openmv/src/omv/img/fmath.c
2016-08-30 22:37:04 +02:00

192 lines
3.9 KiB
C

/*
* This file is part of the OpenMV project.
* Copyright (c) 2013/2014 Ibrahim Abdelkader <i.abdalkader@gmail.com>
* This work is licensed under the MIT license, see the file LICENSE for details.
*
* Fast approximate math functions.
*
*/
#include "fmath.h"
#include "common.h"
#define M_PI 3.14159265f
#define M_PI_2 1.57079632f
#define M_PI_4 0.78539816f
const float __atanf_lut[4] = {
-0.0443265554792128f, //p7
-0.3258083974640975f, //p3
+0.1555786518463281f, //p5
+0.9997878412794807f //p1
};
float ALWAYS_INLINE fast_sqrtf(float x)
{
asm volatile (
"vsqrt.f32 %[r], %[x]\n"
: [r] "=t" (x)
: [x] "t" (x));
return x;
}
int ALWAYS_INLINE fast_floorf(float x)
{
int i;
asm volatile (
"vcvt.S32.f32 %[r], %[x]\n"
: [r] "=t" (i)
: [x] "t" (x));
return i;
}
int ALWAYS_INLINE fast_ceilf(float x)
{
int i;
x += 0.9999f;
asm volatile (
"vcvt.S32.f32 %[r], %[x]\n"
: [r] "=t" (i)
: [x] "t" (x));
return i;
}
int ALWAYS_INLINE fast_roundf(float x)
{
int i;
asm volatile (
"vcvtr.s32.f32 %[r], %[x]\n"
: [r] "=t" (i)
: [x] "t" (x));
return i;
}
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wstrict-aliasing"
typedef union{
uint32_t l;
struct {
uint32_t m : 20;
uint32_t e : 11;
uint32_t s : 1;
};
}exp_t;
float fast_expf(float x)
{
exp_t e;
e.l = (uint32_t)(1512775 * x + 1072632447);
// IEEE binary32 format
e.e = (e.e -1023 + 127) &0xFF; // rebase
uint32_t packed = (e.s << 31) | (e.e << 23) | e.m <<3;
return *((float*)&packed);
}
#pragma GCC diagnostic pop
/*
* From Hackers Delight:
* This is a very approximate but very fast version of acbrt. It is just eight
* integer instructions (shift rights and adds), plus instructions to load the constant.
* 1/3 is approximated as 1/4 + 1/16 + 1/64 + 1/256 + ... + 1/65536.
* The constant 0x2a511cd0 balances the relative error at +-0.0321.
*/
float fast_cbrtf(float x)
{
union {int ix; float x;} v;
v.x = x; // x can be viewed as int.
v.ix = v.ix/4 + v.ix/16; // Approximate divide by 3.
v.ix = v.ix + v.ix/16;
v.ix = v.ix + v.ix/256;
v.ix = 0x2a511cd0 + v.ix; // Initial guess.
return v.x;
}
float ALWAYS_INLINE fast_fabsf(float x)
{
asm volatile (
"vabs.f32 %[r], %[x]\n"
: [r] "=t" (x)
: [x] "t" (x));
return x;
}
inline float fast_atanf(float xx)
{
float x, y, z;
int sign;
x = xx;
/* make argument positive and save the sign */
if( xx < 0.0f )
{
sign = -1;
x = -xx;
}
else
{
sign = 1;
x = xx;
}
/* range reduction */
if( x > 2.414213562373095f ) /* tan 3pi/8 */
{
y = M_PI_2;
x = -( 1.0f/x );
}
else if( x > 0.4142135623730950f ) /* tan pi/8 */
{
y = M_PI_4;
x = (x-1.0f)/(x+1.0f);
}
else
y = 0.0f;
z = x * x;
y +=
((( 8.05374449538e-2f * z
- 1.38776856032E-1f) * z
+ 1.99777106478E-1f) * z
- 3.33329491539E-1f) * z * x + x;
if( sign < 0 )
y = -y;
return( y );
}
float fast_atan2f(float y, float x)
{
if(x > 0 && y >= 0)
return fast_atanf(y/x);
if(x < 0 && y >= 0)
return M_PI - fast_atanf(-y/x);
if(x < 0 && y < 0)
return M_PI + fast_atanf(y/x);
if(x > 0 && y < 0)
return 2*M_PI - fast_atanf(-y/x);
return 0;
}
float fast_log2(float x)
{
union { float f; uint32_t i; } vx = { x };
union { uint32_t i; float f; } mx = { (vx.i & 0x007FFFFF) | 0x3f000000 };
float y = vx.i;
y *= 1.1920928955078125e-7f;
return y - 124.22551499f - 1.498030302f * mx.f
- 1.72587999f / (0.3520887068f + mx.f);
}
float fast_log(float x)
{
return 0.69314718f * fast_log2 (x);
}