diff --git a/src/IntervalArithmetic.jl b/src/IntervalArithmetic.jl
index e35faeea0..e65310c12 100644
--- a/src/IntervalArithmetic.jl
+++ b/src/IntervalArithmetic.jl
@@ -64,7 +64,8 @@ export
     cancelminus, cancelplus, isunbounded,
     .., @I_str, ±,
     pow, extended_div,
-    setformat, @format
+    setformat, @format , vector_sum, vector_dot,
+    vector_sumAbs, vector_sumSquare
 
 if VERSION >= v"1.5.0-DEV.124"
     import Base: isdisjoint
@@ -83,7 +84,6 @@ export showfull
 import Base: rounding, setrounding, setprecision
 
 
-
 ## Multidimensional
 export
     IntervalBox
diff --git a/src/intervals/intervals.jl b/src/intervals/intervals.jl
index 78149832a..8ef815a0a 100644
--- a/src/intervals/intervals.jl
+++ b/src/intervals/intervals.jl
@@ -137,6 +137,7 @@ include("functions.jl")
 include("trigonometric.jl")
 include("hyperbolic.jl")
 include("complex.jl")
+include("reduction.jl")
 
 # Syntax for intervals
 
diff --git a/src/intervals/reduction.jl b/src/intervals/reduction.jl
new file mode 100644
index 000000000..054dc463a
--- /dev/null
+++ b/src/intervals/reduction.jl
@@ -0,0 +1,24 @@
+# This file is part of the IntervalArithmetic.jl package; MIT licensed
+
+"""
+The file contains the reduction functions stated in the section 12.12.12 with correctly rounded results.
+r is the rounding direction which takes 0.0 for RoundingToZero , 0.5 for RoundingNearest , +Inf for RoundingUp and -Inf for RoundingDown.
+"""
+function vector_sum(v :: Vector{T} , r :: RoundingMode) where T
+    sum1 = sum(BigFloat.(v))
+    return T(sum1, r)
+end
+
+function vector_dot(v :: Vector{T}, u :: Vector{T}, r :: RoundingMode) where T
+    sum1 = sum(BigFloat.(v) .* BigFloat.(u))
+    return T(sum1, r)
+end
+
+function vector_sumAbs(v :: Vector{T} , r :: RoundingMode) where T
+    sum1 = sum(BigFloat.(abs.(v)))
+    return T(sum1, r)
+end
+
+function vector_sumSquare(v :: Vector{T} , r :: RoundingMode) where T
+    return vector_dot(v, v, r)
+end
diff --git a/test/ITF1788_tests/ITF1788_tests.jl b/test/ITF1788_tests/ITF1788_tests.jl
index 9dc6c64d4..0e66b8007 100644
--- a/test/ITF1788_tests/ITF1788_tests.jl
+++ b/test/ITF1788_tests/ITF1788_tests.jl
@@ -10,3 +10,4 @@ include("libieeep1788_tests_rev.jl")
 include("libieeep1788_tests_set.jl")
 include("mpfi.jl")
 include("fi_lib.jl")
+include("libieeep1788_reduction.jl")
\ No newline at end of file
diff --git a/test/ITF1788_tests/libieeep1788_reduction.jl b/test/ITF1788_tests/libieeep1788_reduction.jl
new file mode 100644
index 000000000..b862ddd1f
--- /dev/null
+++ b/test/ITF1788_tests/libieeep1788_reduction.jl
@@ -0,0 +1,64 @@
+#=
+ 
+ Unit tests from libieeep1788 for reduction operations
+ (Original author: Marco Nehmeier)
+ converted into portable ITL format by Oliver Heimlich.
+ 
+ Copyright 2013-2015 Marco Nehmeier (nehmeier@informatik.uni-wuerzburg.de)
+ Copyright 2015-2017 Oliver Heimlich (oheim@posteo.de)
+ 
+ Licensed under the Apache License, Version 2.0 (the "License");
+ you may not use this file except in compliance with the License.
+ You may obtain a copy of the License at
+ 
+     http://www.apache.org/licenses/LICENSE-2.0
+ 
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+ 
+=#
+#Language imports
+
+#Test library imports
+using Test
+
+#Arithmetic library imports
+using IntervalArithmetic
+
+#Preamble
+setprecision(256)
+setprecision(Interval, Float64)
+setrounding(Interval, :tight)
+# Set full format, and show decorations
+@format full
+
+@testset "minimal_sum_test" begin
+    @test vector_sum([1.0, 2.0, 3.0], RoundNearest) == 6.0
+    @test isnan(vector_sum([1.0, 2.0, NaN, 3.0], RoundNearest))
+    @test isnan(vector_sum([1.0, -Inf, 2.0, Inf, 3.0], RoundNearest))
+end
+
+@testset "minimal_sum_abs_test" begin
+    @test vector_sumAbs([1.0, -2.0, 3.0], RoundNearest) == 6.0
+    @test isnan(vector_sumAbs([1.0, -2.0, NaN, 3.0], RoundNearest))
+    @test vector_sumAbs([1.0, -Inf, 2.0, Inf, 3.0], RoundNearest) == Inf
+end
+
+@testset "minimal_sum_sqr_test" begin
+    @test vector_sumSquare([1.0, 2.0, 3.0], RoundNearest) == 14.0
+    @test isnan(vector_sumSquare([1.0, 2.0, NaN, 3.0], RoundNearest))
+    @test vector_sumSquare([1.0, -Inf, 2.0, Inf, 3.0], RoundNearest) == Inf
+end
+
+@testset "minimal_dot_test" begin
+    @test vector_dot([1.0, 2.0, 3.0], [1.0, 2.0, 3.0], RoundNearest) == 14.0
+    @test vector_dot([0x10000000000001p0, 0x1p104], [0x0fffffffffffffp0, -1.0], RoundNearest) == -1.0
+    @test isnan(vector_dot([1.0, 2.0, NaN, 3.0], [1.0, 2.0, 3.0, 4.0], RoundNearest))
+    @test isnan(vector_dot([1.0, 2.0, 3.0, 4.0], [1.0, 2.0, NaN, 3.0], RoundNearest))
+    @test isnan(vector_dot([1.0, 2.0, 0.0, 4.0], [1.0, 2.0, Inf, 3.0], RoundNearest))
+    @test isnan(vector_dot([1.0, 2.0, -Inf, 4.0], [1.0, 2.0, 0.0, 3.0], RoundNearest))
+end
+# FactCheck.exitstatus()
diff --git a/test/interval_tests/intervals.jl b/test/interval_tests/intervals.jl
index 34b557122..b90191149 100644
--- a/test/interval_tests/intervals.jl
+++ b/test/interval_tests/intervals.jl
@@ -13,3 +13,4 @@ include("parsing.jl")
 include("rounding.jl")
 include("bisect.jl")
 include("complex.jl")
+include("reduction.jl")
\ No newline at end of file
diff --git a/test/interval_tests/reduction.jl b/test/interval_tests/reduction.jl
new file mode 100644
index 000000000..c4c7e4d3f
--- /dev/null
+++ b/test/interval_tests/reduction.jl
@@ -0,0 +1,22 @@
+using IntervalArithmetic
+using Test
+
+setprecision(Interval, Float64)
+setprecision(256)
+@testset "Reduction Test" begin
+    @test vector_sum([1.0, 2.0, 3.0], RoundDown) == 6.0
+    @test isnan(vector_sum([1.0, 2.0, NaN, 3.0], RoundDown))
+    @test isnan(vector_sum([1.0, -Inf, 2.0, Inf, 3.0], RoundDown))
+    @test vector_sumAbs([1.0, -2.0, 3.0], RoundDown) == 6.0
+    @test isnan(vector_sumAbs([1.0, -2.0, NaN, 3.0], RoundDown))
+    @test vector_sumAbs([1.0, -Inf, 2.0, Inf, 3.0], RoundDown) == Inf
+    @test vector_sumSquare([1.0, 2.0, 3.0], RoundDown) == 14.0
+    @test isnan(vector_sumSquare([1.0, 2.0, NaN, 3.0], RoundDown))
+    @test vector_sumSquare([1.0, -Inf, 2.0, Inf, 3.0], RoundUp) == Inf
+    @test vector_dot([1.0, 2.0, 3.0], [1.0, 2.0, 3.0], RoundUp) == 14.0
+    @test vector_dot([0x10000000000001p0, 0x1p104], [0x0fffffffffffffp0, -1.0], RoundUp) == -1.0
+    @test isnan(vector_dot([1.0, 2.0, NaN, 3.0], [1.0, 2.0, 3.0, 4.0], RoundUp))
+    @test isnan(vector_dot([1.0, 2.0, 3.0, 4.0], [1.0, 2.0, NaN, 3.0], RoundUp))
+    @test vector_sum([sqrt(3), 5^(1/3)], RoundUp) == 3.4420267542455742
+    @test vector_sum([sqrt(3), 5^(1/3)], RoundUp) == 3.4420267542455742
+end