diff --git a/.github/workflows/gradle.yml b/.github/workflows/gradle.yml
new file mode 100644
index 0000000..78510fc
--- /dev/null
+++ b/.github/workflows/gradle.yml
@@ -0,0 +1,35 @@
+name: Testing on various Java versions on Linux, Windows, and MacOS
+
+on:
+  push:
+    branches: [ "master" ]
+  pull_request:
+    branches: [ "master" ]
+
+permissions:
+  contents: read
+
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        os: [ windows-latest, macos-latest, ubuntu-latest ]
+        jdk: [ 11, 17, 20 ]
+    steps:
+    - uses: actions/checkout@v3
+    - name: Set up JDK ${{ matrix.jdk }}
+      uses: actions/setup-java@v3
+      with:
+        java-version: ${{ matrix.jdk }}
+        distribution: 'temurin'
+    - name: Build with Gradle
+      uses: gradle/gradle-build-action@bd5760595778326ba7f1441bcf7e88b49de61a25 # v2.6.0
+      with:
+        arguments: build
+    - name: Store test results
+      if: failure()
+      uses: actions/upload-artifact@v3
+      with:
+        name: test-results
+        path: build/reports
\ No newline at end of file
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..efd6738
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,4 @@
+/.idea
+/.gradle
+/build
+/out
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..6a49c50
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2023 knokko
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/build.gradle b/build.gradle
new file mode 100644
index 0000000..506300f
--- /dev/null
+++ b/build.gradle
@@ -0,0 +1,34 @@
+plugins {
+    id 'java'
+    id 'org.jetbrains.kotlin.jvm' version '1.9.0'
+}
+
+apply plugin: 'java'
+apply plugin: 'org.jetbrains.kotlin.jvm'
+
+repositories {
+    mavenCentral()
+}
+
+compileKotlin {
+    kotlinOptions.jvmTarget = "11"
+}
+
+compileTestKotlin {
+    kotlinOptions.jvmTarget = "11"
+}
+
+java {
+    sourceCompatibility = "11"
+    targetCompatibility = "11"
+}
+
+dependencies {
+    testImplementation platform('org.junit:junit-bom:5.10.0')
+    testImplementation 'org.junit.jupiter:junit-jupiter:5.10.0'
+    testRuntimeOnly("org.junit.platform:junit-platform-launcher")
+}
+
+test {
+    useJUnitPlatform()
+}
diff --git a/gradle/wrapper/gradle-wrapper.jar b/gradle/wrapper/gradle-wrapper.jar
new file mode 100644
index 0000000..033e24c
Binary files /dev/null and b/gradle/wrapper/gradle-wrapper.jar differ
diff --git a/gradle/wrapper/gradle-wrapper.properties b/gradle/wrapper/gradle-wrapper.properties
new file mode 100644
index 0000000..62f495d
--- /dev/null
+++ b/gradle/wrapper/gradle-wrapper.properties
@@ -0,0 +1,7 @@
+distributionBase=GRADLE_USER_HOME
+distributionPath=wrapper/dists
+distributionUrl=https\://services.gradle.org/distributions/gradle-8.2-bin.zip
+networkTimeout=10000
+validateDistributionUrl=true
+zipStoreBase=GRADLE_USER_HOME
+zipStorePath=wrapper/dists
diff --git a/gradlew b/gradlew
new file mode 100644
index 0000000..fcb6fca
--- /dev/null
+++ b/gradlew
@@ -0,0 +1,248 @@
+#!/bin/sh
+
+#
+# Copyright © 2015-2021 the original authors.
+#
+# 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
+#
+#      https://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.
+#
+
+##############################################################################
+#
+#   Gradle start up script for POSIX generated by Gradle.
+#
+#   Important for running:
+#
+#   (1) You need a POSIX-compliant shell to run this script. If your /bin/sh is
+#       noncompliant, but you have some other compliant shell such as ksh or
+#       bash, then to run this script, type that shell name before the whole
+#       command line, like:
+#
+#           ksh Gradle
+#
+#       Busybox and similar reduced shells will NOT work, because this script
+#       requires all of these POSIX shell features:
+#         * functions;
+#         * expansions «$var», «${var}», «${var:-default}», «${var+SET}»,
+#           «${var#prefix}», «${var%suffix}», and «$( cmd )»;
+#         * compound commands having a testable exit status, especially «case»;
+#         * various built-in commands including «command», «set», and «ulimit».
+#
+#   Important for patching:
+#
+#   (2) This script targets any POSIX shell, so it avoids extensions provided
+#       by Bash, Ksh, etc; in particular arrays are avoided.
+#
+#       The "traditional" practice of packing multiple parameters into a
+#       space-separated string is a well documented source of bugs and security
+#       problems, so this is (mostly) avoided, by progressively accumulating
+#       options in "$@", and eventually passing that to Java.
+#
+#       Where the inherited environment variables (DEFAULT_JVM_OPTS, JAVA_OPTS,
+#       and GRADLE_OPTS) rely on word-splitting, this is performed explicitly;
+#       see the in-line comments for details.
+#
+#       There are tweaks for specific operating systems such as AIX, CygWin,
+#       Darwin, MinGW, and NonStop.
+#
+#   (3) This script is generated from the Groovy template
+#       https://github.com/gradle/gradle/blob/HEAD/subprojects/plugins/src/main/resources/org/gradle/api/internal/plugins/unixStartScript.txt
+#       within the Gradle project.
+#
+#       You can find Gradle at https://github.com/gradle/gradle/.
+#
+##############################################################################
+
+# Attempt to set APP_HOME
+
+# Resolve links: $0 may be a link
+app_path=$0
+
+# Need this for daisy-chained symlinks.
+while
+    APP_HOME=${app_path%"${app_path##*/}"}  # leaves a trailing /; empty if no leading path
+    [ -h "$app_path" ]
+do
+    ls=$( ls -ld "$app_path" )
+    link=${ls#*' -> '}
+    case $link in             #(
+      /*)   app_path=$link ;; #(
+      *)    app_path=$APP_HOME$link ;;
+    esac
+done
+
+# This is normally unused
+# shellcheck disable=SC2034
+APP_BASE_NAME=${0##*/}
+APP_HOME=$( cd "${APP_HOME:-./}" && pwd -P ) || exit
+
+# Use the maximum available, or set MAX_FD != -1 to use that value.
+MAX_FD=maximum
+
+warn () {
+    echo "$*"
+} >&2
+
+die () {
+    echo
+    echo "$*"
+    echo
+    exit 1
+} >&2
+
+# OS specific support (must be 'true' or 'false').
+cygwin=false
+msys=false
+darwin=false
+nonstop=false
+case "$( uname )" in                #(
+  CYGWIN* )         cygwin=true  ;; #(
+  Darwin* )         darwin=true  ;; #(
+  MSYS* | MINGW* )  msys=true    ;; #(
+  NONSTOP* )        nonstop=true ;;
+esac
+
+CLASSPATH=$APP_HOME/gradle/wrapper/gradle-wrapper.jar
+
+
+# Determine the Java command to use to start the JVM.
+if [ -n "$JAVA_HOME" ] ; then
+    if [ -x "$JAVA_HOME/jre/sh/java" ] ; then
+        # IBM's JDK on AIX uses strange locations for the executables
+        JAVACMD=$JAVA_HOME/jre/sh/java
+    else
+        JAVACMD=$JAVA_HOME/bin/java
+    fi
+    if [ ! -x "$JAVACMD" ] ; then
+        die "ERROR: JAVA_HOME is set to an invalid directory: $JAVA_HOME
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+    fi
+else
+    JAVACMD=java
+    if ! command -v java >/dev/null 2>&1
+    then
+        die "ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+    fi
+fi
+
+# Increase the maximum file descriptors if we can.
+if ! "$cygwin" && ! "$darwin" && ! "$nonstop" ; then
+    case $MAX_FD in #(
+      max*)
+        # In POSIX sh, ulimit -H is undefined. That's why the result is checked to see if it worked.
+        # shellcheck disable=SC3045
+        MAX_FD=$( ulimit -H -n ) ||
+            warn "Could not query maximum file descriptor limit"
+    esac
+    case $MAX_FD in  #(
+      '' | soft) :;; #(
+      *)
+        # In POSIX sh, ulimit -n is undefined. That's why the result is checked to see if it worked.
+        # shellcheck disable=SC3045
+        ulimit -n "$MAX_FD" ||
+            warn "Could not set maximum file descriptor limit to $MAX_FD"
+    esac
+fi
+
+# Collect all arguments for the java command, stacking in reverse order:
+#   * args from the command line
+#   * the main class name
+#   * -classpath
+#   * -D...appname settings
+#   * --module-path (only if needed)
+#   * DEFAULT_JVM_OPTS, JAVA_OPTS, and GRADLE_OPTS environment variables.
+
+# For Cygwin or MSYS, switch paths to Windows format before running java
+if "$cygwin" || "$msys" ; then
+    APP_HOME=$( cygpath --path --mixed "$APP_HOME" )
+    CLASSPATH=$( cygpath --path --mixed "$CLASSPATH" )
+
+    JAVACMD=$( cygpath --unix "$JAVACMD" )
+
+    # Now convert the arguments - kludge to limit ourselves to /bin/sh
+    for arg do
+        if
+            case $arg in                                #(
+              -*)   false ;;                            # don't mess with options #(
+              /?*)  t=${arg#/} t=/${t%%/*}              # looks like a POSIX filepath
+                    [ -e "$t" ] ;;                      #(
+              *)    false ;;
+            esac
+        then
+            arg=$( cygpath --path --ignore --mixed "$arg" )
+        fi
+        # Roll the args list around exactly as many times as the number of
+        # args, so each arg winds up back in the position where it started, but
+        # possibly modified.
+        #
+        # NB: a `for` loop captures its iteration list before it begins, so
+        # changing the positional parameters here affects neither the number of
+        # iterations, nor the values presented in `arg`.
+        shift                   # remove old arg
+        set -- "$@" "$arg"      # push replacement arg
+    done
+fi
+
+
+# Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+DEFAULT_JVM_OPTS='"-Xmx64m" "-Xms64m"'
+
+# Collect all arguments for the java command;
+#   * $DEFAULT_JVM_OPTS, $JAVA_OPTS, and $GRADLE_OPTS can contain fragments of
+#     shell script including quotes and variable substitutions, so put them in
+#     double quotes to make sure that they get re-expanded; and
+#   * put everything else in single quotes, so that it's not re-expanded.
+
+set -- \
+        "-Dorg.gradle.appname=$APP_BASE_NAME" \
+        -classpath "$CLASSPATH" \
+        org.gradle.wrapper.GradleWrapperMain \
+        "$@"
+
+# Stop when "xargs" is not available.
+if ! command -v xargs >/dev/null 2>&1
+then
+    die "xargs is not available"
+fi
+
+# Use "xargs" to parse quoted args.
+#
+# With -n1 it outputs one arg per line, with the quotes and backslashes removed.
+#
+# In Bash we could simply go:
+#
+#   readarray ARGS < <( xargs -n1 <<<"$var" ) &&
+#   set -- "${ARGS[@]}" "$@"
+#
+# but POSIX shell has neither arrays nor command substitution, so instead we
+# post-process each arg (as a line of input to sed) to backslash-escape any
+# character that might be a shell metacharacter, then use eval to reverse
+# that process (while maintaining the separation between arguments), and wrap
+# the whole thing up as a single "set" statement.
+#
+# This will of course break if any of these variables contains a newline or
+# an unmatched quote.
+#
+
+eval "set -- $(
+        printf '%s\n' "$DEFAULT_JVM_OPTS $JAVA_OPTS $GRADLE_OPTS" |
+        xargs -n1 |
+        sed ' s~[^-[:alnum:]+,./:=@_]~\\&~g; ' |
+        tr '\n' ' '
+    )" '"$@"'
+
+exec "$JAVACMD" "$@"
diff --git a/gradlew.bat b/gradlew.bat
new file mode 100644
index 0000000..93e3f59
--- /dev/null
+++ b/gradlew.bat
@@ -0,0 +1,92 @@
+@rem
+@rem Copyright 2015 the original author or authors.
+@rem
+@rem Licensed under the Apache License, Version 2.0 (the "License");
+@rem you may not use this file except in compliance with the License.
+@rem You may obtain a copy of the License at
+@rem
+@rem      https://www.apache.org/licenses/LICENSE-2.0
+@rem
+@rem Unless required by applicable law or agreed to in writing, software
+@rem distributed under the License is distributed on an "AS IS" BASIS,
+@rem WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+@rem See the License for the specific language governing permissions and
+@rem limitations under the License.
+@rem
+
+@if "%DEBUG%"=="" @echo off
+@rem ##########################################################################
+@rem
+@rem  Gradle startup script for Windows
+@rem
+@rem ##########################################################################
+
+@rem Set local scope for the variables with windows NT shell
+if "%OS%"=="Windows_NT" setlocal
+
+set DIRNAME=%~dp0
+if "%DIRNAME%"=="" set DIRNAME=.
+@rem This is normally unused
+set APP_BASE_NAME=%~n0
+set APP_HOME=%DIRNAME%
+
+@rem Resolve any "." and ".." in APP_HOME to make it shorter.
+for %%i in ("%APP_HOME%") do set APP_HOME=%%~fi
+
+@rem Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+set DEFAULT_JVM_OPTS="-Xmx64m" "-Xms64m"
+
+@rem Find java.exe
+if defined JAVA_HOME goto findJavaFromJavaHome
+
+set JAVA_EXE=java.exe
+%JAVA_EXE% -version >NUL 2>&1
+if %ERRORLEVEL% equ 0 goto execute
+
+echo.
+echo ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:findJavaFromJavaHome
+set JAVA_HOME=%JAVA_HOME:"=%
+set JAVA_EXE=%JAVA_HOME%/bin/java.exe
+
+if exist "%JAVA_EXE%" goto execute
+
+echo.
+echo ERROR: JAVA_HOME is set to an invalid directory: %JAVA_HOME%
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:execute
+@rem Setup the command line
+
+set CLASSPATH=%APP_HOME%\gradle\wrapper\gradle-wrapper.jar
+
+
+@rem Execute Gradle
+"%JAVA_EXE%" %DEFAULT_JVM_OPTS% %JAVA_OPTS% %GRADLE_OPTS% "-Dorg.gradle.appname=%APP_BASE_NAME%" -classpath "%CLASSPATH%" org.gradle.wrapper.GradleWrapperMain %*
+
+:end
+@rem End local scope for the variables with windows NT shell
+if %ERRORLEVEL% equ 0 goto mainEnd
+
+:fail
+rem Set variable GRADLE_EXIT_CONSOLE if you need the _script_ return code instead of
+rem the _cmd.exe /c_ return code!
+set EXIT_CODE=%ERRORLEVEL%
+if %EXIT_CODE% equ 0 set EXIT_CODE=1
+if not ""=="%GRADLE_EXIT_CONSOLE%" exit %EXIT_CODE%
+exit /b %EXIT_CODE%
+
+:mainEnd
+if "%OS%"=="Windows_NT" endlocal
+
+:omega
diff --git a/jitpack.yml b/jitpack.yml
new file mode 100644
index 0000000..46c8529
--- /dev/null
+++ b/jitpack.yml
@@ -0,0 +1,2 @@
+jdk:
+  - openjdk11
\ No newline at end of file
diff --git a/settings.gradle b/settings.gradle
new file mode 100644
index 0000000..9ee668b
--- /dev/null
+++ b/settings.gradle
@@ -0,0 +1 @@
+rootProject.name = 'fixie'
diff --git a/src/main/kotlin/fixie/FixNano64.kt b/src/main/kotlin/fixie/FixNano64.kt
new file mode 100644
index 0000000..1103bd1
--- /dev/null
+++ b/src/main/kotlin/fixie/FixNano64.kt
@@ -0,0 +1,223 @@
+package fixie
+
+import java.math.BigInteger
+import kotlin.math.absoluteValue
+import kotlin.math.roundToLong
+
+private const val RAW_ONE = 1024L * 1024L * 1024L
+
+@JvmInline
+value class FixNano64 private constructor(val raw: Long): Comparable<FixNano64> {
+
+    @Throws(ArithmeticException::class)
+    fun toInt() = Math.toIntExact(toLong())
+
+    fun toLong() = raw / RAW_ONE
+
+    fun toFloat() = toDouble().toFloat()
+
+    fun toDouble() = raw / RAW_ONE.toDouble()
+
+    @Throws(FixedPointException::class)
+    operator fun unaryMinus() = if (raw != Long.MIN_VALUE) FixNano64(-raw) else throw FixedPointException("negating Long.MIN_VALUE")
+
+    @Throws(FixedPointException::class)
+    operator fun plus(other: FixNano64): FixNano64 {
+        try {
+            return FixNano64(Math.addExact(raw, other.raw))
+        } catch (overflow: ArithmeticException) {
+            throw FixedPointException("Tried to compute $this + $other")
+        }
+    }
+
+    @Throws(FixedPointException::class)
+    operator fun minus(right: FixNano64): FixNano64 {
+        try {
+            return FixNano64(Math.subtractExact(raw, right.raw))
+        } catch (overflow: ArithmeticException) {
+            throw FixedPointException("Tried to compute $this - $right")
+        }
+    }
+
+    operator fun times(other: Int) = this * other.toLong()
+
+    operator fun times(other: Long): FixNano64 {
+        try {
+            return FixNano64(Math.multiplyExact(raw, other))
+        } catch (overflow: ArithmeticException) {
+            throw FixedPointException("Tried to compute $this * $other")
+        }
+    }
+
+    operator fun times(other: Float) = this * fromFloat(other)
+
+    operator fun times(other: Double) = this * fromDouble(other)
+
+    operator fun times(other: FixNano64): FixNano64 {
+        /*
+         * Theoretically:
+         *   this = this.raw * 2^-30
+         *   other = other.raw * 2^-30
+         *   result = this * other = this.raw * other.raw * 2^-60 -> result.raw = this.raw * other.raw * 2^-30
+         *
+         * Practically, computing this.raw * other.raw could overflow, so we need a more complicated approach...
+         */
+
+        val highProductBits = Math.multiplyHigh(this.raw, other.raw)
+        if (highProductBits < -(1 shl 29) || highProductBits >= (1 shl 29)) {
+            throw FixedPointException("Attempted to compute $this * $other")
+        }
+
+        val lowProductBits = this.raw * other.raw
+
+        return FixNano64((lowProductBits ushr 30) or (highProductBits shl 34))
+    }
+
+    operator fun div(other: Int) = this / other.toLong()
+
+    operator fun div(other: Long): FixNano64 {
+        if (other == -1L && raw == Long.MIN_VALUE) throw FixedPointException("Attempted to compute $this / -1")
+        if (other == 0L) throw FixedPointException("Attempted to compute $this / 0")
+        return FixNano64(raw / other)
+    }
+
+    operator fun div(other: Float) = this / other.toDouble()
+
+    operator fun div(other: Double): FixNano64 {
+        val doubleResult = this.raw.toDouble() / other
+        if (doubleResult >= Long.MIN_VALUE.toDouble() && doubleResult <= Long.MAX_VALUE.toDouble()) {
+            return FixNano64(doubleResult.roundToLong())
+        } else {
+            throw FixedPointException("Attempted to compute $this / $other")
+        }
+    }
+
+    operator fun div(other: FixNano64): FixNano64 {
+        /*
+         * Theoretically:
+         *   this = this.raw * 2^-30
+         *   other = other.raw * 2^-30
+         *   result = this / other = this.raw / other.raw -> result.raw = 2^30 * this.raw / other.raw
+         *
+         * Practically, computing 2^30 * this.raw could overflow, so we need a more complicated approach...
+         * Unfortunately, I couldn't find a way that avoids BigInteger, so this will be rather slow.
+         */
+
+        // TODO Optimize case when this.raw * 2^30 doesn't overflow
+        val product = BigInteger.valueOf(this.raw) shl 30
+        val bigResult = product / BigInteger.valueOf(other.raw)
+        try {
+            return FixNano64(bigResult.longValueExact())
+        } catch (overflow: ArithmeticException) {
+            throw FixedPointException("Attempted to compute $this / $other")
+        }
+    }
+
+    override fun compareTo(other: FixNano64) = raw.compareTo(other.raw)
+
+    override fun toString(): String {
+        if (raw == Long.MIN_VALUE) return "MIN"
+        if (raw == Long.MAX_VALUE) return "MAX"
+
+        var remaining = (raw.absoluteValue.toBigInteger() * (1000L * 1000L * 1000L).toBigInteger() shr 30).toLong()
+
+        val signString = if (raw < 0) "-" else ""
+
+        if (remaining < 1000) return signString + remaining + "n"
+
+        var numShifts = 0
+        while (remaining / 1_000_000L != 0L) {
+            val shouldRoundUp = (remaining % 1000) >= 500
+            remaining /= 1000
+            if (shouldRoundUp) remaining += 1
+            numShifts += 1
+        }
+
+        val integerPart = (remaining / 1000) % 1000
+        val fractionalPart = remaining % 1000
+
+        val unitString = when (numShifts) {
+            0 -> "u"
+            1 -> "m"
+            2 -> ""
+            3 -> "k"
+            4 -> "M"
+            5 -> "G"
+            else -> throw Error("Unexpected value for numShifts: $numShifts")
+        }
+
+        var fractionalString = if (fractionalPart > 0) {
+            if (fractionalPart < 10) ".00$fractionalPart"
+            else if (fractionalPart < 100) ".0$fractionalPart"
+            else ".$fractionalPart"
+        } else ""
+        while (fractionalString.endsWith("0")) fractionalString = fractionalString.substring(0, fractionalString.length - 1)
+        return signString + integerPart + fractionalString + unitString
+    }
+
+    companion object {
+
+        val ZERO = fromInt(0)
+
+        fun raw(rawValue: Long) = FixNano64(rawValue)
+
+        fun fromInt(value: Int) = FixNano64(value.toLong() * RAW_ONE)
+
+        fun fromLong(value: Long): FixNano64 {
+            try {
+                return FixNano64(Math.multiplyExact(value, RAW_ONE))
+            } catch (overflow: ArithmeticException) {
+                throw FixedPointException("Can't convert $value to FixNano64")
+            }
+        }
+
+        fun fromFloat(value: Float) = fromDouble(value.toDouble())
+
+        fun fromDouble(value: Double): FixNano64 {
+            val doubleValue = RAW_ONE.toDouble() * value
+            if (doubleValue > Long.MAX_VALUE.toDouble() || doubleValue < Long.MIN_VALUE.toDouble()) {
+                throw FixedPointException("Can't represent $value")
+            }
+            return FixNano64(doubleValue.roundToLong())
+        }
+
+        // Note that overflow is impossible since RAW_ONE == 2^30 and |numerator| < 2^31
+        fun fraction(numerator: Int, denominator: Int) = FixNano64(RAW_ONE * numerator / denominator)
+
+        fun fraction(numerator: Long, denominator: Long): FixNano64 {
+            // TODO Optimize common case when RAW_ONE * numerator doesn't overflow
+            try {
+                return FixNano64(
+                    (BigInteger.valueOf(RAW_ONE) * BigInteger.valueOf(numerator) / BigInteger.valueOf(
+                        denominator
+                    )).longValueExact()
+                )
+            } catch (finalOverflow: ArithmeticException) {
+                throw FixedPointException("Can't represent $numerator / $denominator")
+            }
+        }
+    }
+}
+
+operator fun Int.times(other: FixNano64) = other * this
+
+operator fun Long.times(other: FixNano64) = other * this
+
+operator fun Float.times(other: FixNano64) = other * this
+
+operator fun Double.times(other: FixNano64) = other * this
+
+operator fun Int.div(other: FixNano64) = FixNano64.fromInt(this) / other
+
+operator fun Long.div(other: FixNano64) = FixNano64.fromLong(this) / other
+
+operator fun Float.div(other: FixNano64) = FixNano64.fromFloat(this) / other
+
+operator fun Double.div(other: FixNano64) = FixNano64.fromDouble(this) / other
+
+@Throws(AssertionError::class)
+fun assertEquals(expected: FixNano64, actual: FixNano64, margin: Double) {
+    if ((expected.toDouble() - actual.toDouble()).absoluteValue > margin) {
+        throw AssertionError("Expected $expected, but got $actual (difference is ${expected - actual})")
+    }
+}
diff --git a/src/main/kotlin/fixie/FixedPointException.kt b/src/main/kotlin/fixie/FixedPointException.kt
new file mode 100644
index 0000000..8b9b9ad
--- /dev/null
+++ b/src/main/kotlin/fixie/FixedPointException.kt
@@ -0,0 +1,3 @@
+package fixie
+
+class FixedPointException(message: String): RuntimeException(message)
diff --git a/src/main/kotlin/fixie/Norm32.kt b/src/main/kotlin/fixie/Norm32.kt
new file mode 100644
index 0000000..62b676a
--- /dev/null
+++ b/src/main/kotlin/fixie/Norm32.kt
@@ -0,0 +1,87 @@
+package fixie
+
+import java.util.*
+import kotlin.math.roundToLong
+
+@JvmInline
+value class Norm32 private constructor(val raw: Int) : Comparable<Norm32> {
+
+    init {
+        if (raw == Int.MIN_VALUE) throw IllegalStateException("raw value must not be Int.MIN_VALUE")
+    }
+
+    operator fun unaryMinus() = Norm32(-raw)
+
+    @Throws(FixedPointException::class)
+    operator fun plus(other: Norm32): Norm32 {
+        val rawResult = this.raw.toLong() + other.raw.toLong()
+
+        if (rawResult > Int.MAX_VALUE) {
+
+            // Prevent overflow exceptions due to small rounding errors
+            if (rawResult < Int.MAX_VALUE + 1000L) return ONE
+            throw FixedPointException("$this + $other would overflow")
+        }
+
+        if (rawResult < Int.MIN_VALUE) {
+
+            // Prevent underflow exceptions due to small rounding errors
+            if (rawResult > -Int.MAX_VALUE - 1000L) return -ONE
+            throw FixedPointException("$this + $other would underflow")
+        }
+
+        return Norm32(rawResult.toInt())
+    }
+
+    @Throws(FixedPointException::class)
+    operator fun minus(right: Norm32) = this + -right
+
+    fun toFloat() = toDouble().toFloat()
+
+    fun toDouble() = raw.toDouble() / Int.MAX_VALUE.toDouble()
+
+    override fun compareTo(other: Norm32) = raw.compareTo(other.raw)
+
+    override fun toString(): String {
+        val originalString = String.format(Locale.ROOT, "%.4f", toDouble())
+
+        var prefix: String
+        var valueString: String
+        if (originalString.startsWith("-")) {
+            prefix = "-"
+            valueString = originalString.substring(1)
+        } else {
+            prefix = ""
+            valueString = originalString
+        }
+
+        while (valueString.length > 1 && (valueString.endsWith("0") || valueString.endsWith("."))) {
+            valueString = valueString.substring(0 until valueString.length - 1)
+        }
+
+        if (valueString == "0") prefix = ""
+
+        return prefix + valueString
+    }
+
+    companion object {
+
+        val ZERO = Norm32(0)
+        val ONE = Norm32(Int.MAX_VALUE)
+
+        fun fromFloat(value: Float) = fromDouble(value.toDouble())
+
+        @Throws(FixedPointException::class)
+        fun fromDouble(value: Double): Norm32 {
+            val longValue = (value * Int.MAX_VALUE).roundToLong()
+            if (longValue < -Int.MAX_VALUE || longValue > Int.MAX_VALUE) throw FixedPointException("Can't normalize $value")
+
+            return Norm32(longValue.toInt())
+        }
+
+        fun createRaw(rawValue: Int): Norm32 {
+            if (rawValue == Int.MIN_VALUE) throw FixedPointException("Using Int.MIN_VALUE is forbidden")
+            return Norm32(rawValue)
+        }
+    }
+}
diff --git a/src/test/kotlin/Playground.kt b/src/test/kotlin/Playground.kt
new file mode 100644
index 0000000..d984d1b
--- /dev/null
+++ b/src/test/kotlin/Playground.kt
@@ -0,0 +1,56 @@
+import fixie.FixNano64
+import java.util.*
+import kotlin.math.absoluteValue
+import kotlin.system.measureNanoTime
+
+fun main() {
+    tryDoublePerformance()
+}
+
+private fun tryFloatPerformance() {
+    val rng = Random()
+    val values = FloatArray(100_000_000) { 0.5f + rng.nextFloat() }
+
+    val spentTime = measureNanoTime {
+        var result = 0f
+        for (index in 1 until values.size) {
+            result += values[index - 1] * values[index]
+            if (result.absoluteValue > 10_000f) result = 0f
+        }
+        println("result is $result")
+    }
+
+    println("Took ${spentTime / 1_000_000.0} ms")
+}
+
+private fun tryDoublePerformance() {
+    val rng = Random()
+    val values = DoubleArray(100_000_000) { 0.5 + rng.nextDouble() }
+
+    val spentTime = measureNanoTime {
+        var result = 0.0
+        for (index in 1 until values.size) {
+            result += values[index - 1] * values[index]
+            if (result.absoluteValue > 10_000.0) result = 0.0
+        }
+        println("result is $result")
+    }
+
+    println("Took ${spentTime / 1_000_000.0} ms")
+}
+
+private fun tryFixedPerformance() {
+    val rng = Random()
+    val values = LongArray(100_000_000) { FixNano64.fromDouble(0.5 + 50.0 * rng.nextDouble()).raw }
+
+    val spentTime = measureNanoTime {
+        var result = FixNano64.ZERO
+        for (index in 1 until values.size) {
+            result += FixNano64.raw(values[index - 1]) * FixNano64.raw(values[index])
+            if (result.toDouble().absoluteValue > 10_000.0) result = FixNano64.ZERO
+        }
+        println("result is $result")
+    }
+
+    println("Took ${spentTime / 1_000_000.0} ms")
+}
diff --git a/src/test/kotlin/fixie/TestFixNano64.kt b/src/test/kotlin/fixie/TestFixNano64.kt
new file mode 100644
index 0000000..2826404
--- /dev/null
+++ b/src/test/kotlin/fixie/TestFixNano64.kt
@@ -0,0 +1,464 @@
+package fixie
+
+import org.junit.jupiter.api.Assertions.assertEquals
+import org.junit.jupiter.api.Test
+import org.junit.jupiter.api.assertThrows
+
+private fun fi(value: Int) = FixNano64.fromInt(value)
+private fun fl(value: Long) = FixNano64.fromLong(value)
+private fun fd(value: Double) = FixNano64.fromDouble(value)
+
+class TestFixNano64 {
+
+    @Test
+    fun testToFloat() {
+        for (value in arrayOf(-8_000_000_000f, -10f, 0.0001f, 1.2f, 43.2f, 8_000_000_000f)) {
+            assertEquals(value, FixNano64.fromFloat(value).toFloat(), 0.001f)
+        }
+        assertEquals(-5f, fi(-5).toFloat(), 0.001f)
+    }
+
+    @Test
+    fun testToDouble() {
+        for (value in arrayOf(-8_500_000_000.0, -10.0, 0.0001, 1.2, 43.2, 8_500_000_000.0)) {
+            assertEquals(value, fd(value).toDouble(), 0.001)
+        }
+        assertEquals(-5.0, fi(-5).toDouble(), 0.001)
+    }
+
+    @Test
+    fun testFromFloatOverflow() {
+        assertThrows<FixedPointException> { FixNano64.fromFloat(-8_600_000_000f) }
+        assertThrows<FixedPointException> { FixNano64.fromFloat(8_600_000_000f) }
+    }
+
+    @Test
+    fun testFromDoubleOverflow() {
+        assertThrows<FixedPointException> { FixNano64.fromDouble(-8_600_000_000.0) }
+        assertThrows<FixedPointException> { FixNano64.fromDouble(8_600_000_000.0) }
+    }
+
+    @Test
+    fun testToString() {
+        assertEquals("MIN", FixNano64.raw(Long.MIN_VALUE).toString())
+        assertEquals("MAX", FixNano64.raw(Long.MAX_VALUE).toString())
+        assertEquals("8.59G", FixNano64.raw(Long.MAX_VALUE - 1).toString())
+        assertEquals("-8.59G", FixNano64.raw(Long.MIN_VALUE + 1).toString())
+        assertEquals("12M", fd(12_000_000.0).toString())
+        assertEquals("-100.324M", fi(-100_324_000).toString())
+        assertEquals("-1.2k", fd(-1200.0).toString())
+        assertEquals("15", fi(15).toString())
+        assertEquals("-999", fi(-999).toString())
+        assertEquals("1.512", FixNano64.fromFloat(1.512f).toString())
+        assertEquals("100.53m", FixNano64.fromFloat(0.100_53f).toString())
+        assertEquals("13.45u", fd(0.000_013_45).toString())
+        assertEquals("-999.987u", fd(-0.000_999_987).toString())
+        assertEquals("254n", fd(0.000_000_254).toString())
+        assertEquals("100.004k", fl(100_004).toString())
+        assertEquals("100k", fd(100_000.4).toString())
+        assertEquals("100.001k", fd(100_000.6).toString())
+    }
+
+    @Test
+    fun testAdd() {
+        val smallMargin = 0.000_000_01
+        val largeMargin = 0.000_001
+
+        assertEquals(fd(1.8), fi(1) + fd(0.8), smallMargin)
+        assertEquals(FixNano64.fromFloat(-12.45f), fi(-25) + fd(12.55), largeMargin)
+        assertEquals(fi(50), FixNano64.fromFloat(70f) + fd(-20.0), largeMargin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE - 10) + FixNano64.raw(10), smallMargin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), FixNano64.raw(Long.MIN_VALUE + 50) + FixNano64.raw(-50), smallMargin)
+
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MIN_VALUE) + FixNano64.raw(-1) }
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MAX_VALUE) + FixNano64.raw(1) }
+        assertThrows<FixedPointException> { fl(5_000_000_000) + fd(3_600_000_000.0) }
+        assertThrows<FixedPointException> { fd(-5_000_000_000.0) + fl(-3_600_000_000) }
+
+        assertEquals(fd(8_550_000_000.0), fi(2_000_000_000) + fl(6_550_000_000), largeMargin)
+        assertEquals(fd(-8_550_000_000.0), -fi(2_000_000_000) + fl(-6_550_000_000), largeMargin)
+    }
+
+    @Test
+    fun testSubtract() {
+        val smallMargin = 0.000_000_01
+        val largeMargin = 0.000_001
+
+        assertEquals(fd(1.8), fi(1) - fd(-0.8), smallMargin)
+        assertEquals(FixNano64.fromFloat(-12.45f), fi(-25) - fd(-12.55), largeMargin)
+        assertEquals(fi(50), FixNano64.fromFloat(70f) - fd(20.0), largeMargin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE - 10) - FixNano64.raw(-10), smallMargin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), FixNano64.raw(Long.MIN_VALUE + 50) - FixNano64.raw(50), smallMargin)
+
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MIN_VALUE) - FixNano64.raw(1) }
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MAX_VALUE) - FixNano64.raw(-1) }
+        assertThrows<FixedPointException> { fl(5_000_000_000) - fl(-3_600_000_000) }
+        assertThrows<FixedPointException> { fl(-5_000_000_000) - fl(3_600_000_000) }
+
+        assertEquals(fd(8_550_000_000.0), fi(2_000_000_000) - fd(-6_550_000_000.0), largeMargin)
+        assertEquals(fl(-8_550_000_000), -fi(2_000_000_000) - fl(6_550_000_000), largeMargin)
+    }
+
+    @Test
+    fun testMultiplyInt() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(5000), fi(100) * 50, margin)
+        assertEquals(fi(5000), 50 * fi(100), margin)
+
+        assertEquals(fd(0.1), fd(0.02) * 5, margin)
+        assertEquals(fd(-0.1), fd(0.02) * -5, margin)
+        assertEquals(fd(-0.1), fd(-0.02) * 5, margin)
+        assertEquals(fd(0.1), fd(-0.02) * -5, margin)
+
+        assertEquals(fl(8_400_000_000), fi(2_100_000_000) * 4)
+        assertEquals(fl(-8_400_000_000), 2_100_000_000 * -fi(4))
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) * -1 * -1, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), 1 * FixNano64.raw(Long.MAX_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), 1 * FixNano64.raw(Long.MIN_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), -1 * FixNano64.raw(Long.MIN_VALUE + 1), margin)
+
+        assertThrows<FixedPointException> { -1 * FixNano64.raw(Long.MIN_VALUE) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * 8100 }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * 8100 }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * -8100 }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * -8100 }
+    }
+
+    @Test
+    fun testMultiplyLong() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(5000), fi(100) * 50L, margin)
+        assertEquals(fi(5000), 50L * fi(100), margin)
+
+        assertEquals(fd(0.1), fd(0.02) * 5L, margin)
+        assertEquals(fd(-0.1), fd(0.02) * -5L, margin)
+        assertEquals(fd(-0.1), fd(-0.02) * 5L, margin)
+        assertEquals(fd(0.1), fd(-0.02) * -5L, margin)
+
+        assertEquals(fl(8_400_000_000), fi(2_100_000_000) * 4L)
+        assertEquals(fl(-8_400_000_000), 2_100_000_000L * -fi(4))
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) * -1L * -1L, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), 1L * FixNano64.raw(Long.MAX_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), 1L * FixNano64.raw(Long.MIN_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), -1L * FixNano64.raw(Long.MIN_VALUE + 1), margin)
+
+        assertThrows<FixedPointException> { -1L * FixNano64.raw(Long.MIN_VALUE) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * 8100L }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * 8100L }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * -8100L }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * -8100L }
+    }
+
+    @Test
+    fun testMultiplyFloat() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(5000), fi(100) * 50f, margin)
+        assertEquals(fi(5000), 50f * fi(100), margin)
+
+        assertEquals(fd(0.1), fd(0.02) * 5f, margin)
+        assertEquals(fd(-0.1), fd(0.02) * -5f, margin)
+        assertEquals(fd(-0.1), fd(-0.02) * 5f, margin)
+        assertEquals(fd(0.1), fd(-0.02) * -5f, margin)
+
+        assertEquals(fl(8_400_000_000), fi(2_100_000_000) * 4f)
+        assertEquals(fl(-8_400_000_000), 2_100_000_000f * -fi(4))
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) * -1f * -1f, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), 1f * FixNano64.raw(Long.MAX_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), 1f * FixNano64.raw(Long.MIN_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), -1f * FixNano64.raw(Long.MIN_VALUE + 1), margin)
+
+        assertThrows<FixedPointException> { -1f * FixNano64.raw(Long.MIN_VALUE) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * 8100f }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * 8100f }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * -8100f }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * -8100f }
+    }
+
+    @Test
+    fun testMultiplyDouble() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(5000), fi(100) * 50.0, margin)
+        assertEquals(fi(5000), 50.0 * fi(100), margin)
+
+        assertEquals(fd(0.1), fd(0.02) * 5.0, margin)
+        assertEquals(fd(-0.1), fd(0.02) * -5.0, margin)
+        assertEquals(fd(-0.1), fd(-0.02) * 5.0, margin)
+        assertEquals(fd(0.1), fd(-0.02) * -5.0, margin)
+
+        assertEquals(fl(8_400_000_000), fi(2_100_000_000) * 4.0)
+        assertEquals(fl(-8_400_000_000), 2_100_000_000.0 * -fi(4))
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) * -1.0 * -1.0, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), 1.0 * FixNano64.raw(Long.MAX_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), 1.0 * FixNano64.raw(Long.MIN_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), -1.0 * FixNano64.raw(Long.MIN_VALUE + 1), margin)
+
+        assertThrows<FixedPointException> { -1.0 * FixNano64.raw(Long.MIN_VALUE) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * 8100.0 }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * 8100.0 }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * -8100.0 }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * -8100.0 }
+    }
+
+    @Test
+    fun testMultiplyFixed() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(5000), fi(100) * fi(50), margin)
+
+        assertEquals(fd(0.1), fd(0.02) * fi(5), margin)
+        assertEquals(fd(-0.1), fd(0.02) * fi(-5), margin)
+        assertEquals(fd(-0.1), fd(-0.02) * fi(5), margin)
+        assertEquals(fd(0.1), fd(-0.02) * -fi(5), margin)
+
+        assertEquals(fl(8_400_000_000), fi(2_100_000_000) * fi(4))
+        assertEquals(fd(-8_400_000_000.0), fi(2_100_000_000) * -fi(4))
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) * -fi(1) * -fi(1), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), fi(1) * FixNano64.raw(Long.MAX_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), fi(1) * FixNano64.raw(Long.MIN_VALUE), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), fi(-1) * FixNano64.raw(Long.MIN_VALUE + 1), margin)
+
+        assertThrows<FixedPointException> { fi(-1) * FixNano64.raw(Long.MIN_VALUE) }
+        assertThrows<FixedPointException> { fi(2) * FixNano64.raw(Long.MIN_VALUE / 2 - 1) }
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MAX_VALUE / 2 + 1) * fi(2) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * fi(8100) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * fi(8100) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) * fi(-8100) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) * fi(-8100) }
+    }
+
+    @Test
+    fun testDivideInt() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(100), fi(5000) / 50, margin)
+        assertEquals(fi(50), fi(5000) / 100, margin)
+        assertEquals(fi(50), 5000 / fi(100))
+
+        assertEquals(fd(0.02), fd(0.1) / 5, margin)
+        assertEquals(fd(0.02), fd(-0.1) / -5, margin)
+        assertEquals(fd(-0.02), fd(-0.1) / 5, margin)
+        assertEquals(-fd(0.02), fd(0.1) / -5, margin)
+
+        assertEquals(fi(4), fl(8_400_000_000) / 2_100_000_000, margin)
+        assertEquals(-fi(4), fl(8_400_000_000) / -2_100_000_000, margin)
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / -1 / -1, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / 1, margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), FixNano64.raw(Long.MIN_VALUE) / 1, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MIN_VALUE + 1) / -1, margin)
+
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MIN_VALUE) / -1 }
+    }
+
+    @Test
+    fun testDivideLong() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(100), fi(5000) / 50L, margin)
+        assertEquals(fi(50), fi(5000) / 100L, margin)
+        assertEquals(fi(100), 5000L / fi(50))
+
+        assertEquals(fd(0.02), fd(0.1) / 5L, margin)
+        assertEquals(fd(0.02), fd(-0.1) / -5L, margin)
+        assertEquals(fd(-0.02), fd(-0.1) / 5L, margin)
+        assertEquals(-fd(0.02), fd(0.1) / -5L, margin)
+
+        assertEquals(fi(4), fl(8_400_000_000) / 2_100_000_000L, margin)
+        assertEquals(-fi(4), fl(8_400_000_000) / -2_100_000_000L, margin)
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / -1L / -1L, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / 1L, margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), FixNano64.raw(Long.MIN_VALUE) / 1L, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MIN_VALUE + 1L) / -1L, margin)
+
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MIN_VALUE) / -1L }
+    }
+
+    @Test
+    fun testDivideFloat() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(100), fi(5000) / 50f, margin)
+        assertEquals(fi(50), fi(5000) / 100f, margin)
+        assertEquals(fi(100), 5000f / fi(50), margin)
+
+        assertEquals(fd(0.02), fd(0.1) / 5f, margin)
+        assertEquals(fd(0.02), fd(-0.1) / -5f, margin)
+        assertEquals(fd(-0.02), fd(-0.1) / 5f, margin)
+        assertEquals(fd(-0.02), fd(0.1) / -5f, margin)
+
+        assertEquals(fi(5), fd(0.1) / 0.02f, 0.000_001)
+        assertEquals(fi(5), 0.1f / fd(0.02), 0.000_001)
+
+        assertEquals(fi(2_100_000_000), fl(8_400_000_000) / 4f, margin)
+        assertEquals(fi(-2_100_000_000), fl(8_400_000_000) / -4f, margin)
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / -1f / -1f, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / 1f, margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), FixNano64.raw(Long.MIN_VALUE) / 1f, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MIN_VALUE + 1) / -1f, margin)
+
+        assertThrows<FixedPointException> { fi(1_000_000_000) / (1f / 8100f) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) / (1f / 8100f) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) / (1f / -8100f) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) / (1f / -8100f) }
+    }
+
+    @Test
+    fun testDivideDouble() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(100), fi(5000) / 50.0, margin)
+        assertEquals(fi(50), fi(5000) / 100.0, margin)
+        assertEquals(fi(50), 5000.0 / fi(100), margin)
+
+        assertEquals(fd(0.02), fd(0.1) / 5.0, margin)
+        assertEquals(fd(0.02), fd(-0.1) / -5.0, margin)
+        assertEquals(fd(-0.02), fd(-0.1) / 5.0, margin)
+        assertEquals(fd(-0.02), fd(0.1) / -5.0, margin)
+
+        assertEquals(fi(5), fd(0.1) / 0.02, 0.000_001)
+        assertEquals(fi(5), 0.1 / fd(0.02), 0.000_001)
+
+        assertEquals(fi(2_100_000_000), fl(8_400_000_000) / 4.0, margin)
+        assertEquals(fi(-2_100_000_000), fl(8_400_000_000) / -4.0, margin)
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / -1.0 / -1.0, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / 1.0, margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), FixNano64.raw(Long.MIN_VALUE) / 1.0, margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MIN_VALUE + 1) / -1.0, margin)
+
+        assertThrows<FixedPointException> { fi(1_000_000_000) / (1.0 / 8100.0) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) / (1.0 / 8100.0) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) / (1.0 / -8100.0) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) / (1.0 / -8100.0) }
+    }
+
+    @Test
+    fun testDivisionFixed() {
+        val margin = 0.000_000_01
+
+        assertEquals(fi(50), fi(5000) / fi(100), margin)
+
+        assertEquals(fd(0.02), fd(0.1) / fi(5), margin)
+        assertEquals(fd(0.02), fd(-0.1) / fi(-5), margin)
+        assertEquals(fd(-0.02), fd(0.1) / fi(-5), margin)
+        assertEquals(fd(-0.02), fd(-0.1) / fi(5), margin)
+
+        assertEquals(fi(2_100_000_000), fl(8_400_000_000) / fi(4))
+        assertEquals(fi(-2_100_000_000), fl(8_400_000_000) / fi(-4))
+
+        assertEquals(fi(100_000), fi(1) / fd(0.00001), 100.0)
+        assertEquals(fi(1_000_000), fi(1) / fd(0.000001), 1000.0)
+        assertEquals(fi(0), fi(1) / fl(5_000_000_000L))
+
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / -fi(1) / -fi(1), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MAX_VALUE) / fi(1), margin)
+        assertEquals(FixNano64.raw(Long.MIN_VALUE), FixNano64.raw(Long.MIN_VALUE) / fi(1), margin)
+        assertEquals(FixNano64.raw(Long.MAX_VALUE), FixNano64.raw(Long.MIN_VALUE + 1) / fi(-1), margin)
+
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MIN_VALUE) / fi(-1) }
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MIN_VALUE / 2 - 1) / fd(0.5) }
+        assertThrows<FixedPointException> { FixNano64.raw(Long.MAX_VALUE / 2 + 1) / fd(0.5) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) / fd(1.0 / 8100) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) / fd(1.0 / 8100) }
+        assertThrows<FixedPointException> { fi(1_000_000_000) / fd(1.0 / -8100) }
+        assertThrows<FixedPointException> { fi(-1_000_000_000) / fd(1.0 / -8100) }
+        assertThrows<FixedPointException> { fi(1_000_000) / fd(1.0 / 8_600_000.0) }
+    }
+
+    @Test
+    fun testFixedMultiplyAndDivisionEdgeCases() {
+        // Systematically test edge cases
+        for (bitCount1 in 0 until 64) {
+            for (bitCount2 in 0 until 64) {
+
+                val power1 = 1L shl bitCount1
+                val power2 = 1L shl bitCount2
+
+                val ones1 = (Long.MAX_VALUE shr bitCount1 shl bitCount1) xor Long.MAX_VALUE
+                val ones2 = (Long.MAX_VALUE shr bitCount2 shl bitCount2) xor Long.MAX_VALUE
+
+                fun test(value1: Long, value2: Long) {
+                    var shouldOverflow = false
+                    try {
+                        fl(Math.multiplyExact(value1, value2))
+                        fl(value1)
+                        fl(value2)
+                    } catch (overflow: FixedPointException) {
+                        shouldOverflow = true
+                    } catch (overflow: ArithmeticException) {
+                        shouldOverflow = true
+                    }
+
+                    if (shouldOverflow) {
+                        assertThrows<FixedPointException> { println(fl(value1) * fl(value2)) }
+                    } else {
+                        assertEquals(fl(value1 * value2), fl(value1) * fl(value2), 0.001)
+                        if (value2 != 0L) assertEquals(fl(value1), fl(value1 * value2) / fl(value2), 0.001)
+                        if (value1 != 0L) assertEquals(fl(value2), fl(value1 * value2) / fl(value1), 0.001)
+                    }
+                }
+
+                test(power1, power2)
+                test(ones1, ones2)
+                test(power1, ones2)
+            }
+        }
+    }
+
+    @Test
+    fun testFractionInt() {
+
+        val margin = 0.000_000_01
+
+        // Simple cases
+        assertEquals(fd(0.04), FixNano64.fraction(4, 100), margin)
+        assertEquals(fd(-43.71), FixNano64.fraction(4371, -100), margin)
+        assertEquals(fi(82), FixNano64.fraction(-82, -1), margin)
+
+        // Cases with large absolute value
+        assertEquals(fi(100), FixNano64.fraction(2_000_000_000, 20_000_000), margin)
+        assertEquals(fi(-100), FixNano64.fraction(2_000_000_000, -20_000_000), margin)
+        assertEquals(fi(-100), FixNano64.fraction(-2_000_000_000, 20_000_000), margin)
+        assertEquals(fi(100), FixNano64.fraction(-2_000_000_000, -20_000_000), margin)
+        assertEquals(fd(1.5), FixNano64.fraction(1_500_000_000, 1_000_000_000))
+
+        // Cases with the largest possible absolute values
+        assertEquals(fi(Integer.MAX_VALUE), FixNano64.fraction(Integer.MAX_VALUE, 1), margin)
+        assertEquals(fi(Integer.MAX_VALUE), FixNano64.fraction(-Integer.MAX_VALUE, -1), margin)
+        assertEquals(fi(Integer.MIN_VALUE), FixNano64.fraction(Integer.MIN_VALUE, 1), margin)
+        assertEquals(fi(Integer.MIN_VALUE + 1), FixNano64.fraction(-Integer.MAX_VALUE, 1), margin)
+        assertEquals(fi(Integer.MIN_VALUE + 1), FixNano64.fraction(Integer.MAX_VALUE, -1), margin)
+    }
+
+    @Test
+    fun testFractionLong() {
+
+        val margin = 0.000_000_01
+
+        // Simple cases
+        assertEquals(fd(0.04), FixNano64.fraction(4L, 100L), margin)
+        assertEquals(fd(-43.71), FixNano64.fraction(4371L, -100L), margin)
+        assertEquals(fi(82), FixNano64.fraction(-82L, -1L), margin)
+
+        // Cases with large absolute value
+
+        val bil = 1_000_000_000L
+
+        assertEquals(fl(8 * bil), FixNano64.fraction(8 * bil * bil, bil), margin)
+        assertEquals(fl(8 * bil), FixNano64.fraction(-8 * bil * bil, -bil), margin)
+        assertEquals(-fl(8 * bil), FixNano64.fraction(8 * bil * bil, -bil), margin)
+        assertEquals(fl(-8 * bil), FixNano64.fraction(-8 * bil * bil, bil), margin)
+        assertEquals(fd(-1.1234), FixNano64.fraction(-11_234 * bil, 10_000 * bil))
+    }
+}
diff --git a/src/test/kotlin/fixie/TestNorm32.kt b/src/test/kotlin/fixie/TestNorm32.kt
new file mode 100644
index 0000000..ff2f636
--- /dev/null
+++ b/src/test/kotlin/fixie/TestNorm32.kt
@@ -0,0 +1,67 @@
+package fixie
+
+import org.junit.jupiter.api.Assertions.assertEquals
+import org.junit.jupiter.api.Test
+import org.junit.jupiter.api.assertThrows
+
+class TestNorm32 {
+
+    @Test
+    fun testToString() {
+        assertEquals("0.1", Norm32.fromFloat(0.1f).toString())
+        assertEquals("-0.1234", Norm32.fromDouble(-0.1234).toString())
+        assertEquals("0.5294", Norm32.fromDouble(0.5294).toString())
+        assertEquals("-0.529", (-Norm32.fromDouble(0.529)).toString())
+        assertEquals("0.57", Norm32.fromFloat(0.57f).toString())
+        assertEquals("0.0001", Norm32.fromDouble(0.0001).toString())
+        assertEquals("-0.0001", Norm32.fromDouble(-0.0001).toString())
+        assertEquals("0.9999", Norm32.fromDouble(0.9999).toString())
+        assertEquals("-0.9999", (-Norm32.fromDouble(0.9999)).toString())
+        assertEquals("0", Norm32.ZERO.toString())
+        assertEquals("0", Norm32.createRaw(1).toString())
+        assertEquals("0", Norm32.createRaw(-1).toString())
+        assertEquals("1", Norm32.ONE.toString())
+        assertEquals("1", Norm32.fromDouble(0.9999999).toString())
+        assertEquals("-1", (-Norm32.ONE).toString())
+        assertEquals("-1", Norm32.fromDouble(-0.9999999).toString())
+    }
+
+    @Test
+    fun testToFloat() {
+        val margin = 0.0000001f
+
+        for (value in arrayOf(-1f, -0.99f, -0.56f, -0.32f, -0.1f, -0.001f, 0f, 0.001f, 0.1f, 0.32f, 0.56f, 0.99f, 1f)) {
+            assertEquals(value, Norm32.fromFloat(value).toFloat(), margin)
+        }
+    }
+
+    @Test
+    fun testToDouble() {
+        val margin = 0.00000001
+
+        for (value in arrayOf(-1.0, -0.99, -0.56, -0.32, -0.1, -0.001, 0.0, 0.001, 0.1, 0.32, 0.56, 0.99, 1.0)) {
+            assertEquals(value, Norm32.fromDouble(value).toDouble(), margin)
+        }
+    }
+
+    @Test
+    fun testFromFloatOverflow() {
+        for (value in arrayOf(1000f, 100f, 10f, 1.1f, 1.001f)) {
+            assertThrows<FixedPointException> { Norm32.fromFloat(value) }
+            assertThrows<FixedPointException> { Norm32.fromFloat(-value) }
+        }
+    }
+
+    @Test
+    fun testFromDoubleOverflow() {
+        for (value in arrayOf(1000.0, 100.0, 10.0, 1.1, 1.001)) {
+            assertThrows<FixedPointException> { Norm32.fromDouble(value) }
+            assertThrows<FixedPointException> { Norm32.fromDouble(-value) }
+        }
+    }
+
+    @Test
+    fun testAdd() {
+
+    }
+}