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bcomplex.d
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bcomplex.d
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/**
* Compiler implementation of the
* $(LINK2 http://www.dlang.org, D programming language).
*
* Copyright: public domain
* License: public domain
* Source: $(DMDSRC backend/_bcomplex.d)
*/
module dmd.backend.bcomplex;
public import dmd.root.longdouble : targ_ldouble = longdouble;
import core.stdc.math : fabs, fabsl, sqrt;
version(CRuntime_Microsoft)
private import dmd.root.longdouble : fabsl, sqrt; // needed if longdouble is longdouble_soft
extern (C++):
@nogc:
@safe:
nothrow:
// Roll our own for reliable bootstrapping
struct Complex_f
{
float re, im;
static Complex_f div(ref Complex_f x, ref Complex_f y)
{
if (fabs(y.re) < fabs(y.im))
{
const r = y.re / y.im;
const den = y.im + r * y.re;
return Complex_f(cast(float)((x.re * r + x.im) / den),
cast(float)((x.im * r - x.re) / den));
}
else
{
const r = y.im / y.re;
const den = y.re + r * y.im;
return Complex_f(cast(float)((x.re + r * x.im) / den),
cast(float)((x.im - r * x.re) / den));
}
}
static Complex_f mul(ref Complex_f x, ref Complex_f y) pure
{
return Complex_f(x.re * y.re - x.im * y.im,
x.im * y.re + x.re * y.im);
}
static targ_ldouble abs(ref Complex_f z)
{
const targ_ldouble x = fabs(z.re);
const targ_ldouble y = fabs(z.im);
if (x == 0)
return y;
else if (y == 0)
return x;
else if (x > y)
{
const targ_ldouble temp = y / x;
return x * sqrt(1 + temp * temp);
}
else
{
const targ_ldouble temp = x / y;
return y * sqrt(1 + temp * temp);
}
}
static Complex_f sqrtc(ref Complex_f z)
{
if (z.re == 0 && z.im == 0)
{
return Complex_f(0, 0);
}
else
{
const targ_ldouble x = fabs(z.re);
const targ_ldouble y = fabs(z.im);
targ_ldouble r, w;
if (x >= y)
{
r = y / x;
w = sqrt(x) * sqrt(0.5 * (1 + sqrt(1 + r * r)));
}
else
{
r = x / y;
w = sqrt(y) * sqrt(0.5 * (r + sqrt(1 + r * r)));
}
if (z.re >= 0)
{
return Complex_f(cast(float)w, (z.im / cast(float)(w + w)));
}
else
{
const cim = (z.im >= 0) ? w : -w;
return Complex_f((z.im / cast(float)(cim + cim)), cast(float)cim);
}
}
}
}
struct Complex_d
{
double re, im;
static Complex_d div(ref Complex_d x, ref Complex_d y)
{
if (fabs(y.re) < fabs(y.im))
{
const targ_ldouble r = y.re / y.im;
const targ_ldouble den = y.im + r * y.re;
return Complex_d(cast(double)((x.re * r + x.im) / den),
cast(double)((x.im * r - x.re) / den));
}
else
{
const targ_ldouble r = y.im / y.re;
const targ_ldouble den = y.re + r * y.im;
return Complex_d(cast(double)((x.re + r * x.im) / den),
cast(double)((x.im - r * x.re) / den));
}
}
static Complex_d mul(ref Complex_d x, ref Complex_d y) pure
{
return Complex_d(x.re * y.re - x.im * y.im,
x.im * y.re + x.re * y.im);
}
static targ_ldouble abs(ref Complex_d z)
{
const targ_ldouble x = fabs(z.re);
const targ_ldouble y = fabs(z.im);
if (x == 0)
return y;
else if (y == 0)
return x;
else if (x > y)
{
const targ_ldouble temp = y / x;
return x * sqrt(1 + temp * temp);
}
else
{
const targ_ldouble temp = x / y;
return y * sqrt(1 + temp * temp);
}
}
static Complex_d sqrtc(ref Complex_d z)
{
if (z.re == 0 && z.im == 0)
{
return Complex_d(0, 0);
}
else
{
const targ_ldouble x = fabs(z.re);
const targ_ldouble y = fabs(z.im);
targ_ldouble r, w;
if (x >= y)
{
r = y / x;
w = sqrt(x) * sqrt(0.5 * (1 + sqrt(1 + r * r)));
}
else
{
r = x / y;
w = sqrt(y) * sqrt(0.5 * (r + sqrt(1 + r * r)));
}
if (z.re >= 0)
{
return Complex_d(cast(double)w, (z.im / cast(double)(w + w)));
}
else
{
const cim = (z.im >= 0) ? w : -w;
return Complex_d((z.im / cast(double)(cim + cim)), cast(double)cim);
}
}
}
}
struct Complex_ld
{
targ_ldouble re, im;
static Complex_ld div(ref Complex_ld x, ref Complex_ld y)
{
if (fabsl(y.re) < fabsl(y.im))
{
const targ_ldouble r = y.re / y.im;
const targ_ldouble den = y.im + r * y.re;
return Complex_ld((x.re * r + x.im) / den,
(x.im * r - x.re) / den);
}
else
{
const targ_ldouble r = y.im / y.re;
const targ_ldouble den = y.re + r * y.im;
return Complex_ld((x.re + r * x.im) / den,
(x.im - r * x.re) / den);
}
}
static Complex_ld mul(ref Complex_ld x, ref Complex_ld y) pure
{
return Complex_ld(x.re * y.re - x.im * y.im,
x.im * y.re + x.re * y.im);
}
static targ_ldouble abs(ref Complex_ld z)
{
const targ_ldouble x = fabsl(z.re);
const targ_ldouble y = fabsl(z.im);
if (x == 0)
return y;
else if (y == 0)
return x;
else if (x > y)
{
const targ_ldouble temp = y / x;
return x * sqrt(1 + temp * temp);
}
else
{
const targ_ldouble temp = x / y;
return y * sqrt(1 + temp * temp);
}
}
static Complex_ld sqrtc(ref Complex_ld z)
{
if (z.re == 0 && z.im == 0)
{
return Complex_ld(targ_ldouble(0), targ_ldouble(0));
}
else
{
const targ_ldouble x = fabsl(z.re);
const targ_ldouble y = fabsl(z.im);
targ_ldouble r, w;
if (x >= y)
{
r = y / x;
w = sqrt(x) * sqrt(0.5 * (1 + sqrt(1 + r * r)));
}
else
{
r = x / y;
w = sqrt(y) * sqrt(0.5 * (r + sqrt(1 + r * r)));
}
if (z.re >= 0)
{
return Complex_ld(w, z.im / (w + w));
}
else
{
const cim = (z.im >= 0) ? w : -w;
return Complex_ld(z.im / (cim + cim), cim);
}
}
}
}