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# Test accuracy of `repr` conversions.
# This test also increases code coverage for corner cases.
try:
import array, math, random
except ImportError:
print("SKIP")
raise SystemExit
# The largest errors come from seldom used very small numbers, near the
# limit of the representation. So we keep them out of this test to keep
# the max relative error display useful.
if float("1e-100") == 0.0:
# single-precision
float_type = "f"
float_size = 4
# testing range
min_expo = -96 # i.e. not smaller than 1.0e-29
# Expected results (given >=50'000 samples):
# - MICROPY_FLTCONV_IMPL_EXACT: 100% exact conversions
# - MICROPY_FLTCONV_IMPL_APPROX: >=98.53% exact conversions, max relative error <= 1.01e-7
min_success = 0.980 # with only 1200 samples, the success rate is lower
max_rel_err = 1.1e-7
# REPR_C is typically used with FORMAT_IMPL_BASIC, which has a larger error
is_REPR_C = float("1.0000001") == float("1.0")
if is_REPR_C: # REPR_C
min_success = 0.83
max_rel_err = 5.75e-07
else:
# double-precision
float_type = "d"
float_size = 8
# testing range
min_expo = -845 # i.e. not smaller than 1.0e-254
# Expected results (given >=200'000 samples):
# - MICROPY_FLTCONV_IMPL_EXACT: 100% exact conversions
# - MICROPY_FLTCONV_IMPL_APPROX: >=99.83% exact conversions, max relative error <= 2.7e-16
min_success = 0.997 # with only 1200 samples, the success rate is lower
max_rel_err = 2.7e-16
# Deterministic pseudorandom generator. Designed to be uniform
# on mantissa values and exponents, not on the represented number
def pseudo_randfloat():
rnd_buff = bytearray(float_size)
for _ in range(float_size):
rnd_buff[_] = random.getrandbits(8)
return array.array(float_type, rnd_buff)[0]
random.seed(42)
stats = 0
N = 1200
max_err = 0
for _ in range(N):
f = pseudo_randfloat()
while type(f) is not float or math.isinf(f) or math.isnan(f) or math.frexp(f)[1] <= min_expo:
f = pseudo_randfloat()
str_f = repr(f)
f2 = float(str_f)
if f2 == f:
stats += 1
else:
error = abs((f2 - f) / f)
if max_err < error:
max_err = error
print(N, "values converted")
if stats / N >= min_success and max_err <= max_rel_err:
print("float format accuracy OK")
else:
print("FAILED: repr rate=%.3f%% max_err=%.3e" % (100 * stats / N, max_err))
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