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/*
* Copyright 2006 The Android Open Source Project
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "SkCordic.h"
#include "SkMathPriv.h"
#include "Sk64.h"
// 0x20000000 equals pi / 4
const int32_t kATanDegrees[] = { 0x20000000,
0x12E4051D, 0x9FB385B, 0x51111D4, 0x28B0D43, 0x145D7E1, 0xA2F61E, 0x517C55,
0x28BE53, 0x145F2E, 0xA2F98, 0x517CC, 0x28BE6, 0x145F3, 0xA2F9, 0x517C,
0x28BE, 0x145F, 0xA2F, 0x517, 0x28B, 0x145, 0xA2, 0x51, 0x28, 0x14,
0xA, 0x5, 0x2, 0x1 };
const int32_t kFixedInvGain1 = 0x18bde0bb; // 0.607252935
static void SkCircularRotation(int32_t* x0, int32_t* y0, int32_t* z0)
{
int32_t t = 0;
int32_t x = *x0;
int32_t y = *y0;
int32_t z = *z0;
const int32_t* tanPtr = kATanDegrees;
do {
int32_t x1 = y >> t;
int32_t y1 = x >> t;
int32_t tan = *tanPtr++;
if (z >= 0) {
x -= x1;
y += y1;
z -= tan;
} else {
x += x1;
y -= y1;
z += tan;
}
} while (++t < 16); // 30);
*x0 = x;
*y0 = y;
*z0 = z;
}
SkFixed SkCordicSinCos(SkFixed radians, SkFixed* cosp)
{
int32_t scaledRadians = radians * 0x28be; // scale radians to 65536 / PI()
int quadrant = scaledRadians >> 30;
quadrant += 1;
if (quadrant & 2)
scaledRadians = -scaledRadians + 0x80000000;
/* |a| <= 90 degrees as a 1.31 number */
SkFixed sin = 0;
SkFixed cos = kFixedInvGain1;
SkCircularRotation(&cos, &sin, &scaledRadians);
Sk64 scaled;
scaled.setMul(sin, 0x6488d);
sin = scaled.fHi;
scaled.setMul(cos, 0x6488d);
if (quadrant & 2)
scaled.fHi = - scaled.fHi;
*cosp = scaled.fHi;
return sin;
}
SkFixed SkCordicTan(SkFixed a)
{
int32_t cos;
int32_t sin = SkCordicSinCos(a, &cos);
return SkFixedDiv(sin, cos);
}
static int32_t SkCircularVector(int32_t* y0, int32_t* x0, int32_t vecMode)
{
int32_t x = *x0;
int32_t y = *y0;
int32_t z = 0;
int32_t t = 0;
const int32_t* tanPtr = kATanDegrees;
do {
int32_t x1 = y >> t;
int32_t y1 = x >> t;
int32_t tan = *tanPtr++;
if (y < vecMode) {
x -= x1;
y += y1;
z -= tan;
} else {
x += x1;
y -= y1;
z += tan;
}
} while (++t < 16); // 30
Sk64 scaled;
scaled.setMul(z, 0x6488d); // scale back into the SkScalar space (0x100000000/0x28be)
return scaled.fHi;
}
SkFixed SkCordicASin(SkFixed a) {
int32_t sign = SkExtractSign(a);
int32_t z = SkFixedAbs(a);
if (z >= SK_Fixed1)
return SkApplySign(SK_FixedPI>>1, sign);
int32_t x = kFixedInvGain1;
int32_t y = 0;
z *= 0x28be;
z = SkCircularVector(&y, &x, z);
z = SkApplySign(z, ~sign);
return z;
}
SkFixed SkCordicACos(SkFixed a) {
int32_t z = SkCordicASin(a);
z = (SK_FixedPI>>1) - z;
return z;
}
SkFixed SkCordicATan2(SkFixed y, SkFixed x) {
if ((x | y) == 0)
return 0;
int32_t xsign = SkExtractSign(x);
x = SkFixedAbs(x);
int32_t result = SkCircularVector(&y, &x, 0);
if (xsign) {
int32_t rsign = SkExtractSign(result);
if (y == 0)
rsign = 0;
SkFixed pi = SkApplySign(SK_FixedPI, rsign);
result = pi - result;
}
return result;
}
const int32_t kATanHDegrees[] = {
0x1661788D, 0xA680D61, 0x51EA6FC, 0x28CBFDD, 0x1460E34,
0xA2FCE8, 0x517D2E, 0x28BE6E, 0x145F32,
0xA2F98, 0x517CC, 0x28BE6, 0x145F3, 0xA2F9, 0x517C,
0x28BE, 0x145F, 0xA2F, 0x517, 0x28B, 0x145, 0xA2, 0x51, 0x28, 0x14,
0xA, 0x5, 0x2, 0x1 };
const int32_t kFixedInvGain2 = 0x31330AAA; // 1.207534495
static void SkHyperbolic(int32_t* x0, int32_t* y0, int32_t* z0, int mode)
{
int32_t t = 1;
int32_t x = *x0;
int32_t y = *y0;
int32_t z = *z0;
const int32_t* tanPtr = kATanHDegrees;
int k = -3;
do {
int32_t x1 = y >> t;
int32_t y1 = x >> t;
int32_t tan = *tanPtr++;
int count = 2 + (k >> 31);
if (++k == 1)
k = -2;
do {
if (((y >> 31) & mode) | ~((z >> 31) | mode)) {
x += x1;
y += y1;
z -= tan;
} else {
x -= x1;
y -= y1;
z += tan;
}
} while (--count);
} while (++t < 30);
*x0 = x;
*y0 = y;
*z0 = z;
}
SkFixed SkCordicLog(SkFixed a) {
a *= 0x28be;
int32_t x = a + 0x28BE60DB; // 1.0
int32_t y = a - 0x28BE60DB;
int32_t z = 0;
SkHyperbolic(&x, &y, &z, -1);
Sk64 scaled;
scaled.setMul(z, 0x6488d);
z = scaled.fHi;
return z << 1;
}
SkFixed SkCordicExp(SkFixed a) {
int32_t cosh = kFixedInvGain2;
int32_t sinh = 0;
SkHyperbolic(&cosh, &sinh, &a, 0);
return cosh + sinh;
}
#ifdef SK_DEBUG
#include "SkFloatingPoint.h"
void SkCordic_UnitTest()
{
#if defined(SK_SUPPORT_UNITTEST)
float val;
for (float angle = -720; angle < 720; angle += 30) {
float radian = angle * 3.1415925358f / 180.0f;
SkFixed f_angle = SkFloatToFixed(radian);
// sincos
float sine = sinf(radian);
float cosine = cosf(radian);
SkFixed f_cosine;
SkFixed f_sine = SkCordicSinCos(f_angle, &f_cosine);
float sine2 = (float) f_sine / 65536.0f;
float cosine2 = (float) f_cosine / 65536.0f;
float error = fabsf(sine - sine2);
if (error > 0.001)
SkDebugf("sin error : angle = %g ; sin = %g ; cordic = %g\n", angle, sine, sine2);
error = fabsf(cosine - cosine2);
if (error > 0.001)
SkDebugf("cos error : angle = %g ; cos = %g ; cordic = %g\n", angle, cosine, cosine2);
// tan
float _tan = tanf(radian);
SkFixed f_tan = SkCordicTan(f_angle);
float tan2 = (float) f_tan / 65536.0f;
error = fabsf(_tan - tan2);
if (error > 0.05 && fabsf(_tan) < 1e6)
SkDebugf("tan error : angle = %g ; tan = %g ; cordic = %g\n", angle, _tan, tan2);
}
for (val = -1; val <= 1; val += .1f) {
SkFixed f_val = SkFloatToFixed(val);
// asin
float arcsine = asinf(val);
SkFixed f_arcsine = SkCordicASin(f_val);
float arcsine2 = (float) f_arcsine / 65536.0f;
float error = fabsf(arcsine - arcsine2);
if (error > 0.001)
SkDebugf("asin error : val = %g ; asin = %g ; cordic = %g\n", val, arcsine, arcsine2);
}
#if 1
for (val = -1; val <= 1; val += .1f) {
#else
val = .5; {
#endif
SkFixed f_val = SkFloatToFixed(val);
// acos
float arccos = acosf(val);
SkFixed f_arccos = SkCordicACos(f_val);
float arccos2 = (float) f_arccos / 65536.0f;
float error = fabsf(arccos - arccos2);
if (error > 0.001)
SkDebugf("acos error : val = %g ; acos = %g ; cordic = %g\n", val, arccos, arccos2);
}
// atan2
#if 1
for (val = -1000; val <= 1000; val += 500.f) {
for (float val2 = -1000; val2 <= 1000; val2 += 500.f) {
#else
val = 0; {
float val2 = -1000; {
#endif
SkFixed f_val = SkFloatToFixed(val);
SkFixed f_val2 = SkFloatToFixed(val2);
float arctan = atan2f(val, val2);
SkFixed f_arctan = SkCordicATan2(f_val, f_val2);
float arctan2 = (float) f_arctan / 65536.0f;
float error = fabsf(arctan - arctan2);
if (error > 0.001)
SkDebugf("atan2 error : val = %g ; val2 = %g ; atan2 = %g ; cordic = %g\n", val, val2, arctan, arctan2);
}
}
// log
#if 1
for (val = 0.125f; val <= 8.f; val *= 2.0f) {
#else
val = .5; {
#endif
SkFixed f_val = SkFloatToFixed(val);
// acos
float log = logf(val);
SkFixed f_log = SkCordicLog(f_val);
float log2 = (float) f_log / 65536.0f;
float error = fabsf(log - log2);
if (error > 0.001)
SkDebugf("log error : val = %g ; log = %g ; cordic = %g\n", val, log, log2);
}
// exp
#endif
}
#endif
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