| /* |
| * 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 = (int) (radian * 65536.0f); |
| // 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 = (int) (val * 65536.0f); |
| // 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 = (int) (val * 65536.0f); |
| // 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 = (int) (val * 65536.0f); |
| SkFixed f_val2 = (int) (val2 * 65536.0f); |
| 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 = (int) (val * 65536.0f); |
| // 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 |
