( *$ ) [Interval] | a *$ b
multiplies a by b according to interval arithmetic and returns the proper result.
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( *$. ) [Interval] | a *$. x multiplies a by x according to interval arithmetic and returns the proper result.
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( ** ) [Fpu_rename_all] |
Computes x^y
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( ** ) [Fpu_rename] |
Computes x^y
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( **$ ) [Interval] | a **$ b returns interval a raised to b power according to interval arithmetic, considering the restriction of x power y to x >= 0.
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( **$. ) [Interval] | a **$. f returns interval a raised to f power according to interval arithmetic.
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( **.$ ) [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.
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( *. ) [Fpu_rename_all] |
Computes x * y
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( *.$ ) [Interval] | x *$. a multiplies a by x according to interval arithmetic and returns the proper result.
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(+$) [Interval] | a +$ b returns {low=a.low+.b.low;high=a.high+.b.high}
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(+$.) [Interval] | a +$. x returns {low=a.low+.x;high=a.high+.x}
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(+.$) [Interval] | x +.$ a returns {low=a.low+.x;high=a.high+.x}
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(+.) [Fpu_rename_all] |
Computes x + y
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(-$) [Interval] | a -$ b returns {low=a.low-.b.high;high=a.high-.b.low}
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(-$.) [Interval] | a -$. x returns {low=a.low-.x;high=a.high-.x}
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(-.$) [Interval] | x -.$ a returns {low=x-.a.high;high=x-.a.low}
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(-.) [Fpu_rename_all] |
Computes x - y
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(/$) [Interval] | a /$ b divides the first interval by the second according to interval arithmetic and returns the proper result.
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(/$.) [Interval] | a /$. x divides a by x according to interval arithmetic and returns the proper result.
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(/.$) [Interval] | x /.$ a divides x by a according to interval arithmetic and returns the result.
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(/.) [Fpu_rename_all] |
Computes x / y
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(<$.) [Interval] |
Deprecated
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(~-$) [Interval] | ~-$ a returns {low=-a.high;high=-a.low}
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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
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acos [Fpu_rename_all] |
arc-cosine function
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acos [Fpu_rename] |
arc-cosine function
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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} .
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asin [Fpu_rename_all] |
arc-sinus function
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asin [Fpu_rename] |
arc-sinus function
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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} .
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atan [Fpu_rename_all] |
arc-tan function
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atan [Fpu_rename] |
arc-tan function
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atan2 [Fpu_rename_all] |
atan2 function
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atan2 [Fpu_rename] |
atan2 function
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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].
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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].
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atan_I [Interval] | atan_I a returns {low=atan a.low;high=atan a.high}
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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
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cos [Fpu_rename_all] |
Computes cos(x) for x in [-2^63, 2^63]
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cos [Fpu_rename] |
Computes cos(x) for x in [-2^63, 2^63]
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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
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cosh [Fpu_rename_all] |
cosh function
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cosh [Fpu_rename] |
cosh function
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cosh_I [Interval] |
cosh_I is the proper extension of interval arithmetic to cosh
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E | |
e_I [Interval] | e with bounds properly rounded
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exp [Fpu_rename_all] |
exp function
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exp [Fpu_rename] |
exp function
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exp_I [Interval] | exp_I a returns {low=exp a.high;high=exp b.high}
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F | |
facos [Fpu] | |
facos_high [Fpu] |
arc-cosine functions
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facos_low [Fpu] | |
fadd [Fpu] | |
fadd_high [Fpu] |
Floating point addition in nearest, low and high mode
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fadd_low [Fpu] | |
fasin [Fpu] | |
fasin_high [Fpu] |
arc-sinus functions
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fasin_low [Fpu] | |
fatan [Fpu] | |
fatan_high [Fpu] |
fatan x y computes atan2 y x
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fatan_low [Fpu] | |
fcos [Fpu] | |
fcos_high [Fpu] |
Computes cos(x) for x in ]-2^63, 2^63[
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fcos_low [Fpu] | |
fcosh [Fpu] | |
fcosh_high [Fpu] |
Computes cosh(x)
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fcosh_low [Fpu] | |
fdiv [Fpu] | |
fdiv_high [Fpu] |
Floating point division in nearest, low and high mode
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fdiv_low [Fpu] | |
fexp [Fpu] | |
fexp_high [Fpu] |
Floating point exponential in nearest, low and high mode
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fexp_low [Fpu] | |
ffloat [Fpu] | |
ffloat_high [Fpu] | |
ffloat_low [Fpu] |
float() functions.
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float_i [Interval] |
Returns the interval containing the float conversion of an integer
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flog [Fpu] | |
flog_high [Fpu] |
Floating point log in nearest, low and high mode
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flog_low [Fpu] | |
flog_pow [Fpu] | |
flog_pow_high [Fpu] |
Computes x^y for 0 < x < infinity and neg_infinity < y < infinity
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flog_pow_low [Fpu] | |
fmod [Fpu] |
Modulo (result is supposed to be exact)
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fmul [Fpu] | |
fmul_high [Fpu] |
Floating point multiplication in nearest, low and high mode
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fmul_low [Fpu] | |
fpow [Fpu] | |
fpow_high [Fpu] |
Computes x^y expanded to its mathematical limit when it exists
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fpow_low [Fpu] | |
fprintf_I [Interval] |
Prints an interval into an out_channel with the same format applied to both endpoints
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fprintf_X [Interval] |
Prints an interval vector into an out_channel
with the same format applied to all endpoints
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fsin [Fpu] | |
fsin_high [Fpu] |
Computes sin(x) for x in ]-2^63, 2^63[
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fsin_low [Fpu] | |
fsinh [Fpu] | |
fsinh_high [Fpu] |
Computes sinh(x)
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fsinh_low [Fpu] | |
fsqrt [Fpu] | |
fsqrt_high [Fpu] |
Floating point square root in nearest, low and high mode
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fsqrt_low [Fpu] | |
fsub [Fpu] | |
fsub_high [Fpu] |
Floating point substraction in nearest, low and high mode
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fsub_low [Fpu] | |
ftan [Fpu] | |
ftan_high [Fpu] |
Computes tan(x) for x in ]-2^63, 2^63[
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ftan_low [Fpu] | |
ftanh [Fpu] | |
ftanh_high [Fpu] |
Computes tanh(x)
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ftanh_low [Fpu] | |
I | |
inv_I [Interval] | inv_I a returns 1. /.$ a .
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is_neg [Fpu] |
is_neg x returns if x has its sign bit set (true for -0.)
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L | |
log [Fpu_rename_all] |
log function
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log [Fpu_rename] |
log function
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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 .
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M | |
max_I_I [Interval] | max_I_I a b returns {low=max a.low b.low;high=max a.high b.high}
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min_I_I [Interval] | min_I_I a b returns {low=min a.low b.low;high=min a.high b.high}
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mod_I_f [Interval] | mod_I_f a f returns a mod f according to interval arithmetic et ocaml mod_float definition.
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mod_float [Fpu_rename_all] |
Computes x mod y
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mod_float [Fpu_rename] |
Computes x mod y
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O | |
one_I [Interval] |
Neutral element for multiplication
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P | |
pi_I [Interval] | pi with bounds properly rounded
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pow_I_I [Interval] |
Deprecated
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pow_I_f [Interval] |
Deprecated
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pow_I_i [Interval] | Pow_I_i a n with n integer returns interval a raised to nth power according to interval arithmetic.
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print_I [Interval] |
Deprecated
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print_X [Interval] |
Deprecated
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printf_I [Interval] |
Prints an interval with the same format applied to both endpoints.
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printf_X [Interval] |
Prints an interval vector with the same format applied to all endpoints.
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S | |
set_high [Fpu] |
Sets the rounding mod to UPWARD (towards infinity)
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set_low [Fpu] |
Sets the rounding mod to DOWNWARD (towards minus infinity)
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set_nearest [Fpu] |
Sets the rounding mod to NEAREST (default mode)
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sgn_I [Interval] | sgn_I a returns {low=float (compare a.low 0.);high=float (compare a.high 0.)}
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sin [Fpu_rename_all] |
Computes sin(x) for x in [-2^63, 2^63]
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sin [Fpu_rename] |
Computes sin(x) for x in [-2^63, 2^63]
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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
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sinh [Fpu_rename_all] |
sinh function
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sinh [Fpu_rename] |
sinh function
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sinh_I [Interval] |
sinh_I is the proper extension of interval arithmetic to sinh
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size2_X [Interval] |
Deprecated
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size_I [Interval] | size_I a returns a.high-a.low
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size_X [Interval] |
Deprecated
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size_max_X [Interval] |
Computes the size of the largest interval of the interval vector
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size_mean_X [Interval] |
Computes the mean of the size of intervals of the interval vector
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sprintf_I [Interval] |
Returns a string holding the interval printed with the same format applied to both
endpoints
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sprintf_X [Interval] |
Returns a string holding the interval vector printed with the same format applied to all
endpoints
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sqrt [Fpu_rename_all] |
square root function
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sqrt [Fpu_rename] |
square root function
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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 .
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T | |
tan [Fpu_rename_all] |
Computes tan(x) for x in [-2^63, 2^63]
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tan [Fpu_rename] |
Computes tan(x) for x in [-2^63, 2^63]
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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
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tanh [Fpu_rename_all] |
tanh function
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tanh [Fpu_rename] |
tanh function
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tanh_I [Interval] |
tanh_I is the proper extension of interval arithmetic to tanh
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truncate_I [Interval] | truncate_I a returns {low=floor a.low;high=ceil a.high}
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U | |
union_I_I [Interval] | union_I_I a b returns {low=min a.low b.low;high=max a.high b.high}
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Z | |
zero_I [Interval] |
Neutral element for addition
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