Merge "Add a linear transform library to libutils"

include/utils/LinearTransform.h

@@ -0,0 +1,64 @@
+/*
+ * Copyright (C) 2011 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef _LIBS_UTILS_LINEAR_TRANSFORM_H
+#define _LIBS_UTILS_LINEAR_TRANSFORM_H
+
+#include <stdint.h>
+
+namespace android {
+
+// LinearTransform defines a structure which hold the definition of a
+// transformation from single dimensional coordinate system A into coordinate
+// system B (and back again).  Values in A and in B are 64 bit, the linear
+// scale factor is expressed as a rational number using two 32 bit values.
+//
+// Specifically, let
+// f(a) = b
+// F(b) = f^-1(b) = a
+// then
+//
+// f(a) = (((a - a_zero) * a_to_b_numer) / a_to_b_denom) + b_zero;
+//
+// and
+//
+// F(b) = (((b - b_zero) * a_to_b_denom) / a_to_b_numer) + a_zero;
+//
+struct LinearTransform {
+  int64_t  a_zero;
+  int64_t  b_zero;
+  int32_t  a_to_b_numer;
+  uint32_t a_to_b_denom;
+
+  // Transform from A->B
+  // Returns true on success, or false in the case of a singularity or an
+  // overflow.
+  bool doForwardTransform(int64_t a_in, int64_t* b_out) const;
+
+  // Transform from B->A
+  // Returns true on success, or false in the case of a singularity or an
+  // overflow.
+  bool doReverseTransform(int64_t b_in, int64_t* a_out) const;
+
+  // Helpers which will reduce the fraction N/D using Euclid's method.
+  template <class T> static void reduce(T* N, T* D);
+  static void reduce(int32_t* N, uint32_t* D);
+};
+
+
+}
+
+#endif  // _LIBS_UTILS_LINEAR_TRANSFORM_H

libs/utils/Android.mk

@@ -27,6 +27,7 @@ commonSources:= \
 	Debug.cpp \
 	FileMap.cpp \
 	Flattenable.cpp \
+	LinearTransform.cpp \
 	ObbFile.cpp \
 	Pool.cpp \
 	PropertyMap.cpp \

libs/utils/LinearTransform.cpp

@@ -0,0 +1,262 @@
+/*
+ * Copyright (C) 2011 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#define __STDC_LIMIT_MACROS
+
+#include <assert.h>
+#include <stdint.h>
+
+#include <utils/LinearTransform.h>
+
+namespace android {
+
+template<class T> static inline T ABS(T x) { return (x < 0) ? -x : x; }
+
+// Static math methods involving linear transformations
+static bool scale_u64_to_u64(
+        uint64_t val,
+        uint32_t N,
+        uint32_t D,
+        uint64_t* res,
+        bool round_up_not_down) {
+    uint64_t tmp1, tmp2;
+    uint32_t r;
+
+    assert(res);
+    assert(D);
+
+    // Let U32(X) denote a uint32_t containing the upper 32 bits of a 64 bit
+    // integer X.
+    // Let L32(X) denote a uint32_t containing the lower 32 bits of a 64 bit
+    // integer X.
+    // Let X[A, B] with A <= B denote bits A through B of the integer X.
+    // Let (A | B) denote the concatination of two 32 bit ints, A and B.
+    // IOW X = (A | B) => U32(X) == A && L32(X) == B
+    //
+    // compute M = val * N (a 96 bit int)
+    // ---------------------------------
+    // tmp2 = U32(val) * N (a 64 bit int)
+    // tmp1 = L32(val) * N (a 64 bit int)
+    // which means
+    // M = val * N = (tmp2 << 32) + tmp1
+    tmp2 = (val >> 32) * N;
+    tmp1 = (val & UINT32_MAX) * N;
+
+    // compute M[32, 95]
+    // tmp2 = tmp2 + U32(tmp1)
+    //      = (U32(val) * N) + U32(L32(val) * N)
+    //      = M[32, 95]
+    tmp2 += tmp1 >> 32;
+
+    // if M[64, 95] >= D, then M/D has bits > 63 set and we have
+    // an overflow.
+    if ((tmp2 >> 32) >= D) {
+        *res = UINT64_MAX;
+        return false;
+    }
+
+    // Divide.  Going in we know
+    // tmp2 = M[32, 95]
+    // U32(tmp2) < D
+    r = tmp2 % D;
+    tmp2 /= D;
+
+    // At this point
+    // tmp1      = L32(val) * N
+    // tmp2      = M[32, 95] / D
+    //           = (M / D)[32, 95]
+    // r         = M[32, 95] % D
+    // U32(tmp2) = 0
+    //
+    // compute tmp1 = (r | M[0, 31])
+    tmp1 = (tmp1 & UINT32_MAX) | ((uint64_t)r << 32);
+
+    // Divide again.  Keep the remainder around in order to round properly.
+    r = tmp1 % D;
+    tmp1 /= D;
+
+    // At this point
+    // tmp2      = (M / D)[32, 95]
+    // tmp1      = (M / D)[ 0, 31]
+    // r         =  M % D
+    // U32(tmp1) = 0
+    // U32(tmp2) = 0
+
+    // Pack the result and deal with the round-up case (As well as the
+    // remote possiblility over overflow in such a case).
+    *res = (tmp2 << 32) | tmp1;
+    if (r && round_up_not_down) {
+        ++(*res);
+        if (!(*res)) {
+            *res = UINT64_MAX;
+            return false;
+        }
+    }
+
+    return true;
+}
+
+static bool linear_transform_s64_to_s64(
+        int64_t  val,
+        int64_t  basis1,
+        int32_t  N,
+        uint32_t D,
+        int64_t  basis2,
+        int64_t* out) {
+    uint64_t scaled, res;
+    uint64_t abs_val;
+    bool is_neg;
+
+    if (!out)
+        return false;
+
+    // Compute abs(val - basis_64). Keep track of whether or not this delta
+    // will be negative after the scale opertaion.
+    if (val < basis1) {
+        is_neg = true;
+        abs_val = basis1 - val;
+    } else {
+        is_neg = false;
+        abs_val = val - basis1;
+    }
+
+    if (N < 0)
+        is_neg = !is_neg;
+
+    if (!scale_u64_to_u64(abs_val,
+                          ABS(N),
+                          D,
+                          &scaled,
+                          is_neg))
+        return false; // overflow/undeflow
+
+    // if scaled is >= 0x8000<etc>, then we are going to overflow or
+    // underflow unless ABS(basis2) is large enough to pull us back into the
+    // non-overflow/underflow region.
+    if (scaled & INT64_MIN) {
+        if (is_neg && (basis2 < 0))
+            return false; // certain underflow
+
+        if (!is_neg && (basis2 >= 0))
+            return false; // certain overflow
+
+        if (ABS(basis2) <= static_cast<int64_t>(scaled & INT64_MAX))
+            return false; // not enough
+
+        // Looks like we are OK
+        *out = (is_neg ? (-scaled) : scaled) + basis2;
+    } else {
+        // Scaled fits within signed bounds, so we just need to check for
+        // over/underflow for two signed integers.  Basically, if both scaled
+        // and basis2 have the same sign bit, and the result has a different
+        // sign bit, then we have under/overflow.  An easy way to compute this
+        // is
+        // (scaled_signbit XNOR basis_signbit) &&
+        // (scaled_signbit XOR res_signbit)
+        // ==
+        // (scaled_signbit XOR basis_signbit XOR 1) &&
+        // (scaled_signbit XOR res_signbit)
+
+        if (is_neg)
+            scaled = -scaled;
+        res = scaled + basis2;
+
+        if ((scaled ^ basis2 ^ INT64_MIN) & (scaled ^ res) & INT64_MIN)
+            return false;
+
+        *out = res;
+    }
+
+    return true;
+}
+
+bool LinearTransform::doForwardTransform(int64_t a_in, int64_t* b_out) const {
+    if (0 == a_to_b_denom)
+        return false;
+
+    return linear_transform_s64_to_s64(a_in,
+                                       a_zero,
+                                       a_to_b_numer,
+                                       a_to_b_denom,
+                                       b_zero,
+                                       b_out);
+}
+
+bool LinearTransform::doReverseTransform(int64_t b_in, int64_t* a_out) const {
+    if (0 == a_to_b_numer)
+        return false;
+
+    return linear_transform_s64_to_s64(b_in,
+                                       b_zero,
+                                       a_to_b_denom,
+                                       a_to_b_numer,
+                                       a_zero,
+                                       a_out);
+}
+
+template <class T> void LinearTransform::reduce(T* N, T* D) {
+    T a, b;
+    if (!N || !D || !(*D)) {
+        assert(false);
+        return;
+    }
+
+    a = *N;
+    b = *D;
+
+    if (a == 0) {
+        *D = 1;
+        return;
+    }
+
+    // This implements Euclid's method to find GCD.
+    if (a < b) {
+        T tmp = a;
+        a = b;
+        b = tmp;
+    }
+
+    while (1) {
+        // a is now the greater of the two.
+        const T remainder = a % b;
+        if (remainder == 0) {
+            *N /= b;
+            *D /= b;
+            return;
+        }
+        // by swapping remainder and b, we are guaranteeing that a is
+        // still the greater of the two upon entrance to the loop.
+        a = b;
+        b = remainder;
+    }
+};
+
+template void LinearTransform::reduce<uint64_t>(uint64_t* N, uint64_t* D);
+template void LinearTransform::reduce<uint32_t>(uint32_t* N, uint32_t* D);
+
+void LinearTransform::reduce(int32_t* N, uint32_t* D) {
+    if (N && D && *D) {
+        if (*N < 0) {
+            *N = -(*N);
+            reduce(reinterpret_cast<uint32_t*>(N), D);
+            *N = -(*N);
+        } else {
+            reduce(reinterpret_cast<uint32_t*>(N), D);
+        }
+    }
+}
+
+}  // namespace android