math-api | Serverless API to render maths using MathJax for Node | Math library
kandi X-RAY | math-api Summary
kandi X-RAY | math-api Summary
Math API • Render LaTeX and MathML formulas as SVG or PNG. A REST API to do fancy things with formulas, like rendering LaTeX or MathML to SVG or PNG on the server side using MathJax for Node, while leveraging expensive computations on the client.
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QUESTION
I need the square root of a float, in CUDA device code. Hard to say whether speed matters more than accuracy in my use case.
__sqrtf CUDA intrinsic is the natural choice
But then I saw the various __fsqrt with rounding CUDA intrinsics;
What is rounded in these intrinsics; the argument "x" or the return value? Or do I misunderstand the meaning of rounding here?
My testing suggests neither is rounded! I wrote a kernel that evaluates:
...ANSWER
Answered 2021-Jul-14 at 21:59It's a rounding mode for the result. Input arguments are not "rounded" before they are injected into the arithmetic flow.
the "rn" rounding "direction" is "round-to-nearest"
It means that at whatever precision the interim result is being calculated to, that result will be rounded to the nearest available representation. In the case of a float
final result, it will be rounded to the nearest available float
representation.
Let's revisit your example. When I put your problem into the windows 10 calculator, the result I get is 42.001190459319126303634970957554 The way we get from that "correct result at arbitrary precision" to a 32-bit floating point "rn" result is to take the two 32-bit floating point numbers, one which is closest but numerically higher, and one which is closest but numerically lower, and of those 2, select the one that is closest. That is apparently 42.0011902.
QUESTION
Say I have the following function:
...ANSWER
Answered 2020-Oct-04 at 04:15QUESTION
CUDA supports mathematical functions. But do they provide any guarantee like if I compute sin(x)
the result would the closet representable value to the mathematical value of sin(x)
? If the answer is no, is there any alternative if we want to stay in GPU? Something like it always return an upper bound or always a lower bound (but possibly not the closest possible one).
ANSWER
Answered 2020-Jan-31 at 10:23CUDA Appendix Suggests that the value provided by the API are not accurate. There is a difference of, 1/2 ulps in their value. (when compared between host and device).
However, for all practical purposes, these values are accurate.
Anyway if you want to perform symbolic operations with high-level precision, using float precision makes it inaccurate.
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