From ebbc3300e51388c57ccd4718ae4889c686d64e2b Mon Sep 17 00:00:00 2001
From: Andrew Kane <andrew@ankane.org>
Date: Mon, 22 Feb 2021 03:17:06 -0800
Subject: [PATCH] Fixed Math::DomainError with continuity correction

---
 lib/wilson_score.rb       |  6 ++----
 test/wilson_score_test.rb | 10 ++++++++++
 wilson_score.gemspec      |  2 +-
 3 files changed, 13 insertions(+), 5 deletions(-)

diff --git a/lib/wilson_score.rb b/lib/wilson_score.rb
index 639f059..6251cdb 100644
--- a/lib/wilson_score.rb
+++ b/lib/wilson_score.rb
@@ -16,10 +16,8 @@ def self.interval(k, n, *args)
     if correction # continuity correction
       a = 2 * (n + z2)
       b = 2*n*phat + z2
-      c = z * Math.sqrt(z2 - 1.0/n + 4*n*phat*(1 - phat) + (4*phat - 2)) + 1
-      d = z * Math.sqrt(z2 - 1.0/n + 4*n*phat*(1 - phat) - (4*phat - 2)) + 1
-      lower = phat == 0 ? 0 : [0, (b - c) / a].max
-      upper = phat == 1 ? 1 : [1, (b + d) / a].min
+      lower = phat == 0 ? 0 : [0, (b - (z * Math.sqrt(z2 - 1.0/n + 4*n*phat*(1 - phat) + (4*phat - 2)) + 1)) / a].max
+      upper = phat == 1 ? 1 : [1, (b + (z * Math.sqrt(z2 - 1.0/n + 4*n*phat*(1 - phat) - (4*phat - 2)) + 1)) / a].min
       lower..upper
     else
       a = 1 + z2 / n
diff --git a/test/wilson_score_test.rb b/test/wilson_score_test.rb
index 5f98919..4564829 100644
--- a/test/wilson_score_test.rb
+++ b/test/wilson_score_test.rb
@@ -54,6 +54,16 @@ def test_continuity_correction_one_three
     assert_in_delta 0.8747, interval.last
   end
 
+  def test_continuity_correction_p_zero
+    assert_equal 0, WilsonScore.interval(0, 25, confidence: 0.8).first
+    assert_equal 1, WilsonScore.rating_interval(1, 25, 1..5, confidence: 0.8).first
+  end
+
+  def test_continuity_correction_p_one
+    assert_equal 1, WilsonScore.interval(25, 25, confidence: 0.8).last
+    assert_equal 5, WilsonScore.rating_interval(5, 25, 1..5, confidence: 0.8).last
+  end
+
   def test_rating
     interval = WilsonScore.rating_interval(5, 1, 1..5, correction: false)
     assert_in_delta 1.8262, interval.first
diff --git a/wilson_score.gemspec b/wilson_score.gemspec
index c788109..2ca453b 100644
--- a/wilson_score.gemspec
+++ b/wilson_score.gemspec
@@ -18,7 +18,7 @@ Gem::Specification.new do |spec|
   spec.test_files    = spec.files.grep(%r{^(test|spec|features)/})
   spec.require_paths = ["lib"]
 
-  spec.add_development_dependency "bundler", "~> 1.3"
+  spec.add_development_dependency "bundler"
   spec.add_development_dependency "rake"
   spec.add_development_dependency "minitest"
 end