CWE-1339: Insufficient Precision or Accuracy of a Real Number

Description:
The product processes a real number with an implementation in which the number's representation does not preserve required accuracy and precision in its fractional part, causing an incorrect result.

Extended Description:
When a security decision or calculation requires highly precise, accurate numbers such as financial calculations or prices, then small variations in the number could be exploited by an attacker.
             There are multiple ways to store the fractional part of a real number in a computer. In all of these cases, there is a limit to the accuracy of recording a fraction. If the fraction can be represented in a fixed number of digits (binary or decimal), there might not be enough digits assigned to represent the number. In other cases the number cannot be represented in a fixed number of digits due to repeating in decimal or binary notation (e.g. 0.333333...) or due to a transcendental number such as Π or √2. Rounding of numbers can lead to situations where the computer results do not adequately match the result of sufficiently accurate math.

Affected languages: Not Language-Specific
Affected technologies: Not Technology-Specific
Parent weaknesses: CWE-682

Consequences:
  - Availability: DoS: Crash, Exit, or Restart
  - Integrity: Execute Unauthorized Code or Commands
  - Confidentiality: Read Application Data

Detection methods:
  - Automated Static Analysis: Automated static analysis, commonly referred to as Static Application Security Testing (SAST), can find some instances of this weakness by analyzing source code (or binary/compiled code) without havin

Mitigations:
  - [Implementation] The developer or maintainer can move to a more accurate representation of real numbers.  In extreme cases, the programmer can move to representations such as ratios of BigInts which can represent real numbers to extremely fine precision. The programmer can also use the concept of an Unum real. The m

Demonstrative examples:
Muller's Recurrence is a series that is supposed to converge to the number 5. When running this series with the following code, different implementations of real numbers fail at specific iterations:
The chart below shows values for different data structures in the rust language when Muller's recurrence is executed to 80 iterations. The data structure f64 is a 64 bit float. The data structures I<number>F<number> are fixed representations 128 bits in length that use the first number as the size of the integer and the second size as the size of the fraction (e.g. I16F112 uses 16 bits for the integer and 112 bits for the fraction). The data structure of Ratio comes in three different implementations: i32 uses a ratio of 32 bit signed  integers,  i64 uses a ratio of 64 bit signed integers and B

On February 25, 1991, during the eve of the Iraqi invasion of Saudi Arabia, a Scud missile fired from Iraqi positions hit a US Army barracks in Dhahran, Saudi Arabia. It miscalculated time and killed 28 people [REF-1190].

Real-world examples:
  - CVE-2018-16069: Chain: series of floating-point precision errors
			(CWE-1339) in a web browser rendering engine causes out-of-bounds read
			(CWE-125), giving access to cross-origin data
  - CVE-2017-7619: Chain: rounding error in floating-point calculations
			(CWE-1339) in image processor leads to infinite loop (CWE-835)
  - CVE-2021-29529: Chain: machine-learning product can have a heap-based
			buffer overflow (CWE-122) when some integer-oriented bounds are
			calculated by using ceiling() and floor() on floating point values
			(CWE-1
  - CVE-2008-2108: Chain: insufficient precision (CWE-1339) in
			random-number generator causes some zero bits to be reliably
			generated, reducing the amount of entropy (CWE-331)
  - CVE-2006-6499: Chain: web browser crashes due to infinite loop - "bad
			looping logic [that relies on] floating point math [CWE-1339] to exit
			the loop [CWE-835]"