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

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.

Code Examples & CVEs

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 BigInt uses a ratio of signed integer with up to 2^32 digits of base 256. Notice how even with 112 bits of fractions or ratios of 64bit unsigned integers, this math still does not converge to an expected value of 5.

BadRust

fn rec_float(y: f64, z: f64) -> f64  		      { 		       			108.0 - ((815.0 - 1500.0 / z) / y); 		       		      } 		       		      fn float_calc(turns: usize) -> f64  		      { 		       			let mut x: Vec<f64> = vec![4.0, 4.25]; 			(2..turns + 1).for_each(|number|  			{ 			 			  x.push(rec_float(x[number - 1], x[number - 2])); 			 			}); 			 			x[turns] 		       		      }

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:

GoodRust

Use num_rational::BigRational;                        		      fn rec_big(y: BigRational, z: BigRational) -> BigRational 		      { 		       			BigRational::from_integer(BigInt::from(108)) 			 			  - ((BigRational::from_integer(BigInt::from(815)) 			  - BigRational::from_integer(BigInt::from(1500)) / z) 			  / y) 			 		       		      } 		       		      fn big_calc(turns: usize) -> BigRational  		      { 		       			let mut x: Vec<BigRational> = vec![BigRational::from_float(4.0).unwrap(), BigRational::from_float(4.25).unwrap(),]; 			 			(2..turns + 1).for_each(|number|  			{ 			 			  x.push(rec_big(x[number - 1].clone(), x[number - 2].clone())); 			 			}); 			x[turns].clone() 		       		      }

Observed CVE Examples (5)

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

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CVE-2017-7619

Chain: rounding error in floating-point calculations (CWE-1339) in image processor leads to infinite loop (CWE-835)

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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-1339)

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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)

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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]"

View Details

Source-backed guidance

Additional facts reviewed against primary or authoritative security sources.

Verify controls for CWE-1339 with SSDF evidence

Use NIST SSDF verification and vulnerability-response practices to detect CWE-1339, Insufficient Precision or Accuracy of a Real Number, throughout the product lifecycle. Derive review questions, static or dynamic checks, and negative tests from the CWE's causal behavior; define the components and lifecycle stages each check covers; and retain findings with enough evidence to distinguish the root cause from symptoms and impacts. Track escapes and false negatives, then improve the verification plan after every confirmed occurrence.

NIST SP 800-218 Secure Software Development Framework — National Institute of Standards and Technology

Address Insufficient Precision or Accuracy of a Real Number during Implementation

MITRE associates mitigation with Implementation, and Patching and Maintenance; documented detection approaches include Automated Static Analysis; recorded impacts include DoS: Crash, Exit, or Restart, Execute Unauthorized Code or Commands, Read Application Data, and Modify Application Data. Use these source-defined anchors to turn CWE-1339 into implementation, review, and verification checks for the affected component.

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

Triage CWE-1339 against known exploitation evidence

Use CISA's Known Exploited Vulnerabilities catalog to test whether a vulnerability mapped to CWE-1339, Insufficient Precision or Accuracy of a Real Number, has evidence of exploitation in the wild. Confirm the CVE-to-CWE root-cause mapping independently before attaching the example, then capture the affected product, required action, and remediation deadline. A missing KEV match is not evidence that the weakness is unexploited, and a KEV entry must not be generalized to every occurrence of this CWE.

Known Exploited Vulnerabilities Catalog — Cybersecurity and Infrastructure Security Agency

Apply precise root-cause mapping to CWE-1339

Apply MITRE's full root-cause mapping guidance when using CWE-1339, Insufficient Precision or Accuracy of a Real Number. Separate weakness language from attacker prerequisites and technical impact, check the entry's abstraction and vulnerability-mapping notes, and prefer the most specific Base or Variant supported by the evidence. Record the rejected alternatives and require an independent review before the mapping is used for remediation trends or program metrics.

CVE to CWE Root Cause Mapping Guidance — MITRE CWE

Validate CWE-1339 with root-cause mapping checks

Apply MITRE's root-cause mapping quick tips to CWE-1339, Insufficient Precision or Accuracy of a Real Number. Confirm the finding describes the causal weakness rather than an impact or attack pattern, compare the abstraction and mapping notes with plausible alternatives, and have a second reviewer challenge the selection. Preserve the evidence and reasoning so recurring defects can be measured against one consistent identifier.

CVE to CWE Root Cause Mapping Quick Tips — MITRE CWE

Frequently Asked Questions

What is CWE-1339: Insufficient Precision or Accuracy of a Real Number?+

CWE-1339: Insufficient Precision or Accuracy of a Real Number is a Common Weakness Enumeration (CWE) entry maintained by MITRE. 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. 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.

What are the security consequences of Insufficient Precision or Accuracy of a Real Number?+

If exploited, CWE-1339 (Insufficient Precision or Accuracy of a Real Number) it can compromise Availability, Integrity, Confidentiality and Access Control, leading to outcomes such as DoS: Crash, Exit, or Restart, Execute Unauthorized Code or Commands, Read Application Data and Modify Application Data.

How do you prevent or mitigate Insufficient Precision or Accuracy of a Real Number?+

Recommended mitigations for CWE-1339 include: 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 memory and CPU tradeoffs of this change must be examined. Since floating point reals are used in many products and many locations, they are implemented in hardware and most format changes will cause the calculations to be moved into software resulting in slower products.

Which programming languages are affected by Insufficient Precision or Accuracy of a Real Number?+

CWE-1339 commonly affects Not Language-Specific. Note that weaknesses are often language-agnostic patterns, so secure coding practices apply broadly.

What are real-world examples of Insufficient Precision or Accuracy of a Real Number?+

MITRE documents real CVEs mapped to CWE-1339, including CVE-2018-16069, CVE-2017-7619, CVE-2021-29529, CVE-2008-2108 and CVE-2006-6499. You can look up the full details of each CVE, including CVSS scores and remediation guidance, on our CVE Lookup tool.

What is the difference between a CWE and a CVE?+

A CWE (Common Weakness Enumeration) like CWE-1339 describes a category of software weakness — the underlying flaw type. A CVE (Common Vulnerabilities and Exposures) identifies a specific, real-world vulnerability in a particular product. In short, a CWE is the kind of mistake, and a CVE is an instance of that mistake being found in software.

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

Extended Description

Technical Details

Applicable To

Security Consequences

Scope

Impact

Scope

Impact

Scope

Impact

Mitigation Strategies

Phase

Description

Detection Methods

Code Examples & CVEs

Demonstrative Examples

Observed CVE Examples (5)

CWE Relationships

Parent Weaknesses

Source-backed guidance

Verify controls for CWE-1339 with SSDF evidence

Address Insufficient Precision or Accuracy of a Real Number during Implementation

Triage CWE-1339 against known exploitation evidence

Apply precise root-cause mapping to CWE-1339

Validate CWE-1339 with root-cause mapping checks

Frequently Asked Questions

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