Add ClampedNumeric templates

base/numerics/README.md

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+# `base/numerics`
+
+This directory contains templates providing well-defined semantics for safely
+handling a variety of numeric operations, including most common arithmetic
+operations and conversions.
+
+The public API is broken out into the following header files:
+
+*   `checked_math.h` contains the `CheckedNumeric` template class and helper
+    functions for performing arithmetic and conversion operations that detect
+    errors and boundary conditions (e.g. overflow, truncation, etc.).
+*   `clamped_math.h` contains the `ClampedNumeric` template class and
+    helper functions for performing fast, clamped (i.e. non-sticky saturating)
+    arithmetic operations and conversions.
+*   `safe_conversions.h` contains the `StrictNumeric` template class and
+    a collection of custom casting templates and helper functions for safely
+    converting between a range of numeric types.
+*   `safe_math.h` includes all of the previously mentioned headers.
+
+*** aside
+**Note:** The `Numeric` template types implicitly convert from C numeric types
+and `Numeric` templates that are convertable to an underlying C numeric type.
+The conversion priority for `Numeric` type coercions is:
+
+*   `StrictNumeric` coerces to `ClampedNumeric` and `CheckedNumeric`
+*   `ClampedNumeric` coerces to `CheckedNumeric` 
+***
+
+[TOC]
+
+## Conversion functions and `StrictNumeric<>` in `safe_conversions.h`
+
+This header includes a collection of helper `constexpr` templates for safely
+performing a range of conversions, assignments, and tests.
+
+### Safe casting templates
+
+*   `as_signed()` - Returns the supplied integral value as a signed type of
+    the same width.
+*   `as_unsigned()` - Returns the supplied integral value as an unsigned type
+    of the same width.
+*   `checked_cast<>()` - Analogous to `static_cast<>` for numeric types, except
+    that by default it will trigger a crash on an out-of-bounds conversion (e.g.
+    overflow, underflow, NaN to integral) or a compile error if the conversion
+    error can be detected at compile time. The crash handler can be overridden
+    to perform a behavior other than crashing.
+*   `saturated_cast<>()` - Analogous to `static_cast` for numeric types, except
+    that it returns a saturated result when the specified numeric conversion
+    would otherwise overflow or underflow. An NaN source returns 0 by
+    default, but can be overridden to return a different result.
+*   `strict_cast<>()` - Analogous to `static_cast` for numeric types, except
+    this causes a compile failure if the destination type is not large
+    enough to contain any value in the source type. It performs no runtime
+    checking and thus introduces no runtime overhead.
+
+### Other helper and conversion functions
+
+*   `IsValueInRangeForNumericType<>()` - A convenience function that returns
+    true if the type supplied to the template parameter can represent the value
+    passed as an argument to the function.
+*   `IsValueNegative()` - A convenience function that will accept any
+    arithmetic type as an argument and will return whether the value is less
+    than zero. Unsigned types always return false.
+*   `SafeUnsignedAbs()` - Returns the absolute value of the supplied integer
+    parameter as an unsigned result (thus avoiding an overflow if the value
+    is the signed, two's complement minimum).
+
+### `StrictNumeric<>`
+
+`StrictNumeric<>` is a wrapper type that performs assignments and copies via
+the `strict_cast` template, and can perform valid arithmetic comparisons
+across any range of arithmetic types. `StrictNumeric` is the return type for
+values extracted from a `CheckedNumeric` class instance. The raw numeric value
+is extracted via `static_cast` to the underlying type or any type with
+sufficient range to represent the underlying type.
+
+*   `MakeStrictNum()` - Creates a new `StrictNumeric` from the underlying type
+    of the supplied arithmetic or StrictNumeric type.
+*   `SizeT` - Alias for `StrictNumeric<size_t>`.
+
+## `CheckedNumeric<>` in `checked_math.h`
+
+`CheckedNumeric<>` implements all the logic and operators for detecting integer
+boundary conditions such as overflow, underflow, and invalid conversions.
+The `CheckedNumeric` type implicitly converts from floating point and integer
+data types, and contains overloads for basic arithmetic operations (i.e.: `+`,
+`-`, `*`, `/` for all types and `%`, `<<`, `>>`, `&`, `|`, `^` for integers).
+Type promotions are a slightly modified version of the [standard C/C++ numeric
+promotions
+](http://en.cppreference.com/w/cpp/language/implicit_conversion#Numeric_promotions)
+with the two differences being that there is no default promotion to int
+and bitwise logical operations always return an unsigned of the wider type.
+
+### Members
+
+The unary negation, increment, and decrement operators are supported, along
+with the following unary arithmetic methods, which return a new
+`CheckedNumeric` as a result of the operation:
+
+*   `Abs()` - Absolute value.
+*   `UnsignedAbs()` - Absolute value as an equal-width unsigned underlying type
+    (valid for only integral types).
+*   `Max()` - Returns whichever is greater of the current instance or argument.
+    The underlying return type is whichever has the greatest magnitude.
+*   `Min()` - Returns whichever is lowest of the current instance or argument.
+    The underlying return type is whichever has can represent the lowest
+    number in the smallest width (e.g. int8_t over unsigned, int over
+    int8_t, and float over int).
+
+The following are for converting `CheckedNumeric` instances:
+
+*   `type` - The underlying numeric type.
+*   `AssignIfValid()` - Assigns the underlying value to the supplied
+    destination pointer if the value is currently valid and within the
+    range supported by the destination type. Returns true on success.
+*   `Cast<>()` - Instance method returning a `CheckedNumeric` derived from
+    casting the current instance to a `CheckedNumeric` of the supplied
+    destination type.
+
+*** aside
+The following member functions return a `StrictNumeric`, which is valid for
+comparison and assignment operations, but will trigger a compile failure on
+attempts to assign to a type of insufficient range. The underlying value can
+be extracted by an explicit `static_cast` to the underlying type or any type
+with sufficient range to represent the underlying type.
+***
+
+*   `IsValid()` - Returns true if the underlying numeric value is valid (i.e.
+    has not wrapped or saturated and is not the result of an invalid
+    conversion).
+*   `ValueOrDie()` - Returns the underlying value. If the state is not valid
+    this call will trigger a crash by default (but may be overridden by
+    supplying an alternate handler to the template).
+*   `ValueOrDefault()` - Returns the current value, or the supplied default if
+    the state is not valid (but will not crash).
+
+**Comparison operators are explicitly not provided** for `CheckedNumeric`
+types because they could result in a crash if the type is not in a valid state.
+Patterns like the following should be used instead:
+
+```cpp
+CheckedNumeric<size_t> checked_size = untrusted_input_value;
+checked_size += HEADER LENGTH;
+if (checked_size.IsValid() && checked_size.ValueOrDie() < buffer_size) {
+  \\ Do stuff on success...
+} else {
+  \\ Handle an error...
+}
+```
+
+### Non-member helper functions
+
+The following variadic convenience functions, which accept standard arithmetic
+or `CheckedNumeric` types, perform arithmetic operations, and return a
+`CheckedNumeric` result. The supported functions are:
+
+*   `CheckAdd()` - Addition.
+*   `CheckSub()` - Subtraction.
+*   `CheckMul()` - Multiplication.
+*   `CheckDiv()` - Division.
+*   `CheckMod()` - Modulus (integer only).
+*   `CheckLsh()` - Left integer shift (integer only).
+*   `CheckRsh()` - Right integer shift (integer only).
+*   `CheckAnd()` - Bitwise AND (integer only with unsigned result).
+*   `CheckOr()`  - Bitwise OR (integer only with unsigned result).
+*   `CheckXor()` - Bitwise XOR (integer only with unsigned result).
+*   `CheckMax()` - Maximum of supplied arguments.
+*   `CheckMin()` - Minimum of supplied arguments.
+
+The following wrapper functions can be used to avoid the template
+disambiguator syntax when converting a destination type.
+
+*   `IsValidForType<>()` in place of: `a.template IsValid<>()`
+*   `ValueOrDieForType<>()` in place of: `a.template ValueOrDie<>()`
+*   `ValueOrDefaultForType<>()` in place of: `a.template ValueOrDefault<>()`
+
+The following general utility methods is are useful for converting from
+arithmetic types to `CheckedNumeric` types:
+
+*   `MakeCheckedNum()` - Creates a new `CheckedNumeric` from the underlying type
+    of the supplied arithmetic or directly convertible type.
+
+## `ClampedNumeric<>` in `clamped_math.h`
+
+`ClampedNumeric<>` implements all the logic and operators for clamped
+(non-sticky saturating) arithmetic operations and conversions. The
+`ClampedNumeric` type implicitly converts back and forth between floating point
+and integer data types, saturating on assignment as appropriate. It contains
+overloads for basic arithmetic operations (i.e.: `+`, `-`, `*`, `/` for
+all types and `%`, `<<`, `>>`, `&`, `|`, `^` for integers) along with comparison
+operators for arithmetic types of any size. Type promotions are a slightly
+modified version of the [standard C/C++ numeric promotions
+](http://en.cppreference.com/w/cpp/language/implicit_conversion#Numeric_promotions)
+with the two differences being that there is no default promotion to int and
+bitwise logical operations always return an unsigned of the wider type.
+
+*** aside
+Most arithmetic operations saturate normally, to the numeric limit in the
+direction of the sign. The potentially unusual cases are:
+
+*   **Division:** Division by zero returns the saturated limit in the direction
+    of sign of the dividend (first argument). The one exception is 0/0, which
+	returns zero (although logically is NaN).
+*   **Modulus:** Division by zero returns the dividend (first argument).
+*   **Left shift:** Non-zero values saturate in the direction of the signed
+    limit (max/min), even for shifts larger than the bit width. 0 shifted any
+    amount results in 0.
+*   **Right shift:** Negative values saturate to -1. Positive or 0 saturates
+    to 0.
+*   **Bitwise operations:** No saturation; bit pattern is identical to
+    non-saturated bitwise operations.
+***
+
+### Members
+
+The unary negation, increment, and decrement operators are supported, along
+with the following unary arithmetic methods, which return a new
+`ClampedNumeric` as a result of the operation:
+
+*   `Abs()` - Absolute value.
+*   `UnsignedAbs()` - Absolute value as an equal-width unsigned underlying type
+    (valid for only integral types).
+*   `Max()` - Returns whichever is greater of the current instance or argument.
+    The underlying return type is whichever has the greatest magnitude.
+*   `Min()` - Returns whichever is lowest of the current instance or argument.
+    The underlying return type is whichever has can represent the lowest
+    number in the smallest width (e.g. int8_t over unsigned, int over
+    int8_t, and float over int).
+
+The following are for converting `ClampedNumeric` instances:
+
+*   `type` - The underlying numeric type.
+*   `Cast<>()` - Instance method returning a `ClampedNumeric` derived from
+    casting the current instance to a `ClampedNumeric` of the supplied
+    destination type.
+
+### Non-member helper functions
+
+The following variadic convenience functions, which accept standard arithmetic
+or `ClampedNumeric` types, perform arithmetic operations, and return a
+`ClampedNumeric` result. The supported functions are:
+
+*   `ClampAdd()` - Addition.
+*   `ClampSub()` - Subtraction.
+*   `ClampMul()` - Multiplication.
+*   `ClampDiv()` - Division.
+*   `ClampMod()` - Modulus (integer only).
+*   `ClampLsh()` - Left integer shift (integer only).
+*   `ClampRsh()` - Right integer shift (integer only).
+*   `ClampAnd()` - Bitwise AND (integer only with unsigned result).
+*   `ClampOr()`  - Bitwise OR (integer only with unsigned result).
+*   `ClampXor()` - Bitwise XOR (integer only with unsigned result).
+*   `ClampMax()` - Maximum of supplied arguments.
+*   `ClampMin()` - Minimum of supplied arguments.
+
+The following is a general utility method that is useful for converting
+to a `ClampedNumeric` type:
+
+*   `MakeClampedNum()` - Creates a new `ClampedNumeric` from the underlying type
+    of the supplied arithmetic or directly convertible type.