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# Structure Math

Identifier index Structure index

```(* Math -- SML Basis Library *)

type real = real

val pi    : real
val e     : real

val sqrt  : real -> real
val sin   : real -> real
val cos   : real -> real
val tan   : real -> real
val atan  : real -> real
val asin  : real -> real
val acos  : real -> real
val atan2 : real * real -> real
val exp   : real -> real
val pow   : real * real -> real
val ln    : real -> real
val log10 : real -> real
val sinh  : real -> real
val cosh  : real -> real
val tanh  : real -> real

(*
[pi] is the circumference of the circle with diameter 1, that is,
3.14159265358979323846.

[e] is the base of the natural logarithm: 2.7182818284590452354.

[sqrt x] is the square root of x.  Raises Domain if x < 0.0.

[sin r] is the sine of r, where r is in radians.

[cos r] is the cosine of r, where r is in radians.

[tan r] is the tangent of r, where r is in radians.  Raises Domain if
r is a multiple of pi/2.

[atan t] is the arc tangent of t, in the open interval ] ~pi/2, pi/2 [.

[asin t] is the arc sine of t, in the closed interval [ ~pi/2, pi/2 ].
Raises Domain if abs x > 1.

[acos t] is the arc cosine of t, in the closed interval [ 0, pi ].
Raises Domain if abs x > 1.

[atan2(y, x)] is the arc tangent of y/x, in the interval ] ~pi, pi ],
except that atan2(y, 0) = sign y * pi/2.  The quadrant of the result
is the same as the quadrant of the point (x, y).
Hence sign(cos(atan2(y, x))) = sign x
and   sign(sin(atan2(y, x))) = sign y.

[exp x] is e to the x'th power.

[pow (x, y)] is x it the y'th power, defined when
y >= 0 and (y integral or x >= 0)
or y < 0 and ((y integral and x <> 0.0) or x > 0).

We define pow(0, 0) = 1.

[ln x] is the natural logarithm of x (that is, with base e).
Raises Domain if x <= 0.0.

[log10 x] is the base-10 logarithm of x.  Raises Domain if x <= 0.0.

[sinh x] returns the hyperbolic sine of x, mathematically defined as
(exp x - exp (~x)) / 2.  Raises Overflow if x is too large.

[cosh x] returns the hyperbolic cosine of x, mathematically defined as
(exp x + exp (~x)) / 2.  Raises Overflow if x is too large.

[tanh x] returns the hyperbolic tangent of x, mathematically defined
as (sinh x) / (cosh x).  Raises Domain if x is too large.
*)

```

Identifier index Structure index