mathematics: Extend and edit Doxygen

2 files changed, 110 insertions, 33 deletions

diff --git a/libavutil/avutil.h b/libavutil/avutil.h
index 27e9cf0f67..ed1fbfd449 100644
--- a/libavutil/avutil.h
+++ b/libavutil/avutil.h
@@ -98,7 +98,7 @@
  * @{
  * @}
  *
- * @defgroup lavu_math Maths
+ * @defgroup lavu_math Mathematics
  * @{
  *
  * @}
diff --git a/libavutil/mathematics.h b/libavutil/mathematics.h
index 1a6812fc4b..54901800ba 100644
--- a/libavutil/mathematics.h
+++ b/libavutil/mathematics.h
@@ -18,6 +18,12 @@
  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  */
 
+/**
+ * @file
+ * @addtogroup lavu_math
+ * Mathematical utilities for working with timestamp and time base.
+ */
+
 #ifndef AVUTIL_MATHEMATICS_H
 #define AVUTIL_MATHEMATICS_H
 
@@ -63,84 +69,155 @@
 
 /**
  * @addtogroup lavu_math
+ *
  * @{
  */
 
-
+/**
+ * Rounding methods.
+ */
 enum AVRounding {
     AV_ROUND_ZERO     = 0, ///< Round toward zero.
     AV_ROUND_INF      = 1, ///< Round away from zero.
     AV_ROUND_DOWN     = 2, ///< Round toward -infinity.
     AV_ROUND_UP       = 3, ///< Round toward +infinity.
     AV_ROUND_NEAR_INF = 5, ///< Round to nearest and halfway cases away from zero.
-    AV_ROUND_PASS_MINMAX = 8192, ///< Flag to pass INT64_MIN/MAX through instead of rescaling, this avoids special cases for AV_NOPTS_VALUE
+    /**
+     * Flag telling rescaling functions to pass `INT64_MIN`/`MAX` through
+     * unchanged, avoiding special cases for #AV_NOPTS_VALUE.
+     *
+     * Unlike other values of the enumeration AVRounding, this value is a
+     * bitmask that must be used in conjunction with another value of the
+     * enumeration through a bitwise OR, in order to set behavior for normal
+     * cases.
+     *
+     * @code{.c}
+     * av_rescale_rnd(3, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
+     * // Rescaling 3:
+     * //     Calculating 3 * 1 / 2
+     * //     3 / 2 is rounded up to 2
+     * //     => 2
+     *
+     * av_rescale_rnd(AV_NOPTS_VALUE, 1, 2, AV_ROUND_UP | AV_ROUND_PASS_MINMAX);
+     * // Rescaling AV_NOPTS_VALUE:
+     * //     AV_NOPTS_VALUE == INT64_MIN
+     * //     AV_NOPTS_VALUE is passed through
+     * //     => AV_NOPTS_VALUE
+     * @endcode
+     */
+    AV_ROUND_PASS_MINMAX = 8192,
 };
 
 /**
- * Compute the greatest common divisor of a and b.
+ * Compute the greatest common divisor of two integer operands.
  *
- * @return gcd of a and b up to sign; if a >= 0 and b >= 0, return value is >= 0;
+ * @param a,b Operands
+ * @return GCD of a and b up to sign; if a >= 0 and b >= 0, return value is >= 0;
  * if a == 0 and b == 0, returns 0.
  */
 int64_t av_const av_gcd(int64_t a, int64_t b);
 
 /**
  * Rescale a 64-bit integer with rounding to nearest.
- * A simple a*b/c isn't possible as it can overflow.
+ *
+ * The operation is mathematically equivalent to `a * b / c`, but writing that
+ * directly can overflow.
+ *
+ * This function is equivalent to av_rescale_rnd() with #AV_ROUND_NEAR_INF.
+ *
+ * @see av_rescale_rnd(), av_rescale_q(), av_rescale_q_rnd()
  */
 int64_t av_rescale(int64_t a, int64_t b, int64_t c) av_const;
 
 /**
  * Rescale a 64-bit integer with specified rounding.
- * A simple a*b/c isn't possible as it can overflow.
  *
- * @return rescaled value a, or if AV_ROUND_PASS_MINMAX is set and a is
- *         INT64_MIN or INT64_MAX then a is passed through unchanged.
+ * The operation is mathematically equivalent to `a * b / c`, but writing that
+ * directly can overflow, and does not support different rounding methods.
+ *
+ * @see av_rescale(), av_rescale_q(), av_rescale_q_rnd()
  */
 int64_t av_rescale_rnd(int64_t a, int64_t b, int64_t c, enum AVRounding rnd) av_const;
 
 /**
  * Rescale a 64-bit integer by 2 rational numbers.
+ *
+ * The operation is mathematically equivalent to `a * bq / cq`.
+ *
+ * This function is equivalent to av_rescale_q_rnd() with #AV_ROUND_NEAR_INF.
+ *
+ * @see av_rescale(), av_rescale_rnd(), av_rescale_q_rnd()
  */
 int64_t av_rescale_q(int64_t a, AVRational bq, AVRational cq) av_const;
 
 /**
  * Rescale a 64-bit integer by 2 rational numbers with specified rounding.
  *
- * @return rescaled value a, or if AV_ROUND_PASS_MINMAX is set and a is
- *         INT64_MIN or INT64_MAX then a is passed through unchanged.
+ * The operation is mathematically equivalent to `a * bq / cq`.
+ *
+ * @see av_rescale(), av_rescale_rnd(), av_rescale_q()
  */
 int64_t av_rescale_q_rnd(int64_t a, AVRational bq, AVRational cq,
                          enum AVRounding rnd) av_const;
 
 /**
- * Compare 2 timestamps each in its own timebases.
- * The result of the function is undefined if one of the timestamps
- * is outside the int64_t range when represented in the others timebase.
- * @return -1 if ts_a is before ts_b, 1 if ts_a is after ts_b or 0 if they represent the same position
+ * Compare two timestamps each in its own time base.
+ *
+ * @return One of the following values:
+ *         - -1 if `ts_a` is before `ts_b`
+ *         - 1 if `ts_a` is after `ts_b`
+ *         - 0 if they represent the same position
+ *
+ * @warning
+ * The result of the function is undefined if one of the timestamps is outside
+ * the `int64_t` range when represented in the other's timebase.
  */
 int av_compare_ts(int64_t ts_a, AVRational tb_a, int64_t ts_b, AVRational tb_b);
 
 /**
- * Compare 2 integers modulo mod.
- * That is we compare integers a and b for which only the least
- * significant log2(mod) bits are known.
- *
- * @param mod must be a power of 2
- * @return a negative value if a is smaller than b
- *         a positive value if a is greater than b
- *         0                if a equals          b
+ * Compare the remainders of two integer operands divided by a common divisor.
+ *
+ * In other words, compare the least significant `log2(mod)` bits of integers
+ * `a` and `b`.
+ *
+ * @code{.c}
+ * av_compare_mod(0x11, 0x02, 0x10) < 0 // since 0x11 % 0x10  (0x1) < 0x02 % 0x10  (0x2)
+ * av_compare_mod(0x11, 0x02, 0x20) > 0 // since 0x11 % 0x20 (0x11) > 0x02 % 0x20 (0x02)
+ * @endcode
+ *
+ * @param a,b Operands
+ * @param mod Divisor; must be a power of 2
+ * @return
+ *         - a negative value if `a % mod < b % mod`
+ *         - a positive value if `a % mod > b % mod`
+ *         - zero             if `a % mod == b % mod`
  */
 int64_t av_compare_mod(uint64_t a, uint64_t b, uint64_t mod);
 
 /**
  * Rescale a timestamp while preserving known durations.
  *
- * @param in_ts Input timestamp
- * @param in_tb Input timebase
- * @param fs_tb Duration and *last timebase
- * @param duration duration till the next call
- * @param out_tb Output timebase
+ * This function is designed to be called per audio packet to scale the input
+ * timestamp to a different time base. Compared to a simple av_rescale_q()
+ * call, this function is robust against possible inconsistent frame durations.
+ *
+ * The `last` parameter is a state variable that must be preserved for all
+ * subsequent calls for the same stream. For the first call, `*last` should be
+ * initialized to #AV_NOPTS_VALUE.
+ *
+ * @param[in]     in_tb    Input time base
+ * @param[in]     in_ts    Input timestamp
+ * @param[in]     fs_tb    Duration time base; typically this is finer-grained
+ *                         (greater) than `in_tb` and `out_tb`
+ * @param[in]     duration Duration till the next call to this function (i.e.
+ *                         duration of the current packet/frame)
+ * @param[in,out] last     Pointer to a timestamp expressed in terms of
+ *                         `fs_tb`, acting as a state variable
+ * @param[in]     out_tb   Output timebase
+ * @return        Timestamp expressed in terms of `out_tb`
+ *
+ * @note In the context of this function, "duration" is in term of samples, not
+ *       seconds.
  */
 int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int duration, int64_t *last, AVRational out_tb);
 
@@ -150,15 +227,15 @@ int64_t av_rescale_delta(AVRational in_tb, int64_t in_ts,  AVRational fs_tb, int
  * This function guarantees that when the same value is repeatly added that
  * no accumulation of rounding errors occurs.
  *
- * @param ts Input timestamp
- * @param ts_tb Input timestamp timebase
- * @param inc value to add to ts
- * @param inc_tb inc timebase
+ * @param[in] ts     Input timestamp
+ * @param[in] ts_tb  Input timestamp time base
+ * @param[in] inc    Value to be added
+ * @param[in] inc_tb Time base of `inc`
  */
 int64_t av_add_stable(AVRational ts_tb, int64_t ts, AVRational inc_tb, int64_t inc);
 
 
-    /**
+/**
  * @}
  */