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/*
* Copyright © 2018 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice (including the next
* paragraph) shall be included in all copies or substantial portions of the
* Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
* IN THE SOFTWARE.
*/
#ifndef FAST_IDIV_BY_CONST_H
#define FAST_IDIV_BY_CONST_H
/* Imported from:
* https://raw.githubusercontent.com/ridiculousfish/libdivide/master/divide_by_constants_codegen_reference.c
*/
#include <inttypes.h>
#include <limits.h>
#include <assert.h>
#ifdef __cplusplus
extern "C" {
#endif
/* 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.
* Here >> is arithmetic (signed) shift, and >>> is logical shift.
*
* To emit code for n/d, rounding towards zero, use the following sequence:
*
* m = compute_signed_magic_info(D)
* emit("result = (m.multiplier * n) >> SINT_BITS");
* if d > 0 and m.multiplier < 0: emit("result += n")
* if d < 0 and m.multiplier > 0: emit("result -= n")
* if m.post_shift > 0: emit("result >>= m.shift")
* emit("result += (result < 0)")
*
* The shifts by SINT_BITS may be "free" if the high half of the full multiply
* is put in a separate register.
*
* The final add can of course be implemented via the sign bit, e.g.
* result += (result >>> (SINT_BITS - 1))
* or
* result -= (result >> (SINT_BITS - 1))
*
* This code is heavily indebted to Hacker's Delight by Henry Warren.
* See http://www.hackersdelight.org/HDcode/magic.c.txt
* Used with permission from http://www.hackersdelight.org/permissions.htm
*/
struct util_fast_sdiv_info {
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(int64_t D, unsigned SINT_BITS);
/* Computes "magic info" for performing unsigned division by a fixed positive
* 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
* (which may be up to UINT_BITS). To emit code for n/d, use one of the two
* following sequences (here >>> refers to a logical bitshift):
*
* m = compute_unsigned_magic_info(D, num_bits)
* if m.pre_shift > 0: emit("n >>>= m.pre_shift")
* if m.increment: emit("n = saturated_increment(n)")
* emit("result = (m.multiplier * n) >>> UINT_BITS")
* if m.post_shift > 0: emit("result >>>= m.post_shift")
*
* or
*
* m = compute_unsigned_magic_info(D, num_bits)
* if m.pre_shift > 0: emit("n >>>= m.pre_shift")
* emit("result = m.multiplier * n")
* if m.increment: emit("result = result + m.multiplier")
* emit("result >>>= UINT_BITS")
* if m.post_shift > 0: emit("result >>>= m.post_shift")
*
* This second version works even if D is 1. The shifts by UINT_BITS may be
* "free" if the high half of the full multiply is put in a separate register.
*
* saturated_increment(n) means "increment n unless it would wrap to 0," i.e.
* if n == (1 << UINT_BITS)-1: result = n
* else: result = n+1
* A common way to implement this is with the carry bit. For example, on x86:
* add 1
* sbb 0
*
* Some invariants:
* 1: At least one of pre_shift and increment is zero
* 2: multiplier is never zero
*
* This code incorporates the "round down" optimization per ridiculous_fish.
*/
struct util_fast_udiv_info {
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
the two strategies */
};
struct util_fast_udiv_info
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.
*/
/* Full version. */
static inline uint32_t
util_fast_udiv32(uint32_t n, struct util_fast_udiv_info info)
{
n = n >> info.pre_shift;
/* If the divisor is not 1, you can instead use a 32-bit ADD that clamps
* to UINT_MAX. Dividing by 1 needs the full 64-bit ADD.
*
* If you have unsigned 64-bit MAD with 32-bit inputs, you can do:
* increment = increment ? multiplier : 0; // on the CPU
* (n * multiplier + increment) // on the GPU using unsigned 64-bit MAD
*/
n = (((uint64_t)n + info.increment) * info.multiplier) >> 32;
n = n >> info.post_shift;
return n;
}
/* A little more efficient version if n != UINT_MAX, i.e. no unsigned
* wraparound in the computation.
*/
static inline uint32_t
util_fast_udiv32_nuw(uint32_t n, struct util_fast_udiv_info info)
{
assert(n != UINT32_MAX);
n = n >> info.pre_shift;
n = n + info.increment;
n = ((uint64_t)n * info.multiplier) >> 32;
n = n >> info.post_shift;
return n;
}
/* Even faster version but both operands must be 31-bit unsigned integers
* and the divisor must be greater than 1.
*
* info must be computed with num_bits == 31.
*/
static inline uint32_t
util_fast_udiv32_u31_d_not_one(uint32_t n, struct util_fast_udiv_info info)
{
assert(info.pre_shift == 0);
assert(info.increment == 0);
n = ((uint64_t)n * info.multiplier) >> 32;
n = n >> info.post_shift;
return n;
}
#ifdef __cplusplus
} /* extern C */
#endif
#endif /* FAST_IDIV_BY_CONST_H */
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