diff --git a/.github/workflows/Invalidations.yml b/.github/workflows/Invalidations.yml
index a582f3fa..d657cd16 100644
--- a/.github/workflows/Invalidations.yml
+++ b/.github/workflows/Invalidations.yml
@@ -27,7 +27,7 @@ jobs:
           lines = readlines("Project.toml")
           open("Project.toml", "w") do f
               for l in lines
-                  if l == "version = \"0.9.0-dev\""
+                  if startswith(l, "version = ")
                       l = "version = \"0.8.4\""
                   end
                   println(f, l)
@@ -46,7 +46,7 @@ jobs:
           lines = readlines("Project.toml")
           open("Project.toml", "w") do f
               for l in lines
-                  if l == "version = \"0.9.0-dev\""
+                  if startswith(l, "version = ")
                       l = "version = \"0.8.4\""
                   end
                   println(f, l)
diff --git a/Project.toml b/Project.toml
index a76d1e6e..d8abe474 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "FixedPointNumbers"
 uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
-version = "0.9.0"
+version = "0.9.1"
 
 [deps]
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -17,9 +17,7 @@ Aqua = "0.8"
 Documenter = "0.27, 1"
 Random = "<0.0.1, 1"
 StableRNGs = "1"
-# Update this version specifier when Statistics.jl v1.11.2 is released.
-# https://github.com/JuliaStats/Statistics.jl/issues/165
-Statistics = "< 1.11.2"
+Statistics = "1"
 Test = "1"
 julia = "1"
 
diff --git a/src/fixed.jl b/src/fixed.jl
index 1abd7ff4..417a511a 100644
--- a/src/fixed.jl
+++ b/src/fixed.jl
@@ -103,10 +103,10 @@ function _rem(x::Fixed, ::Type{F}) where {T, f, F <: Fixed{T,f}}
 end
 _rem(x::Integer, ::Type{F}) where {T, f, F <: Fixed{T,f}} = F(_unsafe_trunc(T, x) << f, 0)
 function _rem(x::Real, ::Type{F}) where {T, f, F <: Fixed{T,f}}
+    isfinite(x) || return zero(F)
     if bitwidth(T) < 32
         Ti = T
     else
-        isfinite(x) || return zero(F)
         Ti = promote_type(Int64, T)
     end
     Tf = floattype(F)
diff --git a/src/normed.jl b/src/normed.jl
index a8fae420..eec16735 100644
--- a/src/normed.jl
+++ b/src/normed.jl
@@ -112,7 +112,7 @@ _rem(x::N, ::Type{N}) where {N <: Normed} = x
 _rem(x::Normed, ::Type{N}) where {T, N <: Normed{T}} =
     reinterpret(N, _unsafe_trunc(T, round((rawone(N)/rawone(x))*reinterpret(x))))
 function _rem(x::Real, ::Type{N}) where {T, N <: Normed{T}}
-    bitwidth(T) < 32 || isfinite(x) || return zero(N)
+    isfinite(x) || return zero(N)
     reinterpret(N, _unsafe_trunc(T, round(rawone(N) * x)))
 end
 _rem(x::Float16, ::Type{X}) where {X <: Normed} = _rem(Float32(x), X)  # avoid overflow
@@ -283,8 +283,10 @@ end
 function checked_mul(x::N, y::N) where {T <: Union{UInt8,UInt16,UInt32,UInt64}, f, N <: Normed{T,f}}
     f == bitwidth(T) && return wrapping_mul(x, y)
     z = widemul(x.i, y.i)
+    # `rawone(N)` is odd, so `z` rounds to `typemax(N).i` (no overflow) up to
+    # and including `m`; overflow starts at `m + 1`.
     m = widemul(typemax(N).i, rawone(N)) + (rawone(N) >> 0x1)
-    z < m || throw_overflowerror(:*, x, y)
+    z <= m || throw_overflowerror(:*, x, y)
     N(div_2fm1(z, Val(Int(f))) % T, 0)
 end
 
diff --git a/test/common.jl b/test/common.jl
index fdd4cf7b..3a046080 100644
--- a/test/common.jl
+++ b/test/common.jl
@@ -162,9 +162,10 @@ function test_rem_type(TX::Type)
 end
 
 function test_rem_nan(TX::Type)
-    # TODO: avoid undefined behavior
     @testset "nan % $X" for X in target(TX, :i8, :i16, :i32, :i64; ex = :thin)
         @test NaN % X === NaN32 % X === NaN16 % X === zero(X)
+        @test Inf % X === Inf32 % X === Inf16 % X === zero(X)
+        @test -Inf % X === -Inf32 % X === -Inf16 % X === zero(X)
     end
 end
 
diff --git a/test/normed.jl b/test/normed.jl
index b6afb1d2..646b84b1 100644
--- a/test/normed.jl
+++ b/test/normed.jl
@@ -409,6 +409,10 @@ end
             @test_throws OverflowError checked_mul(typemax(N), typemax(N))
         end
     end
+    # products whose exact value rounds to `typemax` must not throw
+    @test checked_mul(reinterpret(N1f7, 0x9c), reinterpret(N1f7, 0xd0)) === typemax(N1f7)
+    @test checked_mul(reinterpret(N7f9, 0x0201), reinterpret(N7f9, 0xff00)) === typemax(N7f9)
+
     test_mul(Normed)
 end