diff --git a/base/array.jl b/base/array.jl
index e90723957afdb..4c75928b47c6f 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -130,9 +130,9 @@ to tell the compiler that indexing operations within the applied expression are
 inbounds and do not need to taint `:consistent` and `:nothrow`.
 """
 macro _safeindex(ex)
-    return esc(_safeindex(__module__, ex))
+    return esc(_safeindex(@__MODULE__, ex))
 end
-function _safeindex(__module__, ex)
+function _safeindex(mod, ex)
     isa(ex, Expr) || return ex
     if ex.head === :(=)
         lhs = ex.args[1]
@@ -141,16 +141,16 @@ function _safeindex(__module__, ex)
             xs = lhs.args[1]
             args = Vector{Any}(undef, length(lhs.args)-1)
             for i = 2:length(lhs.args)
-                args[i-1] = _safeindex(__module__, lhs.args[i])
+                args[i-1] = _safeindex(mod, lhs.args[i])
             end
-            return Expr(:call, GlobalRef(__module__, :__safe_setindex!), xs, _safeindex(__module__, rhs), args...)
+            return Expr(:call, GlobalRef(mod, :__safe_setindex!), xs, _safeindex(mod, rhs), args...)
         end
     elseif ex.head === :ref # xs[i]
-        return Expr(:call, GlobalRef(__module__, :__safe_getindex), ex.args...)
+        return Expr(:call, GlobalRef(mod, :__safe_getindex), ex.args...)
     end
     args = Vector{Any}(undef, length(ex.args))
     for i = 1:length(ex.args)
-        args[i] = _safeindex(__module__, ex.args[i])
+        args[i] = _safeindex(mod, ex.args[i])
     end
     return Expr(ex.head, args...)
 end
diff --git a/base/math.jl b/base/math.jl
index 90b6e726f4f9e..deaab18b52219 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -304,10 +304,10 @@ end
 
 # polynomial evaluation using compensated summation.
 # much more accurate, especially when lo can be combined with other rounding errors
-Base.@assume_effects :terminates_locally @inline function exthorner(x, p::Tuple)
-    hi, lo = p[end], zero(x)
-    for i in length(p)-1:-1:1
-        pi = getfield(p, i) # needed to prove consistency
+Base.@assume_effects :terminates_locally @inline function exthorner(x::T, p::Tuple{T,T,T}) where T<:Union{Float32,Float64}
+    hi, lo = Base.@_safeindex(p[lastindex(p)]), zero(x)
+    Base.@_safeindex for i in length(p)-1:-1:1
+        pi = p[i] # needed to prove consistency
         prod, err = two_mul(hi,x)
         hi = pi+prod
         lo = fma(lo, x, prod - (hi - pi) + err)
diff --git a/base/special/log.jl b/base/special/log.jl
index 488f0c89d48e3..7dd47de474d1a 100644
--- a/base/special/log.jl
+++ b/base/special/log.jl
@@ -155,14 +155,11 @@ logbU(::Type{Float64},::Val{10}) = 0.4342944819032518
 logbL(::Type{Float64},::Val{10}) = 1.098319650216765e-17
 
 # Procedure 1
-# XXX we want to mark :noub here so that this function can be concrete-folded,
-# because the effect analysis currently can't prove it in the presence of `@inbounds` or
-# `:boundscheck`, but still the access to `t_log_Float64` is really safe here
-Base.@assume_effects :consistent :noub @inline function log_proc1(y::Float64,mf::Float64,F::Float64,f::Float64,base=Val(:ℯ))
+@inline function log_proc1(y::Float64,mf::Float64,F::Float64,f::Float64,base=Val(:ℯ))
     jp = unsafe_trunc(Int,128.0*F)-127
 
     ## Steps 1 and 2
-    @inbounds hi,lo = t_log_Float64[jp]
+    Base.@_safeindex hi,lo = t_log_Float64[jp]
     l_hi = mf* 0.6931471805601177 + hi
     l_lo = mf*-1.7239444525614835e-13 + lo
 
@@ -216,14 +213,11 @@ end
 end
 
 # Procedure 1
-# XXX we want to mark :noub here so that this function can be concrete-folded,
-# because the effect analysis currently can't prove it in the presence of `@inbounds` or
-# `:boundscheck`, but still the access to `t_log_Float32` is really safe here
-Base.@assume_effects :consistent :noub @inline function log_proc1(y::Float32,mf::Float32,F::Float32,f::Float32,base=Val(:ℯ))
+@inline function log_proc1(y::Float32,mf::Float32,F::Float32,f::Float32,base=Val(:ℯ))
     jp = unsafe_trunc(Int,128.0f0*F)-127
 
     ## Steps 1 and 2
-    @inbounds hi = t_log_Float32[jp]
+    Base.@_safeindex hi = t_log_Float32[jp]
     l = mf*0.6931471805599453 + hi
 
     ## Step 3
diff --git a/base/special/rem_pio2.jl b/base/special/rem_pio2.jl
index 3086f3ebc02c9..a4c44604177a3 100644
--- a/base/special/rem_pio2.jl
+++ b/base/special/rem_pio2.jl
@@ -126,10 +126,7 @@ function fromfraction(f::Int128)
     return (z1,z2)
 end
 
-# XXX we want to mark :noub here so that this function can be concrete-folded,
-# because the effect analysis currently can't prove it in the presence of `@inbounds` or
-# `:boundscheck`, but still the accesses to `INV_2PI` are really safe here
-Base.@assume_effects :consistent :noub function paynehanek(x::Float64)
+function paynehanek(x::Float64)
     # 1. Convert to form
     #
     #    x = X * 2^k,
@@ -168,15 +165,15 @@ Base.@assume_effects :consistent :noub function paynehanek(x::Float64)
     idx = k >> 6
 
     shift = k - (idx << 6)
-    if shift == 0
-        @inbounds a1 = INV_2PI[idx+1]
-        @inbounds a2 = INV_2PI[idx+2]
-        @inbounds a3 = INV_2PI[idx+3]
+    Base.@_safeindex if shift == 0
+        a1 = INV_2PI[idx+1]
+        a2 = INV_2PI[idx+2]
+        a3 = INV_2PI[idx+3]
     else
         # use shifts to extract the relevant 64 bit window
-        @inbounds a1 = (idx < 0 ? zero(UInt64) : INV_2PI[idx+1] << shift) | (INV_2PI[idx+2] >> (64 - shift))
-        @inbounds a2 = (INV_2PI[idx+2] << shift) | (INV_2PI[idx+3] >> (64 - shift))
-        @inbounds a3 = (INV_2PI[idx+3] << shift) | (INV_2PI[idx+4] >> (64 - shift))
+        a1 = (idx < 0 ? zero(UInt64) : INV_2PI[idx+1] << shift) | (INV_2PI[idx+2] >> (64 - shift))
+        a2 = (INV_2PI[idx+2] << shift) | (INV_2PI[idx+3] >> (64 - shift))
+        a3 = (INV_2PI[idx+3] << shift) | (INV_2PI[idx+4] >> (64 - shift))
     end
 
     # 3. Perform the multiplication:
diff --git a/test/math.jl b/test/math.jl
index df5c0d23d37a4..6dfce98be751c 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -1543,9 +1543,8 @@ end
 
 @testset "constant-foldability of core math functions" begin
     for fn in (:sin, :cos, :tan, :log, :log2, :log10, :log1p, :exponent, :sqrt, :cbrt, :fourthroot,
-            :asin, :atan, :acos, :sinh, :cosh, :tanh, :asinh, :acosh, :atanh,
-            :exp, :exp2, :exp10, :expm1
-            )
+               :asin, :atan, :acos, :sinh, :cosh, :tanh, :asinh, :acosh, :atanh,
+               :exp, :exp2, :exp10, :expm1)
         for T in (Float16, Float32, Float64)
             @testset let f = getfield(@__MODULE__, fn), T = T
                 @test Core.Compiler.is_foldable(Base.infer_effects(f, (T,)))
@@ -1566,6 +1565,29 @@ end;
         end
     end
 end;
+@testset "exception type inference of core math functions" begin
+    for fn in (:sin, :cos, :tan, :log, :log2, :log10, :log1p, :exponent, :sqrt, :cbrt, :fourthroot,
+               :asin, :atan, :acos, :sinh, :cosh, :tanh, :asinh, :acosh, :atanh,
+               :exp, :exp2, :exp10, :expm1)
+        for T in (Float16, Float32, Float64)
+            @testset let f = getfield(@__MODULE__, fn), T = T
+                @test Base.exception_type(f, (T,)) <: Union{DomainError, InexactError}
+                @show f, T, Base.exception_type(f, (T,))
+            end
+        end
+    end
+end;
+@test Base.return_types((Int,)) do x
+    local r = nothing
+    try
+        r = sin(x)
+    catch err
+        if err isa DomainError
+            r = 0.0
+        end
+    end
+    return r
+end |> only === Float64
 
 @testset "BigInt Rationals with special funcs" begin
     @test sinpi(big(1//1)) == big(0.0)