Added csqrt and tests

Author: wlmb

lib/PDL/Ops.pd

@@ -422,6 +422,21 @@ EOF
   Code => '$c() = $r() + $i() * I;'
 );
 
+pp_def('csqrt',
+    GenericTypes => $AF,
+    Pars => 'i(); complex [o] o()',
+    Doc => <<'EOF',
+Take the complex square root of a number choosing that with
+non-negative real part, i.e., a square root with a branch cut
+'infinitesimally' below the negative real axis, the standard choice.
+EOF
+    Code => q{
+        $TFDEGCH(PDL_CFloat,PDL_CDouble,PDL_CLDouble,PDL_CFloat,PDL_CDouble,PDL_CLDouble) tmp=$i();
+        tmp=csqrt(tmp);
+        $o() = tmp;
+    },
+);
+
 pp_def('csqrt_up',
     GenericTypes => $AF,
     Pars => 'i(); complex [o] o()',

t/ops.t

@@ -112,6 +112,34 @@ if ($can_complex_power) {
 is $pa->at(0), '16', 'sqrt orig value ok';
 }
 
+{   # csqrt
+    my $pi=4*atan2(1,1);
+    my $eiO = exp(i()*(sequence(8)-3)*$pi/4);
+    my $eiO2 = exp(i()*(sequence(8)-3)*$pi/8);
+    my $sqrt=csqrt($eiO);
+    is_pdl($sqrt, $eiO2, "csqrt of complex");
+    my $i=csqrt(-1);
+    is_pdl($i, i(), "csqrt of real -1");
+    my $squares="-9 -4 -1 0 1 4 9";
+    my $roots="3i 2i i 0 1 2 3";
+    my $lsqrt=long($squares)->csqrt;
+    is_pdl($lsqrt, cdouble($roots), "csqrt of long");
+    my $llsqrt=longlong($squares)->csqrt;
+    is_pdl($llsqrt, cdouble($roots), "csqrt of longlong");
+    my $fsqrt=float($squares)->csqrt;
+    is_pdl($fsqrt, cfloat($roots), "csqrt of float");
+    my $dsqrt=double($squares)->csqrt;
+    is_pdl($dsqrt,cdouble($roots), "csqrt of double");
+    my $ldsqrt=ldouble($squares)->csqrt;
+    is_pdl($ldsqrt, cldouble($roots), "csqrt of ldouble");
+    my $cfsqrt=cfloat($squares)->csqrt;
+    is_pdl($cfsqrt, cfloat($roots), "csqrt of cfloat");
+    my $cdsqrt=cdouble($squares)->csqrt;
+    is_pdl($cdsqrt,cdouble($roots), "csqrt of cdouble");
+    my $cldsqrt=cldouble($squares)->csqrt;
+    is_pdl($cldsqrt,cldouble($roots), "csqrt of cldouble");
+}
+
 {   # csqrt_up
     my $pi=4*atan2(1,1);
     my $eiO = exp(i()*sequence(8)*$pi/4);