1 2/* 3 * Copyright 2008 The Android Open Source Project 4 * 5 * Use of this source code is governed by a BSD-style license that can be 6 * found in the LICENSE file. 7 */ 8 9 10#include "SkFloat.h" 11#include "SkMathPriv.h" 12 13#define EXP_BIAS (127+23) 14 15static int get_unsigned_exp(uint32_t packed) 16{ 17 return (packed << 1 >> 24); 18} 19 20static unsigned get_unsigned_value(uint32_t packed) 21{ 22 return (packed << 9 >> 9) | (1 << 23); 23} 24 25static int get_signed_value(int32_t packed) 26{ 27 return SkApplySign(get_unsigned_value(packed), SkExtractSign(packed)); 28} 29 30///////////////////////////////////////////////////////////////////////// 31 32int SkFloat::GetShift(int32_t packed, int shift) 33{ 34 if (packed == 0) 35 return 0; 36 37 int exp = get_unsigned_exp(packed) - EXP_BIAS - shift; 38 int value = get_unsigned_value(packed); 39 40 if (exp >= 0) 41 { 42 if (exp > 8) // overflow 43 value = SK_MaxS32; 44 else 45 value <<= exp; 46 } 47 else 48 { 49 exp = -exp; 50 if (exp > 23) // underflow 51 value = 0; 52 else 53 value >>= exp; 54 } 55 return SkApplySign(value, SkExtractSign(packed)); 56} 57 58///////////////////////////////////////////////////////////////////////////////////// 59 60int32_t SkFloat::SetShift(int value, int shift) 61{ 62 if (value == 0) 63 return 0; 64 65 // record the sign and make value positive 66 int sign = SkExtractSign(value); 67 value = SkApplySign(value, sign); 68 69 if (value >> 24) // value is too big (has more than 24 bits set) 70 { 71 int bias = 8 - SkCLZ(value); 72 SkASSERT(bias > 0 && bias < 8); 73 value >>= bias; 74 shift += bias; 75 } 76 else 77 { 78 int zeros = SkCLZ(value << 8); 79 SkASSERT(zeros >= 0 && zeros <= 23); 80 value <<= zeros; 81 shift -= zeros; 82 } 83 // now value is left-aligned to 24 bits 84 SkASSERT((value >> 23) == 1); 85 86 shift += EXP_BIAS; 87 if (shift < 0) // underflow 88 return 0; 89 else 90 { 91 if (shift > 255) // overflow 92 { 93 shift = 255; 94 value = 0x00FFFFFF; 95 } 96 int32_t packed = sign << 31; // set the sign-bit 97 packed |= shift << 23; // store the packed exponent 98 packed |= ((unsigned)(value << 9) >> 9); // clear 24th bit of value (its implied) 99 100#ifdef SK_DEBUG 101 { 102 int n; 103 104 n = SkExtractSign(packed); 105 SkASSERT(n == sign); 106 n = get_unsigned_exp(packed); 107 SkASSERT(n == shift); 108 n = get_unsigned_value(packed); 109 SkASSERT(n == value); 110 } 111#endif 112 return packed; 113 } 114} 115 116int32_t SkFloat::Neg(int32_t packed) 117{ 118 if (packed) 119 packed = packed ^ (1 << 31); 120 return packed; 121} 122 123int32_t SkFloat::Add(int32_t packed_a, int32_t packed_b) 124{ 125 if (packed_a == 0) 126 return packed_b; 127 if (packed_b == 0) 128 return packed_a; 129 130 int exp_a = get_unsigned_exp(packed_a); 131 int exp_b = get_unsigned_exp(packed_b); 132 int exp_diff = exp_a - exp_b; 133 134 int shift_a = 0, shift_b = 0; 135 int exp; 136 137 if (exp_diff >= 0) 138 { 139 if (exp_diff > 24) // B is too small to contribute 140 return packed_a; 141 shift_b = exp_diff; 142 exp = exp_a; 143 } 144 else 145 { 146 exp_diff = -exp_diff; 147 if (exp_diff > 24) // A is too small to contribute 148 return packed_b; 149 shift_a = exp_diff; 150 exp = exp_b; 151 } 152 153 int value_a = get_signed_value(packed_a) >> shift_a; 154 int value_b = get_signed_value(packed_b) >> shift_b; 155 156 return SkFloat::SetShift(value_a + value_b, exp - EXP_BIAS); 157} 158 159#include "Sk64.h" 160 161static inline int32_t mul24(int32_t a, int32_t b) 162{ 163 Sk64 tmp; 164 165 tmp.setMul(a, b); 166 tmp.roundRight(24); 167 return tmp.get32(); 168} 169 170int32_t SkFloat::Mul(int32_t packed_a, int32_t packed_b) 171{ 172 if (packed_a == 0 || packed_b == 0) 173 return 0; 174 175 int exp_a = get_unsigned_exp(packed_a); 176 int exp_b = get_unsigned_exp(packed_b); 177 178 int value_a = get_signed_value(packed_a); 179 int value_b = get_signed_value(packed_b); 180 181 return SkFloat::SetShift(mul24(value_a, value_b), exp_a + exp_b - 2*EXP_BIAS + 24); 182} 183 184int32_t SkFloat::MulInt(int32_t packed, int n) 185{ 186 return Mul(packed, SetShift(n, 0)); 187} 188 189int32_t SkFloat::Div(int32_t packed_n, int32_t packed_d) 190{ 191 SkASSERT(packed_d != 0); 192 193 if (packed_n == 0) 194 return 0; 195 196 int exp_n = get_unsigned_exp(packed_n); 197 int exp_d = get_unsigned_exp(packed_d); 198 199 int value_n = get_signed_value(packed_n); 200 int value_d = get_signed_value(packed_d); 201 202 return SkFloat::SetShift(SkDivBits(value_n, value_d, 24), exp_n - exp_d - 24); 203} 204 205int32_t SkFloat::DivInt(int32_t packed, int n) 206{ 207 return Div(packed, SetShift(n, 0)); 208} 209 210int32_t SkFloat::Invert(int32_t packed) 211{ 212 return Div(packed, SetShift(1, 0)); 213} 214 215int32_t SkFloat::Sqrt(int32_t packed) 216{ 217 if (packed < 0) 218 { 219 SkDEBUGFAIL("can't sqrt a negative number"); 220 return 0; 221 } 222 223 int exp = get_unsigned_exp(packed); 224 int value = get_unsigned_value(packed); 225 226 int nexp = exp - EXP_BIAS; 227 int root = SkSqrtBits(value << (nexp & 1), 26); 228 nexp >>= 1; 229 return SkFloat::SetShift(root, nexp - 11); 230} 231 232#if defined _WIN32 && _MSC_VER >= 1300 // disable warning : unreachable code 233#pragma warning ( push ) 234#pragma warning ( disable : 4702 ) 235#endif 236 237int32_t SkFloat::CubeRoot(int32_t packed) 238{ 239 sk_throw(); 240 return 0; 241} 242 243#if defined _WIN32 && _MSC_VER >= 1300 244#pragma warning ( pop ) 245#endif 246 247static inline int32_t clear_high_bit(int32_t n) 248{ 249 return ((uint32_t)(n << 1)) >> 1; 250} 251 252static inline int int_sign(int32_t a, int32_t b) 253{ 254 return a > b ? 1 : (a < b ? -1 : 0); 255} 256 257int SkFloat::Cmp(int32_t packed_a, int32_t packed_b) 258{ 259 packed_a = SkApplySign(clear_high_bit(packed_a), SkExtractSign(packed_a)); 260 packed_b = SkApplySign(clear_high_bit(packed_b), SkExtractSign(packed_b)); 261 262 return int_sign(packed_a, packed_b); 263} 264 265///////////////////////////////////////////////////////////////////////////////////// 266///////////////////////////////////////////////////////////////////////////////////// 267 268#ifdef SK_DEBUG 269 270#include "SkRandom.h" 271#include "SkFloatingPoint.h" 272 273void SkFloat::UnitTest() 274{ 275#ifdef SK_SUPPORT_UNITTEST 276 SkFloat a, b, c, d; 277 int n; 278 279 a.setZero(); 280 n = a.getInt(); 281 SkASSERT(n == 0); 282 283 b.setInt(5); 284 n = b.getInt(); 285 SkASSERT(n == 5); 286 287 c.setInt(-3); 288 n = c.getInt(); 289 SkASSERT(n == -3); 290 291 d.setAdd(c, b); 292 SkDebugf("SkFloat: %d + %d = %d\n", c.getInt(), b.getInt(), d.getInt()); 293 294 SkRandom rand; 295 296 int i; 297 for (i = 0; i < 1000; i++) 298 { 299 float fa, fb; 300 int aa = rand.nextS() >> 14; 301 int bb = rand.nextS() >> 14; 302 a.setInt(aa); 303 b.setInt(bb); 304 SkASSERT(a.getInt() == aa); 305 SkASSERT(b.getInt() == bb); 306 307 c.setAdd(a, b); 308 int cc = c.getInt(); 309 SkASSERT(cc == aa + bb); 310 311 c.setSub(a, b); 312 cc = c.getInt(); 313 SkASSERT(cc == aa - bb); 314 315 aa >>= 5; 316 bb >>= 5; 317 a.setInt(aa); 318 b.setInt(bb); 319 c.setMul(a, b); 320 cc = c.getInt(); 321 SkASSERT(cc == aa * bb); 322 ///////////////////////////////////// 323 324 aa = rand.nextS() >> 11; 325 a.setFixed(aa); 326 cc = a.getFixed(); 327 SkASSERT(aa == cc); 328 329 bb = rand.nextS() >> 11; 330 b.setFixed(bb); 331 cc = b.getFixed(); 332 SkASSERT(bb == cc); 333 334 cc = SkFixedMul(aa, bb); 335 c.setMul(a, b); 336 SkFixed dd = c.getFixed(); 337 int diff = cc - dd; 338 SkASSERT(SkAbs32(diff) <= 1); 339 340 fa = (float)aa / 65536.0f; 341 fb = (float)bb / 65536.0f; 342 a.assertEquals(fa); 343 b.assertEquals(fb); 344 fa = a.getFloat(); 345 fb = b.getFloat(); 346 347 c.assertEquals(fa * fb, 1); 348 349 c.setDiv(a, b); 350 cc = SkFixedDiv(aa, bb); 351 dd = c.getFixed(); 352 diff = cc - dd; 353 SkASSERT(SkAbs32(diff) <= 3); 354 355 c.assertEquals(fa / fb, 1); 356 357 SkASSERT((aa == bb) == (a == b)); 358 SkASSERT((aa != bb) == (a != b)); 359 SkASSERT((aa < bb) == (a < b)); 360 SkASSERT((aa <= bb) == (a <= b)); 361 SkASSERT((aa > bb) == (a > b)); 362 SkASSERT((aa >= bb) == (a >= b)); 363 364 if (aa < 0) 365 { 366 aa = -aa; 367 fa = -fa; 368 } 369 a.setFixed(aa); 370 c.setSqrt(a); 371 cc = SkFixedSqrt(aa); 372 dd = c.getFixed(); 373 SkASSERT(dd == cc); 374 375 c.assertEquals(sk_float_sqrt(fa), 2); 376 377 // cuberoot 378#if 0 379 a.setInt(1); 380 a.cubeRoot(); 381 a.assertEquals(1.0f, 0); 382 a.setInt(8); 383 a.cubeRoot(); 384 a.assertEquals(2.0f, 0); 385 a.setInt(27); 386 a.cubeRoot(); 387 a.assertEquals(3.0f, 0); 388#endif 389 } 390#endif 391} 392 393#endif 394