1 /* 2 * Copyright (C) 2011 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 #define __STDC_LIMIT_MACROS 18 19 #include <assert.h> 20 #include <stdint.h> 21 22 #include <utils/LinearTransform.h> 23 24 namespace android { 25 26 template<class T> static inline T ABS(T x) { return (x < 0) ? -x : x; } 27 28 // Static math methods involving linear transformations 29 static bool scale_u64_to_u64( 30 uint64_t val, 31 uint32_t N, 32 uint32_t D, 33 uint64_t* res, 34 bool round_up_not_down) { 35 uint64_t tmp1, tmp2; 36 uint32_t r; 37 38 assert(res); 39 assert(D); 40 41 // Let U32(X) denote a uint32_t containing the upper 32 bits of a 64 bit 42 // integer X. 43 // Let L32(X) denote a uint32_t containing the lower 32 bits of a 64 bit 44 // integer X. 45 // Let X[A, B] with A <= B denote bits A through B of the integer X. 46 // Let (A | B) denote the concatination of two 32 bit ints, A and B. 47 // IOW X = (A | B) => U32(X) == A && L32(X) == B 48 // 49 // compute M = val * N (a 96 bit int) 50 // --------------------------------- 51 // tmp2 = U32(val) * N (a 64 bit int) 52 // tmp1 = L32(val) * N (a 64 bit int) 53 // which means 54 // M = val * N = (tmp2 << 32) + tmp1 55 tmp2 = (val >> 32) * N; 56 tmp1 = (val & UINT32_MAX) * N; 57 58 // compute M[32, 95] 59 // tmp2 = tmp2 + U32(tmp1) 60 // = (U32(val) * N) + U32(L32(val) * N) 61 // = M[32, 95] 62 tmp2 += tmp1 >> 32; 63 64 // if M[64, 95] >= D, then M/D has bits > 63 set and we have 65 // an overflow. 66 if ((tmp2 >> 32) >= D) { 67 *res = UINT64_MAX; 68 return false; 69 } 70 71 // Divide. Going in we know 72 // tmp2 = M[32, 95] 73 // U32(tmp2) < D 74 r = tmp2 % D; 75 tmp2 /= D; 76 77 // At this point 78 // tmp1 = L32(val) * N 79 // tmp2 = M[32, 95] / D 80 // = (M / D)[32, 95] 81 // r = M[32, 95] % D 82 // U32(tmp2) = 0 83 // 84 // compute tmp1 = (r | M[0, 31]) 85 tmp1 = (tmp1 & UINT32_MAX) | ((uint64_t)r << 32); 86 87 // Divide again. Keep the remainder around in order to round properly. 88 r = tmp1 % D; 89 tmp1 /= D; 90 91 // At this point 92 // tmp2 = (M / D)[32, 95] 93 // tmp1 = (M / D)[ 0, 31] 94 // r = M % D 95 // U32(tmp1) = 0 96 // U32(tmp2) = 0 97 98 // Pack the result and deal with the round-up case (As well as the 99 // remote possiblility over overflow in such a case). 100 *res = (tmp2 << 32) | tmp1; 101 if (r && round_up_not_down) { 102 ++(*res); 103 if (!(*res)) { 104 *res = UINT64_MAX; 105 return false; 106 } 107 } 108 109 return true; 110 } 111 112 static bool linear_transform_s64_to_s64( 113 int64_t val, 114 int64_t basis1, 115 int32_t N, 116 uint32_t D, 117 int64_t basis2, 118 int64_t* out) { 119 uint64_t scaled, res; 120 uint64_t abs_val; 121 bool is_neg; 122 123 if (!out) 124 return false; 125 126 // Compute abs(val - basis_64). Keep track of whether or not this delta 127 // will be negative after the scale opertaion. 128 if (val < basis1) { 129 is_neg = true; 130 abs_val = basis1 - val; 131 } else { 132 is_neg = false; 133 abs_val = val - basis1; 134 } 135 136 if (N < 0) 137 is_neg = !is_neg; 138 139 if (!scale_u64_to_u64(abs_val, 140 ABS(N), 141 D, 142 &scaled, 143 is_neg)) 144 return false; // overflow/undeflow 145 146 // if scaled is >= 0x8000<etc>, then we are going to overflow or 147 // underflow unless ABS(basis2) is large enough to pull us back into the 148 // non-overflow/underflow region. 149 if (scaled & INT64_MIN) { 150 if (is_neg && (basis2 < 0)) 151 return false; // certain underflow 152 153 if (!is_neg && (basis2 >= 0)) 154 return false; // certain overflow 155 156 if (ABS(basis2) <= static_cast<int64_t>(scaled & INT64_MAX)) 157 return false; // not enough 158 159 // Looks like we are OK 160 *out = (is_neg ? (-scaled) : scaled) + basis2; 161 } else { 162 // Scaled fits within signed bounds, so we just need to check for 163 // over/underflow for two signed integers. Basically, if both scaled 164 // and basis2 have the same sign bit, and the result has a different 165 // sign bit, then we have under/overflow. An easy way to compute this 166 // is 167 // (scaled_signbit XNOR basis_signbit) && 168 // (scaled_signbit XOR res_signbit) 169 // == 170 // (scaled_signbit XOR basis_signbit XOR 1) && 171 // (scaled_signbit XOR res_signbit) 172 173 if (is_neg) 174 scaled = -scaled; 175 res = scaled + basis2; 176 177 if ((scaled ^ basis2 ^ INT64_MIN) & (scaled ^ res) & INT64_MIN) 178 return false; 179 180 *out = res; 181 } 182 183 return true; 184 } 185 186 bool LinearTransform::doForwardTransform(int64_t a_in, int64_t* b_out) const { 187 if (0 == a_to_b_denom) 188 return false; 189 190 return linear_transform_s64_to_s64(a_in, 191 a_zero, 192 a_to_b_numer, 193 a_to_b_denom, 194 b_zero, 195 b_out); 196 } 197 198 bool LinearTransform::doReverseTransform(int64_t b_in, int64_t* a_out) const { 199 if (0 == a_to_b_numer) 200 return false; 201 202 return linear_transform_s64_to_s64(b_in, 203 b_zero, 204 a_to_b_denom, 205 a_to_b_numer, 206 a_zero, 207 a_out); 208 } 209 210 template <class T> void LinearTransform::reduce(T* N, T* D) { 211 T a, b; 212 if (!N || !D || !(*D)) { 213 assert(false); 214 return; 215 } 216 217 a = *N; 218 b = *D; 219 220 if (a == 0) { 221 *D = 1; 222 return; 223 } 224 225 // This implements Euclid's method to find GCD. 226 if (a < b) { 227 T tmp = a; 228 a = b; 229 b = tmp; 230 } 231 232 while (1) { 233 // a is now the greater of the two. 234 const T remainder = a % b; 235 if (remainder == 0) { 236 *N /= b; 237 *D /= b; 238 return; 239 } 240 // by swapping remainder and b, we are guaranteeing that a is 241 // still the greater of the two upon entrance to the loop. 242 a = b; 243 b = remainder; 244 } 245 }; 246 247 template void LinearTransform::reduce<uint64_t>(uint64_t* N, uint64_t* D); 248 template void LinearTransform::reduce<uint32_t>(uint32_t* N, uint32_t* D); 249 250 void LinearTransform::reduce(int32_t* N, uint32_t* D) { 251 if (N && D && *D) { 252 if (*N < 0) { 253 *N = -(*N); 254 reduce(reinterpret_cast<uint32_t*>(N), D); 255 *N = -(*N); 256 } else { 257 reduce(reinterpret_cast<uint32_t*>(N), D); 258 } 259 } 260 } 261 262 } // namespace android 263
