docs: clarify that sqrt must be correctly rounded in accordance with IEEE 754

PR-URL: #882
Closes: #826
Closes: #830
Reviewed-by: Leo Fang <[email protected]>

Author: kgryte

spec/draft/design_topics/accuracy.rst

@@ -23,11 +23,20 @@ including the corresponding element-wise array APIs defined in this standard
 -   multiply
 -   divide
 
-for floating-point operands must return the nearest representable value according to IEEE 754-2019 and a supported rounding mode. By default, the rounding mode should be ``roundTiesToEven`` (i.e., round to nearest with ties rounded toward the nearest value with an even least significant bit).
+for real-valued floating-point operands must return a correctly rounded value according to IEEE 754-2019 and a supported rounding mode. By default, the rounding mode should be ``roundTiesToEven`` (i.e., round to nearest with ties rounded toward the nearest value with an even least significant bit).
+
+IEEE 754-2019 requires support for subnormal (a.k.a., denormal) numbers, which are useful for supporting gradual underflow. However, hardware support for subnormal numbers is not universal, and many platforms (e.g., accelerators) and compilers support toggling denormals-are-zero (DAZ) and/or flush-to-zero (FTZ) behavior to increase performance and to guard against timing attacks. Accordingly, conforming implementations may vary in their support for subnormal numbers.
 
 Mathematical Functions
 ----------------------
 
+The results of the following functions
+
+-   reciprocal
+-   sqrt
+
+for real-valued floating-point operands must return a correctly rounded value according to IEEE 754-2019 and a supported rounding mode.
+
 This specification does **not** precisely define the behavior of the following functions
 
 -   acos
@@ -41,10 +50,12 @@ This specification does **not** precisely define the behavior of the following f
 -   cosh
 -   exp
 -   expm1
+-   hypot
 -   log
 -   log1p
 -   log2
 -   log10
+-   logaddexp
 -   pow
 -   sin
 -   sinh
@@ -75,3 +86,8 @@ Linear Algebra
 --------------
 
 This specification does not specify accuracy requirements for linear algebra functions; however, this specification does expect that a conforming implementation of the array API standard will make a best-effort attempt to ensure that its implementations are theoretically sound and numerically robust.
+
+Operations Involving Complex Numbers
+------------------------------------
+
+This specification does not specify accuracy requirements for arithmetic or functional operations involving complex-valued floating-point operands; however, this specification does expect that a conforming implementation of the array API standard will make a best-effort attempt to ensure that its implementations are theoretically sound and numerically robust.