OLD | NEW |
1 /* | 1 /* |
2 * Copyright 2008 The Android Open Source Project | 2 * Copyright 2008 The Android Open Source Project |
3 * | 3 * |
4 * Use of this source code is governed by a BSD-style license that can be | 4 * Use of this source code is governed by a BSD-style license that can be |
5 * found in the LICENSE file. | 5 * found in the LICENSE file. |
6 */ | 6 */ |
7 | 7 |
8 #include "SkMathPriv.h" | 8 #include "SkMathPriv.h" |
9 #include "SkCordic.h" | |
10 #include "SkFloatBits.h" | 9 #include "SkFloatBits.h" |
11 #include "SkFloatingPoint.h" | 10 #include "SkFloatingPoint.h" |
12 #include "Sk64.h" | 11 #include "Sk64.h" |
13 #include "SkScalar.h" | 12 #include "SkScalar.h" |
14 | 13 |
15 const uint32_t gIEEENotANumber = 0x7FFFFFFF; | 14 const uint32_t gIEEENotANumber = 0x7FFFFFFF; |
16 const uint32_t gIEEEInfinity = 0x7F800000; | 15 const uint32_t gIEEEInfinity = 0x7F800000; |
17 const uint32_t gIEEENegativeInfinity = 0xFF800000; | 16 const uint32_t gIEEENegativeInfinity = 0xFF800000; |
18 | 17 |
19 #define sub_shift(zeros, x, n) \ | 18 #define sub_shift(zeros, x, n) \ |
(...skipping 27 matching lines...) Expand all Loading... |
47 | 46 |
48 int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) { | 47 int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) { |
49 SkASSERT(denom); | 48 SkASSERT(denom); |
50 | 49 |
51 Sk64 tmp; | 50 Sk64 tmp; |
52 tmp.setMul(numer1, numer2); | 51 tmp.setMul(numer1, numer2); |
53 tmp.div(denom, Sk64::kTrunc_DivOption); | 52 tmp.div(denom, Sk64::kTrunc_DivOption); |
54 return tmp.get32(); | 53 return tmp.get32(); |
55 } | 54 } |
56 | 55 |
57 int32_t SkMulShift(int32_t a, int32_t b, unsigned shift) { | |
58 int sign = SkExtractSign(a ^ b); | |
59 | |
60 if (shift > 63) { | |
61 return sign; | |
62 } | |
63 | |
64 a = SkAbs32(a); | |
65 b = SkAbs32(b); | |
66 | |
67 uint32_t ah = a >> 16; | |
68 uint32_t al = a & 0xFFFF; | |
69 uint32_t bh = b >> 16; | |
70 uint32_t bl = b & 0xFFFF; | |
71 | |
72 uint32_t A = ah * bh; | |
73 uint32_t B = ah * bl + al * bh; | |
74 uint32_t C = al * bl; | |
75 | |
76 /* [ A ] | |
77 [ B ] | |
78 [ C ] | |
79 */ | |
80 uint32_t lo = C + (B << 16); | |
81 int32_t hi = A + (B >> 16) + (lo < C); | |
82 | |
83 if (sign < 0) { | |
84 hi = -hi - Sk32ToBool(lo); | |
85 lo = 0 - lo; | |
86 } | |
87 | |
88 if (shift == 0) { | |
89 #ifdef SK_DEBUGx | |
90 SkASSERT(((int32_t)lo >> 31) == hi); | |
91 #endif | |
92 return lo; | |
93 } else if (shift >= 32) { | |
94 return hi >> (shift - 32); | |
95 } else { | |
96 #ifdef SK_DEBUGx | |
97 int32_t tmp = hi >> shift; | |
98 SkASSERT(tmp == 0 || tmp == -1); | |
99 #endif | |
100 // we want (hi << (32 - shift)) | (lo >> shift) but rounded | |
101 int roundBit = (lo >> (shift - 1)) & 1; | |
102 return ((hi << (32 - shift)) | (lo >> shift)) + roundBit; | |
103 } | |
104 } | |
105 | |
106 SkFixed SkFixedMul_portable(SkFixed a, SkFixed b) { | 56 SkFixed SkFixedMul_portable(SkFixed a, SkFixed b) { |
107 #if 0 | 57 #if defined(SkLONGLONG) |
108 Sk64 tmp; | |
109 | |
110 tmp.setMul(a, b); | |
111 tmp.shiftRight(16); | |
112 return tmp.fLo; | |
113 #elif defined(SkLONGLONG) | |
114 return static_cast<SkFixed>((SkLONGLONG)a * b >> 16); | 58 return static_cast<SkFixed>((SkLONGLONG)a * b >> 16); |
115 #else | 59 #else |
116 int sa = SkExtractSign(a); | 60 int sa = SkExtractSign(a); |
117 int sb = SkExtractSign(b); | 61 int sb = SkExtractSign(b); |
118 // now make them positive | 62 // now make them positive |
119 a = SkApplySign(a, sa); | 63 a = SkApplySign(a, sa); |
120 b = SkApplySign(b, sb); | 64 b = SkApplySign(b, sb); |
121 | 65 |
122 uint32_t ah = a >> 16; | 66 uint32_t ah = a >> 16; |
123 uint32_t al = a & 0xFFFF; | 67 uint32_t al = a & 0xFFFF; |
124 uint32_t bh = b >> 16; | 68 uint32_t bh = b >> 16; |
125 uint32_t bl = b & 0xFFFF; | 69 uint32_t bl = b & 0xFFFF; |
126 | 70 |
127 uint32_t R = ah * b + al * bh + (al * bl >> 16); | 71 uint32_t R = ah * b + al * bh + (al * bl >> 16); |
128 | 72 |
129 return SkApplySign(R, sa ^ sb); | 73 return SkApplySign(R, sa ^ sb); |
130 #endif | 74 #endif |
131 } | 75 } |
132 | 76 |
133 SkFract SkFractMul_portable(SkFract a, SkFract b) { | |
134 #if 0 | |
135 Sk64 tmp; | |
136 tmp.setMul(a, b); | |
137 return tmp.getFract(); | |
138 #elif defined(SkLONGLONG) | |
139 return static_cast<SkFract>((SkLONGLONG)a * b >> 30); | |
140 #else | |
141 int sa = SkExtractSign(a); | |
142 int sb = SkExtractSign(b); | |
143 // now make them positive | |
144 a = SkApplySign(a, sa); | |
145 b = SkApplySign(b, sb); | |
146 | |
147 uint32_t ah = a >> 16; | |
148 uint32_t al = a & 0xFFFF; | |
149 uint32_t bh = b >> 16; | |
150 uint32_t bl = b & 0xFFFF; | |
151 | |
152 uint32_t A = ah * bh; | |
153 uint32_t B = ah * bl + al * bh; | |
154 uint32_t C = al * bl; | |
155 | |
156 /* [ A ] | |
157 [ B ] | |
158 [ C ] | |
159 */ | |
160 uint32_t Lo = C + (B << 16); | |
161 uint32_t Hi = A + (B >>16) + (Lo < C); | |
162 | |
163 SkASSERT((Hi >> 29) == 0); // else overflow | |
164 | |
165 int32_t R = (Hi << 2) + (Lo >> 30); | |
166 | |
167 return SkApplySign(R, sa ^ sb); | |
168 #endif | |
169 } | |
170 | |
171 int SkFixedMulCommon(SkFixed a, int b, int bias) { | |
172 // this function only works if b is 16bits | |
173 SkASSERT(b == (int16_t)b); | |
174 SkASSERT(b >= 0); | |
175 | |
176 int sa = SkExtractSign(a); | |
177 a = SkApplySign(a, sa); | |
178 uint32_t ah = a >> 16; | |
179 uint32_t al = a & 0xFFFF; | |
180 uint32_t R = ah * b + ((al * b + bias) >> 16); | |
181 return SkApplySign(R, sa); | |
182 } | |
183 | |
184 #ifdef SK_DEBUGx | |
185 #define TEST_FASTINVERT | |
186 #endif | |
187 | |
188 SkFixed SkFixedFastInvert(SkFixed x) { | |
189 /* Adapted (stolen) from gglRecip() | |
190 */ | |
191 | |
192 if (x == SK_Fixed1) { | |
193 return SK_Fixed1; | |
194 } | |
195 | |
196 int sign = SkExtractSign(x); | |
197 uint32_t a = SkApplySign(x, sign); | |
198 | |
199 if (a <= 2) { | |
200 return SkApplySign(SK_MaxS32, sign); | |
201 } | |
202 | |
203 #ifdef TEST_FASTINVERT | |
204 SkFixed orig = a; | |
205 uint32_t slow = SkFixedDiv(SK_Fixed1, a); | |
206 #endif | |
207 | |
208 // normalize a | |
209 int lz = SkCLZ(a); | |
210 a = a << lz >> 16; | |
211 | |
212 // compute 1/a approximation (0.5 <= a < 1.0) | |
213 uint32_t r = 0x17400 - a; // (2.90625 (~2.914) - 2*a) >> 1 | |
214 | |
215 // Newton-Raphson iteration: | |
216 // x = r*(2 - a*r) = ((r/2)*(1 - a*r/2))*4 | |
217 r = ( (0x10000 - ((a*r)>>16)) * r ) >> 15; | |
218 r = ( (0x10000 - ((a*r)>>16)) * r ) >> (30 - lz); | |
219 | |
220 #ifdef TEST_FASTINVERT | |
221 SkDebugf("SkFixedFastInvert(%x %g) = %x %g Slow[%x %g]\n", | |
222 orig, orig/65536., | |
223 r, r/65536., | |
224 slow, slow/65536.); | |
225 #endif | |
226 | |
227 return SkApplySign(r, sign); | |
228 } | |
229 | |
230 /////////////////////////////////////////////////////////////////////////////// | 77 /////////////////////////////////////////////////////////////////////////////// |
231 | 78 |
232 #define DIVBITS_ITER(n) \ | 79 #define DIVBITS_ITER(n) \ |
233 case n: \ | 80 case n: \ |
234 if ((numer = (numer << 1) - denom) >= 0) \ | 81 if ((numer = (numer << 1) - denom) >= 0) \ |
235 result |= 1 << (n - 1); else numer += denom | 82 result |= 1 << (n - 1); else numer += denom |
236 | 83 |
237 int32_t SkDivBits(int32_t numer, int32_t denom, int shift_bias) { | 84 int32_t SkDivBits(int32_t numer, int32_t denom, int shift_bias) { |
238 SkASSERT(denom != 0); | 85 SkASSERT(denom != 0); |
239 if (numer == 0) { | 86 if (numer == 0) { |
(...skipping 48 matching lines...) Expand 10 before | Expand all | Expand 10 after Loading... |
288 DIVBITS_ITER( 1); | 135 DIVBITS_ITER( 1); |
289 } | 136 } |
290 } | 137 } |
291 | 138 |
292 if (result < 0) { | 139 if (result < 0) { |
293 result = SK_MaxS32; | 140 result = SK_MaxS32; |
294 } | 141 } |
295 return SkApplySign(result, sign); | 142 return SkApplySign(result, sign); |
296 } | 143 } |
297 | 144 |
298 /* mod(float numer, float denom) seems to always return the sign | |
299 of the numer, so that's what we do too | |
300 */ | |
301 SkFixed SkFixedMod(SkFixed numer, SkFixed denom) { | |
302 int sn = SkExtractSign(numer); | |
303 int sd = SkExtractSign(denom); | |
304 | |
305 numer = SkApplySign(numer, sn); | |
306 denom = SkApplySign(denom, sd); | |
307 | |
308 if (numer < denom) { | |
309 return SkApplySign(numer, sn); | |
310 } else if (numer == denom) { | |
311 return 0; | |
312 } else { | |
313 SkFixed div = SkFixedDiv(numer, denom); | |
314 return SkApplySign(SkFixedMul(denom, div & 0xFFFF), sn); | |
315 } | |
316 } | |
317 | |
318 /* www.worldserver.com/turk/computergraphics/FixedSqrt.pdf | 145 /* www.worldserver.com/turk/computergraphics/FixedSqrt.pdf |
319 */ | 146 */ |
320 int32_t SkSqrtBits(int32_t x, int count) { | 147 int32_t SkSqrtBits(int32_t x, int count) { |
321 SkASSERT(x >= 0 && count > 0 && (unsigned)count <= 30); | 148 SkASSERT(x >= 0 && count > 0 && (unsigned)count <= 30); |
322 | 149 |
323 uint32_t root = 0; | 150 uint32_t root = 0; |
324 uint32_t remHi = 0; | 151 uint32_t remHi = 0; |
325 uint32_t remLo = x; | 152 uint32_t remLo = x; |
326 | 153 |
327 do { | 154 do { |
328 root <<= 1; | 155 root <<= 1; |
329 | 156 |
330 remHi = (remHi<<2) | (remLo>>30); | 157 remHi = (remHi<<2) | (remLo>>30); |
331 remLo <<= 2; | 158 remLo <<= 2; |
332 | 159 |
333 uint32_t testDiv = (root << 1) + 1; | 160 uint32_t testDiv = (root << 1) + 1; |
334 if (remHi >= testDiv) { | 161 if (remHi >= testDiv) { |
335 remHi -= testDiv; | 162 remHi -= testDiv; |
336 root++; | 163 root++; |
337 } | 164 } |
338 } while (--count >= 0); | 165 } while (--count >= 0); |
339 | 166 |
340 return root; | 167 return root; |
341 } | 168 } |
342 | 169 |
343 int32_t SkCubeRootBits(int32_t value, int bits) { | |
344 SkASSERT(bits > 0); | |
345 | |
346 int sign = SkExtractSign(value); | |
347 value = SkApplySign(value, sign); | |
348 | |
349 uint32_t root = 0; | |
350 uint32_t curr = (uint32_t)value >> 30; | |
351 value <<= 2; | |
352 | |
353 do { | |
354 root <<= 1; | |
355 uint32_t guess = root * root + root; | |
356 guess = (guess << 1) + guess; // guess *= 3 | |
357 if (guess < curr) { | |
358 curr -= guess + 1; | |
359 root |= 1; | |
360 } | |
361 curr = (curr << 3) | ((uint32_t)value >> 29); | |
362 value <<= 3; | |
363 } while (--bits); | |
364 | |
365 return SkApplySign(root, sign); | |
366 } | |
367 | |
368 SkFixed SkFixedMean(SkFixed a, SkFixed b) { | |
369 Sk64 tmp; | |
370 | |
371 tmp.setMul(a, b); | |
372 return tmp.getSqrt(); | |
373 } | |
374 | |
375 /////////////////////////////////////////////////////////////////////////////// | 170 /////////////////////////////////////////////////////////////////////////////// |
376 | 171 |
377 float SkScalarSinCos(float radians, float* cosValue) { | 172 float SkScalarSinCos(float radians, float* cosValue) { |
378 float sinValue = sk_float_sin(radians); | 173 float sinValue = sk_float_sin(radians); |
379 | 174 |
380 if (cosValue) { | 175 if (cosValue) { |
381 *cosValue = sk_float_cos(radians); | 176 *cosValue = sk_float_cos(radians); |
382 if (SkScalarNearlyZero(*cosValue)) { | 177 if (SkScalarNearlyZero(*cosValue)) { |
383 *cosValue = 0; | 178 *cosValue = 0; |
384 } | 179 } |
(...skipping 111 matching lines...) Expand 10 before | Expand all | Expand 10 after Loading... |
496 SkASSERT(SkAbs32(diff) <= 7); | 291 SkASSERT(SkAbs32(diff) <= 7); |
497 } | 292 } |
498 #endif | 293 #endif |
499 | 294 |
500 if (cosValuePtr) { | 295 if (cosValuePtr) { |
501 *cosValuePtr = cosValue; | 296 *cosValuePtr = cosValue; |
502 } | 297 } |
503 return sinValue; | 298 return sinValue; |
504 } | 299 } |
505 | 300 |
506 /////////////////////////////////////////////////////////////////////////////// | |
507 | |
508 SkFixed SkFixedTan(SkFixed radians) { return SkCordicTan(radians); } | |
509 SkFixed SkFixedASin(SkFixed x) { return SkCordicASin(x); } | |
510 SkFixed SkFixedACos(SkFixed x) { return SkCordicACos(x); } | |
511 SkFixed SkFixedATan2(SkFixed y, SkFixed x) { return SkCordicATan2(y, x); } | |
512 SkFixed SkFixedExp(SkFixed x) { return SkCordicExp(x); } | |
513 SkFixed SkFixedLog(SkFixed x) { return SkCordicLog(x); } | |
OLD | NEW |