Original Post
🔒 Locked
Optimizing reciprocal
Advertisement
sse has one in.
If that''s not the help you''re after then you''re going to have to explain the problem better than what you have. - joanusdmentia
davepermen.net
If that''s not the help you''re after then you''re going to have to explain the problem better than what you have. - joanusdmentia
davepermen.net
well, check out carmacks revsqrt, based on this, you can create a 1/x approx as well.
the carmack one approximates x^-(1/2), you want x^-(1/1).. so all you need to take away is the shift right (wich is division by two), sort of.
i''ve had one once, but thats about 6hd''s back:D
If that''s not the help you''re after then you''re going to have to explain the problem better than what you have. - joanusdmentia
davepermen.net
the carmack one approximates x^-(1/2), you want x^-(1/1).. so all you need to take away is the shift right (wich is division by two), sort of.
i''ve had one once, but thats about 6hd''s back:D
If that''s not the help you''re after then you''re going to have to explain the problem better than what you have. - joanusdmentia
davepermen.net
If it''s not based only on a lut, it''s necessarilly the same concept as the used in the IEE754 + NR trick some name it as "Carmack''s" sqrt. But that was found much before Q3. Well Newton in one sense. You have to understand differentials and the IEEE754 format. That''s all. And yes anyway 1/x is rqsrt(x) squared. This to show you how everything is linked.
I think I''ve a solution to your problem.
It uses the Newton iteration and an initial guess I came up completely by myself (But perhaps some others have discovered similar methods for the initial guess).
The maximum error of the initial guess is about 5,76%.
This error will be halfed by each Newton iteration.
But... The initial guess does NOT work for:
(i) +0; -0; +Inf; -Inf; NaN
(ii) denormal numbers
(iii) if the result would be a denormal number
It uses the Newton iteration and an initial guess I came up completely by myself (But perhaps some others have discovered similar methods for the initial guess).
float frcp_estm(float x) // the initial guess
{
unsigned long rcp = 0x7ef311ef - *(unsigned long*)&x
return *(float*)&rcp
}
float frcp_aprox(float x) // approximation with 1 Newton iteration
{
float y = frcp_estm(x);
y *= 2-x*y; // Newton iteration
return y;
}
The maximum error of the initial guess is about 5,76%.
This error will be halfed by each Newton iteration.
But... The initial guess does NOT work for:
(i) +0; -0; +Inf; -Inf; NaN
(ii) denormal numbers
(iii) if the result would be a denormal number
Topic Locked
This topic has been locked by a moderator. New replies are not allowed.
Sign in to reply to this topic.
Advertisement