Fix(VIM-3827): Fix an incorrect implementation of the >= operator

As a note: This is the first bug in IdeaVim that was fixed by AI (with manual verification, of course).

src/test/java/org/jetbrains/plugins/ideavim/ex/implementation/expressions/operators/GreaterOrEqualsOperatorTest.kt

@@ -0,0 +1,49 @@
+/*
+ * Copyright 2003-2025 The IdeaVim authors
+ *
+ * Use of this source code is governed by an MIT-style
+ * license that can be found in the LICENSE.txt file or at
+ * https://opensource.org/licenses/MIT.
+ */
+
+package org.jetbrains.plugins.ideavim.ex.implementation.expressions.operators
+
+import com.maddyhome.idea.vim.vimscript.model.datatypes.VimInt
+import com.maddyhome.idea.vim.vimscript.parser.VimscriptParser
+import org.jetbrains.plugins.ideavim.VimTestCase
+import org.jetbrains.plugins.ideavim.ex.evaluate
+import org.junit.jupiter.api.Test
+import kotlin.test.assertEquals
+
+class GreaterOrEqualsOperatorTest : VimTestCase() {
+
+  @Test
+  fun `test equal numbers`() {
+    assertEquals(VimInt(1), VimscriptParser.parseExpression("1 >= 1")!!.evaluate())
+  }
+
+  @Test
+  fun `test greater number`() {
+    assertEquals(VimInt(1), VimscriptParser.parseExpression("2 >= 1")!!.evaluate())
+  }
+
+  @Test
+  fun `test smaller number`() {
+    assertEquals(VimInt(0), VimscriptParser.parseExpression("1 >= 2")!!.evaluate())
+  }
+
+  @Test
+  fun `test equal strings`() {
+    assertEquals(VimInt(1), VimscriptParser.parseExpression("'abc' >= 'abc'")!!.evaluate())
+  }
+
+  @Test
+  fun `test greater string`() {
+    assertEquals(VimInt(1), VimscriptParser.parseExpression("'def' >= 'abc'")!!.evaluate())
+  }
+
+  @Test
+  fun `test smaller string`() {
+    assertEquals(VimInt(0), VimscriptParser.parseExpression("'abc' >= 'def'")!!.evaluate())
+  }
+}

vim-engine/src/main/kotlin/com/maddyhome/idea/vim/vimscript/model/expressions/operators/handlers/binary/GreaterOrEqualsCaseSensitiveHandler.kt

@@ -16,9 +16,9 @@ object GreaterOrEqualsCaseSensitiveHandler : BinaryOperatorHandler() {
 
   override fun performOperation(left: VimDataType, right: VimDataType): VimDataType {
     return if (left is VimString || right is VimString) {
-      VimInt(if (left.asString() < right.asString()) 0 else 1)
+      VimInt(if (left.asString() >= right.asString()) 1 else 0)
     } else {
-      VimInt(if (left.asDouble() < right.asDouble()) 0 else 1)
+      VimInt(if (left.asDouble() >= right.asDouble()) 1 else 0)
     }
   }
 }

vim-engine/src/main/kotlin/com/maddyhome/idea/vim/vimscript/model/expressions/operators/handlers/binary/GreaterOrEqualsHandler.kt

@@ -9,4 +9,4 @@
 package com.maddyhome.idea.vim.vimscript.model.expressions.operators.handlers.binary
 
 object GreaterOrEqualsHandler :
-  BinaryOperatorWithIgnoreCaseOption(GreaterIgnoreCaseHandler, GreaterCaseSensitiveHandler)
+  BinaryOperatorWithIgnoreCaseOption(GreaterOrEqualsIgnoreCaseHandler, GreaterOrEqualsCaseSensitiveHandler)

vim-engine/src/main/kotlin/com/maddyhome/idea/vim/vimscript/model/expressions/operators/handlers/binary/GreaterOrEqualsIgnoreCaseHandler.kt

@@ -16,9 +16,9 @@ object GreaterOrEqualsIgnoreCaseHandler : BinaryOperatorHandler() {
 
   override fun performOperation(left: VimDataType, right: VimDataType): VimDataType {
     return if (left is VimString || right is VimString) {
-      VimInt(if (left.asString().compareTo(right.asString(), ignoreCase = true) < 0) 0 else 1)
+      VimInt(if (left.asString().compareTo(right.asString(), ignoreCase = true) >= 0) 1 else 0)
     } else {
-      VimInt(if (left.asDouble() < right.asDouble()) 0 else 1)
+      VimInt(if (left.asDouble() >= right.asDouble()) 1 else 0)
     }
   }
 }