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-rw-r--r--libm/double/polmisc.c309
1 files changed, 309 insertions, 0 deletions
diff --git a/libm/double/polmisc.c b/libm/double/polmisc.c
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+
+/* Square root, sine, cosine, and arctangent of polynomial.
+ * See polyn.c for data structures and discussion.
+ */
+
+#include <stdio.h>
+#include <math.h>
+#ifdef ANSIPROT
+extern double atan2 ( double, double );
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern void polclr ( double *a, int n );
+extern void polmov ( double *a, int na, double *b );
+extern void polmul ( double a[], int na, double b[], int nb, double c[] );
+extern void poladd ( double a[], int na, double b[], int nb, double c[] );
+extern void polsub ( double a[], int na, double b[], int nb, double c[] );
+extern int poldiv ( double a[], int na, double b[], int nb, double c[] );
+extern void polsbt ( double a[], int na, double b[], int nb, double c[] );
+extern void * malloc ( long );
+extern void free ( void * );
+#else
+double atan2(), sqrt(), fabs(), sin(), cos();
+void polclr(), polmov(), polsbt(), poladd(), polsub(), polmul();
+int poldiv();
+void * malloc();
+void free ();
+#endif
+
+/* Highest degree of polynomial to be handled
+ by the polyn.c subroutine package. */
+#define N 16
+/* Highest degree actually initialized at runtime. */
+extern int MAXPOL;
+
+/* Taylor series coefficients for various functions
+ */
+double patan[N+1] = {
+ 0.0, 1.0, 0.0, -1.0/3.0, 0.0,
+ 1.0/5.0, 0.0, -1.0/7.0, 0.0, 1.0/9.0, 0.0, -1.0/11.0,
+ 0.0, 1.0/13.0, 0.0, -1.0/15.0, 0.0 };
+
+double psin[N+1] = {
+ 0.0, 1.0, 0.0, -1.0/6.0, 0.0, 1.0/120.0, 0.0,
+ -1.0/5040.0, 0.0, 1.0/362880.0, 0.0, -1.0/39916800.0,
+ 0.0, 1.0/6227020800.0, 0.0, -1.0/1.307674368e12, 0.0};
+
+double pcos[N+1] = {
+ 1.0, 0.0, -1.0/2.0, 0.0, 1.0/24.0, 0.0,
+ -1.0/720.0, 0.0, 1.0/40320.0, 0.0, -1.0/3628800.0, 0.0,
+ 1.0/479001600.0, 0.0, -1.0/8.7179291e10, 0.0, 1.0/2.0922789888e13};
+
+double pasin[N+1] = {
+ 0.0, 1.0, 0.0, 1.0/6.0, 0.0,
+ 3.0/40.0, 0.0, 15.0/336.0, 0.0, 105.0/3456.0, 0.0, 945.0/42240.0,
+ 0.0, 10395.0/599040.0 , 0.0, 135135.0/9676800.0 , 0.0
+};
+
+/* Square root of 1 + x. */
+double psqrt[N+1] = {
+ 1.0, 1./2., -1./8., 1./16., -5./128., 7./256., -21./1024., 33./2048.,
+ -429./32768., 715./65536., -2431./262144., 4199./524288., -29393./4194304.,
+ 52003./8388608., -185725./33554432., 334305./67108864.,
+ -9694845./2147483648.};
+
+/* Arctangent of the ratio num/den of two polynomials.
+ */
+void
+polatn( num, den, ans, nn )
+ double num[], den[], ans[];
+ int nn;
+{
+ double a, t;
+ double *polq, *polu, *polt;
+ int i;
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ /* arctan( a + b ) = arctan(a) + arctan( b/(1 + ab + a**2) ) */
+ t = num[0];
+ a = den[0];
+ if( (t == 0.0) && (a == 0.0 ) )
+ {
+ t = num[1];
+ a = den[1];
+ }
+ t = atan2( t, a ); /* arctan(num/den), the ANSI argument order */
+ polq = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polu = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polt = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polclr( polq, MAXPOL );
+ i = poldiv( den, nn, num, nn, polq );
+ a = polq[0]; /* a */
+ polq[0] = 0.0; /* b */
+ polmov( polq, nn, polu ); /* b */
+ /* Form the polynomial
+ 1 + ab + a**2
+ where a is a scalar. */
+ for( i=0; i<=nn; i++ )
+ polu[i] *= a;
+ polu[0] += 1.0 + a * a;
+ poldiv( polu, nn, polq, nn, polt ); /* divide into b */
+ polsbt( polt, nn, patan, nn, polu ); /* arctan(b) */
+ polu[0] += t; /* plus arctan(a) */
+ polmov( polu, nn, ans );
+ free( polt );
+ free( polu );
+ free( polq );
+}
+
+
+
+/* Square root of a polynomial.
+ * Assumes the lowest degree nonzero term is dominant
+ * and of even degree. An error message is given
+ * if the Newton iteration does not converge.
+ */
+void
+polsqt( pol, ans, nn )
+ double pol[], ans[];
+ int nn;
+{
+ double t;
+ double *x, *y;
+ int i, n;
+#if 0
+ double z[N+1];
+ double u;
+#endif
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ x = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ y = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polmov( pol, nn, x );
+ polclr( y, MAXPOL );
+
+ /* Find lowest degree nonzero term. */
+ t = 0.0;
+ for( n=0; n<nn; n++ )
+ {
+ if( x[n] != 0.0 )
+ goto nzero;
+ }
+ polmov( y, nn, ans );
+ return;
+
+nzero:
+
+ if( n > 0 )
+ {
+ if (n & 1)
+ {
+ printf("error, sqrt of odd polynomial\n");
+ return;
+ }
+ /* Divide by x^n. */
+ y[n] = x[n];
+ poldiv (y, nn, pol, N, x);
+ }
+
+ t = x[0];
+ for( i=1; i<=nn; i++ )
+ x[i] /= t;
+ x[0] = 0.0;
+ /* series development sqrt(1+x) = 1 + x / 2 - x**2 / 8 + x**3 / 16
+ hopes that first (constant) term is greater than what follows */
+ polsbt( x, nn, psqrt, nn, y);
+ t = sqrt( t );
+ for( i=0; i<=nn; i++ )
+ y[i] *= t;
+
+ /* If first nonzero coefficient was at degree n > 0, multiply by
+ x^(n/2). */
+ if (n > 0)
+ {
+ polclr (x, MAXPOL);
+ x[n/2] = 1.0;
+ polmul (x, nn, y, nn, y);
+ }
+#if 0
+/* Newton iterations */
+for( n=0; n<10; n++ )
+ {
+ poldiv( y, nn, pol, nn, z );
+ poladd( y, nn, z, nn, y );
+ for( i=0; i<=nn; i++ )
+ y[i] *= 0.5;
+ for( i=0; i<=nn; i++ )
+ {
+ u = fabs( y[i] - z[i] );
+ if( u > 1.0e-15 )
+ goto more;
+ }
+ goto done;
+more: ;
+ }
+printf( "square root did not converge\n" );
+done:
+#endif /* 0 */
+
+polmov( y, nn, ans );
+free( y );
+free( x );
+}
+
+
+
+/* Sine of a polynomial.
+ * The computation uses
+ * sin(a+b) = sin(a) cos(b) + cos(a) sin(b)
+ * where a is the constant term of the polynomial and
+ * b is the sum of the rest of the terms.
+ * Since sin(b) and cos(b) are computed by series expansions,
+ * the value of b should be small.
+ */
+void
+polsin( x, y, nn )
+ double x[], y[];
+ int nn;
+{
+ double a, sc;
+ double *w, *c;
+ int i;
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polmov( x, nn, w );
+ polclr( c, MAXPOL );
+ polclr( y, nn );
+ /* a, in the description, is x[0]. b is the polynomial x - x[0]. */
+ a = w[0];
+ /* c = cos (b) */
+ w[0] = 0.0;
+ polsbt( w, nn, pcos, nn, c );
+ sc = sin(a);
+ /* sin(a) cos (b) */
+ for( i=0; i<=nn; i++ )
+ c[i] *= sc;
+ /* y = sin (b) */
+ polsbt( w, nn, psin, nn, y );
+ sc = cos(a);
+ /* cos(a) sin(b) */
+ for( i=0; i<=nn; i++ )
+ y[i] *= sc;
+ poladd( c, nn, y, nn, y );
+ free( c );
+ free( w );
+}
+
+
+/* Cosine of a polynomial.
+ * The computation uses
+ * cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
+ * where a is the constant term of the polynomial and
+ * b is the sum of the rest of the terms.
+ * Since sin(b) and cos(b) are computed by series expansions,
+ * the value of b should be small.
+ */
+void
+polcos( x, y, nn )
+ double x[], y[];
+ int nn;
+{
+ double a, sc;
+ double *w, *c;
+ int i;
+ double sin(), cos();
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polmov( x, nn, w );
+ polclr( c, MAXPOL );
+ polclr( y, nn );
+ a = w[0];
+ w[0] = 0.0;
+ /* c = cos(b) */
+ polsbt( w, nn, pcos, nn, c );
+ sc = cos(a);
+ /* cos(a) cos(b) */
+ for( i=0; i<=nn; i++ )
+ c[i] *= sc;
+ /* y = sin(b) */
+ polsbt( w, nn, psin, nn, y );
+ sc = sin(a);
+ /* sin(a) sin(b) */
+ for( i=0; i<=nn; i++ )
+ y[i] *= sc;
+ polsub( y, nn, c, nn, y );
+ free( c );
+ free( w );
+}
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