math.ps

% PostScript Math Procedures
% by Raymond Luckhurst, scriptit.uk

% constants
/PI 3.141592654 def
/E 2.718281828 def % Euler's number
/I32 1 32 bitshift 0 eq def % true if 32 bit integers

% sign function
/sign {
	dup 0 ne { 0 lt { -1 }{ +1 } ifelse }{ cvi } ifelse % integer
} bind def

% absolute maximum value
/absmax {
	2 copy abs exch abs gt { exch } if pop
} bind def

% absolute minimum value
/absmin {
	2 copy abs exch abs lt { exch } if pop
} bind def

% 32 bit integer addition
//I32 { % 32-bit ints
	/iadd32 {
		2 copy add type /integertype eq {
			add 16#FFFFFFFF and
		}{
			2 copy xor 16#C0000000 and % to xor with carry bits
			2 index 16#3FFFFFFF and 2 index 16#3FFFFFFF and add % 30 bit sum with carry
			2 copy and 5 -2 roll and or 1 bitshift 16#80000000 and % top carry bit
			or % 30 bit sum with both carry bits
			xor % fix top 2 bit sum
		} ifelse
	} bind def
}{ % 64-bit ints
	/iadd32 { add 16#FFFFFFFF and } bind def
} ifelse

% 32 bit integer subtraction
//I32 { % 32-bit ints
	/isub32 {
		dup neg type /integertype eq {
			neg
		}{
			not 1 iadd32
		} ifelse
		iadd32
	} bind def
}{ % 64-bit ints
	/isub32 { sub 16#FFFFFFFF and } bind def
} ifelse

% radians to degrees
% <radians> degrees <degrees>
/degrees {
	180 //PI div mul
} bind def

% degrees to radians
% <degrees> radians <radians>
/radians {
	//PI 180 div mul
} bind def

% root of difference of two squares
% <x> <y> rtdiffsq <d>
/rtdiffsq {
	dup mul exch dup mul sub abs sqrt
} bind def

% arc-cosine
% <adjacent> <hypotenuse> acos <angle>
/acos {
	1 index rtdiffsq exch atan
} bind def

% arc-sine
% <opposite> <hypotenuse> asin <angle>
/asin {
	1 index rtdiffsq atan
} bind def