use new math routines

lang/basic/lib/sin.c

@@ -11,90 +11,74 @@
 #include <math.h>
 
 static double
-sinus(x, quadrant)
+sinus(x, cos_flag)
 	double x;
 {
-	/*	sin(0.5*pi*x) = x * P(x*x)/Q(x*x) for x in [0,1] */
-	/*	Hart & Cheney # 3374 */
+	/*	Algorithm and coefficients from:
+			"Software manual for the elementary functions"
+			by W.J. Cody and W. Waite, Prentice-Hall, 1980
+	*/
 
-	static double p[6] = {
-		 0.4857791909822798473837058825e+10,
-		-0.1808816670894030772075877725e+10,
-		 0.1724314784722489597789244188e+09,
-		-0.6351331748520454245913645971e+07,
-		 0.1002087631419532326179108883e+06,
-		-0.5830988897678192576148973679e+03
+	static double r[] = {
+		-0.16666666666666665052e+0,
+		 0.83333333333331650314e-2,
+		-0.19841269841201840457e-3,
+		 0.27557319210152756119e-5,
+		-0.25052106798274584544e-7,
+		 0.16058936490371589114e-9,
+		-0.76429178068910467734e-12,
+		 0.27204790957888846175e-14
 	};
 
-	static double q[6] = {
-		 0.3092566379840468199410228418e+10,
-		 0.1202384907680254190870913060e+09,
-		 0.2321427631602460953669856368e+07,
-		 0.2848331644063908832127222835e+05,
-		 0.2287602116741682420054505174e+03,
-		 0.1000000000000000000000000000e+01
-	};
-
-	double xsqr;
-	int t;
+	double	xsqr;
+	double	y;
+	int	neg = 0;
 
 	if (x < 0) {
-		quadrant += 2;
 		x = -x;
+		neg = 1;
 	}
-	if (M_PI_2 - x == M_PI_2) {
-		switch(quadrant) {
-		case 0:
-		case 2:
-			return 0.0;
-		case 1:
-			return 1.0;
-		case 3:
-			return -1.0;
-		}
+	if (cos_flag) {
+		neg = 0;
+		y = M_PI_2 + x;
 	}
-	if (x >= M_2PI) {
-	    if (x <= 0x7fffffff) {
-		/*	Use extended precision to calculate reduced argument.
-			Split 2pi in 2 parts a1 and a2, of which the first only
-			uses some bits of the mantissa, so that n * a1 is
-			exactly representable, where n is the integer part of
-			x/pi.
-			Here we used 12 bits of the mantissa for a1.
-			Also split x in integer part x1 and fraction part x2.
-			We then compute x-n*2pi as ((x1 - n*a1) + x2) - n*a2.
-		*/
-#define A1 6.2822265625
-#define A2 0.00095874467958647692528676655900576
-		double n = (long) (x / M_2PI);
-		double x1 = (long) x;
-		double x2 = x - x1;
-		x = x1 - n * A1;
+	else	y = x;
+
+	/* ??? avoid loss of significance, if y is too large, error ??? */
+
+	y = y * M_1_PI + 0.5;
+
+	/*	Use extended precision to calculate reduced argument.
+		Here we used 12 bits of the mantissa for a1.
+		Also split x in integer part x1 and fraction part x2.
+	*/
+#define A1 3.1416015625
+#define A2 -8.908910206761537356617e-6
+	{
+		double x1, x2;
+		extern double	_fif();
+
+		_fif(y, 1.0,  &y);
+		if (_fif(y, 0.5, &x1)) neg = !neg;
+		if (cos_flag) y -= 0.5;
+		x2 = _fif(x, 1.0, &x1);
+		x = x1 - y * A1;
 		x += x2;
-		x -= n * A2;
+		x -= y * A2;
 #undef A1
 #undef A2
-	    }
-	    else {
-		extern double _fif();
-		double dummy;
+	}
 
-		x = _fif(x/M_2PI, 1.0, &dummy) * M_2PI;
-	    }
-	}
-	x /= M_PI_2;
-	t = x;
-	x -= t;
-	quadrant = (quadrant + (int)(t % 4)) % 4;
-	if (quadrant & 01) {
-		x = 1 - x;
-	}
-	if (quadrant > 1) {
+	if (x < 0) {
+		neg = !neg;
 		x = -x;
 	}
-	xsqr = x * x;
-	x = x * POLYNOM5(xsqr, p) / POLYNOM5(xsqr, q);
-	return x;
+
+	/* ??? avoid underflow ??? */
+
+	y = x * x;
+	x += x * y * POLYNOM7(y, r);
+	return neg ? -x : x;
 }
 
 double