
Structure Math
(* 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 base10 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.
*)
