Gmpy2 Newbie Working on Precision

[charlesrkiss]

I am trying to calculate minute angles, and would like precision of at least 15 digits:

But I fail to understand how Python is rounding.

As I vary the value of asin by factors of 10 (from .001 to .00001), the output adds these zeros between the leading numeral 1 and the next numeral 1 (and some sixes after). See the image below.

And this is happening whether I use the gimpy2 or math modules:

Does the Sin-1 actually do this on radians?

Degrees acts similarly: When the input is very small and changes by a factor of ten (eg., .001 - .00001), the output of asin only changes by a factor of ten — the decimal point just moves one place while leaving the significant figures virtually unchanged.



   

Thank you!!

A version of the test code being used is shown below:

import gmpy2
import math
from gmpy2 import *
from gmpy2 import get_context as ctx

ctx().precision = 100

# L = mpfr('1000.0')
F = 0.00001
N = 10.0
B = 0.5

C = gmpy2.div(F, N)
c = F / N
D = 2 * C
d = 2 * c

E = B * gmpy2.asin(D)
e = B * math.asin(d)

g = .000002
e2 = B * math.asin(g)
# F = gmpy2.mul(B, E)
# sin(2 * theta) = 2 * sin(theta)cos(theta)

# print("L: ", L, type(L))
print("F: ", F, type(F))
print("N: ", N, type(N))

print("B: ", B, type(B))
print("C: ", C, type(C))
print("c: ", c, type(c))
print("D: ", D, type(D))
print("d: ", d, type(d))

print("E: ", E, type(E))
print("e: ", e, type(e))

print("e2: ", e2, type(e2))

print(ctx())