def count_horner_compensated6():
print("horner.compensated_k(..., 6) (312n + 818, n >= 5):")
for degree in range(5, 9 + 1):
parent = operation_count.Computation()
x = operation_count.Float(2.0, parent)
coeffs = (operation_count.Float(1.0, parent), ) * (degree + 1)
p = horner.compensated_k(x, coeffs, 6)
assert p.value == 2.0**(degree + 1) - 1
assert parent.count == horner_expected_total(6, degree)
assert parent.fma_count == horner_expected_fma(6, degree)
print(" degree {}: {}".format(degree, parent.display))
def count_horner_compensated5():
print("horner.compensated_k(..., 5) (152n + 350, n >= 4):")
for degree in range(4, 8 + 1):
parent = operation_count.Computation()
x = operation_count.Float(2.0, parent)
coeffs = (operation_count.Float(1.0, parent), ) * (degree + 1)
p = horner.compensated_k(x, coeffs, 5)
assert p.value == 2.0**(degree + 1) - 1
assert parent.count == horner_expected_total(5, degree)
assert parent.fma_count == horner_expected_fma(5, degree)
print(" degree {}: {}".format(degree, parent.display))
def count_horner_compensated3():
print("horner.compensated3() (32n + 46, n >= 2):")
for degree in range(2, 6 + 1):
parent = operation_count.Computation()
x = operation_count.Float(2.0, parent)
coeffs = (operation_count.Float(1.0, parent), ) * (degree + 1)
p = horner.compensated3(x, coeffs)
assert p.value == 2.0**(degree + 1) - 1
assert parent.count == horner_expected_total(3, degree)
assert parent.fma_count == horner_expected_fma(3, degree)
print(" degree {}: {}".format(degree, parent.display))
print("horner.compensated_k(..., 3) (32n + 46, n >= 2):")
for degree in range(2, 6 + 1):
parent = operation_count.Computation()
x = operation_count.Float(2.0, parent)
coeffs = (operation_count.Float(1.0, parent), ) * (degree + 1)
p = horner.compensated_k(x, coeffs, 3)
assert p.value == 2.0**(degree + 1) - 1
assert parent.count == horner_expected_total(3, degree)
assert parent.fma_count == horner_expected_fma(3, degree)
print(" degree {}: {}".format(degree, parent.display))
def count_horner_compensated():
print("horner.compensated() (11n + 1):")
for degree in range(1, 5 + 1):
parent = operation_count.Computation()
x = operation_count.Float(2.0, parent)
coeffs = (operation_count.Float(1.0, parent), ) * (degree + 1)
p = horner.compensated(x, coeffs)
assert p.value == 2.0**(degree + 1) - 1
assert parent.count == 11 * degree + 1
print(" degree {}: {}".format(degree, parent.display))
# NOTE: This is **the same** as ``horner.compensated()`` but uses
# a different algorithm.
print("horner.compensated_k(..., 2) (12n + 10):")
for degree in range(1, 5 + 1):
parent = operation_count.Computation()
x = operation_count.Float(2.0, parent)
coeffs = (operation_count.Float(1.0, parent), ) * (degree + 1)
p = horner.compensated_k(x, coeffs, 2)
assert p.value == 2.0**(degree + 1) - 1
assert parent.count == horner_expected_total(2, degree)
assert parent.fma_count == horner_expected_fma(2, degree)
print(" degree {}: {}".format(degree, parent.display))