double.IsPow2 reports incorrectly for subnormal numbers

[hamarb123]

Description

double.IsPow2 should return true for for all doubles which are a power of 2, and false otherwise. It doesn't appear to work correctly for subnormal numbers.

Reproduction Steps

Execute the following:

double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 16); //not subnormal, = 2^-1022
double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 8); //is subnormal, = 2^-1023
double.IsPow2(double.Epsilon); //is subnormal, = 2^-1074

Expected behavior

double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 16); //true
double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 8); //true
double.IsPow2(double.Epsilon); //true

Actual behavior

double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 16); //true
double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 8); //false
double.IsPow2(double.Epsilon); //false

Regression?

No response

Known Workarounds

No response

Configuration

Reproduces on:
.NET 8.0.0-preview.5.23280.8, 7.0.5.
Windows 10 Pro 10.0.19045.3086 x64
No, it probably isn't specific to this configuration.

Other information

The simplest correct check I can think of for this would be: check the negative bit is not set, check the exponent is not the max exponent (can be combined with previous check), if the exponent is not zero: check the mantissa is 0, if the exponent is zero: check the PopCount is 1.

It seems to also reproduce with float and Half, I only checked T.IsPow2(T.Epsilon), but these should both return true also.

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Issue Details

---

Description

double.IsPow2 should return true for for all doubles which are a power of 2, and false otherwise. It doesn't appear to work correctly for subnormal numbers.

Reproduction Steps

Execute the following:

double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 16); //not subnormal, = 2^-1022
double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 8); //is subnormal, = 2^-1023
double.IsPow2(double.Epsilon); //is subnormal, = 2^-1074

Expected behavior

double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 16); //true
double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 8); //true
double.IsPow2(double.Epsilon); //true

Actual behavior

double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 16); //true
double.IsPow2(double.Epsilon * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 64 * 8); //false
double.IsPow2(double.Epsilon); //false

Regression?

No response

Known Workarounds

No response

Configuration

Reproduces on:
.NET 8.0.0-preview.5.23280.8, 7.0.5.
Windows 10 Pro 10.0.19045.3086 x64
No, it probably isn't specific to this configuration.

Other information

The simplest correct check I can think of for this would be: check the negative bit is not set, check the exponent is not the max exponent (can be combined with previous check), if the exponent is not zero: check the mantissa is 0, if the exponent is zero: check the PopCount is 1.

It seems to also reproduce with float and Half, I only checked T.IsPow2(T.Epsilon), but these should both return true also.

Author:	hamarb123
Assignees:	-
Labels:	area-System.Numerics, untriaged, needs-area-label
Milestone:	-

[danmoseley]

Good catch @hamarb123