Add a linear transform library to libutils
Change-Id: Icdec5a6bebd9d8f24b3f335f8ec8b09a5810a774
diff --git a/include/utils/LinearTransform.h b/include/utils/LinearTransform.h
new file mode 100644
index 0000000..04cb355
--- /dev/null
+++ b/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
diff --git a/libs/utils/Android.mk b/libs/utils/Android.mk
index 093189c..774e8c9 100644
--- a/libs/utils/Android.mk
+++ b/libs/utils/Android.mk
@@ -27,6 +27,7 @@
Debug.cpp \
FileMap.cpp \
Flattenable.cpp \
+ LinearTransform.cpp \
ObbFile.cpp \
Pool.cpp \
PropertyMap.cpp \
diff --git a/libs/utils/LinearTransform.cpp b/libs/utils/LinearTransform.cpp
new file mode 100644
index 0000000..d752415
--- /dev/null
+++ b/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