### 4.2 Routines for floating point emulation

The software floating point library is used on machines which do not have hardware support for floating point. It is also used whenever `-msoft-float` is used to disable generation of floating point instructions. (Not all targets support this switch.)

For compatibility with other compilers, the floating point emulation routines can be renamed with the `DECLARE_LIBRARY_RENAMES` macro (see Library Calls). In this section, the default names are used.

Presently the library does not support `XFmode`, which is used for `long double` on some architectures.

#### 4.2.1 Arithmetic functions

— Runtime Function: float __addsf3 (float a, float b)
— Runtime Function: double __adddf3 (double a, double b)
— Runtime Function: long double __addtf3 (long double a, long double b)
— Runtime Function: long double __addxf3 (long double a, long double b)

> These functions return the sum of a and b.

— Runtime Function: float __subsf3 (float a, float b)
— Runtime Function: double __subdf3 (double a, double b)
— Runtime Function: long double __subtf3 (long double a, long double b)
— Runtime Function: long double __subxf3 (long double a, long double b)

> These functions return the difference between b and a; that is, a - b.

— Runtime Function: float __mulsf3 (float a, float b)
— Runtime Function: double __muldf3 (double a, double b)
— Runtime Function: long double __multf3 (long double a, long double b)
— Runtime Function: long double __mulxf3 (long double a, long double b)

> These functions return the product of a and b.

— Runtime Function: float __divsf3 (float a, float b)
— Runtime Function: double __divdf3 (double a, double b)
— Runtime Function: long double __divtf3 (long double a, long double b)
— Runtime Function: long double __divxf3 (long double a, long double b)

> These functions return the quotient of a and b; that is, a / b.

— Runtime Function: float __negsf2 (float a)
— Runtime Function: double __negdf2 (double a)
— Runtime Function: long double __negtf2 (long double a)
— Runtime Function: long double __negxf2 (long double a)

> These functions return the negation of a. They simply flip the sign bit, so they can produce negative zero and negative NaN.

#### 4.2.2 Conversion functions

— Runtime Function: double __extendsfdf2 (float a)
— Runtime Function: long double __extendsftf2 (float a)
— Runtime Function: long double __extendsfxf2 (float a)
— Runtime Function: long double __extenddftf2 (double a)
— Runtime Function: long double __extenddfxf2 (double a)

> These functions extend a to the wider mode of their return type.

— Runtime Function: double __truncxfdf2 (long double a)
— Runtime Function: double __trunctfdf2 (long double a)
— Runtime Function: float __truncxfsf2 (long double a)
— Runtime Function: float __trunctfsf2 (long double a)
— Runtime Function: float __truncdfsf2 (double a)

> These functions truncate a to the narrower mode of their return type, rounding toward zero.

— Runtime Function: int __fixsfsi (float a)
— Runtime Function: int __fixdfsi (double a)
— Runtime Function: int __fixtfsi (long double a)
— Runtime Function: int __fixxfsi (long double a)

> These functions convert a to a signed integer, rounding toward zero.

— Runtime Function: long __fixsfdi (float a)
— Runtime Function: long __fixdfdi (double a)
— Runtime Function: long __fixtfdi (long double a)
— Runtime Function: long __fixxfdi (long double a)

> These functions convert a to a signed long, rounding toward zero.

— Runtime Function: long long __fixsfti (float a)
— Runtime Function: long long __fixdfti (double a)
— Runtime Function: long long __fixtfti (long double a)
— Runtime Function: long long __fixxfti (long double a)

> These functions convert a to a signed long long, rounding toward zero.

— Runtime Function: unsigned int __fixunssfsi (float a)
— Runtime Function: unsigned int __fixunsdfsi (double a)
— Runtime Function: unsigned int __fixunstfsi (long double a)
— Runtime Function: unsigned int __fixunsxfsi (long double a)

> These functions convert a to an unsigned integer, rounding toward zero. Negative values all become zero.

— Runtime Function: unsigned long __fixunssfdi (float a)
— Runtime Function: unsigned long __fixunsdfdi (double a)
— Runtime Function: unsigned long __fixunstfdi (long double a)
— Runtime Function: unsigned long __fixunsxfdi (long double a)

> These functions convert a to an unsigned long, rounding toward zero. Negative values all become zero.

— Runtime Function: unsigned long long __fixunssfti (float a)
— Runtime Function: unsigned long long __fixunsdfti (double a)
— Runtime Function: unsigned long long __fixunstfti (long double a)
— Runtime Function: unsigned long long __fixunsxfti (long double a)

> These functions convert a to an unsigned long long, rounding toward zero. Negative values all become zero.

— Runtime Function: float __floatsisf (int i)
— Runtime Function: double __floatsidf (int i)
— Runtime Function: long double __floatsitf (int i)
— Runtime Function: long double __floatsixf (int i)

> These functions convert i, a signed integer, to floating point.

— Runtime Function: float __floatdisf (long i)
— Runtime Function: double __floatdidf (long i)
— Runtime Function: long double __floatditf (long i)
— Runtime Function: long double __floatdixf (long i)

> These functions convert i, a signed long, to floating point.

— Runtime Function: float __floattisf (long long i)
— Runtime Function: double __floattidf (long long i)
— Runtime Function: long double __floattitf (long long i)
— Runtime Function: long double __floattixf (long long i)

> These functions convert i, a signed long long, to floating point.

— Runtime Function: float __floatunsisf (unsigned int i)
— Runtime Function: double __floatunsidf (unsigned int i)
— Runtime Function: long double __floatunsitf (unsigned int i)
— Runtime Function: long double __floatunsixf (unsigned int i)

> These functions convert i, an unsigned integer, to floating point.

— Runtime Function: float __floatundisf (unsigned long i)
— Runtime Function: double __floatundidf (unsigned long i)
— Runtime Function: long double __floatunditf (unsigned long i)
— Runtime Function: long double __floatundixf (unsigned long i)

> These functions convert i, an unsigned long, to floating point.

— Runtime Function: float __floatuntisf (unsigned long long i)
— Runtime Function: double __floatuntidf (unsigned long long i)
— Runtime Function: long double __floatuntitf (unsigned long long i)
— Runtime Function: long double __floatuntixf (unsigned long long i)

> These functions convert i, an unsigned long long, to floating point.

#### 4.2.3 Comparison functions

There are two sets of basic comparison functions.

— Runtime Function: int __cmpsf2 (float a, float b)
— Runtime Function: int __cmpdf2 (double a, double b)
— Runtime Function: int __cmptf2 (long double a, long double b)

> These functions calculate a <=> b. That is, if a is less than b, they return −1; if a is greater than b, they return 1; and if a and b are equal they return 0. If either argument is NaN they return 1, but you should not rely on this; if NaN is a possibility, use one of the higher-level comparison functions.

— Runtime Function: int __unordsf2 (float a, float b)
— Runtime Function: int __unorddf2 (double a, double b)
— Runtime Function: int __unordtf2 (long double a, long double b)

> These functions return a nonzero value if either argument is NaN, otherwise 0.

There is also a complete group of higher level functions which correspond directly to comparison operators. They implement the ISO C semantics for floating-point comparisons, taking NaN into account. Pay careful attention to the return values defined for each set. Under the hood, all of these routines are implemented as

           if (__unordXf2 (a, b))
             return E;
           return __cmpXf2 (a, b);

where E is a constant chosen to give the proper behavior for NaN. Thus, the meaning of the return value is different for each set. Do not rely on this implementation; only the semantics documented below are guaranteed.

— Runtime Function: int __eqsf2 (float a, float b)
— Runtime Function: int __eqdf2 (double a, double b)
— Runtime Function: int __eqtf2 (long double a, long double b)

> These functions return zero if neither argument is NaN, and a and b are equal.

— Runtime Function: int __nesf2 (float a, float b)
— Runtime Function: int __nedf2 (double a, double b)
— Runtime Function: int __netf2 (long double a, long double b)

> These functions return a nonzero value if either argument is NaN, or if a and b are unequal.

— Runtime Function: int __gesf2 (float a, float b)
— Runtime Function: int __gedf2 (double a, double b)
— Runtime Function: int __getf2 (long double a, long double b)

> These functions return a value greater than or equal to zero if neither argument is NaN, and a is greater than or equal to b.

— Runtime Function: int __ltsf2 (float a, float b)
— Runtime Function: int __ltdf2 (double a, double b)
— Runtime Function: int __lttf2 (long double a, long double b)

> These functions return a value less than zero if neither argument is NaN, and a is strictly less than b.

— Runtime Function: int __lesf2 (float a, float b)
— Runtime Function: int __ledf2 (double a, double b)
— Runtime Function: int __letf2 (long double a, long double b)

> These functions return a value less than or equal to zero if neither argument is NaN, and a is less than or equal to b.

— Runtime Function: int __gtsf2 (float a, float b)
— Runtime Function: int __gtdf2 (double a, double b)
— Runtime Function: int __gttf2 (long double a, long double b)

> These functions return a value greater than zero if neither argument is NaN, and a is strictly greater than b.

#### 4.2.4 Other floating-point functions

— Runtime Function: float __powisf2 (float a, int b)
— Runtime Function: double __powidf2 (double a, int b)
— Runtime Function: long double __powitf2 (long double a, int b)
— Runtime Function: long double __powixf2 (long double a, int b)

> These functions convert raise a to the power b.

— Runtime Function: complex float __mulsc3 (float a, float b, float c, float d)
— Runtime Function: complex double __muldc3 (double a, double b, double c, double d)
— Runtime Function: complex long double __multc3 (long double a, long double b, long double c, long double d)
— Runtime Function: complex long double __mulxc3 (long double a, long double b, long double c, long double d)

> These functions return the product of a + ib and c + id, following the rules of C99 Annex G.

— Runtime Function: complex float __divsc3 (float a, float b, float c, float d)
— Runtime Function: complex double __divdc3 (double a, double b, double c, double d)
— Runtime Function: complex long double __divtc3 (long double a, long double b, long double c, long double d)
— Runtime Function: complex long double __divxc3 (long double a, long double b, long double c, long double d)

> These functions return the quotient of a + ib and c + id (i.e., (a + ib) / (c + id)), following the rules of C99 Annex G.