diff --git a/base/math/math.jl b/base/math/math.jl
index de6ef0f54cfe93..cf43bc16ea639e 100644
--- a/base/math/math.jl
+++ b/base/math/math.jl
@@ -13,16 +13,16 @@ export exp, exp2, exp10, expm1,
        cotd, cscd, secd, acotd, acscd, asecd,
        rad2deg, deg2rad,
        exponent, significand, ldexp, frexp,
-       sqrt, cbrt, ^, hypot, modf,
+       sqrt, cbrt, ^, hypot, clamp, clamp!,
        max, min, minmax,
-       clamp, clamp!, mod2pi, @evalpoly
+       modf, mod2pi, rem2pi, @evalpoly
 
 import Base: exp, exp2, exp10, expm1,
        log, log2, log10, log1p,
        sin, cos, tan, asin, acos, atan,
        sinh, cosh, tanh, asinh, acosh, atanh,
        sqrt, ^,
-       max, min, minmax, muladd
+       max, min, minmax, rem, muladd
 
 using Base: sign_mask, exponent_mask, exponent_one, exponent_bias,
       exponent_half, exponent_max, exponent_raw_max, fpinttype,
diff --git a/base/mpfr.jl b/base/mpfr.jl
index 325bc6698ea70b..cbb3884682ab6f 100644
--- a/base/mpfr.jl
+++ b/base/mpfr.jl
@@ -24,7 +24,7 @@ import Base.Rounding: rounding_raw, setrounding_raw
 
 import Base.GMP: ClongMax, CulongMax, CdoubleMax, Limb
 
-import Base.SpecFun.lgamma_r
+import Base.SpecialFunctions.lgamma_r
 
 function __init__()
     try
diff --git a/base/special/special.jl b/base/special/special.jl
index faa655591da5af..0885d7f782aae7 100644
--- a/base/special/special.jl
+++ b/base/special/special.jl
@@ -1,6 +1,6 @@
 # This file is a part of Julia. License is MIT: http://julialang.org/license
 
-module SpecFun
+module SpecialFunctions
 
 export erf, erfc, erfcx, erfi, dawson,
        lgamma, gamma, lfact,
@@ -13,7 +13,7 @@ export erf, erfc, erfcx, erfi, dawson,
        beta, lbeta, eta, zeta, polygamma, invdigamma, digamma, trigamma,
        erfinv, erfcinv
 
-import Base.Math: @horner
+using Base.Math: @horner
 
 const libm = Base.libm_name
 const openspecfun = "libopenspecfun"
diff --git a/base/sysimg.jl b/base/sysimg.jl
index 1aee3c08419d56..e0cbe5d626582d 100644
--- a/base/sysimg.jl
+++ b/base/sysimg.jl
@@ -238,7 +238,7 @@ const (∛)=cbrt
 
 # special math functions
 include("special/special.jl")
-importall .SpecFun
+importall .SpecialFunctions
 
 # reduction along dims
 include("reducedim.jl")  # macros in this file relies on string.jl
diff --git a/doc/src/stdlib/math.md b/doc/src/stdlib/math.md
index b4f9d06bf32153..01f92212272ac7 100644
--- a/doc/src/stdlib/math.md
+++ b/doc/src/stdlib/math.md
@@ -153,13 +153,6 @@ Base.flipsign
 Base.sqrt
 Base.isqrt
 Base.Math.cbrt
-Base.SpecFun.erf
-Base.SpecFun.erfc
-Base.SpecFun.erfcx
-Base.SpecFun.erfi
-Base.SpecFun.dawson
-Base.SpecFun.erfinv
-Base.SpecFun.erfcinv
 Base.real(::Complex)
 Base.imag
 Base.reim
@@ -179,44 +172,51 @@ Base.prevpow
 Base.nextprod
 Base.invmod
 Base.powermod
-Base.SpecFun.gamma
-Base.SpecFun.lgamma
-Base.SpecFun.lfact
-Base.SpecFun.digamma
-Base.SpecFun.invdigamma
-Base.SpecFun.trigamma
-Base.SpecFun.polygamma
-Base.SpecFun.airyai
-Base.SpecFun.airyaiprime
-Base.SpecFun.airyaix
-Base.SpecFun.airyaiprimex
-Base.SpecFun.airybi
-Base.SpecFun.airybiprime
-Base.SpecFun.airybix
-Base.SpecFun.airybiprimex
-Base.SpecFun.besselj0
-Base.SpecFun.besselj1
-Base.SpecFun.besselj
-Base.SpecFun.besseljx
-Base.SpecFun.bessely0
-Base.SpecFun.bessely1
-Base.SpecFun.bessely
-Base.SpecFun.besselyx
-Base.SpecFun.hankelh1
-Base.SpecFun.hankelh1x
-Base.SpecFun.hankelh2
-Base.SpecFun.hankelh2x
-Base.SpecFun.besselh
-Base.SpecFun.besselhx
-Base.SpecFun.besseli
-Base.SpecFun.besselix
-Base.SpecFun.besselk
-Base.SpecFun.besselkx
-Base.SpecFun.beta
-Base.SpecFun.lbeta
-Base.SpecFun.eta
-Base.SpecFun.zeta(::Complex)
-Base.SpecFun.zeta(::Any, ::Any)
+Base.SpecialFunctions.erf
+Base.SpecialFunctions.erfc
+Base.SpecialFunctions.erfcx
+Base.SpecialFunctions.erfi
+Base.SpecialFunctions.dawson
+Base.SpecialFunctions.erfinv
+Base.SpecialFunctions.erfcinv
+Base.SpecialFunctions.gamma
+Base.SpecialFunctions.lgamma
+Base.SpecialFunctions.lfact
+Base.SpecialFunctions.digamma
+Base.SpecialFunctions.invdigamma
+Base.SpecialFunctions.trigamma
+Base.SpecialFunctions.polygamma
+Base.SpecialFunctions.airyai
+Base.SpecialFunctions.airyaiprime
+Base.SpecialFunctions.airyaix
+Base.SpecialFunctions.airyaiprimex
+Base.SpecialFunctions.airybi
+Base.SpecialFunctions.airybiprime
+Base.SpecialFunctions.airybix
+Base.SpecialFunctions.airybiprimex
+Base.SpecialFunctions.besselj0
+Base.SpecialFunctions.besselj1
+Base.SpecialFunctions.besselj
+Base.SpecialFunctions.besseljx
+Base.SpecialFunctions.bessely0
+Base.SpecialFunctions.bessely1
+Base.SpecialFunctions.bessely
+Base.SpecialFunctions.besselyx
+Base.SpecialFunctions.hankelh1
+Base.SpecialFunctions.hankelh1x
+Base.SpecialFunctions.hankelh2
+Base.SpecialFunctions.hankelh2x
+Base.SpecialFunctions.besselh
+Base.SpecialFunctions.besselhx
+Base.SpecialFunctions.besseli
+Base.SpecialFunctions.besselix
+Base.SpecialFunctions.besselk
+Base.SpecialFunctions.besselkx
+Base.SpecialFunctions.beta
+Base.SpecialFunctions.lbeta
+Base.SpecialFunctions.eta
+Base.SpecialFunctions.zeta(::Complex)
+Base.SpecialFunctions.zeta(::Any, ::Any)
 Base.ndigits
 Base.widemul
 Base.Math.@evalpoly
diff --git a/test/math.jl b/test/math.jl
index 8faf8cb8296a42..9791f8102c4ce2 100644
--- a/test/math.jl
+++ b/test/math.jl
@@ -426,8 +426,8 @@ end
 end
 
 @testset "airy" begin
-    @test_throws Base.SpecFun.AmosException airyai(200im)
-    @test_throws Base.SpecFun.AmosException airybi(200)
+    @test_throws Base.SpecialFunctions.AmosException airyai(200im)
+    @test_throws Base.SpecialFunctions.AmosException airybi(200)
 
     for T in [Float32, Float64, Complex64,Complex128]
         @test airyai(T(1.8)) ≈ 0.0470362168668458052247
@@ -484,7 +484,7 @@ end
         @test besselh(3,2,3) ≈ conj(true_h133)
         @test besselh(-3,2,3) ≈ -conj(true_h133)
         @testset "Error throwing" begin
-            @test_throws Base.SpecFun.AmosException besselh(1,0)
+            @test_throws Base.SpecialFunctions.AmosException besselh(1,0)
             @test_throws MethodError besselh(1,big(1.0))
             @test_throws MethodError besselh(1,complex(big(1.0)))
             @test_throws MethodError besselhx(1,big(1.0))
@@ -499,7 +499,7 @@ end
         @test besseli(-3,-3) ≈ -true_i33
         @test besseli(Float32(-3),Complex64(-3,0)) ≈ -true_i33
         @testset "Error throwing" begin
-            @test_throws Base.SpecFun.AmosException besseli(1,1000)
+            @test_throws Base.SpecialFunctions.AmosException besseli(1,1000)
             @test_throws DomainError besseli(0.4,-1.0)
             @test_throws MethodError besseli(1,big(1.0))
             @test_throws MethodError besseli(1,complex(big(1.0)))
@@ -544,7 +544,7 @@ end
         @test besselj(1.0,3im) ≈ besselj(1,3im)
         @testset "Error throwing" begin
             @test_throws DomainError    besselj(0.1, -0.4)
-            @test_throws Base.SpecFun.AmosException besselj(20,1000im)
+            @test_throws Base.SpecialFunctions.AmosException besselj(20,1000im)
             @test_throws MethodError besselj(big(1.0),3im)
         end
     end
@@ -559,7 +559,7 @@ end
         # issue #6564
         @test besselk(1.0,0.0) == Inf
         @testset "Error throwing" begin
-            @test_throws Base.SpecFun.AmosException besselk(200,0.01)
+            @test_throws Base.SpecialFunctions.AmosException besselk(200,0.01)
             @test_throws DomainError besselk(3,-3)
             @test_throws MethodError besselk(1,big(1.0))
             @test_throws MethodError besselk(1,complex(big(1.0)))
@@ -577,7 +577,7 @@ end
         @test y33 ≈ -0.53854161610503161800
         @test bessely(3,complex(-3)) ≈ 0.53854161610503161800 - 0.61812544451050328724im
         @testset "Error throwing" begin
-            @test_throws Base.SpecFun.AmosException bessely(200.5,0.1)
+            @test_throws Base.SpecialFunctions.AmosException bessely(200.5,0.1)
             @test_throws DomainError bessely(3,-3)
             @test_throws DomainError bessely(0.4,-1.0)
             @test_throws DomainError bessely(0.4,Float32(-1.0))
@@ -617,11 +617,11 @@ end
         end
         @test besselkx(1, 0) == Inf
         @testset "Error throwing" begin
-            @test_throws Base.SpecFun.AmosException hankelh1x(1, 0)
-            @test_throws Base.SpecFun.AmosException hankelh2x(1, 0)
-            @test_throws Base.SpecFun.AmosException besselix(-1, 0)
-            @test_throws Base.SpecFun.AmosException besseljx(-1, 0)
-            @test_throws Base.SpecFun.AmosException besselyx(1, 0)
+            @test_throws Base.SpecialFunctions.AmosException hankelh1x(1, 0)
+            @test_throws Base.SpecialFunctions.AmosException hankelh2x(1, 0)
+            @test_throws Base.SpecialFunctions.AmosException besselix(-1, 0)
+            @test_throws Base.SpecialFunctions.AmosException besseljx(-1, 0)
+            @test_throws Base.SpecialFunctions.AmosException besselyx(1, 0)
             @test_throws DomainError besselix(0.4,-1.0)
             @test_throws DomainError besseljx(0.4, -1.0)
             @test_throws DomainError besselkx(0.4,-1.0)
@@ -996,8 +996,8 @@ end
     end
 end
 
-@test Base.SpecFun.f32(complex(1.0,1.0)) == complex(Float32(1.),Float32(1.))
-@test Base.SpecFun.f16(complex(1.0,1.0)) == complex(Float16(1.),Float16(1.))
+@test Base.SpecialFunctions.f32(complex(1.0,1.0)) == complex(Float32(1.),Float32(1.))
+@test Base.SpecialFunctions.f16(complex(1.0,1.0)) == complex(Float16(1.),Float16(1.))
 
 # no domain error is thrown for negative values
 @test invoke(cbrt, Tuple{AbstractFloat}, -1.0) == -1.0