Index of values

a *$ b multiplies a by b according to interval arithmetic and returns the proper result.

a *$. x multiplies a by x according to interval arithmetic and returns the proper result.

Computes x^y

Computes x^y

a **$ b returns interval a raised to b power according to interval arithmetic, considering the restriction of x power y to x >= 0.

a **$. f returns interval a raised to f power according to interval arithmetic.

x **.$ a returns float x raised to interval a power according to interval arithmetic, considering the restiction of x power y to x >= 0.

Computes x * y

x *$. a multiplies a by x according to interval arithmetic and returns the proper result.

a +$ b returns {low=a.low+.b.low;high=a.high+.b.high}

a +$. x returns {low=a.low+.x;high=a.high+.x}

x +.$ a returns {low=a.low+.x;high=a.high+.x}

Computes x + y

a -$ b returns {low=a.low-.b.high;high=a.high-.b.low}

a -$. x returns {low=a.low-.x;high=a.high-.x}

x -.$ a returns {low=x-.a.high;high=x-.a.low}

Computes x - y

a /$ b divides the first interval by the second according to interval arithmetic and returns the proper result.

a /$. x divides a by x according to interval arithmetic and returns the proper result.

x /.$ a divides x by a according to interval arithmetic and returns the result.

Computes x / y

Deprecated

~-$ a returns {low=-a.high;high=-a.low}

abs_I a returns {low=a.low;high=a.high} if a.low>=0., {low=-a.high;high=-a.low} if a.high<=0., and {low=0.;high=max -a.low a.high} otherwise

arc-cosine function

arc-cosine function

acos_I a raise Failure "acos_I" if a.low>1. or a.high<-1., else returns {low=if a.high<1. then acos a.high else 0; high=if a.low>-1. then acos a.low else pi}.

arc-sinus function

arc-sinus function

asin_I a raise Failure "asin_I" if a.low>1. or a.high<-1. else returns {low=if a.low>-1. then asin a.low else -pi/2; high=if a.low<1. then asin a.high else pi/2}.

arc-tan function

arc-tan function

atan2 function

atan2 function

Same function as above but when y.low<0 and y.high>0 and x.high<0 the returned interval is [-pi,pi].

atan2mod_I_I y x returns the proper extension of interval arithmetic to atan2 but with values in [-pi,2 pi] instead of [-pi,pi].

atan_I a returns {low=atan a.low;high=atan a.high}

compare_I_f a x returns 1 if a.high<x, 0 if a.low<=x<=a.high and -1 if x<a.low

Computes cos(x) for x in [-2^63, 2^63]

Computes cos(x) for x in [-2^63, 2^63]

cos_I a returns the proper extension of cos to arithmetic interval Returns [-1,1] if one of the bounds is greater or lower than +/-2**53

cosh function

cosh function

cosh_I is the proper extension of interval arithmetic to cosh

e with bounds properly rounded

exp function

exp function

exp_I a returns {low=exp a.high;high=exp b.high}

arc-cosine functions

Floating point addition in nearest, low and high mode

arc-sinus functions

fatan x y computes atan2 y x

Computes cos(x) for x in ]-2^63, 2^63[

Computes cosh(x)

Floating point division in nearest, low and high mode

Floating point exponential in nearest, low and high mode

float() functions.

Returns the interval containing the float conversion of an integer

Floating point log in nearest, low and high mode

Computes x^y for 0 < x < infinity and neg_infinity < y < infinity

Modulo (result is supposed to be exact)

Floating point multiplication in nearest, low and high mode

Computes x^y expanded to its mathematical limit when it exists

Prints an interval into an out_channel with the same format applied to both endpoints

Prints an interval vector into an out_channel with the same format applied to all endpoints

Computes sin(x) for x in ]-2^63, 2^63[

Computes sinh(x)

Floating point square root in nearest, low and high mode

Floating point substraction in nearest, low and high mode

Computes tan(x) for x in ]-2^63, 2^63[

Computes tanh(x)

inv_I a returns 1. /.$ a.

is_neg x returns if x has its sign bit set (true for -0.)

log function

log function

log_I a returns {low=log a.low; high=log a.high} if a.low>0., {low=neg_infinity; high=log a.high} if a.low<0<=a.high.

max_I_I a b returns {low=max a.low b.low;high=max a.high b.high}

min_I_I a b returns {low=min a.low b.low;high=min a.high b.high}

mod_I_f a f returns a mod f according to interval arithmetic et ocaml mod_float definition.

Computes x mod y

Computes x mod y

Neutral element for multiplication

pi with bounds properly rounded

Deprecated

Deprecated

Pow_I_i a n with n integer returns interval a raised to nth power according to interval arithmetic.

Deprecated

Deprecated

Prints an interval with the same format applied to both endpoints.

Prints an interval vector with the same format applied to all endpoints.

Sets the rounding mod to UPWARD (towards infinity)

Sets the rounding mod to DOWNWARD (towards minus infinity)

Sets the rounding mod to NEAREST (default mode)

sgn_I a returns {low=float (compare a.low 0.);high=float (compare a.high 0.)}

Computes sin(x) for x in [-2^63, 2^63]

Computes sin(x) for x in [-2^63, 2^63]

sin_I a returns the proper extension of sin to arithmetic interval Returns [-1,1] if one of the bounds is greater or lower than +/-2**53

sinh function

sinh function

sinh_I is the proper extension of interval arithmetic to sinh

Deprecated

size_I a returns a.high-a.low

Deprecated

Computes the size of the largest interval of the interval vector

Computes the mean of the size of intervals of the interval vector

Returns a string holding the interval printed with the same format applied to both endpoints

Returns a string holding the interval vector printed with the same format applied to all endpoints

square root function

square root function

sqrt_I a returns {low=sqrt a;high=sqrt b} if a>=0., {low=0.;high=sqrt b} if a<0.<=b.

Computes tan(x) for x in [-2^63, 2^63]

Computes tan(x) for x in [-2^63, 2^63]

tan_I a returns the proper extension of tan to arithmetic interval Returns [-Inf,Inf] if one of the bounds is greater or lower than +/-2**53

tanh function

tanh function

tanh_I is the proper extension of interval arithmetic to tanh

truncate_I a returns {low=floor a.low;high=ceil a.high}

union_I_I a b returns {low=min a.low b.low;high=max a.high b.high}

Neutral element for addition