diff --git a/BUILD b/BUILD
index 8da6d15..ea185a0 100644
--- a/BUILD
+++ b/BUILD
@@ -1,9 +1,8 @@
 # An FHE cryptosystem built in JAX
 
-load("@rules_python//python:defs.bzl", "py_library")
-load("@rules_python//python:defs.bzl", "py_test")
 load("@jaxite//bazel:test_oss.bzl", "cpu_gpu_tpu_test", "gpu_tpu_test", "multichip_tpu_test")
 load("@rules_license//rules:license.bzl", "license")
+load("@rules_python//python:defs.bzl", "py_library", "py_test")
 
 package(
     default_applicable_licenses = ["@jaxite//:license"],
diff --git a/jaxite/jaxite_lib/bootstrap.py b/jaxite/jaxite_lib/bootstrap.py
index 60c7c56..a51ecd9 100644
--- a/jaxite/jaxite_lib/bootstrap.py
+++ b/jaxite/jaxite_lib/bootstrap.py
@@ -1,4 +1,4 @@
-"""The API for bootstrapping in TFHE."""
+"""The API for bootstrapping in CGGI."""
 import dataclasses
 import functools
 from typing import Any, Callable, Optional
diff --git a/jaxite/jaxite_lib/decomposition.py b/jaxite/jaxite_lib/decomposition.py
index 568402a..6695858 100644
--- a/jaxite/jaxite_lib/decomposition.py
+++ b/jaxite/jaxite_lib/decomposition.py
@@ -210,7 +210,7 @@ def signed_decomposition(
 
   # reversed because the digits are computed from least-significant bit to
   # highest-significant bit..
-  return result[::-1][:num_levels]
+  return jnp.flip(result, axis=-1)[:num_levels]
 
 
 # Applies the signed decomposition to each coefficient of a polynomial
diff --git a/jaxite/jaxite_lib/matrix_utils.py b/jaxite/jaxite_lib/matrix_utils.py
index 36b019a..0984de6 100644
--- a/jaxite/jaxite_lib/matrix_utils.py
+++ b/jaxite/jaxite_lib/matrix_utils.py
@@ -190,7 +190,6 @@ def _toeplitz(inp_ref, out_ref):
   return pl.pallas_call(
       _toeplitz,
       out_shape=jax.ShapeDtypeStruct((n, n), x.dtype),
-      interpret=(jax.default_backend() == "cpu"),
   )(x)
 
 
@@ -258,27 +257,20 @@ def monomial_mul(
         polynomial
   """
   n = poly.shape[0]
-
-  # After a multiplication by X^{2N}, the polynomial is unchanged.
   degree = degree % (2 * n)
-  flip = degree // n
   shift = degree % n
-
-  # equivalent to "if degree >= n: poly = -poly" because 0 <= degree < 2N
-  poly = jnp.uint32((-1) ** flip) * poly
-  rolled = jnp.roll(poly, shift)
-
-  # trick: generate an array like [1, 1, ..., 1, -1, -1, ..., -1]
-  # and rolling that gives the right argument to use in an element-wise product
-  # with the tail truncated.
-  ones = jnp.ones(n, dtype=jnp.uint32)
-  sign = jnp.roll(jnp.concatenate([ones, -ones]), shift)
-  output = rolled * sign[:n]
+  flip = (degree // n) % 2 == 1
+  indices = jax.lax.broadcasted_iota(
+      dtype=jnp.int32, shape=poly.shape, dimension=0
+  )
+  rolled = jnp.roll(poly, degree)
+  rolled = jnp.where(flip, -rolled, rolled)
+  output = jnp.where(indices < shift, -rolled, rolled)
 
   if 0 < log_modulus < 32:
     output = jnp.mod(output, jnp.uint32(2) ** log_modulus)
 
-  return output
+  return output.astype(poly.dtype)
 
 
 monomial_mul_list = jax.vmap(monomial_mul, in_axes=(0, None, None), out_axes=0)