Added a new algo for sin() function, and a small error analysis to show the precision differences

3 files changed, 37 insertions, 1 deletions

diff --git a/images/error_analysis.ods b/images/error_analysis.ods
new file mode 100644
index 0000000..e410dd3
--- /dev/null
+++ b/images/error_analysis.ods
diff --git a/libfixmath/fix16.h b/libfixmath/fix16.h
index dfb8cb7..7763389 100644
--- 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
index a198b3d..2f92d31 100644
--- 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);