From 7cde4dbcd750dabc74185da058844d43928fa206 Mon Sep 17 00:00:00 2001 From: Jason Ekstrand Date: Fri, 5 Oct 2018 20:29:31 -0500 Subject: [PATCH] util: Generalize fast integer division to be variable bit-width MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit There's nothing inherently fixed-width in the code. All that's required to generalize it is to make everything internally 64-bit and pass UINT_BITS in as a parameter to util_compute_fast_[us]div_info. With that, it can now handle 8, 16, 32, and 64-bit integer division by a constant. We also add support for division by 1 and by other powers of 2. This is useful if you want to divide by a uniform value in a shader where you have the opportunity to adjust the uniform on the CPU before passing it in. Reviewed-by: Marek Olšák --- src/util/fast_idiv_by_const.c | 62 +++++++++++++++++------------------ src/util/fast_idiv_by_const.h | 22 +++++-------- 2 files changed, 39 insertions(+), 45 deletions(-) diff --git a/src/util/fast_idiv_by_const.c b/src/util/fast_idiv_by_const.c index 0bc9b60878b..65a9e640789 100644 --- a/src/util/fast_idiv_by_const.c +++ b/src/util/fast_idiv_by_const.c @@ -42,22 +42,16 @@ #include #include -/* uint_t and sint_t can be replaced by different integer types and the code - * will work as-is. The only requirement is that sizeof(uintN) == sizeof(intN). - */ - struct util_fast_udiv_info -util_compute_fast_udiv_info(uint_t D, unsigned num_bits) +util_compute_fast_udiv_info(uint64_t D, unsigned num_bits, unsigned UINT_BITS) { - /* The numerator must fit in a uint_t */ - assert(num_bits > 0 && num_bits <= sizeof(uint_t) * CHAR_BIT); + /* The numerator must fit in a uint64_t */ + assert(num_bits > 0 && num_bits <= UINT_BITS); assert(D != 0); /* The eventual result */ struct util_fast_udiv_info result; - /* Bits in a uint_t */ - const unsigned UINT_BITS = sizeof(uint_t) * CHAR_BIT; /* The extra shift implicit in the difference between UINT_BITS and num_bits */ @@ -66,23 +60,23 @@ util_compute_fast_udiv_info(uint_t D, unsigned num_bits) /* The initial power of 2 is one less than the first one that can possibly * work. */ - const uint_t initial_power_of_2 = (uint_t)1 << (UINT_BITS-1); + const uint64_t initial_power_of_2 = (uint64_t)1 << (UINT_BITS-1); /* The remainder and quotient of our power of 2 divided by d */ - uint_t quotient = initial_power_of_2 / D; - uint_t remainder = initial_power_of_2 % D; + uint64_t quotient = initial_power_of_2 / D; + uint64_t remainder = initial_power_of_2 % D; /* ceil(log_2 D) */ unsigned ceil_log_2_D; /* The magic info for the variant "round down" algorithm */ - uint_t down_multiplier = 0; + uint64_t down_multiplier = 0; unsigned down_exponent = 0; int has_magic_down = 0; /* Compute ceil(log_2 D) */ ceil_log_2_D = 0; - uint_t tmp; + uint64_t tmp; for (tmp = D; tmp > 0; tmp >>= 1) ceil_log_2_D += 1; @@ -110,14 +104,14 @@ util_compute_fast_udiv_info(uint_t D, unsigned num_bits) * so the check for >= ceil_log_2_D is critical. */ if ((exponent + extra_shift >= ceil_log_2_D) || - (D - remainder) <= ((uint_t)1 << (exponent + extra_shift))) + (D - remainder) <= ((uint64_t)1 << (exponent + extra_shift))) break; /* Set magic_down if we have not set it yet and this exponent works for * the round_down algorithm */ if (!has_magic_down && - remainder <= ((uint_t)1 << (exponent + extra_shift))) { + remainder <= ((uint64_t)1 << (exponent + extra_shift))) { has_magic_down = 1; down_multiplier = quotient; down_exponent = exponent; @@ -140,12 +134,13 @@ util_compute_fast_udiv_info(uint_t D, unsigned num_bits) } else { /* Even divisor, so use a prefix-shifted dividend */ unsigned pre_shift = 0; - uint_t shifted_D = D; + uint64_t shifted_D = D; while ((shifted_D & 1) == 0) { shifted_D >>= 1; pre_shift += 1; } - result = util_compute_fast_udiv_info(shifted_D, num_bits - pre_shift); + result = util_compute_fast_udiv_info(shifted_D, num_bits - pre_shift, + UINT_BITS); /* expect no increment or pre_shift in this path */ assert(result.increment == 0 && result.pre_shift == 0); result.pre_shift = pre_shift; @@ -153,8 +148,14 @@ util_compute_fast_udiv_info(uint_t D, unsigned num_bits) return result; } +static inline int64_t +sign_extend(int64_t x, unsigned SINT_BITS) +{ + return (x << (64 - SINT_BITS)) >> (64 - SINT_BITS); +} + struct util_fast_sdiv_info -util_compute_fast_sdiv_info(sint_t D) +util_compute_fast_sdiv_info(int64_t D, unsigned SINT_BITS) { /* D must not be zero. */ assert(D != 0); @@ -164,33 +165,30 @@ util_compute_fast_sdiv_info(sint_t D) /* Our result */ struct util_fast_sdiv_info result; - /* Bits in an sint_t */ - const unsigned SINT_BITS = sizeof(sint_t) * CHAR_BIT; - /* Absolute value of D (we know D is not the most negative value since * that's a power of 2) */ - const uint_t abs_d = (D < 0 ? -D : D); + const uint64_t abs_d = (D < 0 ? -D : D); /* The initial power of 2 is one less than the first one that can possibly * work */ /* "two31" in Warren */ unsigned exponent = SINT_BITS - 1; - const uint_t initial_power_of_2 = (uint_t)1 << exponent; + const uint64_t initial_power_of_2 = (uint64_t)1 << exponent; /* Compute the absolute value of our "test numerator," * which is the largest dividend whose remainder with d is d-1. * This is called anc in Warren. */ - const uint_t tmp = initial_power_of_2 + (D < 0); - const uint_t abs_test_numer = tmp - 1 - tmp % abs_d; + const uint64_t tmp = initial_power_of_2 + (D < 0); + const uint64_t abs_test_numer = tmp - 1 - tmp % abs_d; /* Initialize our quotients and remainders (q1, r1, q2, r2 in Warren) */ - uint_t quotient1 = initial_power_of_2 / abs_test_numer; - uint_t remainder1 = initial_power_of_2 % abs_test_numer; - uint_t quotient2 = initial_power_of_2 / abs_d; - uint_t remainder2 = initial_power_of_2 % abs_d; - uint_t delta; + uint64_t quotient1 = initial_power_of_2 / abs_test_numer; + uint64_t remainder1 = initial_power_of_2 % abs_test_numer; + uint64_t quotient2 = initial_power_of_2 / abs_d; + uint64_t remainder2 = initial_power_of_2 % abs_d; + uint64_t delta; /* Begin our loop */ do { @@ -217,7 +215,7 @@ util_compute_fast_sdiv_info(sint_t D) delta = abs_d - remainder2; } while (quotient1 < delta || (quotient1 == delta && remainder1 == 0)); - result.multiplier = quotient2 + 1; + result.multiplier = sign_extend(quotient2 + 1, SINT_BITS); if (D < 0) result.multiplier = -result.multiplier; result.shift = exponent - SINT_BITS; return result; diff --git a/src/util/fast_idiv_by_const.h b/src/util/fast_idiv_by_const.h index 1ba9f9a20b8..231311f84be 100644 --- a/src/util/fast_idiv_by_const.h +++ b/src/util/fast_idiv_by_const.h @@ -36,10 +36,6 @@ extern "C" { #endif -/* You can set these to different types to get different precision. */ -typedef int32_t sint_t; -typedef uint32_t uint_t; - /* Computes "magic info" for performing signed division by a fixed integer D. * The type 'sint_t' is assumed to be defined as a signed integer type large * enough to hold both the dividend and the divisor. @@ -68,19 +64,19 @@ typedef uint32_t uint_t; */ struct util_fast_sdiv_info { - sint_t multiplier; /* the "magic number" multiplier */ + int64_t multiplier; /* the "magic number" multiplier */ unsigned shift; /* shift for the dividend after multiplying */ }; struct util_fast_sdiv_info -util_compute_fast_sdiv_info(sint_t D); +util_compute_fast_sdiv_info(int64_t D, unsigned SINT_BITS); /* Computes "magic info" for performing unsigned division by a fixed positive - * integer D. The type 'uint_t' is assumed to be defined as an unsigned - * integer type large enough to hold both the dividend and the divisor. - * num_bits can be set appropriately if n is known to be smaller than - * the largest uint_t; if this is not known then pass - * "(sizeof(uint_t) * CHAR_BIT)" for num_bits. + * integer D. UINT_BITS is the bit size at which the final "magic" + * calculation will be performed; it is assumed to be large enough to hold + * both the dividand and the divisor. num_bits can be set appropriately if n + * is known to be smaller than calc_bits; if this is not known then UINT_BITS + * for num_bits. * * Assume we have a hardware register of width UINT_BITS, a known constant D * which is not zero and not a power of 2, and a variable n of width num_bits @@ -120,7 +116,7 @@ util_compute_fast_sdiv_info(sint_t D); */ struct util_fast_udiv_info { - uint_t multiplier; /* the "magic number" multiplier */ + uint64_t multiplier; /* the "magic number" multiplier */ unsigned pre_shift; /* shift for the dividend before multiplying */ unsigned post_shift; /* shift for the dividend after multiplying */ int increment; /* 0 or 1; if set then increment the numerator, using one of @@ -128,7 +124,7 @@ struct util_fast_udiv_info { }; struct util_fast_udiv_info -util_compute_fast_udiv_info(uint_t D, unsigned num_bits); +util_compute_fast_udiv_info(uint64_t D, unsigned num_bits, unsigned UINT_BITS); /* Below are possible options for dividing by a uniform in a shader where * the divisor is constant but not known at compile time. -- 2.30.2