## Remez algorithm

Change (if needed) interval endpoints, degree, number of gridpoints, and function formula, according to instructions below. It could be made of several statements, like: 1;if(Abs(x)>0.00001){Sin(x)/x}

When ready, use 'Compute' several times (iterations).

If you change parameters and/or function, push on 'Reset'.

Function interpreter by J. Pezzullo; graphics by Grigory - http://mpp.by.ru/

**Operators:** + - * / and parentheses

**Constants:** Pi (=3.14...), e (=2.718...), Deg(=180/Pi = 57.2...)

**Built-in Functions...**

[Unless otherwise indicated, all functions take a single numeric argument,
enclosed in parentheses after the name of the function.]

**Algebraic:** Abs, Sqrt, Power(x,y) [= x raised to power of
y)], Fact [factorial]

**Transcendental:** Exp, Ln [natural], Log10, Log2

**Trigonometric:** Sin, Cos, Tan, Cot, Sec, Csc

**Inverse Trig:** ASin, ACos, ATan, ACot, ASec, ACsc

**Hyperbolic:** SinH, CosH, TanH, CotH, SecH, CscH

**Inverse Hyp:** ASinH, ACosH, ATanH, ACotH, ASecH, ACscH

**Statistical:** Norm, ChiSq(x,df), StudT(t,df), FishF(F,df1,df2)

**Inverse Stat:** ANorm, AChiSq(p,df), AStudT(p,df),
AFishF(p,df1,df2)

Note: Most versions of JavaScript are case-sensitive.
Make sure you type function names *exactly* as you see them above.

Note: The trig functions work in radians. For degrees,
multiply or divide by the Deg variable. For example: Sin(30/Deg) will return
0.5, and ATan(1)*Deg will return 45.

Note: The factorial function is implemented for
all real numbers. For non-integers its accuracy is about 6 significant figures.
For negative integers it returns either a very large number or a division-by-zero
error.

Note: The statistical functions Norm and StudT return
2-tail p-values (eg: Norm(1.96)=0.05), while ChiSq and FishF return 1-tail
values. This is consistent with the way these functions are most frequently
used.

Note: Some of the functions listed above are not
currently implemented in JavaScript, so I have programmed them as user-defined
functions. You can see the algorithms by 'viewing the document source' for
this page. Feel free to copy them if you find them useful.

Disclaimer: I believe this calculator to be reasonably
accurate and reliable, but I make no guarantees and assume no responsibility
for any computational inaccuracies or their consequences.

Return to the Interactive Statistics page,
or to the JCP Home Page

Send e-mail to John C. Pezzullo (this page's author) at
johnp71@aol.com