-- Fixed point I/O
-- ---------------
--- The following documents implementation details of the fixed point
--- input/output routines in the GNAT run time. The first part describes
--- general properties of fixed point types as defined by the Ada 95 standard,
+-- The following text documents implementation details of the fixed point
+-- input/output routines in the GNAT runtime. The first part describes the
+-- general properties of fixed point types as defined by the Ada standard,
-- including the Information Systems Annex.
-- Subsequently these are reduced to implementation constraints and the impact
--- of these constraints on a few possible approaches to I/O are given.
+-- of these constraints on a few possible approaches to input/output is given.
-- Based on this analysis, a specific implementation is selected for use in
--- the GNAT run time. Finally, the chosen algorithm is analyzed numerically in
+-- the GNAT runtime. Finally, the chosen algorithm is analyzed numerically in
-- order to provide user-level documentation on limits for range and precision
-- of fixed point types as well as accuracy of input/output conversions.
-- - General Properties of Fixed Point Types -
-- -------------------------------------------
--- Operations on fixed point values, other than input and output, are not
--- important for the purposes of this document. Only the set of values that a
--- fixed point type can represent and the input and output operations are
--- significant.
+-- Operations on fixed point types, other than input/output, are not important
+-- for the purpose of this document. Only the set of values that a fixed point
+-- type can represent and the input/output operations are significant.
-- Values
-- ------
--- Set set of values of a fixed point type comprise the integral
--- multiples of a number called the small of the type. The small can
--- either be a power of ten, a power of two or (if the implementation
--- allows) an arbitrary strictly positive real value.
+-- The set of values of a fixed point type comprise the integral multiples of
+-- a number called the small of the type. The small can be either a power of
+-- two, a power of ten or (if the implementation allows) an arbitrary strictly
+-- positive real value.
--- Implementations need to support fixed-point types with a precision
--- of at least 24 bits, and (in order to comply with the Information
--- Systems Annex) decimal types need to support at least digits 18.
--- For the rest, however, no requirements exist for the minimal small
--- and range that need to be supported.
+-- Implementations need to support ordinary fixed point types with a precision
+-- of at least 24 bits, and (in order to comply with the Information Systems
+-- Annex) decimal fixed point types with at least 18 digits. For the rest, no
+-- requirements exist for the minimal small and range that must be supported.
-- Operations
-- ----------
-- Implementation Strategies
-- -------------------------
--- * Float arithmetic
+-- * Floating point arithmetic
-- * Arbitrary-precision integer arithmetic
-- * Fixed-precision integer arithmetic
--- Although it seems convenient to convert fixed point numbers to floating-
+-- Although it seems convenient to convert fixed point numbers to floating
-- point and then print them, this leads to a number of restrictions.
-- The first one is precision. The widest floating-point type generally
-- available has 53 bits of mantissa. This means that Fine_Delta cannot
-- be less than 2.0**(-53).
--- In GNAT, Fine_Delta is 2.0**(-63), and Duration for example is a
--- 64-bit type. It would still be possible to use multi-precision
--- floating-point to perform calculations using longer mantissas,
--- but this is a much harder approach.
+-- In GNAT, Fine_Delta is 2.0**(-63), and Duration for example is a 64-bit
+-- type. This means that a floating-point type with 63 bits of mantissa needs
+-- to be used, which is only generally available on the x86 architecture. It
+-- would still be possible to use multi-precision floating point to perform
+-- calculations using longer mantissas, but this is a much harder approach.
--- The base conversions needed for input and output of (non-decimal)
--- fixed point types can be seen as pairs of integer multiplications
--- and divisions.
+-- The base conversions needed for input/output of (non-decimal) fixed point
+-- types can be seen as pairs of integer multiplications and divisions.
--- Arbitrary-precision integer arithmetic would be suitable for the job
--- at hand, but has the draw-back that it is very heavy implementation-wise.
+-- Arbitrary-precision integer arithmetic would be suitable for the job at
+-- hand, but has the drawback that it is very heavy implementation-wise.
-- Especially in embedded systems, where fixed point types are often used,
-- it may not be desirable to require large amounts of storage and time
-- for fixed I/O operations.
-- Fore + Aft + Exp + Extra_Layout_Space
- -- is always long enough for formatting any fixed point number
+ -- is always long enough for formatting any fixed point number.
-- Implementation of Put routines
-- factor 10**E can be trivially handled during final output, by adjusting
-- the decimal point or exponent.
- -- Convert a value X * S of type T to a 64-bit integer value Q equal
- -- to 10.0**D * (X * S) rounded to the nearest integer.
- -- This conversion is a scaled integer divide of the form
+ -- Convert a value X * S of type T to a 64-bit integer value Q equal to
+ -- 10.0**D * (X * S) rounded to the nearest integer. This conversion is
+ -- a scaled integer divide of the form
-- Q := (X * Y) / Z,
-- S * 10.0**D = Y / Z;
-- If S is an integer greater than or equal to one, then Fore must be at
- -- least 20 in order to print T'First, which is at most -2.0**63.
- -- This means D < 0, so use
+ -- least 20 in order to print T'First, which is at most -2.0**63. This
+ -- means that D < 0, so use
-- (1) Y = -S and Z = -10**(-D)
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