NAME
math.ops - Mathematical Opcodes
DESCRIPTION
Operations that perform some sort of mathematics, including both basic math and transcendental functions.
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.
- add(inout INT, in INT)
- add(inout NUM, in NUM)
- add(invar PMC, invar PMC)
- add(invar PMC, in INT)
- add(invar PMC, in NUM) Increase $1 by the amount in $2.
- add(out INT, in INT, in INT)
- add(out NUM, in NUM, in NUM)
- add(invar PMC, invar PMC, invar PMC)
- add(invar PMC, invar PMC, in INT)
- add(invar PMC, invar PMC, in NUM) Set $1 to the sum of $2 and $3.
- cmod(out INT, in INT, in INT)
- cmod(invar PMC, invar PMC, in INT)
- cmod(invar PMC, invar PMC, invar PMC) NOTE: This "uncorrected mod" algorithm uses the C language's built-in mod operator (x % y), which is
- cmod(out NUM, in NUM, in NUM)
- cmod(invar PMC, invar PMC, in NUM) NOTE: This "uncorrected mod" algorithm uses the built-in C math library's fmod() function, which computes
- dec(inout INT)
- dec(inout NUM)
- dec(invar PMC) Decrease $1 by one.
- div(inout INT, in INT)
- div(inout NUM, in NUM)
- div(invar PMC, invar PMC)
- div(invar PMC, in INT)
- div(invar PMC, in NUM) Divide $1 by $2.
- div(out INT, in INT, in INT)
- div(out NUM, in NUM, in NUM)
- div(invar PMC, invar PMC, invar PMC)
- div(invar PMC, invar PMC, in INT)
- div(invar PMC, invar PMC, 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)
- fdiv(invar PMC, invar PMC)
- fdiv(invar PMC, in INT)
- fdiv(invar PMC, in NUM) Floor divide $1 by $2.
- fdiv(out INT, in INT, in INT)
- fdiv(out NUM, in NUM, in NUM)
- fdiv(invar PMC, invar PMC, invar PMC)
- fdiv(invar PMC, invar PMC, in INT)
- fdiv(invar PMC, invar PMC, 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)
- mod(invar PMC, invar PMC, invar PMC)
- mod(invar PMC, invar PMC, in INT)
- mod(invar PMC, invar PMC, in NUM) Sets $1 to the modulus of $2 and $3.
- mod(inout INT, in INT)
- mod(inout NUM, in NUM)
- mod(invar PMC, invar PMC)
- mod(invar PMC, in INT)
- mod(invar PMC, 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:
- mul(inout INT, in INT)
- mul(inout NUM, in NUM)
- mul(invar PMC, invar PMC)
- mul(invar PMC, in INT)
- mul(invar PMC, 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)
- mul(invar PMC, invar PMC, invar PMC)
- mul(invar PMC, invar PMC, in INT)
- mul(invar PMC, invar PMC, 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.
- pow(out NUM, in NUM, in NUM)
- pow(out NUM, in NUM, in INT)
- pow(invar PMC, invar PMC, invar PMC)
- pow(invar PMC, invar PMC, in INT)
- pow(invar PMC, invar PMC, in NUM) Set $1 to $2 raised to the power $3.
- sub(inout INT, in INT)
- sub(inout NUM, in NUM)
- sub(invar PMC, invar PMC)
- sub(invar PMC, in INT)
- sub(invar PMC, in NUM) Decrease $1 by the amount in $2.
- sub(out INT, in INT, in INT)
- sub(out NUM, in NUM, in NUM)
- sub(invar PMC, invar PMC, invar PMC)
- sub(invar PMC, invar PMC, in INT)
- sub(invar PMC, invar PMC, 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
Also:
... 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
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.
[1] Brian W. Kernighan and Dennis M. Ritchie, *The C Programming
Language*, Second Edition. Prentice Hall, 1988.
If the denominator is zero, a 'Divide by zero' exception is thrown.
... 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
In addition, fmod() returns
the remainder, unless y is zero, when the function fails and
errno is set.
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.
[1] Brian W. Kernighan and Dennis M. Ritchie, *The C Programming
Language*, Second Edition. Prentice Hall, 1988.
If the denominator is zero, a 'Divide by zero' exception is thrown.
x mod y = x - y * floor(x / y)For more information on this definition of mod, see section 3.4 of [2], pages 81-85.References:
[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) 2001-2009, Parrot Foundation.
LICENSE
This program is free software. It is subject to the same license as the Parrot interpreter itself.