core.test_math

def test_sqrt_precision():

Test Square Root Precision

Verifies that the square root calculation maintains high precision (50 decimal places) required for financial calculations.

Mathematical Verification

We verify the property: $$(\sqrt{x})^2 \approx x$$

Inputs:

Value ($x$): 3050 (Decimal)

Expected Behavior: The squared result should differ from the original input by less than $10^{-40}$.

$$|(\sqrt{3050})^2 - 3050| < 10^{-40}$$

Calculation:

$y = \text{safe_sqrt}(3050)$
$\text{diff} = |y^2 - 3050|$

This ensures that we are not suffering from floating-point errors (where error $\approx 10^{-15}$).

EXCEL REPRODUCTION

1. Inputs (Cell B1)

Cell	Value
B1	3050

2. Calculation (Cells B2:B3)

Cell	Name	Formula	Expectation
B2	Sqrt	`=SQRT(B1)`	~55.2268
B3	Squared	`=B2^2`	3050

3. Difference (Cell B4)

Cell	Name	Formula	Note
B4	Diff	`=ABS(B3-B1)`\| Should be ~0

def test_normal_cdf():

Test Standard Normal CDF

Verifies the Cumulative Distribution Function $N(x)$ for the standard normal distribution.

Formula

$$N(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{x} e^{-t^2/2} dt$$

We test against known values and properties.

Test Case 1: Symmetry

Property: $N(x) + N(-x) = 1$

Input: $x = 1.5$

Verification: $|N(1.5) + N(-1.5) - 1| < 10^{-20}$

Test Case 2: Zero Point

Property: $N(0) = 0.5$

Verification: $|N(0) - 0.5| < 10^{-7}$

Test Case 3: 1.96 (95% Confidence Interval)

Standard statistical value for $Z=1.96$.

Input: $1.96$

Expected Output: $\approx 0.9750021048$

Verification: Error $< 10^{-6}$

Test Case 4: -1.96

Lower tail probability.

Input: $-1.96$

Expected Output: $\approx 0.0249978951$

Verification: Error $< 10^{-6}$

EXCEL REPRODUCTION

1. Test Table (Columns A, B)

Row	Z Value (A)	CDF Formula (B)	Expected (C)
1	1.5	`=NORM.S.DIST(A1,TRUE)`	~0.9332
2	-1.5	`=NORM.S.DIST(A2,TRUE)`	~0.0668
3	0	`=NORM.S.DIST(A3,TRUE)`	0.5
4	1.96	`=NORM.S.DIST(A4,TRUE)`	~0.9750
5	-1.96	`=NORM.S.DIST(A5,TRUE)`	~0.0250

2. Symmetry Check (Row 6)

Cell	Name	Formula	Expectation
B6	Sum(1.5)	`=B1+B2`\| 1.0

def test_safe_sqrt_low_precision_handling():

Test that safe_sqrt enforces a minimum precision of 50, even if the global context is set lower. This is critical for maintaining accuracy in financial calculations.

def test_safe_sqrt_zero_input():

Test safe_sqrt with zero as an input. Expected behavior: The function should return Decimal('0') without any precision issues or errors.

def test_safe_sqrt_negative_input_error():

Test that safe_sqrt raises a ValueError when given a negative input, as the square root of a negative number is undefined in real numbers.

def test_safe_ln_positive_input():

Test safe_ln with a standard positive input.

def test_safe_ln_zero_input_error():

Test that safe_ln raises a ValueError when given zero, as ln(0) is undefined.

def test_safe_ln_negative_input_error():

Test that safe_ln raises a ValueError when given a negative number.