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

Section: 28.7.3 [c.math.hypot3] Status: New Submitter: Matthias Kretz Opened: 2018-12-06 Last modified: 2018-12-21

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 28.7.3 [c.math.hypot3] is only specified as "Returns: $\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}$.". 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

Proposed resolution:

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 28.7.3 [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: $\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}$.

-?- 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.