add sin, cos implementation

git-svn-id: https://rt-thread.googlecode.com/svn/trunk@949 bbd45198-f89e-11dd-88c7-29a3b14d5316

components/libc/minilibc/math.c

@@ -1,12 +1,169 @@
 #include <math.h>
 
-/* Fix me */
-double sin(double x) 
+/*
+ * COPYRIGHT:        See COPYING in the top level directory
+ * PROJECT:          ReactOS CRT
+ * FILE:             lib/crt/math/cos.c
+ * PURPOSE:          Generic C Implementation of cos
+ * PROGRAMMER:       Timo Kreuzer (timo.kreuzer@reactos.org)
+ */
+
+#define PRECISION 9
+#define M_PI 3.141592653589793238462643
+
+static double cos_off_tbl[] = {0.0, -M_PI/2., 0, -M_PI/2.};
+static double cos_sign_tbl[] = {1,-1,-1,1};
+
+static double sin_off_tbl[] = {0.0, -M_PI/2., 0, -M_PI/2.};
+static double sin_sign_tbl[] = {1,-1,-1,1};
+
+double sin(double x)
 {
-	#warning sin function not supported for this platform
+    int quadrant;
+    double x2, result;
+
+    /* Calculate the quadrant */
+    quadrant = x * (2./M_PI);
+
+    /* Get offset inside quadrant */
+    x = x - quadrant * (M_PI/2.);
+
+    /* Normalize quadrant to [0..3] */
+    quadrant = (quadrant - 1) & 0x3;
+
+    /* Fixup value for the generic function */
+    x += sin_off_tbl[quadrant];
+
+    /* Calculate the negative of the square of x */
+    x2 = - (x * x);
+
+    /* This is an unrolled taylor series using <PRECISION> iterations
+     * Example with 4 iterations:
+     * result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
+     * To save multiplications and to keep the precision high, it's performed
+     * like this:
+     * result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
+     */
+
+    /* Start with 0, compiler will optimize this away */
+    result = 0;
+
+#if (PRECISION >= 10)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
+    result *= x2;
+#endif
+#if (PRECISION >= 9)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
+    result *= x2;
+#endif
+#if (PRECISION >= 8)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
+    result *= x2;
+#endif
+#if (PRECISION >= 7)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
+    result *= x2;
+#endif
+#if (PRECISION >= 6)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
+    result *= x2;
+#endif
+#if (PRECISION >= 5)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10);
+    result *= x2;
+#endif
+    result += 1./(1.*2*3*4*5*6*7*8);
+    result *= x2;
+
+    result += 1./(1.*2*3*4*5*6);
+    result *= x2;
+
+    result += 1./(1.*2*3*4);
+    result *= x2;
+
+    result += 1./(1.*2);
+    result *= x2;
+
+    result += 1;
+
+    /* Apply correct sign */
+    result *= sin_sign_tbl[quadrant];
+
+    return result;
 }
 
-double cos(double x) 
+double cos(double x)
 {
-	#warning cos function not supported for this platform
+    int quadrant;
+    double x2, result;
+
+    /* Calculate the quadrant */
+    quadrant = x * (2./M_PI);
+
+    /* Get offset inside quadrant */
+    x = x - quadrant * (M_PI/2.);
+
+    /* Normalize quadrant to [0..3] */
+    quadrant = quadrant & 0x3;
+
+    /* Fixup value for the generic function */
+    x += cos_off_tbl[quadrant];
+
+    /* Calculate the negative of the square of x */
+    x2 = - (x * x);
+
+    /* This is an unrolled taylor series using <PRECISION> iterations
+     * Example with 4 iterations:
+     * result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
+     * To save multiplications and to keep the precision high, it's performed
+     * like this:
+     * result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
+     */
+
+    /* Start with 0, compiler will optimize this away */
+    result = 0;
+
+#if (PRECISION >= 10)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
+    result *= x2;
+#endif
+#if (PRECISION >= 9)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
+    result *= x2;
+#endif
+#if (PRECISION >= 8)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
+    result *= x2;
+#endif
+#if (PRECISION >= 7)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
+    result *= x2;
+#endif
+#if (PRECISION >= 6)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
+    result *= x2;
+#endif
+#if (PRECISION >= 5)
+    result += 1./(1.*2*3*4*5*6*7*8*9*10);
+    result *= x2;
+#endif
+    result += 1./(1.*2*3*4*5*6*7*8);
+    result *= x2;
+
+    result += 1./(1.*2*3*4*5*6);
+    result *= x2;
+
+    result += 1./(1.*2*3*4);
+    result *= x2;
+
+    result += 1./(1.*2);
+    result *= x2;
+
+    result += 1;
+
+    /* Apply correct sign */
+    result *= cos_sign_tbl[quadrant];
+
+    return result;
 }
+