fixed_point | C Binary Fixed-Point Arithmetic | Build Tool library
kandi X-RAY | fixed_point Summary
kandi X-RAY | fixed_point Summary
The fixed_point library provides a header-only C++11 API for approximating real numbers using binary fixed-point arithmetic. It forms the reference implementation of a standard library proposal presented in paper, P0037 and is developed as part of study groups, SG14 and SG6.
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QUESTION
I have a rather basic question. Suppose I have a templated function:
...ANSWER
Answered 2020-Oct-12 at 18:16The way to handle this is to continue using std::numeric_limits
, and add template specializations for all of the desired input types.
Quoting cppreference:
Implementations may provide specializations of
std::numeric_limits
for implementation-specific types: e.g. GCC providesstd::numeric_limits<__int128>
. Non-standard libraries may add specializations for library-provided types, e.g. OpenEXR providesstd::numeric_limits
for a 16-bit floating-point type.
QUESTION
Say I have a program that uses a built in type such as float
and I want to have the ability to supply a command-line argument to my compiler to change all float
declarations to be fixed_point<8,8>
instead.
Presuming that they're the exact same interface (as in, they can be treated the same with regards to assignment / addition / conversion / etc), is there a way in via compiler or build system (cmake / scons / etc) to swap types during compilation when specifying a specific flag? This would serve a few benefits with regards to determinism, for instance.
...ANSWER
Answered 2020-Sep-17 at 14:38You can declare your variable with an alias type, which is defined conditionally based on a preprocessor definition, like this:
QUESTION
I have a large amount of one-dimensional nonlinear fixed point problems to solve, what is the most efficient numerical solver? I'm currently using scipy.optimize.fixed_point, it takes around 17s to run 1000 of my tasks. Thanks for any suggestions.
...ANSWER
Answered 2020-Aug-13 at 06:00If these are all 1D, you can take the fixed_point source, https://github.com/scipy/scipy/blob/v1.5.2/scipy/optimize/minpack.py#L876 simplify it (can decide once on the acceleration strategy, no need for _lazywhere etc) and compile it with either cython or numba.
QUESTION
I tried to find the root of a²+a³=392 with fixed_point introduced by SICP 1.1.3 functions as general method
...ANSWER
Answered 2019-Dec-31 at 02:45I think this problem is not well suited for solving via a fixed-point procedure. If you print the (abs (- next guess))
for each iteration, you'll see that the value is increasing between iterations, it'll never converge to the specified tolerance - hence the Numerical result out of range
error.
QUESTION
I am reading the fix-point
of SICP:
ANSWER
Answered 2019-Dec-27 at 08:09It's the opposite: it's cleaner and more efficient with try
because it doesn't need to redefine the good-enough-p
.
(also, you're not supposed to use recursion in Python).
The version with try
is better than the version which calls the top function, fixed-point
, because fixed-point
contains inner definitions, of the functions good-enough-p
and try
. A simple-minded compiler would compile it so that on each call it actually makes those definitions anew, again and again, on each call. With try
there's no such concern as it is already inside the fixed-point
's inner environment where good-enough-p
is already defined, and so try
can just run.
(correction/clarification: the above treats your code as if it were Scheme, with internal define
s instead of the Common Lisp with defun
s as you show. SICP is Scheme, after all. In Common Lisp / ELisp there's not even a question -- the internal defun
s will always be performed, on each call to the enclosing function, just (re)defining the same functions at the top level over and over again.)
Incidentally, I like your Python loop translation, it is a verbatim translation of the Scheme's tail-recursive loop, one to one.
Your while
translation is exactly what a Scheme compiler is supposed to be doing given the first tail-recursive Scheme code in your question. The two are exactly the same, down to the "horrible while True ...
with an escape" which, personally, I quite like for its immediacy and clarity. Meaning, I don't need to keep track of which value gets assigned to what variable and which variable gets returned in the end -- instead, a value is just returned, just like it is in Scheme.
QUESTION
I'm practicing rudimentary programming skills on leetcode.com (I highly recommend it. It's great) and I ran into an interesting result.
I'm trying to find the first fixed point of a given array A
with strictly ascending values.
I did this in two ways. First, a binary search / linear time hybrid
...ANSWER
Answered 2019-Sep-08 at 23:56At if A[middle] == middle
: the position of "any index of the fixed point is found". The first version more efficiently finds the start of the midpoint run, assuming that it occurs 'close to' (fsvo) the start of the linear scan: the cost of each binary loop is 'more expensive' (larger C), regardless of number of loops needed (O complexity). For specific degenerate input, it should be possible to construct cases where the pure binary search is better: eg. size of n and distribution of input.
For example, the degenerate case of [0, 0, 0 ..., midpoint=1, 1, 1 ...]
would be be O(n)
in the first version as the linear loop would be over start=0..midpoint=n/2
1. Using this degenerate data, and a large enough value of n, the plain binary search will dominate as it's bounded better. However, assuming that it is 'well distributed random data', then the approach with the linear probe could hone in on a very small linear scan set (smaller C for final loops).
This is similar to why a linear scan is faster for small arrays, and why a merge-sort or quick-sort (eg.) may switch to an insertion sort for near-leaf sorting. Big-O describes the behavior as n -> Inifinity, without consideration of the constant costs.
1The scan could also be midpoint=n/2..start=0
.. in that case the degenerate case shown is the ideal case and corresponding degenerate case would be [0, 1, 1, 1 ...]
.
QUESTION
After reading quite a bit about fixed-point arithmetic I think I can say I've understood the basics, unfortunately I don't know yet how to convert routines that use sin/cos/sqrt or any other fp function.
Consider this simple mcve:
...ANSWER
Answered 2019-Aug-06 at 07:09The basic idea for a lookup table is simple -- you use the fixed point value as an index into an array to look up the value. The problem is if your fixed point values are large, your tables become huge. For a full table with a 32-bit FP type you need 4*232 bytes (16GB) which is impractically large. So what you generally do is use a smaller table (smaller by a factor of N) and the linearly interpolate between two values in the table to do the lookup.
In your case, you appear to want to use a 223 reduction so you need a table with just 513 elements. To do the lookup, you then use the upper 9 bits as an index into the table and use the lower 23 bits to interpolate. eg:
QUESTION
I am trying to find a fixed point in an array using a function that only accepts one input (an array). The problem is, I'm trying to avoid building another function that this function can call. If I could do that, this situation would be solved. These arrays will contain a list of sorted integers for me to iterate through. I am trying to keep its runtime low by using binary search. I've tried this a 100 different ways, and nothing is quite working.
...ANSWER
Answered 2018-Jun-03 at 01:53The fundamental problem with your algorithm as written is that you lose track of where you are in the original array. When you recurse, you return the fixed point of half of the array, but for example in [-4, -2, 0, 2, 4]
when you split the array and find the fixed point in [2, 4]
it doesn't work, because there is no fixed point in [2, 4]
. You need to pass an offset into each recursive call, so you can say something like if mid + offset == a[mid]
.
QUESTION
I would like to add a opus library with wrapper from github to my project, but I have some errors when building. Maybe somebody know what's going on.
Attach a build log.
...ANSWER
Answered 2018-Sep-17 at 23:47$ echo 'D:/GitProject/aliservicescontroller/AliServicesControllerAndroid/opuslib/build/intermediates/ndkBuild/debug/obj/local/armeabi-v7a/objs-debug/senz/D_/GitProject/aliservicescontroller/AliServicesControllerAndroid/opuslib/src/main/jni/opus/silk/code_signs.o.cflags.tmp' | wc -c
266
QUESTION
I have the following parser,
...ANSWER
Answered 2019-Jan-09 at 21:45Use optional parser to not fail if there is no fractional part.
Also you had PRICE_MULT
with 4 zeros, but dec_part
was allowed up to 6 digits.
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