### 4.1 Routines for integer arithmetic

The integer arithmetic routines are used on platforms that don't provide hardware support for arithmetic operations on some modes.

#### 4.1.1 Arithmetic functions

— Runtime Function: int __ashlsi3 (int a, int b)
— Runtime Function: long __ashldi3 (long a, int b)
— Runtime Function: long long __ashlti3 (long long a, int b)

> These functions return the result of shifting a left by b bits.

— Runtime Function: int __ashrsi3 (int a, int b)
— Runtime Function: long __ashrdi3 (long a, int b)
— Runtime Function: long long __ashrti3 (long long a, int b)

> These functions return the result of arithmetically shifting a right by b bits.

— Runtime Function: int __divsi3 (int a, int b)
— Runtime Function: long __divdi3 (long a, long b)
— Runtime Function: long long __divti3 (long long a, long long b)

> These functions return the quotient of the signed division of a and b.

— Runtime Function: int __lshrsi3 (int a, int b)
— Runtime Function: long __lshrdi3 (long a, int b)
— Runtime Function: long long __lshrti3 (long long a, int b)

> These functions return the result of logically shifting a right by b bits.

— Runtime Function: int __modsi3 (int a, int b)
— Runtime Function: long __moddi3 (long a, long b)
— Runtime Function: long long __modti3 (long long a, long long b)

> These functions return the remainder of the signed division of a and b.

— Runtime Function: int __mulsi3 (int a, int b)
— Runtime Function: long __muldi3 (long a, long b)
— Runtime Function: long long __multi3 (long long a, long long b)

> These functions return the product of a and b.

— Runtime Function: long __negdi2 (long a)
— Runtime Function: long long __negti2 (long long a)

> These functions return the negation of a.

— Runtime Function: unsigned int __udivsi3 (unsigned int a, unsigned int b)
— Runtime Function: unsigned long __udivdi3 (unsigned long a, unsigned long b)
— Runtime Function: unsigned long long __udivti3 (unsigned long long a, unsigned long long b)

> These functions return the quotient of the unsigned division of a and b.

— Runtime Function: unsigned long __udivmoddi3 (unsigned long a, unsigned long b, unsigned long *c)
— Runtime Function: unsigned long long __udivti3 (unsigned long long a, unsigned long long b, unsigned long long *c)

> These functions calculate both the quotient and remainder of the unsigned division of a and b. The return value is the quotient, and the remainder is placed in variable pointed to by c.

— Runtime Function: unsigned int __umodsi3 (unsigned int a, unsigned int b)
— Runtime Function: unsigned long __umoddi3 (unsigned long a, unsigned long b)
— Runtime Function: unsigned long long __umodti3 (unsigned long long a, unsigned long long b)

> These functions return the remainder of the unsigned division of a and b.

#### 4.1.2 Comparison functions

The following functions implement integral comparisons. These functions implement a low-level compare, upon which the higher level comparison operators (such as less than and greater than or equal to) can be constructed. The returned values lie in the range zero to two, to allow the high-level operators to be implemented by testing the returned result using either signed or unsigned comparison.

— Runtime Function: int __cmpdi2 (long a, long b)
— Runtime Function: int __cmpti2 (long long a, long long b)

> These functions perform a signed comparison of a and b. If a is less than b, they return 0; if a is greater than b, they return 2; and if a and b are equal they return 1.

— Runtime Function: int __ucmpdi2 (unsigned long a, unsigned long b)
— Runtime Function: int __ucmpti2 (unsigned long long a, unsigned long long b)

> These functions perform an unsigned comparison of a and b. If a is less than b, they return 0; if a is greater than b, they return 2; and if a and b are equal they return 1.

#### 4.1.3 Trapping arithmetic functions

The following functions implement trapping arithmetic. These functions call the libc function `abort` upon signed arithmetic overflow.

— Runtime Function: int __absvsi2 (int a)
— Runtime Function: long __absvdi2 (long a)

> These functions return the absolute value of a.

— Runtime Function: int __addvsi3 (int a, int b)
— Runtime Function: long __addvdi3 (long a, long b)

> These functions return the sum of a and b; that is a`+` b.

— Runtime Function: int __mulvsi3 (int a, int b)
— Runtime Function: long __mulvdi3 (long a, long b)

> The functions return the product of a and b; that is a`*` b.

— Runtime Function: int __negvsi2 (int a)
— Runtime Function: long __negvdi2 (long a)

> These functions return the negation of a; that is `-`a.

— Runtime Function: int __subvsi3 (int a, int b)
— Runtime Function: long __subvdi3 (long a, long b)

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

#### 4.1.4 Bit operations

— Runtime Function: int __clzsi2 (int a)
— Runtime Function: int __clzdi2 (long a)
— Runtime Function: int __clzti2 (long long a)

> These functions return the number of leading 0-bits in a, starting at the most significant bit position. If a is zero, the result is undefined.

— Runtime Function: int __ctzsi2 (int a)
— Runtime Function: int __ctzdi2 (long a)
— Runtime Function: int __ctzti2 (long long a)

> These functions return the number of trailing 0-bits in a, starting at the least significant bit position. If a is zero, the result is undefined.

— Runtime Function: int __ffsdi2 (long a)
— Runtime Function: int __ffsti2 (long long a)

> These functions return the index of the least significant 1-bit in a, or the value zero if a is zero. The least significant bit is index one.

— Runtime Function: int __paritysi2 (int a)
— Runtime Function: int __paritydi2 (long a)
— Runtime Function: int __parityti2 (long long a)

> These functions return the value zero if the number of bits set in a is even, and the value one otherwise.

— Runtime Function: int __popcountsi2 (int a)
— Runtime Function: int __popcountdi2 (long a)
— Runtime Function: int __popcountti2 (long long a)

> These functions return the number of bits set in a.