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### 15.23 Cross Compilation and Floating Point

While all modern machines use twos-complement representation for integers, there are a variety of representations for floating point numbers. This means that in a cross-compiler the representation of floating point numbers in the compiled program may be different from that used in the machine doing the compilation.

Because different representation systems may offer different amounts of range and precision, all floating point constants must be represented in the target machine's format. Therefore, the cross compiler cannot safely use the host machine's floating point arithmetic; it must emulate the target's arithmetic. To ensure consistency, GCC always uses emulation to work with floating point values, even when the host and target floating point formats are identical.

The following macros are provided by real.h for the compiler to use. All parts of the compiler which generate or optimize floating-point calculations must use these macros. They may evaluate their operands more than once, so operands must not have side effects.

— Macro: REAL_VALUE_TYPE

> The C data type to be used to hold a floating point value in the target machine's format. Typically this is a `struct` containing an array of `HOST_WIDE_INT`, but all code should treat it as an opaque quantity.

— Macro: int REAL_VALUES_EQUAL (REAL_VALUE_TYPE x, REAL_VALUE_TYPE y)

> Compares for equality the two values, x and y. If the target floating point format supports negative zeroes and/or NaNs, REAL_VALUES_EQUAL (-0.0, 0.0) is true, and REAL_VALUES_EQUAL (NaN, NaN) is false.

— Macro: int REAL_VALUES_LESS (REAL_VALUE_TYPE x, REAL_VALUE_TYPE y)

> Tests whether x is less than y.

— Macro: HOST_WIDE_INT REAL_VALUE_FIX (REAL_VALUE_TYPE x)

> Truncates x to a signed integer, rounding toward zero.

— Macro: unsigned HOST_WIDE_INT REAL_VALUE_UNSIGNED_FIX (REAL_VALUE_TYPE x)

> Truncates x to an unsigned integer, rounding toward zero. If x is negative, returns zero.

— Macro: REAL_VALUE_TYPE REAL_VALUE_ATOF (const char *string, enum machine_mode mode)

> Converts string into a floating point number in the target machine's representation for mode mode. This routine can handle both decimal and hexadecimal floating point constants, using the syntax defined by the C language for both.

— Macro: int REAL_VALUE_NEGATIVE (REAL_VALUE_TYPE x)

> Returns 1 if x is negative (including negative zero), 0 otherwise.

— Macro: int REAL_VALUE_ISINF (REAL_VALUE_TYPE x)

> Determines whether x represents infinity (positive or negative).

— Macro: int REAL_VALUE_ISNAN (REAL_VALUE_TYPE x)

> Determines whether x represents a “NaN” (not-a-number).

— Macro: void REAL_ARITHMETIC (REAL_VALUE_TYPE output, enum tree_code code, REAL_VALUE_TYPE x, REAL_VALUE_TYPE y)

> Calculates an arithmetic operation on the two floating point values x and y, storing the result in output (which must be a variable).

> The operation to be performed is specified by code. Only the following codes are supported: `PLUS_EXPR`, `MINUS_EXPR`, `MULT_EXPR`, `RDIV_EXPR`, `MAX_EXPR`, `MIN_EXPR`.

> If `REAL_ARITHMETIC` is asked to evaluate division by zero and the target's floating point format cannot represent infinity, it will call `abort`. Callers should check for this situation first, using `MODE_HAS_INFINITIES`. See Storage Layout.

— Macro: REAL_VALUE_TYPE REAL_VALUE_NEGATE (REAL_VALUE_TYPE x)

> Returns the negative of the floating point value x.

— Macro: REAL_VALUE_TYPE REAL_VALUE_ABS (REAL_VALUE_TYPE x)

> Returns the absolute value of x.

— Macro: REAL_VALUE_TYPE REAL_VALUE_TRUNCATE (REAL_VALUE_TYPE mode, enum machine_mode x)

> Truncates the floating point value x to fit in mode. The return value is still a full-size `REAL_VALUE_TYPE`, but it has an appropriate bit pattern to be output as a floating constant whose precision accords with mode mode.

— Macro: void REAL_VALUE_TO_INT (HOST_WIDE_INT low, HOST_WIDE_INT high, REAL_VALUE_TYPE x)

> Converts a floating point value x into a double-precision integer which is then stored into low and high. If the value is not integral, it is truncated.

— Macro: void REAL_VALUE_FROM_INT (REAL_VALUE_TYPE x, HOST_WIDE_INT low, HOST_WIDE_INT high, enum machine_mode mode)

> Converts a double-precision integer found in low and high, into a floating point value which is then stored into x. The value is truncated to fit in mode mode.