fix incorrect mod rounding

base/float.jl

@@ -134,7 +134,17 @@ rem(x::Float64, y::Float64) = box(Float64,rem_float(unbox(Float64,x),unbox(Float
 
 cld{T<:FloatingPoint}(x::T, y::T) = -fld(-x,y)
 
-mod{T<:FloatingPoint}(x::T, y::T) = rem(y+rem(x,y),y)
+function mod{T<:FloatingPoint}(x::T, y::T)
+ r = rem(x,y)
+ if r == 0
+ copysign(r,y)
+ elseif (r > 0) $ (y > 0)
+ r+y
+ else
+ r
+ end
+end
+
 
 ## floating point comparisons ##
 

doc/stdlib/base.rst

@@ -2519,22 +2519,23 @@ Mathematical Operators
 
  Element-wise exponentiation operator.
 
-.. function:: div(a,b)
- ÷(a,b)
+.. function:: div(x, y)
+ ÷(x, y)
 
- Compute a/b, truncating to an integer.
+ The quotient from Euclidean division. Computes ``x/y``, truncated to an integer.
 
-.. function:: fld(a,b)
+.. function:: fld(x, y)
 
- Largest integer less than or equal to a/b.
+ Largest integer less than or equal to ``x/y``.
 
-.. function:: cld(a,b)
+.. function:: cld(x, y)
 
- Smallest integer larger than or equal to a/b.
+ Smallest integer larger than or equal to ``x/y``.
 
-.. function:: mod(x,m)
+.. function:: mod(x, y)
 
- Modulus after division, returning in the range [0,m).
+ Modulus after division, returning in the range [0,``m``), if ``m`` is
+ positive, or (``m``,0] if ``m`` is negative.
 
 .. function:: mod2pi(x)
 
@@ -2545,18 +2546,15 @@ Mathematical Operators
  mod(x,2pi), which would compute the modulus of x relative to division by the
  floating-point number 2pi.
 
-.. function:: rem(x, m)
+.. function:: rem(x, y)
+ %(x, y)
 
- Remainder after division.
+ Remainder from Euclidean division, returning a value of the same sign
+ as``x``, and smaller in magnitude than ``y``. This value is always exact.
 
 .. function:: divrem(x, y)
 
- Returns ``(x/y, x%y)``.
-
-.. _%:
-.. function:: %(x, m)
-
- Remainder after division. The operator form of ``rem``.
+ The quotient and remainder from Euclidean division. Equivalent to ``(x÷y, x%y)``.
 
 .. function:: mod1(x,m)
 

test/numbers.jl

@@ -1263,6 +1263,10 @@ end
 @test div(0.3,0.01) == 29.0
 # see https://github.com/JuliaLang/julia/issues/3127
 
+# issue #8831
+@test rem(prevfloat(1.0),1.0) == prevfloat(1.0)
+@test mod(prevfloat(1.0),1.0) == prevfloat(1.0)
+
 # issue #3046
 @test mod(int64(2),typemax(Int64)) == 2