fix off-by-1 in isqrt. closes #4884

JuliaLang · Dec 22, 2013 · 2e9cccb · 2e9cccb · StefanKarpinski · Dec 22, 2013
1 parent d0d4514
commit 2e9cccb
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diff --git a/base/intfuncs.jl b/base/intfuncs.jl
@@ -310,8 +310,10 @@ end
 isqrt(x::Integer) = oftype(x, trunc(sqrt(x)))
 
 function isqrt(x::Union(Int64,Uint64,Int128,Uint128))
+    x==0 && return x
     s = oftype(x, trunc(sqrt(x)))
     # fix with a Newton iteration, since conversion to float discards
     # too many bits.
-    (s + div(x,s)) >> 1
+    s = (s + div(x,s)) >> 1
+    s*s > x ? s-1 : s
 end
diff --git a/test/math.jl b/test/math.jl
@@ -190,3 +190,15 @@ end
 # isqrt (issue #4884)
 @test isqrt(9223372030926249000) == 3037000498
 @test isqrt(typemax(Int128)) == int128("13043817825332782212")
+@test isqrt(int128(typemax(Int64))^2-1) == 9223372036854775806
+@test isqrt(0) == 0
+for i = 1:1000
+    n = rand(Uint128)
+    s = isqrt(n)
+    @test s*s <= n
+    @test (s+1)*(s+1) > n
+    n = rand(Uint64)
+    s = isqrt(n)
+    @test s*s <= n
+    @test (s+1)*(s+1) > n
+end