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import math
from rpython.rlib.rfloat import isnan, isinf, copysign
# code to deal with special values (infinities, NaNs, ...)
#
# The special types can be:
ST_NINF = 0 # negative infinity
ST_NEG = 1 # negative finite number (nonzero)
ST_NZERO = 2 # -0.
ST_PZERO = 3 # +0.
ST_POS = 4 # positive finite number (nonzero)
ST_PINF = 5 # positive infinity
ST_NAN = 6 # Not a Number
def special_type(d):
if isnan(d):
return ST_NAN
elif isinf(d):
if d > 0.0:
return ST_PINF
else:
return ST_NINF
else:
if d != 0.0:
if d > 0.0:
return ST_POS
else:
return ST_NEG
else:
if copysign(1., d) == 1.:
return ST_PZERO
else:
return ST_NZERO
P = math.pi
P14 = 0.25 * math.pi
P12 = 0.5 * math.pi
P34 = 0.75 * math.pi
INF = 1e200 * 1e200
N = INF / INF
U = -9.5426319407711027e33 # unlikely value, used as placeholder
Z = 0.0 # defined here instead of in the tuples below, because of a bug
# in pypy releases < 1.5
NAN = N
def build_table(lst):
table = []
assert len(lst) == 49
it = iter(lst)
for j in range(7):
row = []
for i in range(7):
(x, y) = it.next()
row.append((x, y))
table.append(row)
return table
acos_special_values = build_table([
(P34,INF), (P,INF), (P,INF), (P,-INF), (P,-INF), (P34,-INF), (N,INF),
(P12,INF), (U,U), (U,U), (U,U), (U,U), (P12,-INF), (N,N),
(P12,INF), (U,U), (P12,Z), (P12,-Z), (U,U), (P12,-INF), (P12,N),
(P12,INF), (U,U), (P12,Z), (P12,-Z), (U,U), (P12,-INF), (P12,N),
(P12,INF), (U,U), (U,U), (U,U), (U,U), (P12,-INF), (N,N),
(P14,INF), (Z,INF), (Z,INF), (Z,-INF), (Z,-INF), (P14,-INF), (N,INF),
(N,INF), (N,N), (N,N), (N,N), (N,N), (N,-INF), (N,N),
])
acosh_special_values = build_table([
(INF,-P34), (INF,-P), (INF,-P), (INF,P), (INF,P), (INF,P34), (INF,N),
(INF,-P12), (U,U), (U,U), (U,U), (U,U), (INF,P12), (N,N),
(INF,-P12), (U,U), (Z,-P12), (Z,P12), (U,U), (INF,P12), (N,N),
(INF,-P12), (U,U), (Z,-P12), (Z,P12), (U,U), (INF,P12), (N,N),
(INF,-P12), (U,U), (U,U), (U,U), (U,U), (INF,P12), (N,N),
(INF,-P14), (INF,-Z), (INF,-Z), (INF,Z), (INF,Z), (INF,P14), (INF,N),
(INF,N), (N,N), (N,N), (N,N), (N,N), (INF,N), (N,N),
])
asinh_special_values = build_table([
(-INF,-P14), (-INF,-Z), (-INF,-Z),(-INF,Z), (-INF,Z), (-INF,P14), (-INF,N),
(-INF,-P12), (U,U), (U,U), (U,U), (U,U), (-INF,P12), (N,N),
(-INF,-P12), (U,U), (-Z,-Z), (-Z,Z), (U,U), (-INF,P12), (N,N),
(INF,-P12), (U,U), (Z,-Z), (Z,Z), (U,U), (INF,P12), (N,N),
(INF,-P12), (U,U), (U,U), (U,U), (U,U), (INF,P12), (N,N),
(INF,-P14), (INF,-Z), (INF,-Z), (INF,Z), (INF,Z), (INF,P14), (INF,N),
(INF,N), (N,N), (N,-Z), (N,Z), (N,N), (INF,N), (N,N),
])
atanh_special_values = build_table([
(-Z,-P12), (-Z,-P12), (-Z,-P12), (-Z,P12), (-Z,P12), (-Z,P12), (-Z,N),
(-Z,-P12), (U,U), (U,U), (U,U), (U,U), (-Z,P12), (N,N),
(-Z,-P12), (U,U), (-Z,-Z), (-Z,Z), (U,U), (-Z,P12), (-Z,N),
(Z,-P12), (U,U), (Z,-Z), (Z,Z), (U,U), (Z,P12), (Z,N),
(Z,-P12), (U,U), (U,U), (U,U), (U,U), (Z,P12), (N,N),
(Z,-P12), (Z,-P12), (Z,-P12), (Z,P12), (Z,P12), (Z,P12), (Z,N),
(Z,-P12), (N,N), (N,N), (N,N), (N,N), (Z,P12), (N,N),
])
log_special_values = build_table([
(INF,-P34), (INF,-P), (INF,-P), (INF,P), (INF,P), (INF,P34), (INF,N),
(INF,-P12), (U,U), (U,U), (U,U), (U,U), (INF,P12), (N,N),
(INF,-P12), (U,U), (-INF,-P), (-INF,P), (U,U), (INF,P12), (N,N),
(INF,-P12), (U,U), (-INF,-Z), (-INF,Z), (U,U), (INF,P12), (N,N),
(INF,-P12), (U,U), (U,U), (U,U), (U,U), (INF,P12), (N,N),
(INF,-P14), (INF,-Z), (INF,-Z), (INF,Z), (INF,Z), (INF,P14), (INF,N),
(INF,N), (N,N), (N,N), (N,N), (N,N), (INF,N), (N,N),
])
sqrt_special_values = build_table([
(INF,-INF), (Z,-INF), (Z,-INF), (Z,INF), (Z,INF), (INF,INF), (N,INF),
(INF,-INF), (U,U), (U,U), (U,U), (U,U), (INF,INF), (N,N),
(INF,-INF), (U,U), (Z,-Z), (Z,Z), (U,U), (INF,INF), (N,N),
(INF,-INF), (U,U), (Z,-Z), (Z,Z), (U,U), (INF,INF), (N,N),
(INF,-INF), (U,U), (U,U), (U,U), (U,U), (INF,INF), (N,N),
(INF,-INF), (INF,-Z), (INF,-Z), (INF,Z), (INF,Z), (INF,INF), (INF,N),
(INF,-INF), (N,N), (N,N), (N,N), (N,N), (INF,INF), (N,N),
])
exp_special_values = build_table([
(Z,Z), (U,U), (Z,-Z), (Z,Z), (U,U), (Z,Z), (Z,Z),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(N,N), (U,U), (1.,-Z), (1.,Z), (U,U), (N,N), (N,N),
(N,N), (U,U), (1.,-Z), (1.,Z), (U,U), (N,N), (N,N),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(INF,N), (U,U), (INF,-Z), (INF,Z), (U,U), (INF,N), (INF,N),
(N,N), (N,N), (N,-Z), (N,Z), (N,N), (N,N), (N,N),
])
cosh_special_values = build_table([
(INF,N), (U,U), (INF,Z), (INF,-Z), (U,U), (INF,N), (INF,N),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(N,Z), (U,U), (1.,Z), (1.,-Z), (U,U), (N,Z), (N,Z),
(N,Z), (U,U), (1.,-Z), (1.,Z), (U,U), (N,Z), (N,Z),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(INF,N), (U,U), (INF,-Z), (INF,Z), (U,U), (INF,N), (INF,N),
(N,N), (N,N), (N,Z), (N,Z), (N,N), (N,N), (N,N),
])
sinh_special_values = build_table([
(INF,N), (U,U), (-INF,-Z), (-INF,Z), (U,U), (INF,N), (INF,N),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(Z,N), (U,U), (-Z,-Z), (-Z,Z), (U,U), (Z,N), (Z,N),
(Z,N), (U,U), (Z,-Z), (Z,Z), (U,U), (Z,N), (Z,N),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(INF,N), (U,U), (INF,-Z), (INF,Z), (U,U), (INF,N), (INF,N),
(N,N), (N,N), (N,-Z), (N,Z), (N,N), (N,N), (N,N),
])
tanh_special_values = build_table([
(-1.,Z), (U,U), (-1.,-Z), (-1.,Z), (U,U), (-1.,Z), (-1.,Z),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(N,N), (U,U), (-Z,-Z), (-Z,Z), (U,U), (N,N), (N,N),
(N,N), (U,U), (Z,-Z), (Z,Z), (U,U), (N,N), (N,N),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(1.,Z), (U,U), (1.,-Z), (1.,Z), (U,U), (1.,Z), (1.,Z),
(N,N), (N,N), (N,-Z), (N,Z), (N,N), (N,N), (N,N),
])
rect_special_values = build_table([
(INF,N), (U,U), (-INF,Z), (-INF,-Z), (U,U), (INF,N), (INF,N),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(Z,Z), (U,U), (-Z,Z), (-Z,-Z), (U,U), (Z,Z), (Z,Z),
(Z,Z), (U,U), (Z,-Z), (Z,Z), (U,U), (Z,Z), (Z,Z),
(N,N), (U,U), (U,U), (U,U), (U,U), (N,N), (N,N),
(INF,N), (U,U), (INF,-Z), (INF,Z), (U,U), (INF,N), (INF,N),
(N,N), (N,N), (N,Z), (N,Z), (N,N), (N,N), (N,N),
])
assert copysign(1., acosh_special_values[5][2][1]) == -1.