diff --git a/base/gmp.jl b/base/gmp.jl
index 70c63e273b2d7..26db033879c7d 100644
--- a/base/gmp.jl
+++ b/base/gmp.jl
@@ -8,7 +8,8 @@ import Base: *, +, -, /, <, <<, >>, >>>, <=, ==, >, >=, ^, (~), (&), (|), ($),
              binomial, cmp, convert, div, divrem, factorial, fld, gcd, gcdx, lcm, mod,
              ndigits, promote_rule, rem, show, isqrt, string, powermod,
              sum, trailing_zeros, trailing_ones, count_ones, base, tryparse_internal,
-             bin, oct, dec, hex, isequal, invmod, prevpow2, nextpow2, ndigits0z, widen, signed, unsafe_trunc, trunc
+             bin, oct, dec, hex, isequal, invmod, prevpow2, nextpow2, ndigits0z,
+             ndigits0znb, widen, signed, unsafe_trunc, trunc
 
 if Clong == Int32
     typealias ClongMax Union{Int8, Int16, Int32}
@@ -526,6 +527,7 @@ end
 
 function ndigits0z(x::BigInt, b::Integer=10)
     b < 2 && throw(DomainError())
+    x.size == 0 && return 0 # for consistency with other ndigits0z methods
     if ispow2(b) && 2 <= b <= 62 # GMP assumes b is in this range
         Int(ccall((:__gmpz_sizeinbase,:libgmp), Csize_t, (Ptr{BigInt}, Cint), &x, b))
     else
@@ -545,7 +547,6 @@ function ndigits0z(x::BigInt, b::Integer=10)
         end
     end
 end
-ndigits(x::BigInt, b::Integer=10) = x.size == 0 ? 1 : ndigits0z(x,b)
 
 prevpow2(x::BigInt) = x.size < 0 ? -prevpow2(-x) : (x <= 2 ? x : one(BigInt) << (ndigits(x, 2)-1))
 nextpow2(x::BigInt) = x.size < 0 ? -nextpow2(-x) : (x <= 2 ? x : one(BigInt) << ndigits(x-1, 2))
diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index a46a3046be5a8..b352e65c1ae5a 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -216,10 +216,13 @@ function ndigits0z(x::UInt128)
     return n + ndigits0z(UInt64(x))
 end
 ndigits0z(x::Integer) = ndigits0z(unsigned(abs(x)))
+ndigits(x::Integer) = x==0 ? 1 : ndigits0z(x)
 
 const ndigits_max_mul = Core.sizeof(Int) == 4 ? 69000000 : 290000000000000000
 
-function ndigits0znb(n::Signed, b::Int)
+# The suffix "nb" stands for "negative base"
+function ndigits0znb(n::Integer, b::Integer)
+    # precondition: b < -1 && !(typeof(n) <: Unsigned)
     d = 0
     while n != 0
         n = cld(n,b)
@@ -228,36 +231,38 @@ function ndigits0znb(n::Signed, b::Int)
     return d
 end
 
+ndigits0znb(n::Unsigned, b::Integer) = ndigits0znb(signed(n), b)
+
 function ndigits0z(n::Unsigned, b::Int)
+    # precondition: b > 1
     d = 0
-    if b < 0
-        d = ndigits0znb(signed(n), b)
-    else
-        b == 2  && return (sizeof(n)<<3-leading_zeros(n))
-        b == 8  && return div((sizeof(n)<<3)-leading_zeros(n)+2,3)
-        b == 16 && return (sizeof(n)<<1)-(leading_zeros(n)>>2)
-        b == 10 && return ndigits0z(n)
-        while ndigits_max_mul < n
-            n = div(n,b)
-            d += 1
-        end
-        m = 1
-        while m <= n
-            m *= b
-            d += 1
-        end
+    b == 2  && return (sizeof(n)<<3-leading_zeros(n))
+    b == 8  && return div((sizeof(n)<<3)-leading_zeros(n)+2,3)
+    b == 16 && return (sizeof(n)<<1)-(leading_zeros(n)>>2)
+    b == 10 && return ndigits0z(n)
+    while ndigits_max_mul < n
+        n = div(n,b)
+        d += 1
+    end
+    m = 1
+    while m <= n
+        m *= b
+        d += 1
     end
     return d
 end
-ndigits0z(x::Integer, b::Integer) = ndigits0z(unsigned(abs(x)),Int(b))
 
-ndigitsnb(x::Integer, b::Integer) = x==0 ? 1 : ndigits0znb(x, b)
+ndigits0z(x::Integer, b::Integer) = ndigits0z(unsigned(abs(x)), Int(b))
 
-ndigits(x::Unsigned, b::Integer) = x==0 ? 1 : ndigits0z(x,Int(b))
-ndigits(x::Unsigned)             = x==0 ? 1 : ndigits0z(x)
-
-ndigits(x::Integer, b::Integer) = b >= 0 ? ndigits(unsigned(abs(x)),Int(b)) : ndigitsnb(x, b)
-ndigits(x::Integer) = ndigits(unsigned(abs(x)))
+function ndigits(x::Integer, b::Integer)
+    if b < -1
+        x == 0 ? 1 : ndigits0znb(x, b)
+    elseif b > 1
+        x == 0 ? 1 : ndigits0z(x, b)
+    else
+        throw(DomainError())
+    end
+end
 
 ## integer to string functions ##
 
@@ -352,7 +357,6 @@ bits(x::Union{Int128,UInt128})            = bin(reinterpret(UInt128,x),128)
 digits{T<:Integer}(n::Integer, base::T=10, pad::Integer=1) = digits(T, n, base, pad)
 
 function digits{T<:Integer}(::Type{T}, n::Integer, base::Integer=10, pad::Integer=1)
-    2 <= base || throw(ArgumentError("base must be ≥ 2, got $base"))
     digits!(zeros(T, max(pad, ndigits0z(n,base))), n, base)
 end
 
diff --git a/test/bigint.jl b/test/bigint.jl
index 0478b28f8b286..4f29b748ac048 100644
--- a/test/bigint.jl
+++ b/test/bigint.jl
@@ -275,10 +275,10 @@ ndigits_mismatch(n) = ndigits(n) != ndigits(BigInt(n))
 @test !any(ndigits_mismatch, 8192:9999)
 
 # The following should not crash (#16579)
-ndigits(rand(big(-999:999)), rand(63:typemax(Int)))
-ndigits(rand(big(-999:999)), big(2)^rand(2:999))
+ndigits(big(rand(Int)), rand(63:typemax(Int)))
+ndigits(big(rand(Int)), big(2)^rand(2:999))
 
-for i in big([-20:-1;1:20])
+for i in big([-20:-1;1:20; rand(Int)])
     for b in -10:1
         @test_throws DomainError ndigits(i, b)
     end
diff --git a/test/intfuncs.jl b/test/intfuncs.jl
index 822bad6805a07..6eb976cbcc316 100644
--- a/test/intfuncs.jl
+++ b/test/intfuncs.jl
@@ -84,8 +84,14 @@ end
 
 @test ndigits(146, -3) == 5
 
-let n = rand(Int)
+let (n, b) = rand(Int, 2)
+    -1 <= b <= 1 && (b = 2) # invalid bases
     @test ndigits(n) == ndigits(big(n)) == ndigits(n, 10)
+    @test ndigits(n, b) == ndigits(big(n), b)
+end
+
+for b in -1:1
+    @test_throws DomainError ndigits(rand(Int), b)
 end
 
 @test bin('3') == "110011"