Added a new algo for sin() function, and a small error analysis to sh…

…ow the precision differences
digitalentity · Jun 8, 2011 · 3b63453 · 3b63453
1 parent 297e94e
commit 3b63453
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Showing 3 changed files with 37 additions and 1 deletion.
diff --git a/images/error_analysis.ods b/images/error_analysis.ods
diff --git a/libfixmath/fix16.h b/libfixmath/fix16.h
@@ -10,6 +10,10 @@ extern "C"
 
 typedef int32_t fix16_t;
 
+static const fix16_t FOUR_DIV_PI  = 0x145F3;			/*!< Fix16 value of 4/PI */
+static const fix16_t _FOUR_DIV_PI2 = 0xFFFF9840; 		/*!< Fix16 value of -4/PI² */
+static const fix16_t X4_CORRECTION_COMPONENT = 0x399A; 	/*!< Fix16 value of 0.225 */
+
 static const fix16_t fix16_max = 0x7FFFFFFF; /*!< the maximum value of fix16_t */
 static const fix16_t fix16_min = 0x80000000; /*!< the minimum value of fix16_t */
 
@@ -80,7 +84,9 @@ extern fix16_t fix16_lerp16(fix16_t inArg0, fix16_t inArg1, uint16_t inFract);
 extern fix16_t fix16_lerp32(fix16_t inArg0, fix16_t inArg1, uint32_t inFract);
 #endif
 
-
+/*! Returns the sine of the given fix16_t.
+*/
+extern fix16_t fix16_sin_parabola(fix16_t inAngle);
 
 /*! Returns the sine of the given fix16_t.
 */

diff --git a/libfixmath/fix16_trig.c b/libfixmath/fix16_trig.c
@@ -1,3 +1,4 @@
+#include <limits.h>
 #include "fix16.h"
 
 #if defined(FIXMATH_SIN_LUT)
@@ -13,6 +14,35 @@ static fix16_t _fix16_atan_cache_value[4096] = { 0 };
 #endif
 
 
+fix16_t fix16_sin_parabola(fix16_t inAngle)
+{
+	fix16_t abs_inAngle, abs_retval, retval;
+	fix16_t mask;
+
+	/* Absolute function */
+	mask = (inAngle >> (sizeof(fix16_t)*CHAR_BIT-1));
+	abs_inAngle = (inAngle + mask) ^ mask;
+
+	/* On 0->PI, sin looks like x² that is :
+	   - centered on PI/2,
+	   - equals 1 on PI/2,
+	   - equals 0 on 0 and PI
+	  that means :  4/PI * x  - 4/PI² * x²
+	  Use abs(x) to handle (-PI) -> 0 zone.
+	 */
+	retval = fix16_mul(FOUR_DIV_PI, inAngle) + fix16_mul( fix16_mul(_FOUR_DIV_PI2, inAngle), abs_inAngle );
+	/* At this point, retval equals sin(inAngle) on important points ( -PI, -PI/2, 0, PI/2, PI),
+	   but is not very precise between these points
+	 */
+	#ifndef FIXMATH_FAST_SIN
+	/* Absolute value of retval */
+	mask = (retval >> (sizeof(fix16_t)*CHAR_BIT-1));
+	abs_retval = (retval + mask) ^ mask;
+	/* So improve its precision by adding some x^4 component to retval */
+	retval += fix16_mul(X4_CORRECTION_COMPONENT, fix16_mul(retval, abs_retval) - retval );
+	#endif
+	return retval;
+}
 
 fix16_t fix16_sin(fix16_t inAngle) {
 	fix16_t tempAngle = inAngle % (fix16_pi << 1);