Special case NaNs in all statistical functions

Author: honno

spec/API_specification/statistical_functions.md

@@ -24,6 +24,12 @@ Calculates the maximum value of the input array `x`.
 When the number of elements over which to compute the maximum value is zero, the maximum value is implementation-defined. Specification-compliant libraries may choose to error, return a sentinel value (e.g., if `x` is a floating-point input array, return `NaN`), or return the minimum possible value for the input array `x` data type (e.g., if `x` is a floating-point array, return `-infinity`).
 ```
 
+#### Special Cases
+
+Let `x_i` be an element over which to compute the maximum value. For floating-point operands,
+
+-   if `x_i` is `NaN`, the maximum value is `NaN` (i.e., `NaN` values propagate).
+
 #### Parameters
 
 -   **x**: _<array>_
@@ -55,6 +61,11 @@ For a floating-point input array `x`, let `N` equal the number of elements over
 
 -   if `N` is `0`, the arithmetic mean is `NaN`.
 
+Let `x_i` be an element over which to compute the arithmetic mean. For floating-point operands,
+
+-   if `x_i` is `NaN`, the arithmetic mean is `NaN` (i.e., `NaN` values propagate).
+
+
 #### Parameters
 
 -   **x**: _<array>_
@@ -88,6 +99,12 @@ Calculates the minimum value of the input array `x`.
 When the number of elements over which to compute the minimum value is zero, the minimum value is implementation-defined. Specification-compliant libraries may choose to error, return a sentinel value (e.g., if `x` is a floating-point input array, return `NaN`), or return the maximum possible value for the input array `x` data type (e.g., if `x` is a floating-point array, return `+infinity`).
 ```
 
+#### Special Cases
+
+Let `x_i` be an element over which to compute the minimum value. For floating-point operands,
+
+-   if `x_i` is `NaN`, the minimum value is `NaN` (i.e., `NaN` values propagate).
+
 #### Parameters
 
 -   **x**: _<array>_
@@ -119,6 +136,10 @@ For an input array `x`, let `N` equal the number of elements over which to compu
 
 -   if `N` is `0`, the product is `1` (i.e., the empty product).
 
+Let `x_i` be an element over which to compute the product. For floating-point operands,
+
+-   if `x_i` is `NaN`, the product is `NaN` (i.e., `NaN` values propagate).
+
 #### Parameters
 
 -   **x**: _<array>_
@@ -163,6 +184,10 @@ For a floating-point input array `x`, let `N` equal the number of elements over
 
 -  if `N - correction` is less than or equal to `0`, the standard deviation is `NaN`.
 
+Let `x_i` be an element over which to compute the standard deviation. For floating-point operands,
+
+-   if `x_i` is `NaN`, the standard deviation is `NaN` (i.e., `NaN` values propagate).
+
 #### Parameters
 
 -   **x**: _<array>_
@@ -202,6 +227,10 @@ For an input array `x`, let `N` equal the number of elements over which to compu
 
 -   if `N` is `0`, the sum is `0` (i.e., the empty sum).
 
+Let `x_i` be an element over which to compute the sum. For floating-point operands,
+
+-   if `x_i` is `NaN`, the sum is `NaN` (i.e., `NaN` values propagate).
+
 #### Parameters
 
 -   **x**: _<array>_
@@ -246,6 +275,10 @@ For a floating-point input array `x`, let `N` equal the number of elements over
 
 -  if `N - correction` is less than or equal to `0`, the variance is `NaN`.
 
+Let `x_i` be an element over which to compute the variance. For floating-point operands,
+
+-   if `x_i` is `NaN`, the variance is `NaN` (i.e., `NaN` values propagate).
+
 #### Parameters
 
 -   **x**: _<array>_