[Python] polynomial evaluation Decimal precision [closed]

I'm struggling to implement two functions that need to pass specific pytest cases I can't modify. The first evaluates a polynomial with precision requirements, and the second solves a system of equations with Decimal arithmetic.

Problem 1: Polynomial Evaluation (code1.py) The test requires:

Exact float evaluation (y_e)

Term-by-term evaluation with truncation (y_p)

Nested (Horner) evaluation (y_a) All with Decimal precision (3 digits) and ROUND_FLOOR rounding.

Test Cases(code 1):

,,, import code1 as q import numpy from decimal import * import pytest

@pytest.mark.timeout(5)
def pytest_code1():
getcontext().prec = 3
getcontext().rounding = ROUND_FLOOR

# Test case 1
y_e, y_p, y_a = q.eval_poly(numpy.array([1, -7, 8, 0.35], dtype=numpy.float64),
numpy.float64(1.37))
assert y_e == pytest.approx(0.743053)
assert y_p == Decimal('0.549')
assert y_a == Decimal('0.732')

# Test case 2
y_e, y_p, y_a = q.eval_poly(numpy.array([1, -6.1, 3.2, 1.5], dtype=numpy.float64),
numpy.float64(4.71))
assert y_e == pytest.approx(-14.263899)
assert y_p == Decimal('-15.5')
assert y_a == Decimal('-14.6')

# Type checks
with pytest.raises(TypeError):
q.eval_poly([1, -6.1, 3.2, 1.5], 4.71)
with pytest.raises(TypeError):
q.eval_poly(numpy.array([1, -6.1, 3.2, 1.5], dtype=numpy.float64), 4.71)


,,, my attempt (code1); ,,, import numpy as np from decimal import Decimal, getcontext, ROUND_FLOOR, localcontext

def trunc(x, sig=3):
"""Truncate x to sig significant figures using Decimal."""
if x == 0:
return Decimal('0')

x = Decimal(str(x))
exponent = x.adjusted()
shift = sig - exponent - 1

if shift < 0:
shift = 0

with localcontext() as ctx:
ctx.prec = sig
ctx.rounding = ROUND_FLOOR
truncated = (x.scaleb(shift).to_integral_value()).scaleb(-shift)
return truncated

def eval_poly(a: np.ndarray, x0: float):
if not isinstance(a, np.ndarray) or not isinstance(x0, float):
raise TypeError("Invalid input types")

# Exact evaluation
y_e = a[0] * x0**3 + a[1] * x0**2 + a[2] * x0 + a[3]

# Decimal conversions
x0_d = Decimal(str(x0))
a_d = [Decimal(str(coef)) for coef in a]

# Partial evaluation
def calculate_yp():
with localcontext() as ctx:
ctx.prec = 3
ctx.rounding = ROUND_FLOOR
terms = [
trunc(a_d[0] * x0_d**3),
trunc(a_d[1] * x0_d**2),
trunc(a_d[2] * x0_d),
trunc(a_d[3])
]
yield trunc(sum(terms))

# Horner's method
def calculate_ya():
with localcontext() as ctx:
ctx.prec = 3
ctx.rounding = ROUND_FLOOR
h = trunc(a_d[0])
h = trunc(h * x0_d + a_d[1])
h = trunc(h * x0_d + a_d[2])
yield trunc(h * x0_d + a_d[3])

return (y_e, next(calculate_yp()), next(calculate_ya()))


,,, Test Cases(code 2):

,,, import code2 as q from decimal import * import pytest

@pytest.mark.timeout(5)
def pytest_code2():
getcontext().prec = 4
# Test case 1
a, b, e = 1.130, -6.990, 14.20
c, d, f = 1.013, -6.099, 14.22
x, y = q.two_eq_system(a, b, c, d, e, f)
assert (float(x), float(y)) == (float(Decimal('68.15')), float(Decimal('8.987')))

# Test case 2
a, b, e = 8.110, 12.20, -0.1370
c, d, f = -18.11, 112.2, -0.1376
x, y = q.two_eq_system(a, b, c, d, e, f)
assert (float(x), float(y)) == (float(Decimal('-0.01211')),
float(Decimal('-0.003183')))


,,,

my attempt (code2); ,,, from decimal import Decimal, getcontext, ROUND_FLOOR

def two_eq_system(a, b, e, c, d, f): getcontext().prec = 6 getcontext().rounding = ROUND_FLOOR

a_d = Decimal(str(a))
b_d = Decimal(str(b))
e_d = Decimal(str(e))
c_d = Decimal(str(c))
d_d = Decimal(str(d))
f_d = Decimal(str(f))

det = (a_d * d_d - b_d * c_d).quantize(Decimal('1.0000'))
x = (e_d * d_d - b_d * f_d) / det
y = (a_d * f_d - e_d * c_d) / det

return (
x.quantize(Decimal('1.00') if abs(x) > 1 else Decimal('1.0000')),
y.quantize(Decimal('1.000') if abs(y) > 1 else Decimal('1.0000'))
)


,,,

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