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docs: clarify that sqrt must be correctly rounded in accordance with IEEE 754 #882

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docs: clarify that sqrt must be correctly rounded in accordance with IEEE 754 #882

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16 changes: 15 additions & 1 deletion spec/draft/design_topics/accuracy.rst
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Expand Up @@ -23,11 +23,18 @@ 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 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).
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I suggest changing nearest representable to correctly rounded.
If the rounding mode is not roundTiesToEven the value will be correctly rounded, but in general, it will not be the nearest representable. For example, if the rounding mode is roundTowardPositive, then the correctly rounded value is rounded up regardless of whether the rounded down value is nearer to the infinitely precise mathematical result.


Mathematical Functions
----------------------

The results of the following functions

- reciprocal
- sqrt

for real-valued floating-point operands must return the nearest representable value according to IEEE 754-2019 and a supported rounding mode.
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I suggest changing nearest representable to correctly rounded.


This specification does **not** precisely define the behavior of the following functions

- acos
Expand All @@ -41,10 +48,12 @@ This specification does **not** precisely define the behavior of the following f
- cosh
- exp
- expm1
- hypot
- log
- log1p
- log2
- log10
- logaddexp
- pow
- sin
- sinh
Expand Down Expand Up @@ -75,3 +84,8 @@ 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.
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