Creating arithmetic sequences

[mmm]

I wrote the code below to create simple arithmetic sequences that are
iter-able
I.e.,  this would basically combine the NUMPY arange(start,end,step)
to range(start,end),  with step not necessarily an integer.

The code below is in its simplest form and I want to generalize the
sequence types (multiplicative, cumulative, gauss ...), but first I
need the simple SEQA( ) function to be more robust.   The problem is
the three test code functions produces different results based on
step. I understand why steps such as 0.1 have rounding and  machine
math issues, and before I try to solve this I thought it was worth
asking if this problem has been solved (so I do not re-invent the
wheel).

Another way to put my question, is there a PYTHON function that
emulates SEQA() in APTECH’s GAUSS language and produces iterable
lists ?

Note I originally wrote the three versions below see which is fastest,
but each is fast enough such that I care more about robustness now.


## Python arithmetic sequence implimentation
##   MDB April 16  2008

from numpy import array, arange, floor
import time

# simple arithmetic sequence
def seqa1(start,end,step=1):
    n= floor( (end-start) / float(step) )
    x= [start,]
    for i in xrange(0,n):
        x.append(x[-1]+step)
    return x

##faster seq creation
def seqa2(start,end,step=1):
    n= floor( (end-start) / float(step) )
    x= [ start+i*step for i in xrange(0,n) ]
    return x

##fastest seq creation as array, also allow array --> different type
def seqa3(start,end,step=1.0,type=array):
    x=arange(start,end,step)
    if type==array:  pass
    elif type==list or type==None or type=='' :
        x=list(x)
    elif type==tuple:
        x=tuple(x)
    elif type==dict:
        x= dict(zip(range(1,len(x)),tuple(x)))
    elif type==set:
        x= set(x)
    return x

if (1):
    start=1
    end=2
    step= 0.10

    t0=time.time()
    x1=seqa1(start,end,step)
    print 'SEQA1 Time= ', time.time()-t0

    t0=time.time()
    x2=seqa2(start,end+step,step)
    print 'SEQA2 Time= ', time.time()-t0

    print 'Check for X1,X2 equivalence-- ', (x1==x2)

    t0=time.time()
    x3=seqa3(start,end+step,step,list)
    print 'SEQA3 Time= ', time.time()-t0

    print 'Check for X2,X3 equivalence-- ', (x2==x3)