Bignum

An infinite-precision calculator and function library for Miranda

Input syntax for Miranda version

(The Haskell version just creates a new type BigFloat, to which all the usual operations apply)

Calculated constants

bn_0

The bignum version of zero

bn_1

The bignum version of one

bn_2

The bignum version of two

bn_e

2.7182818...

bn_pi

3.1415926535...

bn_pi_2, bn_pi_4 and bn_2_pi

pi/2, pi/4 and twice pi

Functions taking a single parameter

bn

takes a character string containing a decimal number and converts it to a bignum. The string can have an arbitrary number of decimal places after the decimal point.

ibn

takes an integer and converts it to a bignum (Note: an integer, not a floating point value, nor the result of a floating point calculation. You can try converting those using "bn (show x)", or more simply with the compound function "(bn.show), but entirely at your own risk!)

showbignum

is the inverse function of bn. It converts a bignum to a printable form. Miranda calls this function automatically whenever it has to display a bignum.

bn_twice

doubles its parameter (faster than "bn_times 2 x")

bn_half

halves its parameter (faster than "bn_quot x 2")

bn_sqr

returns the square of its argument (faster than "bn_mul x x")

bn_sqrt

returns the square root of its argument

bn_neg

negates its argument

bn_rnd

takes a positive integer seed as its parameter and returns a pseudo-random bignum in the range 0 <= n < 1

Functions taking two parameters

bn_add

takes two bignum parameters and returns their sum.

bn_sub

subtracts its second bignum parameter from its first, returning the difference.

bn_times

takes an integer and a bignum and returns their bignum product. The integer is the first of the two parameters, so as to ease partial parameterisazion.

bn_mul

multiplies two bignums

bn_quot

divides a bignum by an positive integer. If you want to partially parameterise the integer divisor, use "($bn_quot n)".

bn_div

performs long division of two bignums

bn_raise

takes a bignum and an integer and returns the bignum raised to that integral power

bn_pow

takes two bignums and returns the first raised to the power of the second

Trigonometric functions

bn_ln

returns the natural logarithm (in base e) of its parameter

bn_exp

returns the inverse natural logarithm of its parameter

bn_sin

returns the sine of its parameter. It is fastest for values between -pi/2 and +pi/2

bn_cos

returns the cosine of its parameter (defined using sin).

bn_tan

returns the tangent of its parameter (defined using sin/cos).

bn_asin

returns the arcsine (in the range -pi/2 to pi/2) of its parameter (defined using atan)

bn_acos

returns the arccosine (in the range -pi/2 to pi/2) of its parameter (defined using atan)

bn_atan

returns the arctangent (in the range -pi/2 to pi/2) of its parameter.

bn_sinh, bn_cosh, bn_tanh, bn_asinh, bn_acosh, bn_atanh

return hyperbolic sine, cosine and tangent and their inverses.

Logical functions

bn_is_zero

tells you whether a bignum is zero.

bn_is_neg

tells you whether a bignum has a negative value.

bn_cmp

compares two bignums and returns:
0 if the two numbers have the same value,
1 if the first number is greater than the second
-1 if the second number is greater than the first.

bn_eq, bn_ne, bn_gt, bn_lt, bn_ge, bn_le

The six usual comparison functions,
equal to, not equal to, greater than, less than,
greater than or equal to, less than or equal to.
They all take two bignum parameters and return a boolean value.

Examples

bn_sqrt bn_2

The square root of two.

bn_raise ( bn_mul (bn "1.5") (bn "0.75") ) 6

The interval obtained by tuning up by a perfect fifth and down by a perfect fourth, six times (not quite an octave!)

bn_quot (bn_add bn_1 (bn_sqrt (bn "5"))) 2

The golden ratio, calculated as (1 + sqrt(5)) / 2