NAME 
math.ops - Mathematical Operations
DESCRIPTION
Operations that perform some sort of mathematics, including both basic math and transcendental functions.
The variants with a prepended n_ like <n_abs> generate a new target PMC.
If possible,
they use the appropriate language type,
specified with .HLL.
General infix operations
These operations take an infix operation number and PMC arguments.
- infix(inconst INT, invar PMC, in INT)
- infix(inconst INT, invar PMC, in NUM)
- infix(inconst INT, invar PMC, in STR)
- infix(inconst INT, invar PMC, invar PMC)
- General inplace infix dispatch opcode. $1 is the MMD function number.
- infix(inconst INT, out PMC, invar PMC, in INT)
- infix(inconst INT, out PMC, invar PMC, in NUM)
- infix(inconst INT, out PMC, invar PMC, in STR)
- infix(inconst INT, out PMC, invar PMC, invar PMC)
- General infix dispatch opcode. $1 is the MMD function number.
- n_infix(inconst INT, out PMC, invar PMC, in INT)
- n_infix(inconst INT, out PMC, invar PMC, in NUM)
- n_infix(inconst INT, out PMC, invar PMC, in STR)
- n_infix(inconst INT, out PMC, invar PMC, invar PMC)
- General infix dispatch opcode. $1 is the MMD function number. These opcodes return a new result PMC $2.
Arithmetic operations
These operations store the results of arithmetic on other registers and constants into their destination register, $1.
- abs(inout INT)
- abs(inout NUM)
- abs(invar PMC)
- Set $1 to its absolute value.
- abs(out INT, in INT)
- abs(out NUM, in NUM)
- abs(out PMC, invar PMC)
- Set $1 to absolute value of $2.
- n_abs(out PMC, invar PMC)
- Create new $1 as the absolute of $2.
- add(inout INT, in INT)
- add(inout NUM, in NUM)
- Increase $1 by the amount in $2.
- add(out INT, in INT, in INT)
- add(out NUM, in NUM, in NUM)
- Set $1 to the sum of $2 and $3.
- Please note that all PMC variants of all infix functions are handled by the
infixandn_infixopcodes. Thus there is no distinct implementation of e.g.add_p_p_p. - cmod(out INT, in INT, in INT)
- NOTE: This "uncorrected mod" algorithm uses the C language's built-in mod operator (x % y), which is
- Also:
- This op is provided for those who need it (such as speed-sensitive applications with heavy use of mod, but using it only with positive arguments), but a more mathematically useful mod based on ** floor(x/y) and defined with y == 0 is provided by the mod op.
- If the denominator is zero, a 'Divide by zero' exception is thrown.
- cmod(out NUM, in NUM, in NUM)
- NOTE: This "uncorrected mod" algorithm uses the built-in C math library's fmod() function, which computes
- In addition, fmod() returns
- According to page 251 of [1], the result when y is zero is implementation- defined.
- This op is provided for those who need it, but a more mathematically useful numeric mod based on floor(x/y) instead of truncate(x/y) and defined with y == 0 is provided by the mod op.
- If the denominator is zero, a 'Divide by zero' exception is thrown.
- dec(inout INT)
- dec(inout NUM)
- dec(invar PMC)
- Decrease $1 by one.
- div(inout INT, in INT)
- div(inout NUM, in NUM)
- Divide $1 by $2.
- div(out INT, in INT, in INT)
- div(out NUM, in NUM, in NUM)
- Set $1 to the quotient of $2 divided by $3. In the case of INTVAL division, the result is truncated (NOT rounded or floored). If the denominator is zero, a 'Divide by zero' exception is thrown.
- fdiv(inout INT, in INT)
- fdiv(inout NUM, in NUM)
- Floor divide $1 by $2.
- fdiv(out INT, in INT, in INT)
- fdiv(out NUM, in NUM, in NUM)
- Set $1 to the quotient of $2 divided by $3. The result is the floor() of the division i.e. the next whole integer towards -inf. If the denominator is zero, a 'Divide by zero' exception is thrown.
- ceil(inout NUM)
- Set $1 to the smallest integral value greater than or equal to $1.
- ceil(out INT, in NUM)
- ceil(out NUM, in NUM)
- Set $1 to the smallest integral value greater than or equal to $2.
- floor(inout NUM)
- Set $1 to the largest integral value less than or equal to $1.
- floor(out INT, in NUM)
- floor(out NUM, in NUM)
- Set $1 to the largest integral value less than or equal to $2.
- inc(inout INT)
- inc(inout NUM)
- inc(invar PMC)
- Increase $1 by one.
- mod(out INT, in INT, in INT)
- mod(out NUM, in NUM, in NUM)
- Sets $1 to the modulus of $2 and $3.
- mod(inout INT, in INT)
- mod(inout NUM, in NUM)
- Sets $1 to the modulus of $1 and $2.
- NOTE: This "corrected mod" algorithm is based on the C code on page 70 of [1]. Assuming correct behavior of the built-in mod operator (%) with positive arguments, this algorithm implements a mathematically convenient version of mod, defined thus:
- For more information on this definition of mod, see section 3.4 of [2], pages 81-85.
- References:
- mul(inout INT, in INT)
- mul(inout NUM, in NUM)
- Set $1 to the product of $1 and $2.
- mul(out INT, in INT, in INT)
- mul(out NUM, in NUM, in NUM)
- Set $1 to the product of $2 and $3.
- neg(inout INT)
- neg(inout NUM)
- neg(invar PMC)
- Set $1 to its negative.
- neg(out INT, in INT)
- neg(out NUM, in NUM)
- neg(out PMC, invar PMC)
- Set $1 to the negative of $2.
- n_neg(out PMC, invar PMC)
- Create $1 as the negative of $2.
- pow(out NUM, in NUM, in NUM)
- Set $1 to $2 raised to the power $3.
- sub(inout INT, in INT)
- sub(inout NUM, in NUM)
- Decrease $1 by the amount in $2.
- sub(out INT, in INT, in INT)
- sub(out NUM, in NUM, in NUM)
- Set $1 to $2 minus $3.
- sqrt(out NUM, in NUM)
- Set $1 to the square root of $2.
... the remainder when x is divided by y, and thus is zero
when y divides x exactly.
...
The direction of truncation for / and the sign of the result
for % are machine-dependent for negative operands, as is the
action taken on overflow or underflow.
-- [1], page 41
... if the second operand is 0, the result is undefined.
Otherwise, it is always true that (a/b)*b + a%b is equal to z. If
both operands are non-negative, then the remainder is non-
negative and smaller than the divisor; if not, it is guaranteed
only that the absolute value of the remainder is smaller than
the absolute value of the divisor.
-- [1], page 205
[1] Brian W. Kernighan and Dennis M. Ritchie, *The C Programming
Language*, Second Edition. Prentice Hall, 1988.
... the remainder of dividing x by y. The return value is
x - n * y, where n is the quotient of x / y, rounded towards
zero to an integer.
-- fmod() manpage on RedHat Linux 7.0
the remainder, unless y is zero, when the function fails and
errno is set.
[1] Brian W. Kernighan and Dennis M. Ritchie, *The C Programming
Language*, Second Edition. Prentice Hall, 1988.
x mod y = x - y * floor(x / y)
[1] Donald E. Knuth, *MMIXware: A RISC Computer for the Third
Millennium* Springer, 1999.
[2] Ronald L. Graham, Donald E. Knuth and Oren Patashnik, *Concrete
Mathematics*, Second Edition. Addison-Wesley, 1994.
Transcendental mathematical operations
These operations perform various transcendental operations such as logarithmics and trigonometrics.
- acos(out NUM, in NUM)
- Set $1 to the arc cosine (in radians) of $2.
- asec(out NUM, in NUM)
- Set $1 to the arc secant (in radians) of $2.
- asin(out NUM, in NUM)
- Set $1 to the arc sine (in radians) of $2.
- atan(out NUM, in NUM)
- atan(out NUM, in NUM, in NUM)
- The two-argument versions set $1 to the arc tangent (in radians) of $2.
- The three-argument versions set $1 to the arc tangent (in radians) of $2 / $3, taking account of the signs of the arguments in determining the quadrant of the result.
- cos(out NUM, in NUM)
- Set $1 to the cosine of $2 (given in radians).
- cosh(out NUM, in NUM)
- Set $1 to the hyperbolic cosine of $2 (given in radians).
- exp(out NUM, in NUM)
- Set $1 to e raised to the power $2. e is the base of the natural logarithm.
- ln(out NUM, in NUM)
- Set $1 to the natural (base e) logarithm of $2.
- log10(out NUM, in NUM)
- Set $1 to the base 10 logarithm of $2.
- log2(out NUM, in NUM)
- Set $1 to the base 2 logarithm of $2.
- sec(out NUM, in NUM)
- Set $1 to the secant of $2 (given in radians).
- sech(out NUM, in NUM)
- Set $1 to the hyperbolic secant of $2 (given in radians).
- sin(out NUM, in NUM)
- Set $1 to the sine of $2 (given in radians).
- sinh(out NUM, in NUM)
- Set $1 to the hyperbolic sine of $2 (given in radians).
- tan(out NUM, in NUM)
- Set $1 to the tangent of $2 (given in radians).
- tanh(out NUM, in NUM)
- Set $1 to the hyperbolic tangent of $2 (given in radians).
Other mathematical operations
Implementations of various mathematical operations
- gcd(out INT, in INT, in INT)
- Greatest Common divisor of $2 and $3.
- lcm(out INT, in INT, in INT)
- Least Common Multiple of $2 and $3
- fact(out INT, in INT)
- fact(out NUM, in INT)
- Factorial, n!. Calculates the product of 1 to N.
COPYRIGHT
Copyright (C) 2001-2004, The Perl Foundation.
LICENSE
This program is free software. It is subject to the same license as the Parrot interpreter itself.
