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Merged
merged 5 commits into from
Feb 6, 2025
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docs: clarify that sqrt must be correctly rounded in accordance with IEEE 754 #882

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docs: require that `sqrt` be correctly rounded in accordance with IEE…
kgryte Jan 9, 2025
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Merge branch 'main' of https://github.com/data-apis/array-api into fe…
kgryte Feb 6, 2025
ced123a
docs: update copy to use "correctly rounded"
kgryte Feb 6, 2025
10c6d26
docs: include blurb regarding subnormal support
kgryte Feb 6, 2025
c85425e
docs: specify that results must be "correctly rounded"
kgryte Feb 6, 2025
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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).

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.

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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