## FP16 **Kind**: global class **this**: {FP16} * [FP16](#FP16) * [new FP16()](#new_FP16_new) * [.reduce()](#FP16+reduce) * [.norm()](#FP16+norm) * [.iszilch()](#FP16+iszilch) * [.isunity()](#FP16+isunity) * [.cmove(g, d)](#FP16+cmove) * [.isreal()](#FP16+isreal) * [.real()](#FP16+real) * [.geta()](#FP16+geta) * [.getb()](#FP16+getb) * [.equals(x)](#FP16+equals) * [.copy(x)](#FP16+copy) * [.zero()](#FP16+zero) * [.one(x)](#FP16+one) * [.set(c, d)](#FP16+set) * [.seta(c)](#FP16+seta) * [.neg()](#FP16+neg) * [.conj()](#FP16+conj) * [.nconj()](#FP16+nconj) * [.add(x)](#FP16+add) * [.sub(x)](#FP16+sub) * [.pmul(s)](#FP16+pmul) * [.qmul(s)](#FP16+qmul) * [.imul(s)](#FP16+imul) * [.sqr()](#FP16+sqr) * [.mul(y)](#FP16+mul) * [.toString()](#FP16+toString) * [.inverse()](#FP16+inverse) * [.times_i()](#FP16+times_i) * [.times_i2()](#FP16+times_i2) * [.times_i4()](#FP16+times_i4) * [.frob(f)](#FP16+frob) * [.pow(e)](#FP16+pow) * [.xtr_A(w, y, z)](#FP16+xtr_A) * [.xtr_D()](#FP16+xtr_D) * [.xtr_pow(n)](#FP16+xtr_pow) * [.xtr_pow2()](#FP16+xtr_pow2) ### new FP16() Creates an instance of FP16. ### fP16.reduce() Reduces all components of possibly unreduced FP16 mod Modulus **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.norm() Normalises the components of an FP16 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.iszilch() Tests for FP16 equal to zero **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.isunity() Tests for FP16 equal to unity **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.cmove(g, d) Conditional copy of FP16 number **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | g | FP16 instance | | d | copy depends on this value | ### fP16.isreal() test is w real? That is in a+ib test b is zero **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.real() extract real part a **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.geta() extract a from this **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.getb() extract b from this **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.equals(x) Tests for equality of two FP16s **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | x | FP16 instance to compare | ### fP16.copy(x) Copy FP16 to another FP16 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | x | FP16 instance to be copied | ### fP16.zero() Set FP16 to zero **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.one(x) Set FP16 to unity **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | x | FP16 instance to be set to one | ### fP16.set(c, d) Set FP16 from two FP8 values **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | c | FP8 instance | | d | FP8 instance | ### fP16.seta(c) Set FP16 from one FP8 value **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | c | FP8 instance | ### fP16.neg() this=-this **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.conj() Conjugation of FP16 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.nconj() Negative conjugation of FP16 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.add(x) addition of two FP16s **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | x | FP16 instance | ### fP16.sub(x) subtraction of two FP16s **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | x | FP16 instance | ### fP16.pmul(s) Multiplication of an FP16 by an FP8 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | s | FP8 instance | ### fP16.qmul(s) Multiplication of an FP16 by an FP2 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | s | FP2 instance | ### fP16.imul(s) Multiplication of an FP16 by a small integer **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | s | integer | ### fP16.sqr() Fast Squaring of an FP16 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.mul(y) Full unconditional Multiplication of two FP16s **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | y | FP16 instance, the multiplier | ### fP16.toString() convert this to hex string **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.inverse() Inverting an FP16 **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.times\_i() multiplies an FP16 instance by irreducible polynomial sqrt(1+sqrt(-1)) **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.times\_i2() multiplies an FP16 instance by irreducible polynomial (1+sqrt(-1)) **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.times\_i4() multiplies an FP16 instance by irreducible polynomial (1+sqrt(-1)) **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.frob(f) Raises an FP16 to the power of the internal modulus p, using the Frobenius **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | f | Modulus | ### fP16.pow(e) Raises an FP16 to the power of a BIG **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | e | BIG instance exponent | ### fP16.xtr\_A(w, y, z) Calculates the XTR addition function r=w*x-conj(x)*y+z **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | w | FP16 instance | | y | FP16 instance | | z | FP16 instance | ### fP16.xtr\_D() Calculates the XTR doubling function r=x^2-2*conj(x) **Kind**: instance method of [FP16](#FP16) **this**: {FP16} ### fP16.xtr\_pow(n) Calculates FP16 trace of an FP16 raised to the power of a BIG number **Kind**: instance method of [FP16](#FP16) **this**: {FP16} | Param | Description | | --- | --- | | n | Big number | ### fP16.xtr\_pow2() Calculates FP16 trace of c^a.d^b, where c and d are derived from FP16 traces of FP16s **Kind**: instance method of [FP16](#FP16) **this**: {FP16}