mirror of
https://gitlab.freedesktop.org/gstreamer/gstreamer.git
synced 2024-12-18 22:36:33 +00:00
gstutils: Refactor gst_util_uint64_scale()
This will later make it possible to provide rounding versions of it without much code duplication. Partially fixes bug #590919.
This commit is contained in:
Kipp Cannon
Sebastian Dröge
parent
824a0b5f5f
commit
3d359729af
1 changed files with 191 additions and 162 deletions
353
gst/gstutils.c
353
gst/gstutils.c
|
|
@ -204,83 +204,19 @@ typedef union
|
|||
} l;
|
||||
} GstUInt64;
|
||||
|
||||
/* based on Hacker's Delight p152 */
|
||||
static guint64
|
||||
gst_util_div128_64 (GstUInt64 c1, GstUInt64 c0, guint64 denom)
|
||||
/* multiply two 64-bit unsigned ints into a 128-bit unsigned int. the high
|
||||
* and low 64 bits of the product are placed in c1 and c0 respectively.
|
||||
* this operation cannot overflow. */
|
||||
static void
|
||||
gst_util_uint64_mul_uint64 (GstUInt64 * c1, GstUInt64 * c0, guint64 arg1,
|
||||
guint64 arg2)
|
||||
{
|
||||
GstUInt64 q1, q0, rhat;
|
||||
GstUInt64 v, cmp1, cmp2;
|
||||
guint s;
|
||||
|
||||
v.ll = denom;
|
||||
|
||||
/* count number of leading zeroes, we know they must be in the high
|
||||
* part of denom since denom > G_MAXUINT32. */
|
||||
s = v.l.high | (v.l.high >> 1);
|
||||
s |= (s >> 2);
|
||||
s |= (s >> 4);
|
||||
s |= (s >> 8);
|
||||
s = ~(s | (s >> 16));
|
||||
s = s - ((s >> 1) & 0x55555555);
|
||||
s = (s & 0x33333333) + ((s >> 2) & 0x33333333);
|
||||
s = (s + (s >> 4)) & 0x0f0f0f0f;
|
||||
s += (s >> 8);
|
||||
s = (s + (s >> 16)) & 0x3f;
|
||||
|
||||
if (s > 0) {
|
||||
/* normalize divisor and dividend */
|
||||
v.ll <<= s;
|
||||
c1.ll = (c1.ll << s) | (c0.l.high >> (32 - s));
|
||||
c0.ll <<= s;
|
||||
}
|
||||
|
||||
q1.ll = c1.ll / v.l.high;
|
||||
rhat.ll = c1.ll - q1.ll * v.l.high;
|
||||
|
||||
cmp1.l.high = rhat.l.low;
|
||||
cmp1.l.low = c0.l.high;
|
||||
cmp2.ll = q1.ll * v.l.low;
|
||||
|
||||
while (q1.l.high || cmp2.ll > cmp1.ll) {
|
||||
q1.ll--;
|
||||
rhat.ll += v.l.high;
|
||||
if (rhat.l.high)
|
||||
break;
|
||||
cmp1.l.high = rhat.l.low;
|
||||
cmp2.ll -= v.l.low;
|
||||
}
|
||||
c1.l.high = c1.l.low;
|
||||
c1.l.low = c0.l.high;
|
||||
c1.ll -= q1.ll * v.ll;
|
||||
q0.ll = c1.ll / v.l.high;
|
||||
rhat.ll = c1.ll - q0.ll * v.l.high;
|
||||
|
||||
cmp1.l.high = rhat.l.low;
|
||||
cmp1.l.low = c0.l.low;
|
||||
cmp2.ll = q0.ll * v.l.low;
|
||||
|
||||
while (q0.l.high || cmp2.ll > cmp1.ll) {
|
||||
q0.ll--;
|
||||
rhat.ll += v.l.high;
|
||||
if (rhat.l.high)
|
||||
break;
|
||||
cmp1.l.high = rhat.l.low;
|
||||
cmp2.ll -= v.l.low;
|
||||
}
|
||||
q0.l.high += q1.l.low;
|
||||
|
||||
return q0.ll;
|
||||
}
|
||||
|
||||
static guint64
|
||||
gst_util_uint64_scale_int64_unchecked (guint64 val, guint64 num, guint64 denom)
|
||||
{
|
||||
GstUInt64 a0, a1, b0, b1, c0, ct, c1, result;
|
||||
GstUInt64 a1, b0;
|
||||
GstUInt64 v, n;
|
||||
|
||||
/* prepare input */
|
||||
v.ll = val;
|
||||
n.ll = num;
|
||||
v.ll = arg1;
|
||||
n.ll = arg2;
|
||||
|
||||
/* do 128 bits multiply
|
||||
* nh nl
|
||||
|
|
@ -291,79 +227,169 @@ gst_util_uint64_scale_int64_unchecked (guint64 val, guint64 num, guint64 denom)
|
|||
* b0 = vh * nl
|
||||
* b1 = + vh * nh
|
||||
* -------------------
|
||||
* c1,c0
|
||||
* c1h c1l c0h c0l
|
||||
*
|
||||
* "a0" is optimized away, result is stored directly in c0. "b1" is
|
||||
* optimized away, result is stored directly in c1.
|
||||
*/
|
||||
a0.ll = (guint64) v.l.low * n.l.low;
|
||||
c0->ll = (guint64) v.l.low * n.l.low;
|
||||
a1.ll = (guint64) v.l.low * n.l.high;
|
||||
b0.ll = (guint64) v.l.high * n.l.low;
|
||||
b1.ll = (guint64) v.l.high * n.l.high;
|
||||
|
||||
/* and sum together with carry into 128 bits c1, c0 */
|
||||
c0.l.low = a0.l.low;
|
||||
ct.ll = (guint64) a0.l.high + a1.l.low + b0.l.low;
|
||||
c0.l.high = ct.l.low;
|
||||
c1.ll = (guint64) a1.l.high + b0.l.high + ct.l.high + b1.ll;
|
||||
/* add the high word of a0 to the low words of a1 and b0 using c1 as
|
||||
* scrach space to capture the carry. the low word of the result becomes
|
||||
* the final high word of c0 */
|
||||
c1->ll = (guint64) c0->l.high + a1.l.low + b0.l.low;
|
||||
c0->l.high = c1->l.low;
|
||||
|
||||
/* if high bits bigger than denom, we overflow */
|
||||
if (G_UNLIKELY (c1.ll >= denom))
|
||||
goto overflow;
|
||||
/* add the carry from the result above (found in the high word of c1) and
|
||||
* the high words of a1 and b0 to b1, the result is c1. */
|
||||
c1->ll = (guint64) v.l.high * n.l.high + c1->l.high + a1.l.high + b0.l.high;
|
||||
}
|
||||
|
||||
/* shortcut for division by 1, c1.ll should be 0 because of the
|
||||
* overflow check above. */
|
||||
if (denom == 1)
|
||||
return c0.ll;
|
||||
|
||||
/* and 128/64 bits division, result fits 64 bits */
|
||||
if (denom <= G_MAXUINT32) {
|
||||
guint32 den = (guint32) denom;
|
||||
|
||||
/* easy case, (c1,c0)128/(den)32 division */
|
||||
c1.l.high %= den;
|
||||
c1.l.high = c1.ll % den;
|
||||
c1.l.low = c0.l.high;
|
||||
c0.l.high = c1.ll % den;
|
||||
result.l.high = c1.ll / den;
|
||||
result.l.low = c0.ll / den;
|
||||
} else {
|
||||
result.ll = gst_util_div128_64 (c1, c0, denom);
|
||||
/* compute the quotient and remainder of 2^64 / d. returns 0 if the
|
||||
* quotient overflows (meaning d = 1). */
|
||||
static guint64
|
||||
gst_util_two_to_the_64_over_d (guint64 d, guint64 * remainder)
|
||||
{
|
||||
guint64 quotient = G_MAXUINT64 / d;
|
||||
*remainder = G_MAXUINT64 % d + 1;
|
||||
if (*remainder == d) {
|
||||
quotient++;
|
||||
*remainder = 0;
|
||||
}
|
||||
return result.ll;
|
||||
return quotient;
|
||||
}
|
||||
|
||||
overflow:
|
||||
{
|
||||
/* divide a 128-bit unsigned int by a 64-bit unsigned int when we know the
|
||||
* quotient fits into 64 bits. */
|
||||
static guint64
|
||||
gst_util_div128_64 (guint64 c1, guint64 c0, guint64 denom, guint64 * remainder)
|
||||
{
|
||||
/* we are trying to compute
|
||||
*
|
||||
* c1 * 2^64 + c0
|
||||
* --------------
|
||||
* d
|
||||
*
|
||||
* this can be re-written as:
|
||||
*
|
||||
* c1 * 2^64 + c0 2^64 c0
|
||||
* -------------- = c1 * ---- + --
|
||||
* d d d
|
||||
*
|
||||
* ( 2^64 % d ) c0
|
||||
* = c1 * (2^64 // d + ---------) + --
|
||||
* ( d ) d
|
||||
*
|
||||
* c1 * (2^64 % d) + c0
|
||||
* = c1 * (2^64 // d) + --------------------
|
||||
* d
|
||||
*
|
||||
* where "//" indicates the integer quotient and "%" indicates remainder.
|
||||
* note that 2^64 // d != 0 because d fits in 64 bits, and therefore if
|
||||
* c1 != 0 the first term on the right-hand-side is != 0 and therefore
|
||||
* the numerator in the fraction on the right-hand-side must be less than
|
||||
* the numerator in the fraction on the left-hand-side.
|
||||
*
|
||||
* this provides us with an algorithm to compute both the quotient and
|
||||
* remainder iteratively --- essentially a base-2^64 version of long
|
||||
* division. initializing the quotient to 0, the first term on the
|
||||
* right-hand side is computed and added to the quotient (this can't
|
||||
* overflow because we know the final answer fits in 64 bits). the
|
||||
* numerator of the second term is then computed and the high and low
|
||||
* words stored in c1 and c0 respectively. this is repeated until c1 is
|
||||
* 0, at which point the problem has been reduced to computing the
|
||||
* quotient and remainder of a 64-bit unsigned integer (c0) divided by a
|
||||
* 64-bit unsigned integer (denom) which can be completed using regular
|
||||
* integer arithmetic operations.
|
||||
*
|
||||
* note that gst_util_two_to_the_64_over_d() returns 0 if that quotient
|
||||
* overflows. this can only happen if d = 1, but because we know that
|
||||
* our quotient must fit into 64 bits c1 must be 0 when d = 1, so the
|
||||
* algorithm produces the correct result.
|
||||
*/
|
||||
|
||||
guint64 quotient = 0;
|
||||
|
||||
while (c1) {
|
||||
guint64 a;
|
||||
/* add c1 * (2^64 // d) to quotient, store 2^64 % d in a */
|
||||
quotient += c1 * gst_util_two_to_the_64_over_d (denom, &a);
|
||||
/* store the high and low words of c1 * (2^64 % d) in c1 and a
|
||||
* respectively */
|
||||
gst_util_uint64_mul_uint64 ((GstUInt64 *) & c1, (GstUInt64 *) & a, c1, a);
|
||||
/* add a to c0, with a carry into c1 if the result rolls over */
|
||||
if (G_MAXUINT64 - c0 < a)
|
||||
c1++;
|
||||
c0 += a;
|
||||
}
|
||||
|
||||
/* c1 is 0. use regular integer arithmetic with c0 to complete result */
|
||||
*remainder = c0 % denom;
|
||||
return quotient + c0 / denom;
|
||||
}
|
||||
|
||||
/* multiply a 64-bit unsigned int by a 32-bit unsigned int into a 96-bit
|
||||
* unsigned int. the high 64 bits and low 32 bits of the product are
|
||||
* placed in c1 and c0 respectively. this operation cannot overflow. */
|
||||
static void
|
||||
gst_util_uint64_mul_uint32 (GstUInt64 * c1, GstUInt64 * c0, guint64 arg1,
|
||||
guint32 arg2)
|
||||
{
|
||||
GstUInt64 a;
|
||||
|
||||
a.ll = arg1;
|
||||
|
||||
c0->ll = (guint64) a.l.low * arg2;
|
||||
c1->ll = (guint64) a.l.high * arg2 + c0->l.high;
|
||||
c0->l.high = 0;
|
||||
}
|
||||
|
||||
/* divide a 96-bit unsigned int by a 32-bit unsigned int when we know the
|
||||
* quotient fits into 64 bits. the high 64 bits and low 32 bits of the
|
||||
* numerator are expected in c1 and c0 respectively. */
|
||||
static guint64
|
||||
gst_util_div96_32 (guint64 c1, guint64 c0, guint32 denom, guint32 * remainder)
|
||||
{
|
||||
c0 += (c1 % denom) << 32;
|
||||
*remainder = c0 % denom;
|
||||
return ((c1 / denom) << 32) + (c0 / denom);
|
||||
}
|
||||
|
||||
static guint64
|
||||
gst_util_uint64_scale_uint64_unchecked (guint64 val, guint64 num,
|
||||
guint64 denom, guint64 * remainder)
|
||||
{
|
||||
guint64 c1, c0;
|
||||
|
||||
/* compute 128-bit numerator product */
|
||||
gst_util_uint64_mul_uint64 ((GstUInt64 *) & c1, (GstUInt64 *) & c0, val, num);
|
||||
|
||||
/* high word as big as or bigger than denom --> overflow */
|
||||
if (G_UNLIKELY (c1 >= denom))
|
||||
return G_MAXUINT64;
|
||||
}
|
||||
|
||||
/* compute quotient, fits in 64 bits */
|
||||
return gst_util_div128_64 (c1, c0, denom, remainder);
|
||||
}
|
||||
|
||||
static inline guint64
|
||||
gst_util_uint64_scale_int_unchecked (guint64 val, gint num, gint denom)
|
||||
gst_util_uint64_scale_uint32_unchecked (guint64 val, guint32 num,
|
||||
guint32 denom, guint32 * remainder)
|
||||
{
|
||||
GstUInt64 result;
|
||||
GstUInt64 low, high;
|
||||
GstUInt64 c1, c0;
|
||||
|
||||
/* do 96 bits mult/div */
|
||||
low.ll = val;
|
||||
result.ll = ((guint64) low.l.low) * num;
|
||||
high.ll = ((guint64) low.l.high) * num + (result.l.high);
|
||||
/* compute 96-bit numerator product */
|
||||
gst_util_uint64_mul_uint32 (&c1, &c0, val, num);
|
||||
|
||||
low.ll = high.ll / denom;
|
||||
result.l.high = high.ll % denom;
|
||||
result.ll /= denom;
|
||||
|
||||
/* avoid overflow */
|
||||
if (G_UNLIKELY (low.ll + result.l.high > G_MAXUINT32))
|
||||
goto overflow;
|
||||
|
||||
result.l.high += low.l.low;
|
||||
|
||||
return result.ll;
|
||||
|
||||
overflow:
|
||||
{
|
||||
/* high 32 bits as big as or bigger than denom --> overflow */
|
||||
if (G_UNLIKELY (c1.l.high >= denom))
|
||||
return G_MAXUINT64;
|
||||
}
|
||||
}
|
||||
|
||||
/* compute quotient, fits in 64 bits */
|
||||
return gst_util_div96_32 (c1.ll, c0.ll, denom, remainder);
|
||||
}
|
||||
|
||||
/**
|
||||
* gst_util_uint64_scale:
|
||||
|
|
@ -371,16 +397,19 @@ overflow:
|
|||
* @num: the numerator of the scale ratio
|
||||
* @denom: the denominator of the scale ratio
|
||||
*
|
||||
* Scale @val by @num / @denom, trying to avoid overflows.
|
||||
* Scale @val by the rational number @num / @denom, avoiding overflows and
|
||||
* underflows and without loss of precision.
|
||||
*
|
||||
* This function can potentially be very slow if denom > G_MAXUINT32.
|
||||
* This function can potentially be very slow if val and num are both
|
||||
* greater than G_MAXUINT32.
|
||||
*
|
||||
* Returns: @val * @num / @denom, trying to avoid overflows.
|
||||
* In the case of an overflow, this function returns G_MAXUINT64.
|
||||
* Returns: @val * @num / @denom. In the case of an overflow, this
|
||||
* function returns G_MAXUINT64.
|
||||
*/
|
||||
guint64
|
||||
gst_util_uint64_scale (guint64 val, guint64 num, guint64 denom)
|
||||
{
|
||||
guint64 remainder;
|
||||
g_return_val_if_fail (denom != 0, G_MAXUINT64);
|
||||
|
||||
if (G_UNLIKELY (num == 0))
|
||||
|
|
@ -389,27 +418,22 @@ gst_util_uint64_scale (guint64 val, guint64 num, guint64 denom)
|
|||
if (G_UNLIKELY (num == denom))
|
||||
return val;
|
||||
|
||||
/* if the denom is high, we need to do a 64 muldiv */
|
||||
if (G_UNLIKELY (denom > G_MAXINT32))
|
||||
goto do_int64;
|
||||
/* deneom is low --> try to use 96 bit muldiv */
|
||||
if (G_LIKELY (denom <= G_MAXUINT32)) {
|
||||
guint32 remainder;
|
||||
/* num is low --> use 96 bit muldiv */
|
||||
if (G_LIKELY (num <= G_MAXUINT32))
|
||||
return gst_util_uint64_scale_uint32_unchecked (val, (guint32) num,
|
||||
(guint32) denom, &remainder);
|
||||
|
||||
/* if num and denom are low we can do a 32 bit muldiv */
|
||||
if (G_LIKELY (num <= G_MAXINT32))
|
||||
goto do_int32;
|
||||
/* num is high but val is low --> swap and use 96-bit muldiv */
|
||||
if (G_LIKELY (val <= G_MAXUINT32))
|
||||
return gst_util_uint64_scale_uint32_unchecked (num, (guint32) val,
|
||||
(guint32) denom, &remainder);
|
||||
}
|
||||
|
||||
/* val and num are high, we need 64 muldiv */
|
||||
if (G_UNLIKELY (val > G_MAXINT32))
|
||||
goto do_int64;
|
||||
|
||||
/* val is low and num is high, we can swap them and do 32 muldiv */
|
||||
return gst_util_uint64_scale_int_unchecked (num, (gint) val, (gint) denom);
|
||||
|
||||
do_int32:
|
||||
return gst_util_uint64_scale_int_unchecked (val, (gint) num, (gint) denom);
|
||||
|
||||
do_int64:
|
||||
/* to the more heavy implementations... */
|
||||
return gst_util_uint64_scale_int64_unchecked (val, num, denom);
|
||||
/* val is high and num is high --> use 128-bit muldiv */
|
||||
return gst_util_uint64_scale_uint64_unchecked (val, num, denom, &remainder);
|
||||
}
|
||||
|
||||
/**
|
||||
|
|
@ -418,17 +442,17 @@ do_int64:
|
|||
* @num: numerator of the scale factor.
|
||||
* @denom: denominator of the scale factor.
|
||||
*
|
||||
* Scale a guint64 by a factor expressed as a fraction (num/denom), avoiding
|
||||
* overflows and loss of precision.
|
||||
* Scale @val by the rational number @num / @denom, avoiding overflows and
|
||||
* underflows and without loss of precision. @num must be non-negative and
|
||||
* @denom must be positive.
|
||||
*
|
||||
* @num and @denom must be positive integers. @denom cannot be 0.
|
||||
*
|
||||
* Returns: @val * @num / @denom, avoiding overflow and loss of precision.
|
||||
* In the case of an overflow, this function returns G_MAXUINT64.
|
||||
* Returns: @val * @num / @denom. In the case of an overflow, this
|
||||
* function returns G_MAXUINT64.
|
||||
*/
|
||||
guint64
|
||||
gst_util_uint64_scale_int (guint64 val, gint num, gint denom)
|
||||
{
|
||||
guint32 remainder;
|
||||
g_return_val_if_fail (denom > 0, G_MAXUINT64);
|
||||
g_return_val_if_fail (num >= 0, G_MAXUINT64);
|
||||
|
||||
|
|
@ -438,11 +462,16 @@ gst_util_uint64_scale_int (guint64 val, gint num, gint denom)
|
|||
if (G_UNLIKELY (num == denom))
|
||||
return val;
|
||||
|
||||
if (val <= G_MAXUINT32)
|
||||
/* simple case */
|
||||
return val * num / denom;
|
||||
if (val <= G_MAXUINT32) {
|
||||
/* simple case, use two statements to prevent optimizer from screwing
|
||||
* up result. num and denom are not negative so casts are OK */
|
||||
val *= (guint64) num;
|
||||
return val / (guint64) denom;
|
||||
}
|
||||
|
||||
return gst_util_uint64_scale_int_unchecked (val, num, denom);
|
||||
/* num and denom are not negative so casts are OK */
|
||||
return gst_util_uint64_scale_uint32_unchecked (val, (guint32) num,
|
||||
(guint32) denom, &remainder);
|
||||
}
|
||||
|
||||
/**
|
||||
|
|
|
|||
Loading…
Reference in a new issue