Add complex number support to cosh

[kgryte]

This PR

• adds complex number support to cosh by documenting special cases. The hyperbolic cosine is an entire function in the complex plane. Thus, the function has no branch cuts.
• updates the input and output array data types to be any floating-point data type, not just real-valued floating-point data types.
• derives special cases from C99 and tested against NumPy (script found below).

Details

importnumpyasnpimportmathdefis_equal_float(x, y):
"""Test whether two floating-point numbers are equal with special consideration for zeros and NaNs. Parameters ---------- x : float First input number. y : float Second input number. Returns ------- bool Boolean indicating whether two floating-point numbers are equal. Examples -------- >>> is_equal_float(0.0, -0.0) False >>> is_equal_float(-0.0, -0.0) True """# Handle +-0:ifx==0.0andy==0.0:
returnmath.copysign(1.0, x) ==math.copysign(1.0, y)
# Handle NaNs:ifx!=x:
returny!=y# Everything else, including infinities:returnx==ydefis_equal(x, y):
"""Test whether two complex numbers are equal with special consideration for zeros and NaNs. Parameters ---------- x : complex First input number. y : complex Second input number. Returns ------- bool Boolean indicating whether two complex numbers are equal. Examples -------- >>> import numpy as np >>> is_equal(complex(np.nan, np.nan), complex(np.nan, np.nan)) True """returnis_equal_float(x.real, y.real) andis_equal_float(x.imag, y.imag)
# Strided array consisting of input values and expected values:values= [
complex(0.0, 0.0), # 0complex(1.0, 0.0), # 0complex(-0.0, 0.0), # 1complex(1.0, -0.0), # 1complex(0.0, np.inf), # 2complex(np.nan, 0), # 2complex(0.0, np.nan), # 3complex(np.nan, 0.0), # 3complex(1.0, np.inf), # 4complex(np.nan, np.nan), # 4complex(1.0, np.nan), # 5complex(np.nan, np.nan), # 5complex(np.inf, 0.0), # 6complex(np.inf, 0.0), # 6complex(np.inf, -0.0), # 7complex(np.inf, -0.0), # 7complex(np.inf, 1.0), # 8complex(np.inf, np.inf), # 8complex(np.inf, np.inf), # 9complex(np.inf, np.nan), # 9complex(np.inf, np.nan), # 10complex(np.inf, np.nan), # 10complex(np.nan, 0.0), # 11complex(np.nan, 0.0), # 11complex(np.nan, 1.0), # 12complex(np.nan, np.nan), # 12complex(np.nan, 1.0), # 13complex(np.nan, np.nan), # 13complex(np.nan, np.nan), # 14complex(np.nan, np.nan) # 14
]
foriinrange(len(values)//2):
j=i*2v=values[j]
e=values[j+1]
actual=np.cosh(v)
print('Value: {value}'.format(value=str(v)))
print('Actual: {actual}'.format(actual=str(actual)))
print('Expected: {expected}'.format(expected=str(e)))
print('Equal: {is_equal}'.format(is_equal=str(is_equal(actual, e))))
print('\n')

Value: 0j
Actual: (1+0j)
Expected: (1+0j)
Equal: True
Value: (-0+0j)
Actual: (1-0j)
Expected: (1-0j)
Equal: True
/path/to/ccosh.py:116: RuntimeWarning: invalid value encountered in cosh
actual = np.cosh(v)
Value: infj
Actual: (nan+0j)
Expected: (nan+0j)
Equal: True
Value: nanj
Actual: (nan+0j)
Expected: (nan+0j)
Equal: True
Value: (1+infj)
Actual: (nan+nanj)
Expected: (nan+nanj)
Equal: True
Value: (1+nanj)
Actual: (nan+nanj)
Expected: (nan+nanj)
Equal: True
Value: (inf+0j)
Actual: (inf+0j)
Expected: (inf+0j)
Equal: True
Value: (inf-0j)
Actual: (inf-0j)
Expected: (inf-0j)
Equal: True
Value: (inf+1j)
Actual: (inf+infj)
Expected: (inf+infj)
Equal: True
Value: (inf+infj)
Actual: (inf+nanj)
Expected: (inf+nanj)
Equal: True
Value: (inf+nanj)
Actual: (inf+nanj)
Expected: (inf+nanj)
Equal: True
Value: (nan+0j)
Actual: (nan+0j)
Expected: (nan+0j)
Equal: True
Value: (nan+1j)
Actual: (nan+nanj)
Expected: (nan+nanj)
Equal: True
Value: (nan+1j)
Actual: (nan+nanj)
Expected: (nan+nanj)
Equal: True
Value: (nan+nanj)
Actual: (nan+nanj)
Expected: (nan+nanj)
Equal: True

[kgryte]

As cosh does not involve branch cuts and the special cases introduced in this PR follow prior art, will merge. Further revisions can be addressed in subsequent PRs...