# [RFC,PATCHv2] fixp-arith: replace sin/cos table by a better precision one

Message ID 20141217195448.156e3a38@recife.lan (mailing list archive) New, archived show

## Commit Message

Mauro Carvalho Chehab Dec. 17, 2014, 9:54 p.m. UTC
```Em Wed, 17 Dec 2014 19:11:33 +0000

> Hi Mauro,
>
> I was able to test your patch with vivid sdr tone generation. It calls
> sin/cos functions with radians as argument. I find that the sine wave
> generated using fixp_sin32_rad() show discontinuities, especially around
> 90, 180 degrees. After debugging it further, these discontinuities seems
> to be originating due to division of negative number. Please find it below
>
> On 17/12/14 7:12 pm, "Mauro Carvalho Chehab" <mchehab@osg.samsung.com>
> wrote:
>
> >
> >+ */
> > {
> >+	int degrees;
> >+	s32 v1, v2, dx, dy;
> >+	s64 tmp;
> >+	degrees = (radians * 360) / twopi;
>
> Not sure if we should use higher precision here. But just a question - in
> case, caller function uses higher precision for representing radians,
> (radians * 360) can probably overflow, right ? So, could we possibly
> specify on max precision for representing radian fraction cannot be more
> than 18 bits.

True. We could call BUG_ON() if this routine is called with a
number of bits higher than a given amount.

>
> >+	v1 = fixp_sin32(degrees);
> >+	v2 = fixp_sin32(degrees + 1);
> >+	dx = twopi / 360;
> >+	dy = v2 - v1;
> >+	tmp = radians - (degrees * twopi) / 360;
>
> Same as above.
>
> >+	tmp *= dy;
> >+	do_div(tmp, dx);
>
> tmp can go negative. do_div() cannot handle negative number. We could
> probably avoid do_div and do tmp / dx here. If we want to use do_div(), we
> could still do it by modifying radian to degree calculation.

Well, we should then use div_s64(), as defined at include/linux/math64.h.
This is likely better than adding some magic.

> tmp goes negative when the slope sine waveform is negative, that is 2nd
> and 3rd quadrant. We could avoid it by deciding the quadrant based on
> radians and then calling fixp_sin32(). I modified the function on lines of
> fixp_sin32() and tested. It works fine. Attaching a diff for fixp-arith.h
> for with the this change to avoid negative values of tmp in

Please check if the enclosed patch is better.

Thanks!
Mauro

fixp-arith: replace sin/cos table by a better precision one

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>

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## Patch

```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..f3b3d2cbfcbe 100644
--- a/include/linux/fixp-arith.h
+++ b/include/linux/fixp-arith.h
@@ -1,6 +1,8 @@
#ifndef _FIXP_ARITH_H
#define _FIXP_ARITH_H

+#include <linux/math64.h>
+
/*
* Simplistic fixed-point arithmetics.
* Hmm, I'm probably duplicating some code :(
@@ -29,59 +31,126 @@

#include <linux/types.h>

-/* The type representing fixed-point values */
-typedef s16 fixp_t;
+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
+};

-#define FRAC_N 8
+/**
+ * __fixp_sin32() returns the sin of an angle in degrees
+ *
+ * @degrees: angle, in degrees, from 0 to 360.
+ *
+ * The returned value ranges from -0x7fffffff to +0x7fffffff.
+ */
+static inline s32 __fixp_sin32(int degrees)
+{
+	s32 ret;
+	bool negative = false;

-/* 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
-};
+	if (degrees > 180) {
+		negative = true;
+		degrees -= 180;
+	}
+	if (degrees > 90)
+		degrees = 180 - degrees;

+	ret = sin_table[degrees];

-/* a: 123 -> 123.0 */
-static inline fixp_t fixp_new(s16 a)
-{
-	return a<<FRAC_N;
+	return negative ? -ret : ret;
}

-/* a: 0xFFFF -> -1.0
-      0x8000 -> 1.0
-      0x0000 -> 0.0
-*/
-static inline fixp_t fixp_new16(s16 a)
+/**
+ * fixp_sin32() returns the sin of an angle in degrees
+ *
+ * @degrees: angle, in degrees. The angle can be positive or negative
+ *
+ * The returned value ranges from -0x7fffffff to +0x7fffffff.
+ */
+static inline s32 fixp_sin32(int degrees)
{
-	return ((s32)a)>>(16-FRAC_N);
+	degrees = (degrees % 360 + 360) % 360;
+
+	return __fixp_sin32(degrees);
}

-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
+ *
+ * @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.
+ *
+ * Please notice that two high numbers for twopi could cause
+ * overflows, so the routine will not allow values of twopi
+ * bigger than 1^18.
+ */
{
-	int quadrant = (degrees / 90) & 3;
-	unsigned int i = degrees % 90;
+	int degrees;
+	s32 v1, v2, dx, dy;
+	s64 tmp;

-		i = 90 - i;
+	/*
+	 * Avoid too large values for twopi, as we don't want overflows.
+	 */
+	BUG_ON(twopi > 1 << 18);

-	i >>= 1;
+	degrees = (radians * 360) / twopi;

-	return (quadrant == 1 || quadrant == 2)? -cos_table[i] : cos_table[i];
-}
+	degrees = (degrees % 360 + 360) % 360;
+	v1 = __fixp_sin32(degrees);

-static inline fixp_t fixp_sin(unsigned int degrees)
-{
-	return -fixp_cos(degrees + 90);
-}
+	v2 = fixp_sin32(degrees + 1);

-static inline fixp_t fixp_mult(fixp_t a, fixp_t b)
-{
-	return ((s32)(a*b))>>FRAC_N;
+	dx = twopi / 360;
+	dy = v2 - v1;
+
+	tmp = radians - (degrees * twopi) / 360;
+	tmp *= dy;
+
+	return v1 +  div_s64(tmp, dx);
}

+/* cos(x) = sin(x + pi/2 radians) */
+