Index of values


( *$ ) [Interval]
a *$ b multiplies a by b according to interval arithmetic and returns the proper result.
( *$. ) [Interval]
a *$. x multiplies a by x according to interval arithmetic and returns the proper result.
( ** ) [Fpu_rename_all]
Computes x^y
( ** ) [Fpu_rename]
Computes x^y
( **$ ) [Interval]
a **$ b returns interval a raised to b power according to interval arithmetic, considering the restriction of x power y to x >= 0.
( **$. ) [Interval]
a **$. f returns interval a raised to f power according to interval arithmetic.
( **.$ ) [Interval]
x **.$ a returns float x raised to interval a power according to interval arithmetic, considering the restiction of x power y to x >= 0.
( *. ) [Fpu_rename_all]
Computes x * y
( *.$ ) [Interval]
x *$. a multiplies a by x according to interval arithmetic and returns the proper result.
(+$) [Interval]
a +$ b returns {low=a.low+.b.low;high=a.high+.b.high}
(+$.) [Interval]
a +$. x returns {low=a.low+.x;high=a.high+.x}
(+.$) [Interval]
x +.$ a returns {low=a.low+.x;high=a.high+.x}
(+.) [Fpu_rename_all]
Computes x + y
(-$) [Interval]
a -$ b returns {low=a.low-.b.high;high=a.high-.b.low}
(-$.) [Interval]
a -$. x returns {low=a.low-.x;high=a.high-.x}
(-.$) [Interval]
x -.$ a returns {low=x-.a.high;high=x-.a.low}
(-.) [Fpu_rename_all]
Computes x - y
(/$) [Interval]
a /$ b divides the first interval by the second according to interval arithmetic and returns the proper result.
(/$.) [Interval]
a /$. x divides a by x according to interval arithmetic and returns the proper result.
(/.$) [Interval]
x /.$ a divides x by a according to interval arithmetic and returns the result.
(/.) [Fpu_rename_all]
Computes x / y
(<$.) [Interval]
Deprecated
(~-$) [Interval]
~-$ a returns {low=-a.high;high=-a.low}

A
abs_I [Interval]
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
acos [Fpu_rename_all]
arc-cosine function
acos [Fpu_rename]
arc-cosine function
acos_I [Interval]
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}.
asin [Fpu_rename_all]
arc-sinus function
asin [Fpu_rename]
arc-sinus function
asin_I [Interval]
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}.
atan [Fpu_rename_all]
arc-tan function
atan [Fpu_rename]
arc-tan function
atan2 [Fpu_rename_all]
atan2 function
atan2 [Fpu_rename]
atan2 function
atan2_I_I [Interval]
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 [Interval]
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 [Interval]
atan_I a returns {low=atan a.low;high=atan a.high}

C
compare_I_f [Interval]
compare_I_f a x returns 1 if a.high<x, 0 if a.low<=x<=a.high and -1 if x<a.low
cos [Fpu_rename_all]
Computes cos(x) for x in [-2^63, 2^63]
cos [Fpu_rename]
Computes cos(x) for x in [-2^63, 2^63]
cos_I [Interval]
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 [Fpu_rename_all]
cosh function
cosh [Fpu_rename]
cosh function
cosh_I [Interval]
cosh_I is the proper extension of interval arithmetic to cosh

E
e_I [Interval]
e with bounds properly rounded
exp [Fpu_rename_all]
exp function
exp [Fpu_rename]
exp function
exp_I [Interval]
exp_I a returns {low=exp a.high;high=exp b.high}

F
facos [Fpu]
facos_high [Fpu]
arc-cosine functions
facos_low [Fpu]
fadd [Fpu]
fadd_high [Fpu]
Floating point addition in nearest, low and high mode
fadd_low [Fpu]
fasin [Fpu]
fasin_high [Fpu]
arc-sinus functions
fasin_low [Fpu]
fatan [Fpu]
fatan_high [Fpu]
fatan x y computes atan2 y x
fatan_low [Fpu]
fcos [Fpu]
fcos_high [Fpu]
Computes cos(x) for x in ]-2^63, 2^63[
fcos_low [Fpu]
fcosh [Fpu]
fcosh_high [Fpu]
Computes cosh(x)
fcosh_low [Fpu]
fdiv [Fpu]
fdiv_high [Fpu]
Floating point division in nearest, low and high mode
fdiv_low [Fpu]
fexp [Fpu]
fexp_high [Fpu]
Floating point exponential in nearest, low and high mode
fexp_low [Fpu]
ffloat [Fpu]
ffloat_high [Fpu]
ffloat_low [Fpu]
float() functions.
float_i [Interval]
Returns the interval containing the float conversion of an integer
flog [Fpu]
flog_high [Fpu]
Floating point log in nearest, low and high mode
flog_low [Fpu]
flog_pow [Fpu]
flog_pow_high [Fpu]
Computes x^y for 0 < x < infinity and neg_infinity < y < infinity
flog_pow_low [Fpu]
fmod [Fpu]
Modulo (result is supposed to be exact)
fmul [Fpu]
fmul_high [Fpu]
Floating point multiplication in nearest, low and high mode
fmul_low [Fpu]
fpow [Fpu]
fpow_high [Fpu]
Computes x^y expanded to its mathematical limit when it exists
fpow_low [Fpu]
fprintf_I [Interval]
Prints an interval into an out_channel with the same format applied to both endpoints
fprintf_X [Interval]
Prints an interval vector into an out_channel with the same format applied to all endpoints
fsin [Fpu]
fsin_high [Fpu]
Computes sin(x) for x in ]-2^63, 2^63[
fsin_low [Fpu]
fsinh [Fpu]
fsinh_high [Fpu]
Computes sinh(x)
fsinh_low [Fpu]
fsqrt [Fpu]
fsqrt_high [Fpu]
Floating point square root in nearest, low and high mode
fsqrt_low [Fpu]
fsub [Fpu]
fsub_high [Fpu]
Floating point substraction in nearest, low and high mode
fsub_low [Fpu]
ftan [Fpu]
ftan_high [Fpu]
Computes tan(x) for x in ]-2^63, 2^63[
ftan_low [Fpu]
ftanh [Fpu]
ftanh_high [Fpu]
Computes tanh(x)
ftanh_low [Fpu]

I
inv_I [Interval]
inv_I a returns 1. /.$ a.
is_neg [Fpu]
is_neg x returns if x has its sign bit set (true for -0.)

L
log [Fpu_rename_all]
log function
log [Fpu_rename]
log function
log_I [Interval]
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.

M
max_I_I [Interval]
max_I_I a b returns {low=max a.low b.low;high=max a.high b.high}
min_I_I [Interval]
min_I_I a b returns {low=min a.low b.low;high=min a.high b.high}
mod_I_f [Interval]
mod_I_f a f returns a mod f according to interval arithmetic et ocaml mod_float definition.
mod_float [Fpu_rename_all]
Computes x mod y
mod_float [Fpu_rename]
Computes x mod y

O
one_I [Interval]
Neutral element for multiplication

P
pi_I [Interval]
pi with bounds properly rounded
pow_I_I [Interval]
Deprecated
pow_I_f [Interval]
Deprecated
pow_I_i [Interval]
Pow_I_i a n with n integer returns interval a raised to nth power according to interval arithmetic.
print_I [Interval]
Deprecated
print_X [Interval]
Deprecated
printf_I [Interval]
Prints an interval with the same format applied to both endpoints.
printf_X [Interval]
Prints an interval vector with the same format applied to all endpoints.

S
set_high [Fpu]
Sets the rounding mod to UPWARD (towards infinity)
set_low [Fpu]
Sets the rounding mod to DOWNWARD (towards minus infinity)
set_nearest [Fpu]
Sets the rounding mod to NEAREST (default mode)
sgn_I [Interval]
sgn_I a returns {low=float (compare a.low 0.);high=float (compare a.high 0.)}
sin [Fpu_rename_all]
Computes sin(x) for x in [-2^63, 2^63]
sin [Fpu_rename]
Computes sin(x) for x in [-2^63, 2^63]
sin_I [Interval]
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 [Fpu_rename_all]
sinh function
sinh [Fpu_rename]
sinh function
sinh_I [Interval]
sinh_I is the proper extension of interval arithmetic to sinh
size2_X [Interval]
Deprecated
size_I [Interval]
size_I a returns a.high-a.low
size_X [Interval]
Deprecated
size_max_X [Interval]
Computes the size of the largest interval of the interval vector
size_mean_X [Interval]
Computes the mean of the size of intervals of the interval vector
sprintf_I [Interval]
Returns a string holding the interval printed with the same format applied to both endpoints
sprintf_X [Interval]
Returns a string holding the interval vector printed with the same format applied to all endpoints
sqrt [Fpu_rename_all]
square root function
sqrt [Fpu_rename]
square root function
sqrt_I [Interval]
sqrt_I a returns {low=sqrt a;high=sqrt b} if a>=0., {low=0.;high=sqrt b} if a<0.<=b.

T
tan [Fpu_rename_all]
Computes tan(x) for x in [-2^63, 2^63]
tan [Fpu_rename]
Computes tan(x) for x in [-2^63, 2^63]
tan_I [Interval]
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 [Fpu_rename_all]
tanh function
tanh [Fpu_rename]
tanh function
tanh_I [Interval]
tanh_I is the proper extension of interval arithmetic to tanh
truncate_I [Interval]
truncate_I a returns {low=floor a.low;high=ceil a.high}

U
union_I_I [Interval]
union_I_I a b returns {low=min a.low b.low;high=max a.high b.high}

Z
zero_I [Interval]
Neutral element for addition