github.com/primecitizens/pcz/std@v0.2.1/builtin/complex/complex128.go (about) 1 // SPDX-License-Identifier: Apache-2.0 2 // Copyright 2023 The Prime Citizens 3 // 4 // Copyright 2010 The Go Authors. All rights reserved. 5 // Use of this source code is governed by a BSD-style 6 // license that can be found in the LICENSE file. 7 8 package stdcomplex 9 10 import ( 11 stdfloat "github.com/primecitizens/pcz/std/builtin/float" 12 ) 13 14 func Complex128Div(n, m complex128) complex128 { 15 var e, f float64 // complex(e, f) = n/m 16 17 // Algorithm for robust complex division as described in 18 // Robert L. Smith: Algorithm 116: Complex division. Commun. ACM 5(8): 435 (1962). 19 if stdfloat.Abs(real(m)) >= stdfloat.Abs(imag(m)) { 20 ratio := imag(m) / real(m) 21 denom := real(m) + ratio*imag(m) 22 e = (real(n) + imag(n)*ratio) / denom 23 f = (imag(n) - real(n)*ratio) / denom 24 } else { 25 ratio := real(m) / imag(m) 26 denom := imag(m) + ratio*real(m) 27 e = (real(n)*ratio + imag(n)) / denom 28 f = (imag(n)*ratio - real(n)) / denom 29 } 30 31 if stdfloat.IsNaN(e) && stdfloat.IsNaN(f) { 32 // Correct final result to infinities and zeros if applicable. 33 // Matches C99: ISO/IEC 9899:1999 - G.5.1 Multiplicative operators. 34 35 a, b := real(n), imag(n) 36 c, d := real(m), imag(m) 37 38 switch { 39 case m == 0 && (!stdfloat.IsNaN(a) || !stdfloat.IsNaN(b)): 40 e = stdfloat.CopySign(inf, c) * a 41 f = stdfloat.CopySign(inf, c) * b 42 43 case (stdfloat.IsInf(a) || stdfloat.IsInf(b)) && stdfloat.IsFinite(c) && stdfloat.IsFinite(d): 44 a = inf2one(a) 45 b = inf2one(b) 46 e = inf * (a*c + b*d) 47 f = inf * (b*c - a*d) 48 49 case (stdfloat.IsInf(c) || stdfloat.IsInf(d)) && stdfloat.IsFinite(a) && stdfloat.IsFinite(b): 50 c = inf2one(c) 51 d = inf2one(d) 52 e = 0 * (a*c + b*d) 53 f = 0 * (b*c - a*d) 54 } 55 } 56 57 return complex(e, f) 58 } 59 60 // inf2one returns a signed 1 if f is an infinity and a signed 0 otherwise. 61 // The sign of the result is the sign of f. 62 func inf2one(f float64) float64 { 63 g := 0.0 64 if stdfloat.IsInf(f) { 65 g = 1.0 66 } 67 return stdfloat.CopySign(g, f) 68 }