I want to add/subtract for any float some smallest values which will change this float value about one bit of mantissa/significant part. How to calculate such small number efficiently.
For example I have such array of x:
xs = [1e300, 1e0, 1e-300]
What will be function for it to generate the smallest value? All assertion should be valid.
for x in xs:
assert x < x + smallestChange(x)
assert x > x - smallestChange(x)
Consider that 1e308 + 1 == 1e308 since 1 does means 0 for mantissa so `smallestChange' should be dynamic.
Pure Python solution will be the best.
Why this is not duplicate of Increment a python floating point value by the smallest possible amount - two simple tests prove it with invalid results.
(1) The question is not aswered in Increment a python floating point value by the smallest possible amount difference:
Increment a python floating point value by the smallest possible amount just not works try this code:
import math
epsilon = math.ldexp(1.0, -53) # smallest double that 0.5+epsilon != 0.5
maxDouble = float(2**1024 - 2**971) # From the IEEE 754 standard
minDouble = math.ldexp(1.0, -1022) # min positive normalized double
smallEpsilon = math.ldexp(1.0, -1074) # smallest increment for doubles < minFloat
infinity = math.ldexp(1.0, 1023) * 2
def nextafter(x,y):
"""returns the next IEEE double after x in the direction of y if possible"""
if y==x:
return y #if x==y, no increment
# handle NaN
if x!=x or y!=y:
return x + y
if x >= infinity:
return infinity
if x <= -infinity:
return -infinity
if -minDouble < x < minDouble:
if y > x:
return x + smallEpsilon
else:
return x - smallEpsilon
m, e = math.frexp(x)
if y > x:
m += epsilon
else:
m -= epsilon
return math.ldexp(m,e)
print nextafter(1e307, 1e308), 'nextafter(1e307, 1e308)'
print nextafter(1e308, 1e307), 'nextafter(1e308, 1e307)'
Results of [Increment a python floating point value by the smallest possible amount] is invalid:
1e+307 nextafter(1e307, 1e308) # invalid 2e307 is possible!!!
1e+308 nextafter(1e308, 1e307) # invalid 9e307 is possible!!!
(2) It was not asked how to add/substract the smallest value but was asked how to add/substract value in specific direction - propose solution is need to know x and y. Here is required to know only x.
(3) Propose solution in Increment a python floating point value by the smallest possible amount will not work on border conditions.
