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From: Taco Hoekwater <taco.hoekwater@wkap.nl>
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Subject: Re: mp-tool
Date: Fri, 10 Sep 1999 09:03:06 +0000 (GMT)
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>>>>> "David" == David Arnold <darnold@northcoast.com> writes:

    David> All,
    David> Defined in mp-tool is

    David> def sqr  (expr x) = (x*x)                            enddef;
    David> def ln   (expr x) = (if x=0: 0 else: mlog(x)/256 fi) enddef;
    David> def exp  (expr x) = ((mexp 256)**x) enddef;
    David> def pow  (expr x) = (x**power) enddef;
    David> def inv  (expr x) = (if x=0: 0 else: x**-1 fi)       enddef;

There are some really tricky ones that are above my mp knowledge that
would be a great addition, like a macro that can fake 

	  2**2.5 

and another for 

	{\root .5 \of 2}. 

Also something like 

	 binom(10,9)

(which quickly goes over 4096)

    David> def tand (expr x) = (sind(x)/cosd(x))                enddef;
    David> def asin (expr x) = (x+(x**3)/6+3(x**5)/40)          enddef;
    David> def acos (expr x) = (asin(-x))                       enddef;
    David> def atan (expr x) = (x-(x**3)/3+(x**5)/5-(x**7)/7)   enddef;

    David> It would be useful to add to this list. Specifically, cos, sin, tan for
    David> radian measure, and create a value for pi. Maybe,

    David> pi=4*atan(1);

gives 2.89526???????????????

I'd rather see the definitions from grafbase for the trig. These defs
are both shorter and more accurate:

[DHL==Daniel Luecking]

%D START.
pi := 3.1415926
2pi*radian= 180*deg;

%D Extra Trigonometric and Hyperbolic Functions.
%D tand, cotd, acos, asin;
%D exp, ln, cosh, sinh, acosh, asinh.
%D NOTE:  acos and asin return angle in degrees.

def tand (expr x) = (sind (x) / cosd (x)) enddef;
def cotd (expr x) = (cosd (x) / sind (x)) enddef;

%D DHL: I \emph{MUST} have these!
%D one can say sin(pi/2) or sind((pi/2)*radian)
def sin (expr x) = (sind (x*radian)) enddef;
def cos (expr x) = (cosd (x*radian)) enddef;
def tan (expr x) = (sin (x) / cos (x)) enddef;
def cot (expr x) = (cos (x) / sin (x)) enddef;

def acos (expr x) = angle ((x, 1+-+x)) enddef;
def asin (expr y) = angle ((1+-+y, y)) enddef;

def invcos (expr x) = ((acos (x))/radian) enddef;
def invsin (expr y) = ((asin (x))/radian) enddef;  
vardef cosh primary X =
  save temp;
  temp = exp X;
  (temp + 1/temp) / 2
enddef;

vardef sinh primary X =
  save temp;
  temp = exp X;
  (temp - 1/temp) / 2
enddef;

def acosh (expr y) = ln (y + (y+-+1)) enddef;
def asinh (expr y) = ln (y + (y++1)) enddef;

%D END. 

Greetings, Taco