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BUG: Simplified fix, Overflow in tan and tanh for large complex values. #5518

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Merged
charris merged 7 commits into from
Feb 13, 2015
Merged

BUG: Simplified fix, Overflow in tan and tanh for large complex values. #5518

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de681b7
ENH: Detect all functions in complex.h
charris Jan 28, 2015
c1f7e0b
ENH: Implement more fallback complex functions for npy_math.
ewmoore Jan 28, 2015
6906823
ENH: Use the new complex functions in npymath for our ufuncs.
ewmoore Jan 28, 2015
34b5f9f
TST: Add tests for complex ufuncs.
ewmoore Jan 29, 2015
44d0c52
BUG: Do not use system cpow directly.
charris Jan 29, 2015
3a4127b
BUG: Disable broken complex trig functions for early linux glibc.
charris Jan 30, 2015
f9c3776
DOC: Document changes in npymath library.
charris Feb 13, 2015
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TST: Add tests for complex ufuncs. 
The test for precision needed to have difference changed from 2*eps to
2.1*eps for the system supplied sinh.
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@ewmoore @charris
ewmoore authored and charris committed Feb 13, 2015
commit 34b5f9f631fe268559c4a896fdf19e91aedd4a35
104 changes: 60 additions & 44 deletions numpy/core/tests/test_umath.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1363,45 +1363,53 @@ def test_precisions_consistent(self) :

def test_branch_cuts(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True

yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, -1j], 1, -1
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, -1j], 1, -1
yield _check_branch_cut, np.arctan, [-2j, 2j], [1, -1 ], -1, 1
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1 ], -1, 1, True

yield _check_branch_cut, np.arcsinh, [-2j, 2j], [-1, 1], -1, 1
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, -1j], 1, -1
yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True

# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1

yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1 ], 1, 1
yield _check_branch_cut, np.arccosh, [-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [-2j, 2j, 0], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1

@dec.knownfailureif(True, "These branch cuts are known to fail")
def test_branch_cuts_failing(self):
# XXX: signed zero not OK with ICC on 64-bit platform for log, see
# http://permalink.gmane.org/gmane.comp.python.numeric.general/25335
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True
# XXX: signed zeros are not OK for sqrt or for the arc* functions
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True
yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, -1j], 1, -1, True
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, -1j], 1, -1, True
yield _check_branch_cut, np.arctan, [-2j, 2j], [1, -1 ], -1, 1, True
yield _check_branch_cut, np.arcsinh, [-2j, 2j], [-1, 1], -1, 1, True
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, -1j], 1, -1, True
def test_branch_cuts_complex64(self):
# check branch cuts and continuity on them
yield _check_branch_cut, np.log, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log2, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log10, -0.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.log1p, -1.5, 1j, 1, -1, True, np.complex64
yield _check_branch_cut, np.sqrt, -0.5, 1j, 1, -1, True, np.complex64

yield _check_branch_cut, np.arcsin, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arccos, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctan, [0-2j, 2j], [1, 1 ], -1, 1, True, np.complex64

yield _check_branch_cut, np.arcsinh, [0-2j, 2j], [1, 1], -1, 1, True, np.complex64
yield _check_branch_cut, np.arccosh, [ -1, 0.5], [1j, 1j], 1, -1, True, np.complex64
yield _check_branch_cut, np.arctanh, [ -2, 2], [1j, 1j], 1, -1, True, np.complex64

# check against bogus branch cuts: assert continuity between quadrants
yield _check_branch_cut, np.arcsin, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccos, [0-2j, 2j], [ 1, 1], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctan, [ -2, 2], [1j, 1j], 1, 1, False, np.complex64

yield _check_branch_cut, np.arcsinh, [ -2, 2, 0], [1j, 1j, 1 ], 1, 1, False, np.complex64
yield _check_branch_cut, np.arccosh, [0-2j, 2j, 2], [1, 1, 1j], 1, 1, False, np.complex64
yield _check_branch_cut, np.arctanh, [0-2j, 2j, 0], [1, 1, 1j], 1, 1, False, np.complex64

def test_against_cmath(self):
import cmath, sys
Expand Down Expand Up @@ -1466,7 +1474,7 @@ def check(x, rtol):
# So, give more leeway for long complex tests here:
check(x_series, 50*eps)
else:
check(x_series, 2*eps)
check(x_series, 2.1*eps)
check(x_basic, 2*eps/1e-3)

# Check a few points
Expand Down Expand Up @@ -1565,8 +1573,12 @@ def _check_branch_cut(f, x0, dx, re_sign=1, im_sign=-1, sig_zero_ok=False,
x0 = np.atleast_1d(x0).astype(dtype)
dx = np.atleast_1d(dx).astype(dtype)

scale = np.finfo(dtype).eps * 1e3
atol = 1e-4
if np.dtype(dtype).char == 'F':
scale = np.finfo(dtype).eps * 1e2
atol = np.float32(1e-2)
else:
scale = np.finfo(dtype).eps * 1e3
atol = 1e-4

y0 = f(x0)
yp = f(x0 + dx*scale*np.absolute(x0)/np.absolute(dx))
Expand All @@ -1581,16 +1593,20 @@ def _check_branch_cut(f, x0, dx, re_sign=1, im_sign=-1, sig_zero_ok=False,
# check that signed zeros also work as a displacement
jr = (x0.real == 0) & (dx.real != 0)
ji = (x0.imag == 0) & (dx.imag != 0)

x = -x0
x.real[jr] = 0.*dx.real
x.imag[ji] = 0.*dx.imag
x = -x
ym = f(x)
ym = ym[jr | ji]
y0 = y0[jr | ji]
assert_(np.all(np.absolute(y0.real - ym.real*re_sign) < atol), (y0, ym))
assert_(np.all(np.absolute(y0.imag - ym.imag*im_sign) < atol), (y0, ym))
if np.any(jr):
x = x0[jr]
x.real = np.NZERO
ym = f(x)
assert_(np.all(np.absolute(y0[jr].real - ym.real*re_sign) < atol), (y0[jr], ym))
assert_(np.all(np.absolute(y0[jr].imag - ym.imag*im_sign) < atol), (y0[jr], ym))


if np.any(ji):
x = x0[ji]
x.imag = np.NZERO
ym = f(x)
assert_(np.all(np.absolute(y0[ji].real - ym.real*re_sign) < atol), (y0[ji], ym))
assert_(np.all(np.absolute(y0[ji].imag - ym.imag*im_sign) < atol), (y0[ji], ym))

def test_copysign():
assert_(np.copysign(1, -1) == -1)
Expand Down