1 files changed, 227 insertions, 0 deletions
diff --git a/libm/double/polrt.c b/libm/double/polrt.c
new file mode 100644
index 000000000..b1cd88087
--- /dev/null
+++ b/libm/double/polrt.c
@@ -0,0 +1,227 @@
+/*							polrt.c
+ *
+ *	Find roots of a polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ *	{
+ *	double r;
+ *	double i;
+ *	}cmplx;
+ *
+ * double xcof[], cof[];
+ * int m;
+ * cmplx root[];
+ *
+ * polrt( xcof, cof, m, root )
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Iterative determination of the roots of a polynomial of
+ * degree m whose coefficient vector is xcof[].  The
+ * coefficients are arranged in ascending order; i.e., the
+ * coefficient of x**m is xcof[m].
+ *
+ * The array cof[] is working storage the same size as xcof[].
+ * root[] is the output array containing the complex roots.
+ *
+ *
+ * ACCURACY:
+ *
+ * Termination depends on evaluation of the polynomial at
+ * the trial values of the roots.  The values of multiple roots
+ * or of roots that are nearly equal may have poor relative
+ * accuracy after the first root in the neighborhood has been
+ * found.
+ *
+ */
+
+/*							polrt	*/
+/* Complex roots of real polynomial */
+/* number of coefficients is m + 1 ( i.e., m is degree of polynomial) */
+
+#include <math.h>
+/*
+typedef struct
+	{
+	double r;
+	double i;
+	}cmplx;
+*/
+#ifdef ANSIPROT
+extern double fabs ( double );
+#else
+double fabs();
+#endif
+
+int polrt( xcof, cof, m, root )
+double xcof[], cof[];
+int m;
+cmplx root[];
+{
+register double *p, *q;
+int i, j, nsav, n, n1, n2, nroot, iter, retry;
+int final;
+double mag, cofj;
+cmplx x0, x, xsav, dx, t, t1, u, ud;
+
+final = 0;
+n = m;
+if( n <= 0 )
+	return(1);
+if( n > 36 )
+	return(2);
+if( xcof[m] == 0.0 )
+	return(4);
+
+n1 = n;
+n2 = n;
+nroot = 0;
+nsav = n;
+q = &xcof[0];
+p = &cof[n];
+for( j=0; j<=nsav; j++ )
+	*p-- = *q++;	/*	cof[ n-j ] = xcof[j];*/
+xsav.r = 0.0;
+xsav.i = 0.0;
+
+nxtrut:
+x0.r = 0.00500101;
+x0.i = 0.01000101;
+retry = 0;
+
+tryagn:
+retry += 1;
+x.r = x0.r;
+
+x0.r = -10.0 * x0.i;
+x0.i = -10.0 * x.r;
+
+x.r = x0.r;
+x.i = x0.i;
+
+finitr:
+iter = 0;
+
+while( iter < 500 )
+{
+u.r = cof[n];
+if( u.r == 0.0 )
+	{		/* this root is zero */
+	x.r = 0;
+	n1 -= 1;
+	n2 -= 1;
+	goto zerrut;
+	}
+u.i = 0;
+ud.r = 0;
+ud.i = 0;
+t.r = 1.0;
+t.i = 0;
+p = &cof[n-1];
+for( i=0; i<n; i++ )
+	{
+	t1.r = x.r * t.r  -  x.i * t.i;
+	t1.i = x.r * t.i  +  x.i * t.r;
+	cofj = *p--;		/* evaluate polynomial */
+	u.r += cofj * t1.r;
+	u.i += cofj * t1.i;
+	cofj = cofj * (i+1);	/* derivative */
+	ud.r += cofj * t.r;
+	ud.i -= cofj * t.i;
+	t.r = t1.r;
+	t.i = t1.i;
+	}
+
+mag = ud.r * ud.r  +  ud.i * ud.i;
+if( mag == 0.0 )
+	{
+	if( !final )
+		goto tryagn;
+	x.r = xsav.r;
+	x.i = xsav.i;
+	goto findon;
+	}
+dx.r = (u.i * ud.i  -  u.r * ud.r)/mag;
+x.r += dx.r;
+dx.i = -(u.r * ud.i  +  u.i * ud.r)/mag;
+x.i += dx.i;
+if( (fabs(dx.i) + fabs(dx.r)) < 1.0e-6 )
+	goto lupdon;
+iter += 1;
+}	/* while iter < 500 */
+
+if( final )
+	goto lupdon;
+if( retry < 5 )
+	goto tryagn;
+return(3);
+
+lupdon:
+/* Swap original and reduced polynomials */
+q = &xcof[nsav];
+p = &cof[0];
+for( j=0; j<=n2; j++ )
+	{
+	cofj = *q;
+	*q-- = *p;
+	*p++ = cofj;
+	}
+i = n;
+n = n1;
+n1 = i;
+
+if( !final )
+	{
+	final = 1;
+	if( fabs(x.i/x.r) < 1.0e-4 )
+		x.i = 0.0;
+	xsav.r = x.r;
+	xsav.i = x.i;
+	goto finitr;	/* do final iteration on original polynomial */
+	}
+
+findon:
+final = 0;
+if( fabs(x.i/x.r) >= 1.0e-5 )
+	{
+	cofj = x.r + x.r;
+	mag = x.r * x.r  +  x.i * x.i;
+	n -= 2;
+	}
+else
+	{		/* root is real */
+zerrut:
+	x.i = 0;
+	cofj = x.r;
+	mag = 0;
+	n -= 1;
+	}
+/* divide working polynomial cof(z) by z - x */
+p = &cof[1];
+*p += cofj * *(p-1);
+for( j=1; j<n; j++ )
+	{
+	*(p+1) += cofj * *p  -  mag * *(p-1);
+	p++;
+	}
+
+setrut:
+root[nroot].r = x.r;
+root[nroot].i = x.i;
+nroot += 1;
+if( mag != 0.0 )
+	{
+	x.i = -x.i;
+	mag = 0;
+	goto setrut;	/* fill in the complex conjugate root */
+	}
+if( n > 0 )
+	goto nxtrut;
+return(0);
+}