[error] Improve display of error messages (colours, auto-inferred file name and line number) (#195)

This PR refactors Decimo’s error handling to produce Python-style
tracebacks with ANSI coloring, and updates many call sites to raise
typed `DecimoError[...]` variants (e.g., `ValueError`, `OverflowError`)
with consistent metadata (message/function/previous error).

**Changes:**
- Reworked `DecimoError` formatting to mimic Python tracebacks,
including chained errors and ANSI colors.
- Updated many modules to raise structured `DecimoError` variants
instead of raw string `Error(...)` messages.
- Removed explicit `file=` parameters at many raise sites in favor of
auto-captured file/line via `call_location()`.

Author: forfudan

src/decimo/bigdecimal/arithmetics.mojo

@@ -20,6 +20,7 @@ Implements functions for mathematical operations on BigDecimal objects.
 
 from std import math
 
+from decimo.errors import ZeroDivisionError
 from decimo.rounding_mode import RoundingMode
 
 # ===----------------------------------------------------------------------=== #
@@ -319,7 +320,12 @@ def true_divide(
     """
     # Check for division by zero
     if y.coefficient.is_zero():
-        raise Error("bigdecimal.arithmetics.true_divide(): Division by zero")
+        raise Error(
+            ZeroDivisionError(
+                message="Division by zero.",
+                function="true_divide()",
+            )
+        )
 
     # Handle dividend of zero
     if x.coefficient.is_zero():
@@ -692,7 +698,12 @@ def true_divide_inexact(
 
     # Check for division by zero
     if x2.coefficient.is_zero():
-        raise Error("Division by zero")
+        raise Error(
+            ZeroDivisionError(
+                message="Division by zero.",
+                function="true_divide_inexact()",
+            )
+        )
 
     # Handle dividend of zero
     if x1.coefficient.is_zero():
@@ -905,7 +916,12 @@ def truncate_divide(x1: BigDecimal, x2: BigDecimal) raises -> BigDecimal:
     """
     # Check for division by zero
     if x2.coefficient.is_zero():
-        raise Error("Division by zero")
+        raise Error(
+            ZeroDivisionError(
+                message="Division by zero.",
+                function="truncate_divide()",
+            )
+        )
 
     # Handle dividend of zero
     if x1.coefficient.is_zero():
@@ -945,7 +961,12 @@ def truncate_modulo(
     """
     # Check for division by zero
     if x2.coefficient.is_zero():
-        raise Error("Division by zero")
+        raise Error(
+            ZeroDivisionError(
+                message="Division by zero.",
+                function="truncate_modulo()",
+            )
+        )
 
     return subtract(
         x1,

src/decimo/bigdecimal/bigdecimal.mojo

@@ -27,7 +27,7 @@ from std.memory import UnsafePointer
 from std.python import PythonObject
 from std import testing
 
-from decimo.errors import DecimoError
+from decimo.errors import DecimoError, ConversionError, ValueError
 from decimo.rounding_mode import RoundingMode
 from decimo.bigdecimal.rounding import round_to_precision
 from decimo.bigint10.bigint10 import BigInt10
@@ -362,14 +362,22 @@ struct BigDecimal(
             return Self(coefficient=BigUInt.zero(), scale=0, sign=False)
 
         if value != value:  # Check for NaN
-            raise Error("`from_scalar()`: Cannot convert NaN to BigUInt")
+            raise Error(
+                ValueError(
+                    message="Cannot convert NaN to BigDecimal.",
+                    function="BigDecimal.from_scalar()",
+                )
+            )
         # Convert to string with full precision
         try:
             return Self.from_string(String(value))
         except e:
             raise Error(
-                "`from_scalar()`: Cannot get decimal from string\nTrace back: "
-                + String(e),
+                ConversionError(
+                    message="Cannot convert scalar to BigDecimal.",
+                    function="BigDecimal.from_scalar()",
+                    previous_error=e^,
+                )
             )
 
     @staticmethod
@@ -537,11 +545,9 @@ struct BigDecimal(
 
         except e:
             raise Error(
-                DecimoError(
-                    file="src/decimo/bigdecimal/bigdecimal.mojo",
-                    function="from_python_decimal()",
-                    message="Failed to convert Python Decimal to BigDecimal: "
-                    + "as_tuple() returned invalid data or conversion failed.",
+                ConversionError(
+                    message="Failed to convert Python Decimal to BigDecimal.",
+                    function="BigDecimal.from_python_decimal()",
                     previous_error=e^,
                 ),
             )

src/decimo/bigdecimal/constants.mojo

@@ -18,6 +18,7 @@
 """
 
 from decimo.bigdecimal.bigdecimal import BigDecimal
+from decimo.errors import ValueError
 from decimo.bigint10.bigint10 import BigInt10
 from decimo.rounding_mode import RoundingMode
 
@@ -164,7 +165,11 @@ def pi(precision: Int) raises -> BigDecimal:
     """
 
     if precision < 0:
-        raise Error("Precision must be non-negative")
+        raise Error(
+            ValueError(
+                message="Precision must be non-negative", function="pi()"
+            )
+        )
 
     # TODO: When global variables are supported,
     # we can check if we have a cached value for the requested precision.

src/decimo/bigdecimal/exponential.mojo

@@ -19,6 +19,7 @@
 from std import math
 
 from decimo.bigdecimal.bigdecimal import BigDecimal
+from decimo.errors import ValueError, OverflowError, ZeroDivisionError
 from decimo.rounding_mode import RoundingMode
 
 # ===----------------------------------------------------------------------=== #
@@ -235,11 +236,20 @@ def power(
     # Special cases
     if base.coefficient.is_zero():
         if exponent.coefficient.is_zero():
-            raise Error("Error in power: 0^0 is undefined")
+            raise Error(
+                ValueError(
+                    message="0^0 is undefined.",
+                    function="power()",
+                )
+            )
         elif exponent.sign:
             raise Error(
-                "Error in power: Division by zero (negative exponent with zero"
-                " base)"
+                ZeroDivisionError(
+                    message=(
+                        "Division by zero (negative exponent with zero base)."
+                    ),
+                    function="power()",
+                )
             )
         else:
             return BigDecimal(BigUInt.zero(), 0, False)
@@ -264,8 +274,13 @@ def power(
     # Check for negative base with non-integer exponent
     if base.sign and not exponent.is_integer():
         raise Error(
-            "Error in power: Negative base with non-integer exponent would"
-            " produce a complex result"
+            ValueError(
+                message=(
+                    "Negative base with non-integer exponent would produce"
+                    " a complex result."
+                ),
+                function="power()",
+            )
         )
 
     # Optimization for integer exponents
@@ -434,7 +449,12 @@ def root(x: BigDecimal, n: BigDecimal, precision: Int) raises -> BigDecimal:
 
     # Check for n = 0
     if n.coefficient.is_zero():
-        raise Error("Error in `root`: Cannot compute zeroth root")
+        raise Error(
+            ValueError(
+                message="Cannot compute zeroth root.",
+                function="root()",
+            )
+        )
 
     # Special case for integer roots - use more efficient implementation
     if not n.sign:
@@ -493,8 +513,13 @@ def root(x: BigDecimal, n: BigDecimal, precision: Int) raises -> BigDecimal:
         var n_is_odd_reciprocal = is_odd_reciprocal(n)
         if not n_is_integer and not n_is_odd_reciprocal:
             raise Error(
-                "Error in `root`: Cannot compute non-odd-integer root of a"
-                " negative number"
+                ValueError(
+                    message=(
+                        "Cannot compute non-odd-integer root of a negative"
+                        " number."
+                    ),
+                    function="root()",
+                )
             )
         elif n_is_integer:
             var result = integer_root(x, n, precision)
@@ -549,13 +574,28 @@ def integer_root(
 
     # Handle special case: n must be a positive integer
     if n.sign:
-        raise Error("Error in `root`: Root value must be positive")
+        raise Error(
+            ValueError(
+                message="Root value must be positive.",
+                function="integer_root()",
+            )
+        )
 
     if not n.is_integer():
-        raise Error("Error in `root`: Root value must be an integer")
+        raise Error(
+            ValueError(
+                message="Root value must be an integer.",
+                function="integer_root()",
+            )
+        )
 
     if n.coefficient.is_zero():
-        raise Error("Error in `root`: Cannot compute zeroth root")
+        raise Error(
+            ValueError(
+                message="Cannot compute zeroth root.",
+                function="integer_root()",
+            )
+        )
 
     # Special case: n = 1 (1st root is just the number itself)
     if n.is_one():
@@ -594,7 +634,10 @@ def integer_root(
             result_sign = True
         else:  # n_uint.words[0] % 2 == 0:  # Even root
             raise Error(
-                "Error in `root`: Cannot compute even root of a negative number"
+                ValueError(
+                    message="Cannot compute even root of a negative number.",
+                    function="integer_root()",
+                )
             )
 
     # Extract n as Int for Newton's method
@@ -1183,7 +1226,10 @@ def sqrt_exact(x: BigDecimal, precision: Int) raises -> BigDecimal:
     # Handle special cases
     if x.sign:
         raise Error(
-            "Error in `sqrt`: Cannot compute square root of negative number"
+            ValueError(
+                message="Cannot compute square root of a negative number.",
+                function="sqrt_exact()",
+            )
         )
 
     if x.coefficient.is_zero():
@@ -1316,7 +1362,10 @@ def sqrt_reciprocal(x: BigDecimal, precision: Int) raises -> BigDecimal:
     # Handle special cases
     if x.sign:
         raise Error(
-            "Error in `sqrt`: Cannot compute square root of negative number"
+            ValueError(
+                message="Cannot compute square root of a negative number.",
+                function="sqrt_reciprocal()",
+            )
         )
 
     if x.coefficient.is_zero():
@@ -1498,7 +1547,10 @@ def sqrt_newton(x: BigDecimal, precision: Int) raises -> BigDecimal:
     # Handle special cases
     if x.sign:
         raise Error(
-            "Error in `sqrt`: Cannot compute square root of negative number"
+            ValueError(
+                message="Cannot compute square root of a negative number.",
+                function="sqrt_newton()",
+            )
         )
 
     if x.coefficient.is_zero():
@@ -1583,7 +1635,10 @@ def sqrt_decimal_approach(x: BigDecimal, precision: Int) raises -> BigDecimal:
     # Handle special cases
     if x.sign:
         raise Error(
-            "Error in `sqrt`: Cannot compute square root of negative number"
+            ValueError(
+                message="Cannot compute square root of a negative number.",
+                function="sqrt_decimal_approach()",
+            )
         )
 
     if x.coefficient.is_zero():
@@ -1765,7 +1820,11 @@ def exp(x: BigDecimal, precision: Int) raises -> BigDecimal:
     # For very large positive values, result will overflow BigDecimal capacity
     # TODO: Use BigInt10 as scale can avoid overflow in this case
     if not x.sign and x.adjusted() >= 20:  # x > 10^20
-        raise Error("Error in `exp`: Result too large to represent")
+        raise Error(
+            OverflowError(
+                message="Result too large to represent", function="exp()"
+            )
+        )
 
     # For very large negative values, result will be effectively zero
     if x.sign and x.adjusted() >= 20:  # x < -10^20
@@ -1973,10 +2032,17 @@ def ln(
     # Handle special cases
     if x.sign:
         raise Error(
-            "Error in `ln`: Cannot compute logarithm of negative number"
+            ValueError(
+                message="Cannot compute logarithm of negative number",
+                function="ln()",
+            )
         )
     if x.coefficient.is_zero():
-        raise Error("Error in `ln`: Cannot compute logarithm of zero")
+        raise Error(
+            ValueError(
+                message="Cannot compute logarithm of zero", function="ln()"
+            )
+        )
     if x == BigDecimal(BigUInt.one(), 0, False):
         return BigDecimal(BigUInt.zero(), 0, False)  # ln(1) = 0
 
@@ -2066,21 +2132,36 @@ def log(x: BigDecimal, base: BigDecimal, precision: Int) raises -> BigDecimal:
     # Special cases
     if x.sign:
         raise Error(
-            "Error in log(): Cannot compute logarithm of a negative number"
+            ValueError(
+                message="Cannot compute logarithm of a negative number",
+                function="log()",
+            )
         )
     if x.coefficient.is_zero():
-        raise Error("Error in log(): Cannot compute logarithm of zero")
+        raise Error(
+            ValueError(
+                message="Cannot compute logarithm of zero", function="log()"
+            )
+        )
 
     # Base validation
     if base.sign:
-        raise Error("Error in log(): Cannot use a negative base")
+        raise Error(
+            ValueError(message="Cannot use a negative base", function="log()")
+        )
     if base.coefficient.is_zero():
-        raise Error("Error in log(): Cannot use zero as a base")
+        raise Error(
+            ValueError(message="Cannot use zero as a base", function="log()")
+        )
     if (
         base.coefficient.number_of_digits() == base.scale + 1
         and base.coefficient.words[-1] == 1
     ):
-        raise Error("Error in log(): Cannot use base 1 for logarithm")
+        raise Error(
+            ValueError(
+                message="Cannot use base 1 for logarithm", function="log()"
+            )
+        )
 
     # Special cases
     if (
@@ -2129,10 +2210,17 @@ def log10(x: BigDecimal, precision: Int) raises -> BigDecimal:
     # Special cases
     if x.sign:
         raise Error(
-            "Error in log10(): Cannot compute logarithm of a negative number"
+            ValueError(
+                message="Cannot compute logarithm of a negative number",
+                function="log10()",
+            )
         )
     if x.coefficient.is_zero():
-        raise Error("Error in log10(): Cannot compute logarithm of zero")
+        raise Error(
+            ValueError(
+                message="Cannot compute logarithm of zero", function="log10()"
+            )
+        )
 
     # Fast path: Powers of 10 are handled directly
     if x.coefficient.is_power_of_10():