interval<T> neg(interval<T> x)[source]
interval<T> neg(interval<T> x)
Returns the additive inverse of the interval −x-x−x.
−:IR→IR-: \mathbb{IR} \rightarrow \mathbb{IR}−:IR→IR
interval<T> add(interval<T> a, interval<T> b)[source]
interval<T> add(interval<T> a, interval<T> b)
Returns the interval sum a+ba + ba+b.
+:IR×IR→IR+: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}+:IR×IR→IR
interval<T> sub(interval<T> a, interval<T> b)[source]
interval<T> sub(interval<T> a, interval<T> b)
Returns the interval difference a−ba - ba−b.
−:IR×IR→IR-: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}−:IR×IR→IR
interval<T> mul(interval<T> a, interval<T> b)[source]
interval<T> mul(interval<T> a, interval<T> b)
Returns the interval product a×ba \times ba×b.
×:IR×IR→IR\times: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}×:IR×IR→IR
interval<T> div(interval<T> x, interval<T> y)[source]
interval<T> div(interval<T> x, interval<T> y)
Returns the interval quotient x/yx / yx/y.
÷:IR×IR→IR\div: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}÷:IR×IR→IR
interval<T> recip(interval<T> a)[source]
interval<T> recip(interval<T> a)
Returns the reciprocal interval 1/x1/x1/x.
1/x:IR→IR1/x: \mathbb{IR} \rightarrow \mathbb{IR}1/x:IR→IR
interval<T> sqr(interval<T> x)[source]
interval<T> sqr(interval<T> x)
Returns the interval square x2x^2x2.
x2:IR→IR≥0x^2: \mathbb{IR} \rightarrow \mathbb{IR}_{\ge \mathbf{0}}x2:IR→IR≥0
interval<T> sqrt(interval<T> x)[source]
interval<T> sqrt(interval<T> x)
Returns the interval square root x\sqrt{x}x.
x:IR≥0→IR≥0\sqrt{x}: \mathbb{IR}_{\ge \mathbf{0}} \rightarrow \mathbb{IR}_{\ge \mathbf{0}}x:IR≥0→IR≥0
interval<T> fma(interval<T> x, interval<T> y, interval<T> z)[source]
interval<T> fma(interval<T> x, interval<T> y, interval<T> z)
Returns the fused multiply-add x⋅y+zx \cdot y + zx⋅y+z.
x⋅y+z:IR×IR×IR→IRx\cdot y + z: \mathbb{IR}\times\mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}x⋅y+z:IR×IR×IR→IR
T mig(interval<T> x)[source]
T mig(interval<T> x)
Returns the midpoint-inclusion generator for interval xxx.
mig:IR→R\mathrm{mig}: \mathbb{IR} \rightarrow \mathbb{R}mig:IR→R
T mag(interval<T> x)[source]
T mag(interval<T> x)
Returns the magnitude (maximum absolute value) of interval xxx.
mag:IR→R\mathrm{mag}: \mathbb{IR} \rightarrow \mathbb{R}mag:IR→R
T rad(interval<T> x)[source]
T rad(interval<T> x)
Returns the radius (half-width) of interval xxx.
rad:IR→R\mathrm{rad}: \mathbb{IR} \rightarrow \mathbb{R}rad:IR→R
interval<T> abs(interval<T> x)[source]
interval<T> abs(interval<T> x)
Returns the absolute value interval ∣x∣|x|∣x∣.
∣x∣:IR→IR≥0\left|x\right|: \mathbb{IR} \rightarrow \mathbb{IR}_{\ge \mathbf{0}}∣x∣:IR→IR≥0
interval<T> min(interval<T> x, interval<T> y)[source]
interval<T> min(interval<T> x, interval<T> y)
Returns the interval minimum of xxx and yyy.
min:IR×IR→IR\min: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}min:IR×IR→IR
interval<T> max(interval<T> x, interval<T> y)[source]
interval<T> max(interval<T> x, interval<T> y)
Returns the interval maximum of xxx and yyy.
max:IR×IR→IR\max: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}max:IR×IR→IR
interval<T> cbrt(interval<T> x)[source]
interval<T> cbrt(interval<T> x)
Returns the interval cube root x3\sqrt[3]{x}3x.
x3:IR→IR\sqrt[3]{x}: \mathbb{IR} \rightarrow \mathbb{IR}3x:IR→IR
interval<T> fabs(interval<T> x)[source]
interval<T> fabs(interval<T> x)
Returns the interval absolute value ∣x∣|x|∣x∣.
interval<T> fmax(interval<T> x, interval<T> y)[source]
interval<T> fmax(interval<T> x, interval<T> y)
fmax:IR×IR→IR\mathrm{fmax}: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}fmax:IR×IR→IR
interval<T> fmin(interval<T> x, interval<T> y)[source]
interval<T> fmin(interval<T> x, interval<T> y)
fmin:IR×IR→IR\mathrm{fmin}: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{IR}fmin:IR×IR→IR