def mpi_cos_sin(x, prec):
a, b = x
# Guaranteed to contain both -1 and 1
if finf in (a, b) or fninf in (a, b):
return (fnone, fone), (fnone, fone)
y, yswaps, yn = reduce_angle(a, prec+20)
z, zswaps, zn = reduce_angle(b, prec+20)
# Guaranteed to contain both -1 and 1
if zn - yn >= 4:
return (fnone, fone), (fnone, fone)
# Both points in the same quadrant -- cos and sin both strictly monotonous
if yn == zn:
m = yn % 4
if m == 0:
cb, sa = calc_cos_sin(0, y, yswaps, prec, round_ceiling, round_floor)
ca, sb = calc_cos_sin(0, z, zswaps, prec, round_floor, round_ceiling)
if m == 1:
cb, sb = calc_cos_sin(0, y, yswaps, prec, round_ceiling, round_ceiling)
ca, sa = calc_cos_sin(0, z, zswaps, prec, round_floor, round_ceiling)
if m == 2:
ca, sb = calc_cos_sin(0, y, yswaps, prec, round_floor, round_ceiling)
cb, sa = calc_cos_sin(0, z, zswaps, prec, round_ceiling, round_floor)
if m == 3:
ca, sa = calc_cos_sin(0, y, yswaps, prec, round_floor, round_floor)
cb, sb = calc_cos_sin(0, z, zswaps, prec, round_ceiling, round_ceiling)
return (ca, cb), (sa, sb)
# Intervals spanning multiple quadrants
yn %= 4
zn %= 4
case = (yn, zn)
if case == (0, 1):
cb, sy = calc_cos_sin(0, y, yswaps, prec, round_ceiling, round_floor)
ca, sz = calc_cos_sin(0, z, zswaps, prec, round_floor, round_floor)
return (ca, cb), (MIN(sy, sz), fone)
ca, sb = calc_cos_sin(0, y, yswaps, prec, round_floor, round_ceiling)
cb, sa = calc_cos_sin(0, z, zswaps, prec, round_ceiling, round_floor)
if m == 3:
ca, sa = calc_cos_sin(0, y, yswaps, prec, round_floor, round_floor)
cb, sb = calc_cos_sin(0, z, zswaps, prec, round_ceiling, round_ceiling)
return (ca, cb), (sa, sb)
# Intervals spanning multiple quadrants
yn %= 4
zn %= 4
case = (yn, zn)
if case == (0, 1):
cb, sy = calc_cos_sin(0, y, yswaps, prec, round_ceiling, round_floor)
ca, sz = calc_cos_sin(0, z, zswaps, prec, round_floor, round_floor)
return (ca, cb), (MIN(sy, sz), fone)
if case == (3, 0):
cy, sa = calc_cos_sin(0, y, yswaps, prec, round_floor, round_floor)
cz, sb = calc_cos_sin(0, z, zswaps, prec, round_floor, round_ceiling)
return (MIN(cy, cz), fone), (sa, sb)
raise NotImplementedError("cos/sin spanning multiple quadrants")
def mpi_cos(x, prec):
return mpi_cos_sin(x, prec)[0]
def mpi_sin(x, prec):
return mpi_cos_sin(x, prec)[1]
def mpi_tan(x, prec):
cos, sin = mpi_cos_sin(x, prec+20)
return mpi_div(sin, cos, prec)
def mpi_cos_sin(x, prec):
a, b = x
# Guaranteed to contain both -1 and 1
if finf in (a, b) or fninf in (a, b):
return (fnone, fone), (fnone, fone)
y, yswaps, yn = reduce_angle(a, prec + 20)
z, zswaps, zn = reduce_angle(b, prec + 20)
# Guaranteed to contain both -1 and 1
if zn - yn >= 4:
return (fnone, fone), (fnone, fone)
# Both points in the same quadrant -- cos and sin both strictly monotonous
if yn == zn:
m = yn % 4
if m == 0:
cb, sa = calc_cos_sin(0, y, yswaps, prec, round_ceiling, round_floor)
ca, sb = calc_cos_sin(0, z, zswaps, prec, round_floor, round_ceiling)
if m == 1:
cb, sb = calc_cos_sin(0, y, yswaps, prec, round_ceiling, round_ceiling)
ca, sa = calc_cos_sin(0, z, zswaps, prec, round_floor, round_ceiling)
if m == 2:
ca, sb = calc_cos_sin(0, y, yswaps, prec, round_floor, round_ceiling)
cb, sa = calc_cos_sin(0, z, zswaps, prec, round_ceiling, round_floor)
if m == 3:
ca, sa = calc_cos_sin(0, y, yswaps, prec, round_floor, round_floor)
cb, sb = calc_cos_sin(0, z, zswaps, prec, round_ceiling, round_ceiling)
return (ca, cb), (sa, sb)
# Intervals spanning multiple quadrants
yn %= 4
zn %= 4
case = (yn, zn)
if case == (0, 1):
cb, sy = calc_cos_sin(0, y, yswaps, prec, round_ceiling, round_floor)
ca, sz = calc_cos_sin(0, z, zswaps, prec, round_floor, round_floor)
return (ca, cb), (MIN(sy, sz), fone)
if case == (3, 0):
cy, sa = calc_cos_sin(0, y, yswaps, prec, round_floor, round_floor)
cz, sb = calc_cos_sin(0, z, zswaps, prec, round_floor, round_ceiling)
return (MIN(cy, cz), fone), (sa, sb)
raise NotImplementedError("cos/sin spanning multiple quadrants")