[RFC PATCH] fixp-arith: replace sin/cos table by a better precision one

[Mauro Carvalho Chehab <mchehab@osg.samsung.com>]

The cos table used at fixp-arith.h has only 8 bits of precision.
That causes problems if it is reused on other drivers.

As some media drivers require a higher precision sin/cos
implementation, replace the current implementation by one that
will provide 32 bits precision.

The values generated by the new implementation matches the
32 bit precision of glibc's sin for an angle measured in
integer degrees.

It also provides support for fractional angles via linear
interpolation. On experimental calculus, when used a table
with a 0.001 degree angle, the maximum error for sin is
0.000038, with is likely good enough for practical purposes.

There are some logic there that seems to be specific to the
usage inside ff-memless.c. Move those logic to there, as they're
not needed elsewhere.

Signed-off-by: Mauro Carvalho Chehab <mchehab@osg.samsung.com>

---

Instead of adding yet-another implementation of integer sin()/cos(),
let's fix the one that already exists on a worldwide header for one
that would provide the needed precision.

While I tested the implementation on userspace, I didn't actually
check if ff-memless and ov534 drivers are working properly with
this change. Please test.

diff --git a/drivers/input/ff-memless.c b/drivers/input/ff-memless.c
index 74c0d8c6002a..fcc6c3368182 100644
--- a/drivers/input/ff-memless.c
+++ b/drivers/input/ff-memless.c
@@ -237,6 +237,18 @@ static u16 ml_calculate_direction(u16 direction, u16 force,
 		(force + new_force)) << 1;
 }
 
+#define FRAC_N 8
+static inline s16 fixp_new16(s16 a)
+{
+	return ((s32)a) >> (16 - FRAC_N);
+}
+
+static inline s16 fixp_mult(s16 a, s16 b)
+{
+	a = ((s32)a * 0x100) / 0x7fff;
+	return ((s32)(a * b)) >> FRAC_N;
+}
+
 /*
  * Combine two effects and apply gain.
  */
@@ -247,7 +259,7 @@ static void ml_combine_effects(struct ff_effect *effect,
 	struct ff_effect *new = state->effect;
 	unsigned int strong, weak, i;
 	int x, y;
-	fixp_t level;
+	s16 level;
 
 	switch (new->type) {
 	case FF_CONSTANT:
@@ -255,8 +267,8 @@ static void ml_combine_effects(struct ff_effect *effect,
 		level = fixp_new16(apply_envelope(state,
 					new->u.constant.level,
 					&new->u.constant.envelope));
-		x = fixp_mult(fixp_sin(i), level) * gain / 0xffff;
-		y = fixp_mult(-fixp_cos(i), level) * gain / 0xffff;
+		x = fixp_mult(fixp_sin16(i), level) * gain / 0xffff;
+		y = fixp_mult(-fixp_cos16(i), level) * gain / 0xffff;
 		/*
 		 * here we abuse ff_ramp to hold x and y of constant force
 		 * If in future any driver wants something else than x and y
diff --git a/drivers/media/usb/gspca/ov534.c b/drivers/media/usb/gspca/ov534.c
index 90f0d637cd9d..50b72f6dfdc6 100644
--- a/drivers/media/usb/gspca/ov534.c
+++ b/drivers/media/usb/gspca/ov534.c
@@ -810,21 +810,16 @@ static void sethue(struct gspca_dev *gspca_dev, s32 val)
 		s16 huesin;
 		s16 huecos;
 
-		/* fixp_sin and fixp_cos accept only positive values, while
-		 * our val is between -90 and 90
-		 */
-		val += 360;
-
 		/* According to the datasheet the registers expect HUESIN and
 		 * HUECOS to be the result of the trigonometric functions,
 		 * scaled by 0x80.
 		 *
-		 * The 0x100 here represents the maximun absolute value
+		 * The 0x7fff here represents the maximum absolute value
 		 * returned byt fixp_sin and fixp_cos, so the scaling will
 		 * consider the result like in the interval [-1.0, 1.0].
 		 */
-		huesin = fixp_sin(val) * 0x80 / 0x100;
-		huecos = fixp_cos(val) * 0x80 / 0x100;
+		huesin = fixp_sin16(val) * 0x80 / 0x7fff;
+		huecos = fixp_cos16(val) * 0x80 / 0x7fff;
 
 		if (huesin < 0) {
 			sccb_reg_write(gspca_dev, 0xab,
diff --git a/include/linux/fixp-arith.h b/include/linux/fixp-arith.h
index 3089d7382325..857e7f782140 100644
--- a/include/linux/fixp-arith.h
+++ b/include/linux/fixp-arith.h
@@ -29,59 +29,104 @@
 
 #include <linux/types.h>
 
-/* The type representing fixed-point values */
-typedef s16 fixp_t;
-
-#define FRAC_N 8
-#define FRAC_MASK ((1<<FRAC_N)-1)
-
-/* Not to be used directly. Use fixp_{cos,sin} */
-static const fixp_t cos_table[46] = {
-	0x0100,	0x00FF,	0x00FF,	0x00FE,	0x00FD,	0x00FC,	0x00FA,	0x00F8,
-	0x00F6,	0x00F3,	0x00F0,	0x00ED,	0x00E9,	0x00E6,	0x00E2,	0x00DD,
-	0x00D9,	0x00D4,	0x00CF,	0x00C9,	0x00C4,	0x00BE,	0x00B8,	0x00B1,
-	0x00AB,	0x00A4,	0x009D,	0x0096,	0x008F,	0x0087,	0x0080,	0x0078,
-	0x0070,	0x0068,	0x005F,	0x0057,	0x004F,	0x0046,	0x003D,	0x0035,
-	0x002C,	0x0023,	0x001A,	0x0011,	0x0008, 0x0000
+static const s32 sin_table[] = {
+	0x00000000, 0x023be165, 0x04779632, 0x06b2f1d2, 0x08edc7b6, 0x0b27eb5c,
+	0x0d61304d, 0x0f996a26, 0x11d06c96, 0x14060b67, 0x163a1a7d, 0x186c6ddd,
+	0x1a9cd9ac, 0x1ccb3236, 0x1ef74bf2, 0x2120fb82, 0x234815ba, 0x256c6f9e,
+	0x278dde6e, 0x29ac379f, 0x2bc750e8, 0x2ddf003f, 0x2ff31bdd, 0x32037a44,
+	0x340ff241, 0x36185aee, 0x381c8bb5, 0x3a1c5c56, 0x3c17a4e7, 0x3e0e3ddb,
+	0x3fffffff, 0x41ecc483, 0x43d464fa, 0x45b6bb5d, 0x4793a20f, 0x496af3e1,
+	0x4b3c8c11, 0x4d084650, 0x4ecdfec6, 0x508d9210, 0x5246dd48, 0x53f9be04,
+	0x55a6125a, 0x574bb8e5, 0x58ea90c2, 0x5a827999, 0x5c135399, 0x5d9cff82,
+	0x5f1f5ea0, 0x609a52d1, 0x620dbe8a, 0x637984d3, 0x64dd894f, 0x6639b039,
+	0x678dde6d, 0x68d9f963, 0x6a1de735, 0x6b598ea1, 0x6c8cd70a, 0x6db7a879,
+	0x6ed9eba0, 0x6ff389de, 0x71046d3c, 0x720c8074, 0x730baeec, 0x7401e4bf,
+	0x74ef0ebb, 0x75d31a5f, 0x76adf5e5, 0x777f903b, 0x7847d908, 0x7906c0af,
+	0x79bc384c, 0x7a6831b8, 0x7b0a9f8c, 0x7ba3751c, 0x7c32a67c, 0x7cb82884,
+	0x7d33f0c8, 0x7da5f5a3, 0x7e0e2e31, 0x7e6c924f, 0x7ec11aa3, 0x7f0bc095,
+	0x7f4c7e52, 0x7f834ecf, 0x7fb02dc4, 0x7fd317b3, 0x7fec09e1, 0x7ffb025e,
+	0x7fffffff
 };
 
+/**
+ * fixp_sin32() returns the sin of an angle in degrees
+ *
+ * @degrees: angle, in degrees. It can be positive or negative
+ *
+ * The returned value ranges from -0x7fffffff to +0x7fffffff.
+ */
 
-/* a: 123 -> 123.0 */
-static inline fixp_t fixp_new(s16 a)
+static inline s32 fixp_sin32(int degrees)
 {
-	return a<<FRAC_N;
-}
+	s32 ret;
+	bool negative = false;
 
-/* a: 0xFFFF -> -1.0
-      0x8000 -> 1.0
-      0x0000 -> 0.0
-*/
-static inline fixp_t fixp_new16(s16 a)
-{
-	return ((s32)a)>>(16-FRAC_N);
+	degrees = (degrees % 360 + 360) % 360;
+	if (degrees > 180) {
+		negative = true;
+		degrees -= 180;
+	}
+	if (degrees > 90)
+		degrees = 180 - degrees;
+
+	ret = sin_table[degrees];
+
+	return negative ? -ret : ret;
 }
 
-static inline fixp_t fixp_cos(unsigned int degrees)
+/* cos(x) = sin(x + 90 degrees) */
+#define fixp_cos32(v) fixp_sin32((v) + 90)
+
+/*
+ * 16 bits variants
+ *
+ * The returned value ranges from -0x7fff to 0x7fff
+ */
+
+#define fixp_sin16(v) (fixp_sin32(v) >> 16)
+#define fixp_cos16(v) (fixp_cos32(v) >> 16)
+
+/**
+ * fixp_sin32_rad() - calculates the sin of an angle in radians
+ *
+ * @radians: angle, in radians
+ * @twopi: value to be used for 2*pi
+ *
+ * Provides a variant for the cases where just 360
+ * values is not enough. This function uses linear
+ * interpolation to a wider range of values given by
+ * twopi var.
+ *
+ * Experimental tests gave a maximum difference of
+ * 0.000038 between the value calculated by sin() and
+ * the one produced by this function, when twopi is
+ * equal to 360000. That seems to be enough precision
+ * for practical purposes.
+ */
+static inline s32 fixp_sin32_rad(u32 radians, u32 twopi)
 {
-	int quadrant = (degrees / 90) & 3;
-	unsigned int i = degrees % 90;
+	int degrees;
+	s32 v1, v2, dx, dy;
+	s64 tmp;
 
-	if (quadrant == 1 || quadrant == 3)
-		i = 90 - i;
+	degrees = (radians * 360) / twopi;
 
-	i >>= 1;
+	v1 = fixp_sin32(degrees);
+	v2 = fixp_sin32(degrees + 1);
 
-	return (quadrant == 1 || quadrant == 2)? -cos_table[i] : cos_table[i];
-}
+	dx = twopi / 360;
+	dy = v2 - v1;
 
-static inline fixp_t fixp_sin(unsigned int degrees)
-{
-	return -fixp_cos(degrees + 90);
-}
+	tmp = radians - (degrees * twopi) / 360;
+	tmp *= dy;
+	do_div(tmp, dx);
 
-static inline fixp_t fixp_mult(fixp_t a, fixp_t b)
-{
-	return ((s32)(a*b))>>FRAC_N;
+	return v1 + tmp;
 }
 
+/* cos(x) = sin(x + pi radians) */
+
+#define fixp_cos32_rad(rad, twopi)	\
+	fixp_sin32_rad(rad + twopi/2, twopi)
+
 #endif
-- 
2.1.0