102 lines
3.8 KiB
TypeScript
102 lines
3.8 KiB
TypeScript
import {Complex} from './type.js'
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import type {
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Dependencies, Signature, Returns, RealType, AliasOf
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} from '../interfaces/type.js'
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declare module "../interfaces/type" {
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interface Signatures<T> {
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addReal: AliasOf<'add', (a: T, b: RealType<T>) => T>
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divideReal: AliasOf<'divide', (a: T, b: RealType<T>) => T>
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}
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}
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export const add =
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<T>(dep: Dependencies<'add' | 'complex', T>): Signature<'add', Complex<T>> =>
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(w, z) => dep.complex(dep.add(w.re, z.re), dep.add(w.im, z.im))
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export const addReal =
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<T>(dep: Dependencies<'addReal' | 'complex', T>):
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Signature<'addReal', Complex<T>> =>
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(z, r) => dep.complex(dep.addReal(z.re, r), z.im)
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export const unaryMinus =
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<T>(dep: Dependencies<'unaryMinus' | 'complex', T>):
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Signature<'unaryMinus', Complex<T>> =>
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z => dep.complex(dep.unaryMinus(z.re), dep.unaryMinus(z.im))
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export const conj =
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<T>(dep: Dependencies<'unaryMinus' | 'conj' | 'complex', T>):
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Signature<'conj', Complex<T>> =>
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z => dep.complex(dep.conj(z.re), dep.unaryMinus(z.im))
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export const subtract =
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<T>(dep: Dependencies<'subtract' | 'complex', T>):
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Signature<'subtract', Complex<T>> =>
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(w, z) => dep.complex(dep.subtract(w.re, z.re), dep.subtract(w.im, z.im))
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export const multiply =
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<T>(dep: Dependencies<
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'add' | 'subtract' | 'multiply' | 'conj' | 'complex', T>):
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Signature<'multiply', Complex<T>> =>
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(w, z) => {
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const mult = dep.multiply
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const realpart = dep.subtract(
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mult( w.re, z.re), mult(dep.conj(w.im), z.im))
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const imagpart = dep.add(
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mult(dep.conj(w.re), z.im), mult( w.im, z.re))
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return dep.complex(realpart, imagpart)
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}
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export const absquare =
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<T>(dep: Dependencies<'absquare', T>
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& Dependencies<'add', Returns<'absquare', T>>):
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Signature<'absquare', Complex<T>> =>
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z => dep.add(dep.absquare(z.re), dep.absquare(z.im))
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export const divideReal =
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<T>(dep: Dependencies<'divideReal' | 'complex', T>):
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Signature<'divideReal', Complex<T>> =>
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(z, r) => dep.complex(dep.divideReal(z.re, r), dep.divideReal(z.im, r))
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export const reciprocal =
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<T>(dep: Dependencies<'conj' | 'absquare' | 'divideReal', Complex<T>>):
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Signature<'reciprocal', Complex<T>> =>
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z => dep.divideReal(dep.conj(z), dep.absquare(z))
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export const divide =
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<T>(dep: Dependencies<'multiply' | 'reciprocal', Complex<T>>):
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Signature<'divide', Complex<T>> =>
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(w, z) => dep.multiply(w, dep.reciprocal(z))
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// The dependencies are slightly tricky here, because there are three types
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// involved: Complex<T>, T, and RealType<T>, all of which might be different,
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// and we have to get it straight which operations we need on each type, and
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// in fact, we need `addReal` on both T and Complex<T>, hence the dependency
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// with a custom name, not generated via Dependencies<...>
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export const sqrt =
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<T>(dep: Dependencies<'equal' | 'conservativeSqrt' | 'unaryMinus', RealType<T>>
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& Dependencies<'zero' | 'complex', T>
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& Dependencies<'absquare' | 're' | 'divideReal', Complex<T>>
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& {
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addTR: Signature<'addReal', T>,
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addRR: Signature<'add', RealType<T>>,
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addCR: Signature<'addReal', Complex<T>>
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}):
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Signature<'sqrt', Complex<T>> =>
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z => {
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const myabs = dep.conservativeSqrt(dep.absquare(z))
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const r = dep.re(z)
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const negr = dep.unaryMinus(r)
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if (dep.equal(myabs, negr)) {
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// pure imaginary square root; z.im already zero
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return dep.complex(
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dep.zero(z.re), dep.addTR(z.im, dep.conservativeSqrt(negr)))
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}
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const num = dep.addCR(z, myabs)
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const denomsq = dep.addRR(dep.addRR(myabs, myabs), dep.addRR(r, r))
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const denom = dep.conservativeSqrt(denomsq)
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return dep.divideReal(num, denom)
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}
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export const conservativeSqrt = sqrt
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