require File.expand_path('../../../spec_helper', __FILE__)

describe "Math.gamma" do
  before :all do
    @factorial1 = 1
    @factorial2 = 1124000727777607680000  # 22!
  end

  it "returns +infinity given 0" do
    Math.gamma(0).should == Float::INFINITY
  end

  it "returns -infinity given -0.0" do
    Math.gamma(-0.0).should == -Float::INFINITY
  end

  it "returns Math.sqrt(Math::PI) given 0.5" do
    Math.gamma(0.5).should be_close(Math.sqrt(Math::PI), TOLERANCE)
  end

  # stop at n == 23 because 23! cannot be exactly represented by IEEE 754 double
  2.upto(23) do |n|
    it "returns exactly #{n-1}! given #{n}" do
      @factorial1 *= n - 1
      Math.gamma(n).should == @factorial1
    end
  end

  24.upto(30) do |n|
    it "returns approximately #{n-1}! given #{n}" do
      @factorial2 *= n - 1
      # compare only the first 12 places, tolerate the rest
      Math.gamma(n).should be_close(@factorial2, @factorial2.to_s[12..-1].to_i)
    end
  end

  it "returns good numerical approximation for gamma(3.2)" do
    Math.gamma(3.2).should be_close(2.423965, TOLERANCE)
  end

  it "returns good numerical approximation for gamma(-2.15)" do
    Math.gamma(-2.15).should be_close(-2.999619, TOLERANCE)
  end

  it "returns good numerical approximation for gamma(0.00001)" do
    Math.gamma(0.00001).should be_close(99999.422794, TOLERANCE)
  end

  it "returns good numerical approximation for gamma(-0.00001)" do
    Math.gamma(-0.00001).should be_close(-100000.577225, TOLERANCE)
  end

  it "raises Math::DomainError given -1" do
    lambda { Math.gamma(-1) }.should raise_error(Math::DomainError)
  end

  # See http://redmine.ruby-lang.org/issues/show/2189
  it "returns +infinity given +infinity" do
    Math.gamma(infinity_value).infinite?.should == 1
  end

  it "raises Math::DomainError given negative infinity" do
    lambda { Math.gamma(-Float::INFINITY) }.should raise_error(Math::DomainError)
  end

  it "returns NaN given NaN" do
    Math.gamma(nan_value).nan?.should be_true
  end
end
