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