2024 Updates (Fork) #2

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TAbdiukov wants to merge 10 commits into alidasdan:master from TAbdiukov:staging

ad_gcd_lcm.py

            
                      Original file line number
                      Diff line number
                      Diff line change
                  
    @@ -1,4 +1,4 @@
  
    #!/usr/bin/python

    #!/usr/bin/python3

    # find the gcd and lcm of a given list of floating-point numbers. this

    # code uses a best rational approximation algorithm to solve the

    @@ -7,19 +7,35 @@
  
    # rational numbers.

    # author: ali dasdan

    # updated 2024 onwards by Tim Abdiukov.

    import sys

    import getopt

    import re

    from math import *

    from ad_rat_by_fast_farey import *

    USE_NUMPY_HI_PRECISION = True

    if(USE_NUMPY_HI_PRECISION):

        try:

            import numpy as np

            float2 = lambda x: np.longdouble(x)

        except ModuleNotFoundError:

            print("Please disable USE_NUMPY_HI_PRECISION or install prerequisite,")

            print("```")

            print("pip install numpy")

            print("```")

            exit()

    else:

        print("WARN: High precision NumPy logic is not used")

        float2 = lambda x: float(x)

    def show_usage():

        print "Usage:  " + sys.argv[0] + " -l/--limit=int>=1 -n/--nums=quoted list of at least 2 numbers or math expression returning float (w/o spaces)"

        print("Usage:  " + sys.argv[0] + " -l/--limit=int>=1 -n/--nums=quoted list of at least 2 numbers or math expression returning float (w/o spaces)")

    def at_exit(msg):

        if msg != '' and msg != None:

            print "Error:", msg

            print("Error:", msg)

        show_usage()

        sys.exit(0)

    @@ -84,7 +100,7 @@ def main():
  
        try:

            opts, args = getopt.getopt(sys.argv[1:], 'l:n:', ['limit=', 'nums'])

        except getopt.GetoptError, msg:

        except getopt.GetoptError as msg:

            at_exit(msg)

        for o, a in opts:

    @@ -96,15 +112,15 @@ def main():
  
                    if l < 1: raise Exception()

                else:

                    raise Exception()

            except Exception, msg:

            except Exception as msg:

                at_exit(msg)

        if s == None:

            at_exit(None)

        # get the list from the input string

        lst = re.split("[\s,;|:]+", s)

        print "input:", lst

        print("input:", lst)

        if len(lst) <= 1 or l == None:

            at_exit("Bad args")

    @@ -113,10 +129,10 @@ def main():
  
        for x in lst:

            try:

                nums.append(eval(x))

            except Exception, msg:

            except Exception as msg:

                at_exit(msg)

        print "input evaluated:", nums

        print("input evaluated:", nums)

        # convert to best rational approximations

        ns = []

    @@ -130,17 +146,17 @@ def main():
  
        for n, d in zip(ns, ds):

            rats.append(str(n) + "/" + str(d))

        srats = ", ".join(rats)

        print "best_rats= [" + srats + "]"

        print("best_rats= [" + srats + "]")

        # compute gcd and lcm of the elts in the list

        n_gcd, d_gcd = rgcd_lst(ns, ds)

        n_lcm, d_lcm = rlcm_lst(ns, ds)

        gcd = float(n_gcd) / d_gcd

        lcm = float(n_lcm) / d_lcm

        gcd = float2(n_gcd) / d_gcd

        lcm = float2(n_lcm) / d_lcm

        print("gcd: rat= %d / %d val= %g" % (n_gcd, d_gcd, gcd))    

        print("lcm: rat= %d / %d val= %g lcm/gcd= %g" % (n_lcm, d_lcm, lcm, float(lcm)/gcd))

        print("lcm: rat= %d / %d val= %g lcm/gcd= %g" % (n_lcm, d_lcm, lcm, float2(lcm)/gcd))

        # compute the ratios and measure error (difference from the

        # closest int)

    @@ -150,21 +166,21 @@ def main():
  
        n_div_gcd = []

        lcm_div_n = []

        for x in nums:

            r = float(x) / gcd

            r = float2(x) / gcd

            r_int = int(round(r))

            err = abs(r - r_int)

            if err > max_err_gcd:

                max_err_gcd = err

            n_div_gcd.append(r_int)

            r = float(lcm) / x

            r = float2(lcm) / x

            r_int = int(round(r))

            err = abs(r - r_int)

            if err > max_err_lcm:

                max_err_lcm = err

            lcm_div_n.append(r_int)

        print "nums_div_gcd= ", n_div_gcd, "max_err= %g" % (max_err_gcd)

        print "lcm_div_nums= ", lcm_div_n, "max_err= %g" % (max_err_lcm)

        print("nums_div_gcd= ", n_div_gcd, "max_err= %g" % (max_err_gcd))

        print("lcm_div_nums= ", lcm_div_n, "max_err= %g" % (max_err_lcm))

    if __name__ == "__main__":

        main()

ad_rat_by_cont_frac.py

            
                      Original file line number
                      Diff line number
                      Diff line change
                  
    @@ -1,4 +1,4 @@
  
    #!/usr/bin/python

    #!/usr/bin/python3

    # find the best rational approximation n/d where d <= l to the given

    # target number t. here the best means the one with the smallest

    @@ -15,17 +15,33 @@
  
    # just keep the last partial product of these matrics.

    # author: ali dasdan (based on the C code by d. eppstein)

    # updated 2024 onwards by Tim Abdiukov.

    import sys

    import getopt

    from math import *

    USE_NUMPY_HI_PRECISION = True

    if(USE_NUMPY_HI_PRECISION):

        try:

            import numpy as np

            float2 = lambda x: np.longdouble(x)

        except ModuleNotFoundError:

            print("Please disable USE_NUMPY_HI_PRECISION or install prerequisite,")

            print("```")

            print("pip install numpy")

            print("```")

            exit()

    else:

        print("WARN: High precision NumPy logic is not used")

        float2 = lambda x: float(x)

    def show_usage():

        print sys.argv[0] + " -h/--help [-e/--error=float>=0] -l/--limit=int>1 -t/--target=float or quoted math expr returning float"

        print(sys.argv[0] + " -h/--help [-e/--error=float>=0] -l/--limit=int>1 -t/--target=float or quoted math expr returning float")

    def at_exit(msg):

        if msg != "" and msg != None:

            print "Error:", msg

            print("Error:", msg)

        show_usage()

        sys.exit(0)

    @@ -61,8 +77,8 @@ def find_best_rat(l, t):
  
            tmp = m10 * ai + m11

            m11 = m10

            m10 = tmp

            if (x == float(ai)): break

            x = float(1.0) / (x - float(ai))

            if (x == float2(ai)): break

            x = float2(1.0) / (x - float2(ai))

            ai = int(x)

        # now remaining x is between 0 and 1/ai. approx as either o or 1/m

    @@ -71,18 +87,22 @@ def find_best_rat(l, t):
  
        # first try zero

        n1 = m00

        d1 = m10

        err1 = (t - float(n1) / d1)

        err1 = (t - float2(n1) / d1)

        # try the other possibility

        ai = int(float(l - m11) / m10)

        ai = int(float2(l - m11) / m10)

        n2 = m00 * ai + m01

        d2 = m10 * ai + m11

        err2 = (t - float(n2) / d2)

        err2 = (t - float2(n2) / d2)

        if abs(err1) <= abs(err2):

            return err1, n1, d1, niter

        else:

            return err2, n2, d2, niter

        # optimization

        best_err = min(abs(err1), abs(err2))

        # assert precision wasn't lost

        assert(type(best_err) == type(float2(pi)))

        # return data

        return best_err, n2, d2, niter

    # this function takes in an error bound err_in, an int limit l, and

    # the target fraction to approximate t and returns err_out, n, d,

    @@ -110,28 +130,28 @@ def main():
  
            opts, args = getopt.getopt(sys.argv[1:],

                                       'he:l:t:',

                                       ['help', 'error=', 'limit=', 'target='])

        except getopt.GetoptError, msg:

        except getopt.GetoptError as msg:

            at_exit(msg)

        for o, a in opts:

            try:

                if o in ('-h', '--help'):

                    raise Exception()

                elif o in ('-e', '--error'):

                    eps = float(a)

                    eps = float2(a)

                    if eps <= 0: raise Exception()

                elif o in ('-l', '--limit'):

                    l = int(a)

                    if l < 1: raise Exception()

                elif o in ('-t', '--target'):

                    try:

                        t = float(eval(a))

                    except Exception, msg:

                        t = float2(eval(a))

                    except Exception as msg:

                        at_exit(msg)

                    if t <= 0: raise Exception()

                else:

                    raise Exception()

            except Exception, msg:

            except Exception as msg:

                at_exit(msg)

        if t == None or l==None:

    @@ -147,7 +167,7 @@ def main():
  
        if eps == None:

            print("target= %f best_rat= %d / %d max_denom= %d err= %g abs_err= %g niter= %d" % (t, n, d, l, err, abs(err), niter))

        else:

            print("target= %f best_rat= %d / %d max_denom= %d err= %g abs_err= %g abs_err/error= %g niter= %d" % (t, n, d, l, err, abs(err), float(abs(err)) / eps, niter))

            print("target= %f best_rat= %d / %d max_denom= %d err= %g abs_err= %g abs_err/error= %g niter= %d" % (t, n, d, l, err, abs(err), float2(abs(err)) / eps, niter))

    if __name__ == '__main__':

        main()

ad_rat_by_exhaustive.py

            
                      Original file line number
                      Diff line number
                      Diff line change
                  
    @@ -1,4 +1,4 @@
  
    #!/usr/bin/python

    #!/usr/bin/python3

    # find the best rational approximation n/d where d <= l to the given

    # target number t. here the best means the one with the smallest

    @@ -8,17 +8,34 @@
  
    # up to and including l.

    # author: ali dasdan

    # updated 2024 onwards by Tim Abdiukov.

    import sys

    import getopt

    from math import *

    USE_NUMPY_HI_PRECISION = True

    if(USE_NUMPY_HI_PRECISION):

        try:

            import numpy as np

            float2 = lambda x: np.longdouble(x)

        except ModuleNotFoundError:

            print("Please disable USE_NUMPY_HI_PRECISION or install prerequisite,")

            print("```")

            print("pip install numpy")

            print("```")

            exit()

    else:

        print("WARN: High precision NumPy logic is not used")

        float2 = lambda x: float(x)

    def show_usage():

        print sys.argv[0] + " -h/--help [-e/--error=float>=0] -l/--limit=int=>1 -t/--target=float or quoted math expr returning float"

        print(sys.argv[0] + " -h/--help [-e/--error=float>=0] -l/--limit=int=>1 -t/--target=float or quoted math expr returning float")

    def at_exit(msg):

        if msg != "" and msg != None:

            print "Error:", msg

            print("Error:", msg)

        show_usage()

        sys.exit(0)

    @@ -40,11 +57,15 @@ def find_best_rat(l, t):
  
            for n in range(1, l + 1):

                niter += 1

                err = abs(t - float(n) / d)

                err = abs(t - float2(n) / d)

                if err < best_err:

                    best_err = err

                    best_n, best_d = n, d

        # assert precision wasn't lost

        assert(type(best_err) == type(float2(pi)))

        # return data

        return best_err, best_n, best_d, niter

    # this function takes in an error bound err_in, an int limit l, and

    @@ -73,28 +94,28 @@ def main():
  
            opts, args = getopt.getopt(sys.argv[1:],

                                       'he:l:t:',

                                       ['help', 'error=', 'limit=', 'target='])

        except getopt.GetoptError, msg:

        except getopt.GetoptError as msg:

            at_exit(msg)

        for o, a in opts:

            try:

                if o in ('-h', '--help'):

                    raise Exception()

                elif o in ('-e', '--error'):

                    eps = float(a)

                    eps = float2(a)

                    if eps <= 0: raise Exception()

                elif o in ('-l', '--limit'):

                    l = int(a)

                    if l < 1: raise Exception()

                elif o in ('-t', '--target'):

                    try:

                        t = float(eval(a))

                    except Exception, msg:

                        t = float2(eval(a))

                    except Exception as msg:

                        at_exit(msg)

                    if t <= 0: raise Exception()

                else:

                    raise Exception()

            except Exception, msg:

            except Exception as msg:

                at_exit(msg)

        if t == None or l==None:

    @@ -108,11 +129,11 @@ def main():
  
        else:

            err, n, d, niter = find_best_rat_with_err_bound(eps, l, t_frac)

        n += t_int * d

        err = (t - float(n) / d)

        err = (t - float2(n) / d)

        if eps == None:

            print("target= %f best_rat= %d / %d max_denom= %d err= %g abs_err= %g niter= %d" % (t, n, d, l, err, abs(err), niter))

        else:

            print("target= %f best_rat= %d / %d max_denom= %d err= %g abs_err= %g abs_err/error= %g niter= %d" % (t, n, d, l, err, abs(err), float(abs(err)) / eps, niter))

            print("target= %f best_rat= %d / %d max_denom= %d err= %g abs_err= %g abs_err/error= %g niter= %d" % (t, n, d, l, err, abs(err), float2(abs(err)) / eps, niter))

    if __name__ == '__main__':

        main()

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