def _sinpi_real(x):
if x < 0:
return -_sinpi_real(-x)
n, r = divmod(x, 0.5)
r *= pi
n %= 4
if n == 0: return math.sin(r)
if n == 1: return math.cos(r)
if n == 2: return -math.sin(r)
if n == 3: return -math.cos(r)
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