-                    %(z)s = (
-                        %(x)s < -103.0f ? 0.0 :
-                        %(x)s < -37.0f ? exp(%(x)s) :
-                        %(x)s < 18.0f ? log1p(exp(%(x)s)) :
-                        %(x)s < 33.3f ? %(x)s + exp(-%(x)s) :
-                        %(x)s
+                return dedent(
+                    f"""
+                    {z} = (
+                        {x} < -37.0f ? exp({x}) :
+                        {x} < 18.0f ? log1p(exp({x})) :
+                        {x} < 33.3f ? {x} + exp(-{x}) :
+                        {x}
                     );
                     """
-                    % locals()
                 )
         else:
             raise NotImplementedError("only floatingpoint is implemented")
 
     def c_code_cache_version(self):
         v = super().c_code_cache_version()
         if v:
-            return (2,) + v
+            return (3,) + v
         else:
             return v