[cairo-commit] src/cairo.c src/cairo-gstate.c src/cairo-misc.c src/Makefile.am
Behdad Esfahbod
behdad at kemper.freedesktop.org
Sat Feb 16 23:32:43 PST 2008
src/Makefile.am | 1
src/cairo-gstate.c | 79 ----------
src/cairo-misc.c | 407 +++++++++++++++++++++++++++++++++++++++++++++++++++++
src/cairo.c | 287 -------------------------------------
4 files changed, 408 insertions(+), 366 deletions(-)
New commits:
commit c7204adcf3ff6614aae75c4c1c5ef0fc5269d834
Author: Behdad Esfahbod <behdad at behdad.org>
Date: Sun Feb 17 02:32:00 2008 -0500
[cairo-misc.c] Add misc functions to this file
Anything functions that doesn't group with other functions enough to
justify its own file should go here now.
diff --git a/src/Makefile.am b/src/Makefile.am
index c149a69..525ca66 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -31,6 +31,7 @@ cairo_base_sources = \
cairo-hull.c \
cairo-image-surface.c \
cairo-lzw.c \
+ cairo-misc.c \
cairo-malloc-private.h \
cairo-matrix.c \
cairo-mutex.c \
diff --git a/src/cairo-gstate.c b/src/cairo-gstate.c
index 37a8031..b6ddcb3 100644
--- a/src/cairo-gstate.c
+++ b/src/cairo-gstate.c
@@ -900,85 +900,6 @@ _cairo_gstate_paint (cairo_gstate_t *gstate)
return status;
}
-/**
- * _cairo_operator_bounded_by_mask:
- * @op: a #cairo_operator_t
- *
- * A bounded operator is one where mask pixel
- * of zero results in no effect on the destination image.
- *
- * Unbounded operators often require special handling; if you, for
- * example, draw trapezoids with an unbounded operator, the effect
- * extends past the bounding box of the trapezoids.
- *
- * Return value: %TRUE if the operator is bounded by the mask operand
- **/
-cairo_bool_t
-_cairo_operator_bounded_by_mask (cairo_operator_t op)
-{
- switch (op) {
- case CAIRO_OPERATOR_CLEAR:
- case CAIRO_OPERATOR_SOURCE:
- case CAIRO_OPERATOR_OVER:
- case CAIRO_OPERATOR_ATOP:
- case CAIRO_OPERATOR_DEST:
- case CAIRO_OPERATOR_DEST_OVER:
- case CAIRO_OPERATOR_DEST_OUT:
- case CAIRO_OPERATOR_XOR:
- case CAIRO_OPERATOR_ADD:
- case CAIRO_OPERATOR_SATURATE:
- return TRUE;
- case CAIRO_OPERATOR_OUT:
- case CAIRO_OPERATOR_IN:
- case CAIRO_OPERATOR_DEST_IN:
- case CAIRO_OPERATOR_DEST_ATOP:
- return FALSE;
- }
-
- ASSERT_NOT_REACHED;
- return FALSE;
-}
-
-/**
- * _cairo_operator_bounded_by_source:
- * @op: a #cairo_operator_t
- *
- * A bounded operator is one where source pixels of zero
- * (in all four components, r, g, b and a) effect no change
- * in the resulting destination image.
- *
- * Unbounded operators often require special handling; if you, for
- * example, copy a surface with the SOURCE operator, the effect
- * extends past the bounding box of the source surface.
- *
- * Return value: %TRUE if the operator is bounded by the source operand
- **/
-cairo_bool_t
-_cairo_operator_bounded_by_source (cairo_operator_t op)
-{
- switch (op) {
- case CAIRO_OPERATOR_OVER:
- case CAIRO_OPERATOR_ATOP:
- case CAIRO_OPERATOR_DEST:
- case CAIRO_OPERATOR_DEST_OVER:
- case CAIRO_OPERATOR_DEST_OUT:
- case CAIRO_OPERATOR_XOR:
- case CAIRO_OPERATOR_ADD:
- case CAIRO_OPERATOR_SATURATE:
- return TRUE;
- case CAIRO_OPERATOR_CLEAR:
- case CAIRO_OPERATOR_SOURCE:
- case CAIRO_OPERATOR_OUT:
- case CAIRO_OPERATOR_IN:
- case CAIRO_OPERATOR_DEST_IN:
- case CAIRO_OPERATOR_DEST_ATOP:
- return FALSE;
- }
-
- ASSERT_NOT_REACHED;
- return FALSE;
-}
-
cairo_status_t
_cairo_gstate_mask (cairo_gstate_t *gstate,
cairo_pattern_t *mask)
diff --git a/src/cairo-misc.c b/src/cairo-misc.c
new file mode 100644
index 0000000..a2250ff
--- /dev/null
+++ b/src/cairo-misc.c
@@ -0,0 +1,407 @@
+/* -*- Mode: c; c-basic-offset: 4; indent-tabs-mode: t; tab-width: 8; -*- */
+/* cairo - a vector graphics library with display and print output
+ *
+ * Copyright © 2002 University of Southern California
+ * Copyright © 2005 Red Hat, Inc.
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (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.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ *
+ * The Original Code is the cairo graphics library.
+ *
+ * The Initial Developer of the Original Code is University of Southern
+ * California.
+ *
+ * Contributor(s):
+ * Carl D. Worth <cworth at cworth.org>
+ */
+
+#include "cairoint.h"
+
+
+/**
+ * cairo_status_to_string:
+ * @status: a cairo status
+ *
+ * Provides a human-readable description of a #cairo_status_t.
+ *
+ * Returns: a string representation of the status
+ */
+const char *
+cairo_status_to_string (cairo_status_t status)
+{
+ switch (status) {
+ case CAIRO_STATUS_SUCCESS:
+ return "success";
+ case CAIRO_STATUS_NO_MEMORY:
+ return "out of memory";
+ case CAIRO_STATUS_INVALID_RESTORE:
+ return "cairo_restore without matching cairo_save";
+ case CAIRO_STATUS_INVALID_POP_GROUP:
+ return "cairo_pop_group without matching cairo_push_group";
+ case CAIRO_STATUS_NO_CURRENT_POINT:
+ return "no current point defined";
+ case CAIRO_STATUS_INVALID_MATRIX:
+ return "invalid matrix (not invertible)";
+ case CAIRO_STATUS_INVALID_STATUS:
+ return "invalid value for an input cairo_status_t";
+ case CAIRO_STATUS_NULL_POINTER:
+ return "NULL pointer";
+ case CAIRO_STATUS_INVALID_STRING:
+ return "input string not valid UTF-8";
+ case CAIRO_STATUS_INVALID_PATH_DATA:
+ return "input path data not valid";
+ case CAIRO_STATUS_READ_ERROR:
+ return "error while reading from input stream";
+ case CAIRO_STATUS_WRITE_ERROR:
+ return "error while writing to output stream";
+ case CAIRO_STATUS_SURFACE_FINISHED:
+ return "the target surface has been finished";
+ case CAIRO_STATUS_SURFACE_TYPE_MISMATCH:
+ return "the surface type is not appropriate for the operation";
+ case CAIRO_STATUS_PATTERN_TYPE_MISMATCH:
+ return "the pattern type is not appropriate for the operation";
+ case CAIRO_STATUS_INVALID_CONTENT:
+ return "invalid value for an input cairo_content_t";
+ case CAIRO_STATUS_INVALID_FORMAT:
+ return "invalid value for an input cairo_format_t";
+ case CAIRO_STATUS_INVALID_VISUAL:
+ return "invalid value for an input Visual*";
+ case CAIRO_STATUS_FILE_NOT_FOUND:
+ return "file not found";
+ case CAIRO_STATUS_INVALID_DASH:
+ return "invalid value for a dash setting";
+ case CAIRO_STATUS_INVALID_DSC_COMMENT:
+ return "invalid value for a DSC comment";
+ case CAIRO_STATUS_INVALID_INDEX:
+ return "invalid index passed to getter";
+ case CAIRO_STATUS_CLIP_NOT_REPRESENTABLE:
+ return "clip region not representable in desired format";
+ case CAIRO_STATUS_TEMP_FILE_ERROR:
+ return "error creating or writing to a temporary file";
+ case CAIRO_STATUS_INVALID_STRIDE:
+ return "invalid value for stride";
+ }
+
+ return "<unknown error status>";
+}
+
+/**
+ * _cairo_operator_bounded_by_mask:
+ * @op: a #cairo_operator_t
+ *
+ * A bounded operator is one where mask pixel
+ * of zero results in no effect on the destination image.
+ *
+ * Unbounded operators often require special handling; if you, for
+ * example, draw trapezoids with an unbounded operator, the effect
+ * extends past the bounding box of the trapezoids.
+ *
+ * Return value: %TRUE if the operator is bounded by the mask operand
+ **/
+cairo_bool_t
+_cairo_operator_bounded_by_mask (cairo_operator_t op)
+{
+ switch (op) {
+ case CAIRO_OPERATOR_CLEAR:
+ case CAIRO_OPERATOR_SOURCE:
+ case CAIRO_OPERATOR_OVER:
+ case CAIRO_OPERATOR_ATOP:
+ case CAIRO_OPERATOR_DEST:
+ case CAIRO_OPERATOR_DEST_OVER:
+ case CAIRO_OPERATOR_DEST_OUT:
+ case CAIRO_OPERATOR_XOR:
+ case CAIRO_OPERATOR_ADD:
+ case CAIRO_OPERATOR_SATURATE:
+ return TRUE;
+ case CAIRO_OPERATOR_OUT:
+ case CAIRO_OPERATOR_IN:
+ case CAIRO_OPERATOR_DEST_IN:
+ case CAIRO_OPERATOR_DEST_ATOP:
+ return FALSE;
+ }
+
+ ASSERT_NOT_REACHED;
+ return FALSE;
+}
+
+/**
+ * _cairo_operator_bounded_by_source:
+ * @op: a #cairo_operator_t
+ *
+ * A bounded operator is one where source pixels of zero
+ * (in all four components, r, g, b and a) effect no change
+ * in the resulting destination image.
+ *
+ * Unbounded operators often require special handling; if you, for
+ * example, copy a surface with the SOURCE operator, the effect
+ * extends past the bounding box of the source surface.
+ *
+ * Return value: %TRUE if the operator is bounded by the source operand
+ **/
+cairo_bool_t
+_cairo_operator_bounded_by_source (cairo_operator_t op)
+{
+ switch (op) {
+ case CAIRO_OPERATOR_OVER:
+ case CAIRO_OPERATOR_ATOP:
+ case CAIRO_OPERATOR_DEST:
+ case CAIRO_OPERATOR_DEST_OVER:
+ case CAIRO_OPERATOR_DEST_OUT:
+ case CAIRO_OPERATOR_XOR:
+ case CAIRO_OPERATOR_ADD:
+ case CAIRO_OPERATOR_SATURATE:
+ return TRUE;
+ case CAIRO_OPERATOR_CLEAR:
+ case CAIRO_OPERATOR_SOURCE:
+ case CAIRO_OPERATOR_OUT:
+ case CAIRO_OPERATOR_IN:
+ case CAIRO_OPERATOR_DEST_IN:
+ case CAIRO_OPERATOR_DEST_ATOP:
+ return FALSE;
+ }
+
+ ASSERT_NOT_REACHED;
+ return FALSE;
+}
+
+
+void
+_cairo_restrict_value (double *value, double min, double max)
+{
+ if (*value < min)
+ *value = min;
+ else if (*value > max)
+ *value = max;
+}
+
+/* This function is identical to the C99 function lround(), except that it
+ * performs arithmetic rounding (instead of away-from-zero rounding) and
+ * has a valid input range of (INT_MIN, INT_MAX] instead of
+ * [INT_MIN, INT_MAX]. It is much faster on both x86 and FPU-less systems
+ * than other commonly used methods for rounding (lround, round, rint, lrint
+ * or float (d + 0.5)).
+ *
+ * The reason why this function is much faster on x86 than other
+ * methods is due to the fact that it avoids the fldcw instruction.
+ * This instruction incurs a large performance penalty on modern Intel
+ * processors due to how it prevents efficient instruction pipelining.
+ *
+ * The reason why this function is much faster on FPU-less systems is for
+ * an entirely different reason. All common rounding methods involve multiple
+ * floating-point operations. Each one of these operations has to be
+ * emulated in software, which adds up to be a large performance penalty.
+ * This function doesn't perform any floating-point calculations, and thus
+ * avoids this penalty.
+ */
+int
+_cairo_lround (double d)
+{
+ uint32_t top, shift_amount, output;
+ union {
+ double d;
+ uint64_t ui64;
+ uint32_t ui32[2];
+ } u;
+
+ u.d = d;
+
+ /* If the integer word order doesn't match the float word order, we swap
+ * the words of the input double. This is needed because we will be
+ * treating the whole double as a 64-bit unsigned integer. Notice that we
+ * use WORDS_BIGENDIAN to detect the integer word order, which isn't
+ * exactly correct because WORDS_BIGENDIAN refers to byte order, not word
+ * order. Thus, we are making the assumption that the byte order is the
+ * same as the integer word order which, on the modern machines that we
+ * care about, is OK.
+ */
+#if ( defined(FLOAT_WORDS_BIGENDIAN) && !defined(WORDS_BIGENDIAN)) || \
+ (!defined(FLOAT_WORDS_BIGENDIAN) && defined(WORDS_BIGENDIAN))
+ {
+ uint32_t temp = u.ui32[0];
+ u.ui32[0] = u.ui32[1];
+ u.ui32[1] = temp;
+ }
+#endif
+
+#ifdef WORDS_BIGENDIAN
+ #define MSW (0) /* Most Significant Word */
+ #define LSW (1) /* Least Significant Word */
+#else
+ #define MSW (1)
+ #define LSW (0)
+#endif
+
+ /* By shifting the most significant word of the input double to the
+ * right 20 places, we get the very "top" of the double where the exponent
+ * and sign bit lie.
+ */
+ top = u.ui32[MSW] >> 20;
+
+ /* Here, we calculate how much we have to shift the mantissa to normalize
+ * it to an integer value. We extract the exponent "top" by masking out the
+ * sign bit, then we calculate the shift amount by subtracting the exponent
+ * from the bias. Notice that the correct bias for 64-bit doubles is
+ * actually 1075, but we use 1053 instead for two reasons:
+ *
+ * 1) To perform rounding later on, we will first need the target
+ * value in a 31.1 fixed-point format. Thus, the bias needs to be one
+ * less: (1075 - 1: 1074).
+ *
+ * 2) To avoid shifting the mantissa as a full 64-bit integer (which is
+ * costly on certain architectures), we break the shift into two parts.
+ * First, the upper and lower parts of the mantissa are shifted
+ * individually by a constant amount that all valid inputs will require
+ * at the very least. This amount is chosen to be 21, because this will
+ * allow the two parts of the mantissa to later be combined into a
+ * single 32-bit representation, on which the remainder of the shift
+ * will be performed. Thus, we decrease the bias by an additional 21:
+ * (1074 - 21: 1053).
+ */
+ shift_amount = 1053 - (top & 0x7FF);
+
+ /* We are done with the exponent portion in "top", so here we shift it off
+ * the end.
+ */
+ top >>= 11;
+
+ /* Before we perform any operations on the mantissa, we need to OR in
+ * the implicit 1 at the top (see the IEEE-754 spec). We needn't mask
+ * off the sign bit nor the exponent bits because these higher bits won't
+ * make a bit of difference in the rest of our calculations.
+ */
+ u.ui32[MSW] |= 0x100000;
+
+ /* If the input double is negative, we have to decrease the mantissa
+ * by a hair. This is an important part of performing arithmetic rounding,
+ * as negative numbers must round towards positive infinity in the
+ * halfwase case of -x.5. Since "top" contains only the sign bit at this
+ * point, we can just decrease the mantissa by the value of "top".
+ */
+ u.ui64 -= top;
+
+ /* By decrementing "top", we create a bitmask with a value of either
+ * 0x0 (if the input was negative) or 0xFFFFFFFF (if the input was positive
+ * and thus the unsigned subtraction underflowed) that we'll use later.
+ */
+ top--;
+
+ /* Here, we shift the mantissa by the constant value as described above.
+ * We can emulate a 64-bit shift right by 21 through shifting the top 32
+ * bits left 11 places and ORing in the bottom 32 bits shifted 21 places
+ * to the right. Both parts of the mantissa are now packed into a single
+ * 32-bit integer. Although we severely truncate the lower part in the
+ * process, we still have enough significant bits to perform the conversion
+ * without error (for all valid inputs).
+ */
+ output = (u.ui32[MSW] << 11) | (u.ui32[LSW] >> 21);
+
+ /* Next, we perform the shift that converts the X.Y fixed-point number
+ * currently found in "output" to the desired 31.1 fixed-point format
+ * needed for the following rounding step. It is important to consider
+ * all possible values for "shift_amount" at this point:
+ *
+ * - {shift_amount < 0} Since shift_amount is an unsigned integer, it
+ * really can't have a value less than zero. But, if the shift_amount
+ * calculation above caused underflow (which would happen with
+ * input > INT_MAX or input <= INT_MIN) then shift_amount will now be
+ * a very large number, and so this shift will result in complete
+ * garbage. But that's OK, as the input was out of our range, so our
+ * output is undefined.
+ *
+ * - {shift_amount > 31} If the magnitude of the input was very small
+ * (i.e. |input| << 1.0), shift_amount will have a value greater than
+ * 31. Thus, this shift will also result in garbage. After performing
+ * the shift, we will zero-out "output" if this is the case.
+ *
+ * - {0 <= shift_amount < 32} In this case, the shift will properly convert
+ * the mantissa into a 31.1 fixed-point number.
+ */
+ output >>= shift_amount;
+
+ /* This is where we perform rounding with the 31.1 fixed-point number.
+ * Since what we're after is arithmetic rounding, we simply add the single
+ * fractional bit into the integer part of "output", and just keep the
+ * integer part.
+ */
+ output = (output >> 1) + (output & 1);
+
+ /* Here, we zero-out the result if the magnitude if the input was very small
+ * (as explained in the section above). Notice that all input out of the
+ * valid range is also caught by this condition, which means we produce 0
+ * for all invalid input, which is a nice side effect.
+ *
+ * The most straightforward way to do this would be:
+ *
+ * if (shift_amount > 31)
+ * output = 0;
+ *
+ * But we can use a little trick to avoid the potential branch. The
+ * expression (shift_amount > 31) will be either 1 or 0, which when
+ * decremented will be either 0x0 or 0xFFFFFFFF (unsigned underflow),
+ * which can be used to conditionally mask away all the bits in "output"
+ * (in the 0x0 case), effectively zeroing it out. Certain, compilers would
+ * have done this for us automatically.
+ */
+ output &= ((shift_amount > 31) - 1);
+
+ /* If the input double was a negative number, then we have to negate our
+ * output. The most straightforward way to do this would be:
+ *
+ * if (!top)
+ * output = -output;
+ *
+ * as "top" at this point is either 0x0 (if the input was negative) or
+ * 0xFFFFFFFF (if the input was positive). But, we can use a trick to
+ * avoid the branch. Observe that the following snippet of code has the
+ * same effect as the reference snippet above:
+ *
+ * if (!top)
+ * output = 0 - output;
+ * else
+ * output = output - 0;
+ *
+ * Armed with the bitmask found in "top", we can condense the two statements
+ * into the following:
+ *
+ * output = (output & top) - (output & ~top);
+ *
+ * where, in the case that the input double was negative, "top" will be 0,
+ * and the statement will be equivalent to:
+ *
+ * output = (0) - (output);
+ *
+ * and if the input double was positive, "top" will be 0xFFFFFFFF, and the
+ * statement will be equivalent to:
+ *
+ * output = (output) - (0);
+ *
+ * Which, as pointed out earlier, is equivalent to the original reference
+ * snippet.
+ */
+ output = (output & top) - (output & ~top);
+
+ return output;
+#undef MSW
+#undef LSW
+}
diff --git a/src/cairo.c b/src/cairo.c
index 7f5e1ec..68b5d55 100644
--- a/src/cairo.c
+++ b/src/cairo.c
@@ -3616,290 +3616,3 @@ cairo_status (cairo_t *cr)
return cr->status;
}
slim_hidden_def (cairo_status);
-
-/**
- * cairo_status_to_string:
- * @status: a cairo status
- *
- * Provides a human-readable description of a #cairo_status_t.
- *
- * Returns: a string representation of the status
- */
-const char *
-cairo_status_to_string (cairo_status_t status)
-{
- switch (status) {
- case CAIRO_STATUS_SUCCESS:
- return "success";
- case CAIRO_STATUS_NO_MEMORY:
- return "out of memory";
- case CAIRO_STATUS_INVALID_RESTORE:
- return "cairo_restore without matching cairo_save";
- case CAIRO_STATUS_INVALID_POP_GROUP:
- return "cairo_pop_group without matching cairo_push_group";
- case CAIRO_STATUS_NO_CURRENT_POINT:
- return "no current point defined";
- case CAIRO_STATUS_INVALID_MATRIX:
- return "invalid matrix (not invertible)";
- case CAIRO_STATUS_INVALID_STATUS:
- return "invalid value for an input cairo_status_t";
- case CAIRO_STATUS_NULL_POINTER:
- return "NULL pointer";
- case CAIRO_STATUS_INVALID_STRING:
- return "input string not valid UTF-8";
- case CAIRO_STATUS_INVALID_PATH_DATA:
- return "input path data not valid";
- case CAIRO_STATUS_READ_ERROR:
- return "error while reading from input stream";
- case CAIRO_STATUS_WRITE_ERROR:
- return "error while writing to output stream";
- case CAIRO_STATUS_SURFACE_FINISHED:
- return "the target surface has been finished";
- case CAIRO_STATUS_SURFACE_TYPE_MISMATCH:
- return "the surface type is not appropriate for the operation";
- case CAIRO_STATUS_PATTERN_TYPE_MISMATCH:
- return "the pattern type is not appropriate for the operation";
- case CAIRO_STATUS_INVALID_CONTENT:
- return "invalid value for an input cairo_content_t";
- case CAIRO_STATUS_INVALID_FORMAT:
- return "invalid value for an input cairo_format_t";
- case CAIRO_STATUS_INVALID_VISUAL:
- return "invalid value for an input Visual*";
- case CAIRO_STATUS_FILE_NOT_FOUND:
- return "file not found";
- case CAIRO_STATUS_INVALID_DASH:
- return "invalid value for a dash setting";
- case CAIRO_STATUS_INVALID_DSC_COMMENT:
- return "invalid value for a DSC comment";
- case CAIRO_STATUS_INVALID_INDEX:
- return "invalid index passed to getter";
- case CAIRO_STATUS_CLIP_NOT_REPRESENTABLE:
- return "clip region not representable in desired format";
- case CAIRO_STATUS_TEMP_FILE_ERROR:
- return "error creating or writing to a temporary file";
- case CAIRO_STATUS_INVALID_STRIDE:
- return "invalid value for stride";
- }
-
- return "<unknown error status>";
-}
-
-void
-_cairo_restrict_value (double *value, double min, double max)
-{
- if (*value < min)
- *value = min;
- else if (*value > max)
- *value = max;
-}
-
-/* This function is identical to the C99 function lround(), except that it
- * performs arithmetic rounding (instead of away-from-zero rounding) and
- * has a valid input range of (INT_MIN, INT_MAX] instead of
- * [INT_MIN, INT_MAX]. It is much faster on both x86 and FPU-less systems
- * than other commonly used methods for rounding (lround, round, rint, lrint
- * or float (d + 0.5)).
- *
- * The reason why this function is much faster on x86 than other
- * methods is due to the fact that it avoids the fldcw instruction.
- * This instruction incurs a large performance penalty on modern Intel
- * processors due to how it prevents efficient instruction pipelining.
- *
- * The reason why this function is much faster on FPU-less systems is for
- * an entirely different reason. All common rounding methods involve multiple
- * floating-point operations. Each one of these operations has to be
- * emulated in software, which adds up to be a large performance penalty.
- * This function doesn't perform any floating-point calculations, and thus
- * avoids this penalty.
- */
-int
-_cairo_lround (double d)
-{
- uint32_t top, shift_amount, output;
- union {
- double d;
- uint64_t ui64;
- uint32_t ui32[2];
- } u;
-
- u.d = d;
-
- /* If the integer word order doesn't match the float word order, we swap
- * the words of the input double. This is needed because we will be
- * treating the whole double as a 64-bit unsigned integer. Notice that we
- * use WORDS_BIGENDIAN to detect the integer word order, which isn't
- * exactly correct because WORDS_BIGENDIAN refers to byte order, not word
- * order. Thus, we are making the assumption that the byte order is the
- * same as the integer word order which, on the modern machines that we
- * care about, is OK.
- */
-#if ( defined(FLOAT_WORDS_BIGENDIAN) && !defined(WORDS_BIGENDIAN)) || \
- (!defined(FLOAT_WORDS_BIGENDIAN) && defined(WORDS_BIGENDIAN))
- {
- uint32_t temp = u.ui32[0];
- u.ui32[0] = u.ui32[1];
- u.ui32[1] = temp;
- }
-#endif
-
-#ifdef WORDS_BIGENDIAN
- #define MSW (0) /* Most Significant Word */
- #define LSW (1) /* Least Significant Word */
-#else
- #define MSW (1)
- #define LSW (0)
-#endif
-
- /* By shifting the most significant word of the input double to the
- * right 20 places, we get the very "top" of the double where the exponent
- * and sign bit lie.
- */
- top = u.ui32[MSW] >> 20;
-
- /* Here, we calculate how much we have to shift the mantissa to normalize
- * it to an integer value. We extract the exponent "top" by masking out the
- * sign bit, then we calculate the shift amount by subtracting the exponent
- * from the bias. Notice that the correct bias for 64-bit doubles is
- * actually 1075, but we use 1053 instead for two reasons:
- *
- * 1) To perform rounding later on, we will first need the target
- * value in a 31.1 fixed-point format. Thus, the bias needs to be one
- * less: (1075 - 1: 1074).
- *
- * 2) To avoid shifting the mantissa as a full 64-bit integer (which is
- * costly on certain architectures), we break the shift into two parts.
- * First, the upper and lower parts of the mantissa are shifted
- * individually by a constant amount that all valid inputs will require
- * at the very least. This amount is chosen to be 21, because this will
- * allow the two parts of the mantissa to later be combined into a
- * single 32-bit representation, on which the remainder of the shift
- * will be performed. Thus, we decrease the bias by an additional 21:
- * (1074 - 21: 1053).
- */
- shift_amount = 1053 - (top & 0x7FF);
-
- /* We are done with the exponent portion in "top", so here we shift it off
- * the end.
- */
- top >>= 11;
-
- /* Before we perform any operations on the mantissa, we need to OR in
- * the implicit 1 at the top (see the IEEE-754 spec). We needn't mask
- * off the sign bit nor the exponent bits because these higher bits won't
- * make a bit of difference in the rest of our calculations.
- */
- u.ui32[MSW] |= 0x100000;
-
- /* If the input double is negative, we have to decrease the mantissa
- * by a hair. This is an important part of performing arithmetic rounding,
- * as negative numbers must round towards positive infinity in the
- * halfwase case of -x.5. Since "top" contains only the sign bit at this
- * point, we can just decrease the mantissa by the value of "top".
- */
- u.ui64 -= top;
-
- /* By decrementing "top", we create a bitmask with a value of either
- * 0x0 (if the input was negative) or 0xFFFFFFFF (if the input was positive
- * and thus the unsigned subtraction underflowed) that we'll use later.
- */
- top--;
-
- /* Here, we shift the mantissa by the constant value as described above.
- * We can emulate a 64-bit shift right by 21 through shifting the top 32
- * bits left 11 places and ORing in the bottom 32 bits shifted 21 places
- * to the right. Both parts of the mantissa are now packed into a single
- * 32-bit integer. Although we severely truncate the lower part in the
- * process, we still have enough significant bits to perform the conversion
- * without error (for all valid inputs).
- */
- output = (u.ui32[MSW] << 11) | (u.ui32[LSW] >> 21);
-
- /* Next, we perform the shift that converts the X.Y fixed-point number
- * currently found in "output" to the desired 31.1 fixed-point format
- * needed for the following rounding step. It is important to consider
- * all possible values for "shift_amount" at this point:
- *
- * - {shift_amount < 0} Since shift_amount is an unsigned integer, it
- * really can't have a value less than zero. But, if the shift_amount
- * calculation above caused underflow (which would happen with
- * input > INT_MAX or input <= INT_MIN) then shift_amount will now be
- * a very large number, and so this shift will result in complete
- * garbage. But that's OK, as the input was out of our range, so our
- * output is undefined.
- *
- * - {shift_amount > 31} If the magnitude of the input was very small
- * (i.e. |input| << 1.0), shift_amount will have a value greater than
- * 31. Thus, this shift will also result in garbage. After performing
- * the shift, we will zero-out "output" if this is the case.
- *
- * - {0 <= shift_amount < 32} In this case, the shift will properly convert
- * the mantissa into a 31.1 fixed-point number.
- */
- output >>= shift_amount;
-
- /* This is where we perform rounding with the 31.1 fixed-point number.
- * Since what we're after is arithmetic rounding, we simply add the single
- * fractional bit into the integer part of "output", and just keep the
- * integer part.
- */
- output = (output >> 1) + (output & 1);
-
- /* Here, we zero-out the result if the magnitude if the input was very small
- * (as explained in the section above). Notice that all input out of the
- * valid range is also caught by this condition, which means we produce 0
- * for all invalid input, which is a nice side effect.
- *
- * The most straightforward way to do this would be:
- *
- * if (shift_amount > 31)
- * output = 0;
- *
- * But we can use a little trick to avoid the potential branch. The
- * expression (shift_amount > 31) will be either 1 or 0, which when
- * decremented will be either 0x0 or 0xFFFFFFFF (unsigned underflow),
- * which can be used to conditionally mask away all the bits in "output"
- * (in the 0x0 case), effectively zeroing it out. Certain, compilers would
- * have done this for us automatically.
- */
- output &= ((shift_amount > 31) - 1);
-
- /* If the input double was a negative number, then we have to negate our
- * output. The most straightforward way to do this would be:
- *
- * if (!top)
- * output = -output;
- *
- * as "top" at this point is either 0x0 (if the input was negative) or
- * 0xFFFFFFFF (if the input was positive). But, we can use a trick to
- * avoid the branch. Observe that the following snippet of code has the
- * same effect as the reference snippet above:
- *
- * if (!top)
- * output = 0 - output;
- * else
- * output = output - 0;
- *
- * Armed with the bitmask found in "top", we can condense the two statements
- * into the following:
- *
- * output = (output & top) - (output & ~top);
- *
- * where, in the case that the input double was negative, "top" will be 0,
- * and the statement will be equivalent to:
- *
- * output = (0) - (output);
- *
- * and if the input double was positive, "top" will be 0xFFFFFFFF, and the
- * statement will be equivalent to:
- *
- * output = (output) - (0);
- *
- * Which, as pointed out earlier, is equivalent to the original reference
- * snippet.
- */
- output = (output & top) - (output & ~top);
-
- return output;
-#undef MSW
-#undef LSW
-}
More information about the cairo-commit
mailing list