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Is 1.0 identity element of multiplication?

A simple script that checks whether 1.0 is really the identity element of multiplication for 32bit floating-point numbers.

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open System

// Step 100 takes about 3 sec on my machine
// so we can iterate over all flaot32 values
// in something like 5 minutes :-)
let step = 100 

// This can quite likely be optimized too :-)
for v in Int32.MinValue .. step .. Int32.MaxValue do
  let f = BitConverter.ToSingle(BitConverter.GetBytes(v), 0)
  // If they are both NaN, then that's okay, but since
  // NaN <> NaN, we need to check that case explicitly
  if Single.IsNaN(f) <> Single.IsNaN(1.0f * f) && 
     f <> 1.0f * f then 
    failwithf "Failed for: %f" f

namespace System

val step : int

Full name: Script.step

val v : int

type Int32 =
  struct
    member CompareTo : value:obj -> int + 1 overload
    member Equals : obj:obj -> bool + 1 overload
    member GetHashCode : unit -> int
    member GetTypeCode : unit -> TypeCode
    member ToString : unit -> string + 3 overloads
    static val MaxValue : int
    static val MinValue : int
    static member Parse : s:string -> int + 3 overloads
    static member TryParse : s:string * result:int -> bool + 1 overload
  end

Full name: System.Int32

field int.MinValue = -2147483648

field int.MaxValue = 2147483647

val f : float32

type BitConverter =
  static val IsLittleEndian : bool
  static member DoubleToInt64Bits : value:float -> int64
  static member GetBytes : value:bool -> byte[] + 9 overloads
  static member Int64BitsToDouble : value:int64 -> float
  static member ToBoolean : value:byte[] * startIndex:int -> bool
  static member ToChar : value:byte[] * startIndex:int -> char
  static member ToDouble : value:byte[] * startIndex:int -> float
  static member ToInt16 : value:byte[] * startIndex:int -> int16
  static member ToInt32 : value:byte[] * startIndex:int -> int
  static member ToInt64 : value:byte[] * startIndex:int -> int64
  ...

Full name: System.BitConverter

BitConverter.ToSingle(value: byte [], startIndex: int) : float32

BitConverter.GetBytes(value: float) : byte []
BitConverter.GetBytes(value: float32) : byte []
BitConverter.GetBytes(value: uint64) : byte []
BitConverter.GetBytes(value: uint32) : byte []
BitConverter.GetBytes(value: uint16) : byte []
BitConverter.GetBytes(value: int64) : byte []
BitConverter.GetBytes(value: int) : byte []
BitConverter.GetBytes(value: int16) : byte []
BitConverter.GetBytes(value: char) : byte []
BitConverter.GetBytes(value: bool) : byte []

type Single =
  struct
    member CompareTo : value:obj -> int + 1 overload
    member Equals : obj:obj -> bool + 1 overload
    member GetHashCode : unit -> int
    member GetTypeCode : unit -> TypeCode
    member ToString : unit -> string + 3 overloads
    static val MinValue : float32
    static val Epsilon : float32
    static val MaxValue : float32
    static val PositiveInfinity : float32
    static val NegativeInfinity : float32
    ...
  end

Full name: System.Single

Single.IsNaN(f: float32) : bool

val failwithf : format:Printf.StringFormat<'T,'Result> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.failwithf

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More information

Link:	http://fssnip.net/n3
Posted:	10 years ago
Author:	Tomas Petricek
Tags:	floating point