Project:ISO JTC1/SC22/WG21:
Programming Language C++
Author:Lawrence Crowl

Narrowing and Widening Conversions


Generalizing narrowing conversions can admit new primitive numeric types without further updates to the standard. Giving priority to select widening conversions in overload resolution will ease the construction and use of overloaded functions.




Overload resolution relies on finding the best implicit conversion sequence from each argument type to its corresponding parameter type in all candidate functions. When no one function has all the best sequences, the function call is ambiguous and therefore ill-formed.

While many standard conversions may appear in a conversion sequence, only one user-defined conversion may appear.

The standard distinguishes between information-preserving (widening) conversions and information-destroying (narrowing) conversions in two ways. First, the standard promotions are widening conversions. Second, initializer-list initialization defines some conversions as narrowing conversions and permits them only when the source is constexpr and the value is within the value set of the destination type.


Consider the following declarations.

float atan2( float, float );
double atan2( double, double );
long double atan2( long double, long double );

Of the nine possible call argument-type combinations (32), six are ambiguous. However, all combinations have a best overload, which preserves all the information in the arguments and operates at the least cost.

int main() {
  float f; double d; long double ld;
  atan2(  f,  f ); // matches float
  atan2(  f,  d ); // ambiguous, want double
  atan2(  f, ld ); // ambiguous, want long double
  atan2(  d,  f ); // ambiguous, want double
  atan2(  d,  d ); // matches double
  atan2(  d, ld ); // ambiguous, want long double
  atan2( ld,  f ); // ambiguous, want long double
  atan2( ld,  d ); // ambiguous, want long double
  atan2( ld, ld ); // matches long double

The problem extends to user-defined types and functions as well.

class cardinal {
  unsigned int c;

class integral {
  int c;
  integral( cardinal );
  operator cardinal();

class rational {
  integral n, d;
  rational( cardinal );
  operator cardinal();
  rational( integral );
  operator integral();

cardinal add( cardinal, cardinal );
integral add( integral, integral );
rational add( rational, rational );

int main() {
  cardinal c; integral i; rational r;
  add( c, c ); // matches cardinal
  add( c, i ); // ambiguous, want integral
  add( c, r ); // ambiguous, want rational
  add( i, c ); // ambiguous, want integral
  add( i, i ); // matches integral
  add( i, r ); // ambiguous, want rational
  add( r, c ); // ambiguous, want rational
  add( r, i ); // ambiguous, want rational
  add( r, r ); // matches rational

A related problem is that adding a new overload into a header may introduce an ambiguity in client code. Such problems may not be found until well after products have shipped.

Workarounds for Library Users

The user of library must necessarily be able to work around such issues.

Explicit Argument Casting

The typical workaround to ambiguity for library users is to add explicit casts to the call sites.

int main() {
  atan2( f, f );
  atan2( static_cast<double>(f), d );
  atan2( static_cast<long double>(f), ld );
  atan2( d, static_cast<double>(f) );
  atan2( d, d );
  atan2( static_cast<long double>(d), ld );
  atan2( ld, static_cast<long double>(f) );
  atan2( ld, static_cast<long double>(d) );
  atan2( ld, ld );

Static Function Declaration

One workaround to this problem is to define a local static function with exactly the needed arguments..

static long double atan2( float f, double d )
  return atan2( static_cast<double>(f), d );

int main() {
  float f; double d;
  atan2( f, d );

Local Extern Declaration

One workaround to this problem is Daveed Vandervorde's technique that adds a local extern function declaration to force a particular overload.

int main() {
  float f; double d;
  extern long double atan2( double, double );
  return atan2( f, d );

This technique is effective, but not well known. It lacks generality in that it does not apply to member functions. More importantly, as more overloads are used within the function, the ambiguity problem resurfaces.

Workarounds for Library Authors

Library authors can anticipate some problems.

Add Additional Overloads

The primary workaround is to add more overloaded functions. Unfortunately, argument-dependent lookup problems may arise when the new functions and the original functions are in different namespaces.

double atan2( float f, double d )
  { return atan2( static_cast(c), i ); }
long double atan2( float f, long double ld )
  { return atan2( static_cast(c), r ); }
double atan2( double d, float f )
  { return atan2( i, static_cast(c) ); }
long double atan2( double d, long double ld )
  { return atan2( static_cast(i), r ); }
long double atan2( long double ld, float f )
  { return atan2( r, static_cast(c) ); }
long double atan2( long double ld, double d )
  { return atan2( r, static_cast(i) ); }

Unfortunately, number of additional overloads needed grows dramatically with increasing number of types and parameters. This growth places a specification burden on the library author. It also places a burden on the library user, because the number of overloads that must be excluded by a call also grows.

Make Lossy Conversions Explicit

Problematic conversion can be excluded from overloading by making them explicit. However, this approach requires casting even when there would otherwise be no ambiguity.

Common Type Template

Another approach to solving the problem is to write templates that convert arguments to a common type (e.g. [P0880R2]). Unfortunately this approach has difficulty with argument-dependent lookup and namespaces.


In the examples above, there is always one least-common information-preserving overload. There are two mechanisms that make identifying this overload possible. First, we prefer conversions that preserve information over those that lose information. Second, we prefer the promotion that covers the least distance.

In [N3387], Jens Maurer applied these principles to integer types by adjusting the rules for integer conversion rank and promotion. The paper was not persued. We intend to generalize the approach to user-defined types.


We propose to introduce a distinction between narrowing and widening conversions in C++ programs. We then propose to alter overload resolution rules to prefer widening conversion over narrowing conversions.

For built-in types:

For user-defined types:


The proposal only removes ambiguity, it does not introduce it. So, all existing code is correct and unchanged.

The two's complement representation for builtin integer types, implies signed&darrow;unsigned conversions are not widening.

When programmers change existing user-defined conversions to widening conversions, option 1 will not introduce user-defined conversions where none existed before. It is unclear whether option 2 may do so.

The parameter types have widening conversions, adding new overloads reduces the chance that existing calls will become ambiguous.

In the case where an existing call would be ambiguous, overload resolution would become more expensive. This expense must be evaluated with respect to the workarounds.


All wording edits are relative to N4800 Working Draft, Standard for Programming Language C++.


5.11 Keywords [lex.key]

Add widening to Table 5 — Keywords.

7.3 Standard conversions [conv]

9.3.4 List-initialization [dcl.init.list]

paragraph 7 defines narrowing conversion

10.3.4 Constructors [class.ctor]

11.3.3 Best viable function [] Implicit conversion sequences []


N3387 Overload resolution tiebreakers for integer types; 2012-09-12;
N3387 Numbers interaction; 2019-01-15;
N4800 Working Draft, Standard for Programming Language C++; 2019-01-21;