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3172. 3-arg std::hypot is underspecified compared to the 2-arg overload

Section: 29.7.3 [c.math.hypot3] Status: Ready Submitter: Matthias Kretz Opened: 2018-12-06 Last modified: 2026-07-17

Priority: 3

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Discussion:

The 2-arg hypot function specified in the C standard is required to avoid overflow and underflow (7.12.7.3 p2). Furthermore C's Annex F (IEC 60559 floating-point arithmetic) defines special cases for inputs of ±0 and ±inf (F. 10.4.3). The 3-arg hypot function 29.7.3 [c.math.hypot3] is only specified as "Returns: x2+ y2+z2.". This is inconsistent with the 2-arg overload.

It is not clear whether C's Annex F is "imported" into the C++ standard. [cmath.syn] p1 suggests that it is: "The contents and meaning of the header <cmath> are the same as the C standard library header <math.h>, […]".

[2018-12-21 Reflector prioritization]

Set Priority to 3

Previous resolution [SUPERSEDED]

This wording is relative to N4778.

[Drafting Note: Two mutually exclusive options are prepared, depicted below by Option A and Option B, respectively.]

Option A

  1. Modify 29.7.3 [c.math.hypot3] as indicated:

    float hypot(float x, float y, float z);
double hypot(double x, double y, double z);
long double hypot(long double x, long double y, long double z);

    -?- Effects: The hypot functions compute the square root of the sum of the squares of x, y, and z, without undue overflow or underflow. A range error may occur.

    -1- Returns: x2+ y2+z2.

    -?- Remarks: If __STDC_IEC_559__ is defined, the following guarantees hold:

    • hypot(x, y, z), hypot(x, z, y), hypot(z, y, x), and hypot(x, y, -z) are equivalent.

    • if y2 + z2 == ±0, hypot(x, y, z) is equivalent to fabs(x).

    • hypot(±∞, y, z) returns +∞, even if y and/or z is a NaN.

Option B

  1. Add a note that clarifies that the behavior of the 3-arg hypot function differs from the C specification. I.e. that no special guarantees wrt. over-/underflow or special values are given.

[2026-06-10; Tim provides new wording]

LWG in Brno is in favor of the direction of Option A. However, __STDC_IEC_559__ is not defined in C++. The wording has been updated following the current C WD, taking into account WG14 N2714.

[Brno 2026-06-12; Status changed: New → Ready.]

Previous resolution [SUPERSEDED]

This wording is relative to N5050.

  1. Modify 29.7.3 [c.math.hypot3] as indicated:

    constexpr floating-point-type hypot(floating-point-type x, floating-point-type y,
                                    floating-point-type z);

    -?- Effects: Compute the square root of the sum of the squares of x, y, and z, without undue overflow or underflow. A range error may occur.

    -1- Returns: x2+ y2+z2.

    -?- Remarks: If numeric_limits<floating-point-type>::is_iec559 is true, the following guarantees hold:

    • hypot(x, y, z), hypot(x, z, y), hypot(z, y, x), and hypot(x, y, -z) are equivalent.

    • if y and z are zero and x is not a NaN, hypot(x, y, z) returns the absolute value of x.

    • if x is positive or negative infinity, hypot(x, y, z) returns positive infinity, even if y and/or z is a NaN.

    • if x is a NaN and neither y nor z is positive or negative infinity, hypot(x, y, z) returns a NaN.

[2026-06-30; Tim reopens and provides new wording. Status changed: Ready → Open.]

Matthias Kretz pointed out that is_iec559 is the wrong test as it only concerns representation and not behavior.

Until C++ gets its own floating point annex, this wording downgrades the Remarks: to a Recommended practice: and ties the condition to whether the binary version of hypot conforms to C's Annex F.

[2026-07-17 LWG telecon; Change status New → Ready.]

Proposed resolution:

This wording is relative to N5050.

  1. Modify 29.7.3 [c.math.hypot3] as indicated:

    constexpr floating-point-type hypot(floating-point-type x, floating-point-type y,
                                    floating-point-type z);

    -?- Effects: Compute the square root of the sum of the squares of x, y, and z, without undue overflow or underflow. A range error may occur.

    -1- Returns: x2+ y2+z2.

    -?- Recommended practice: An implementation whose two-parameter overload of hypot conforms to ISO/IEC 9899:2024 Annex F should provide the following guarantees:

    • hypot(x, y, z), hypot(x, z, y), hypot(z, y, x), and hypot(x, y, -z) are equivalent.

    • if y and z are zero and x is not a NaN, hypot(x, y, z) returns the absolute value of x.

    • if x is positive or negative infinity, hypot(x, y, z) returns positive infinity, even if y and/or z is a NaN.

    • if x is a NaN and neither y nor z is positive or negative infinity, hypot(x, y, z) returns a NaN.