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Removed divideByConstantCodegen

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tevador 2019-02-22 13:47:47 +01:00
parent 18ca8b5020
commit 9d5f621d5c
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169
src/divideByConstantCodegen.c
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/*
Reference implementations of computing and using the "magic number" approach to dividing
by constants, including codegen instructions. The unsigned division incorporates the
"round down" optimization per ridiculous_fish.
This is free and unencumbered software. Any copyright is dedicated to the Public Domain.
*/
#include <limits.h> //for CHAR_BIT
#include <assert.h>
#include "divideByConstantCodegen.h"
struct magicu_info compute_unsigned_magic_info(unsigned_type D, unsigned num_bits) {
//The numerator must fit in a unsigned_type
assert(num_bits > 0 && num_bits <= sizeof(unsigned_type) * CHAR_BIT);
// D must be larger than zero and not a power of 2
assert(D & (D - 1));
// The eventual result
struct magicu_info result;
// Bits in a unsigned_type
const unsigned UINT_BITS = sizeof(unsigned_type) * CHAR_BIT;
// The extra shift implicit in the difference between UINT_BITS and num_bits
const unsigned extra_shift = UINT_BITS - num_bits;
// The initial power of 2 is one less than the first one that can possibly work
const unsigned_type initial_power_of_2 = (unsigned_type)1 << (UINT_BITS - 1);
// The remainder and quotient of our power of 2 divided by d
unsigned_type quotient = initial_power_of_2 / D, remainder = initial_power_of_2 % D;
// ceil(log_2 D)
unsigned ceil_log_2_D;
// The magic info for the variant "round down" algorithm
unsigned_type down_multiplier = 0;
unsigned down_exponent = 0;
int has_magic_down = 0;
// Compute ceil(log_2 D)
ceil_log_2_D = 0;
unsigned_type tmp;
for (tmp = D; tmp > 0; tmp >>= 1)
ceil_log_2_D += 1;
// Begin a loop that increments the exponent, until we find a power of 2 that works.
unsigned exponent;
for (exponent = 0; ; exponent++) {
// Quotient and remainder is from previous exponent; compute it for this exponent.
if (remainder >= D - remainder) {
// Doubling remainder will wrap around D
quotient = quotient * 2 + 1;
remainder = remainder * 2 - D;
}
else {
// Remainder will not wrap
quotient = quotient * 2;
remainder = remainder * 2;
}
// We're done if this exponent works for the round_up algorithm.
// Note that exponent may be larger than the maximum shift supported,
// so the check for >= ceil_log_2_D is critical.
if ((exponent + extra_shift >= ceil_log_2_D) || (D - remainder) <= ((unsigned_type)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 <= ((unsigned_type)1 << (exponent + extra_shift))) {
has_magic_down = 1;
down_multiplier = quotient;
down_exponent = exponent;
}
}
if (exponent < ceil_log_2_D) {
// magic_up is efficient
result.multiplier = quotient + 1;
result.pre_shift = 0;
result.post_shift = exponent;
result.increment = 0;
}
else if (D & 1) {
// Odd divisor, so use magic_down, which must have been set
assert(has_magic_down);
result.multiplier = down_multiplier;
result.pre_shift = 0;
result.post_shift = down_exponent;
result.increment = 1;
}
else {
// Even divisor, so use a prefix-shifted dividend
unsigned pre_shift = 0;
unsigned_type shifted_D = D;
while ((shifted_D & 1) == 0) {
shifted_D >>= 1;
pre_shift += 1;
}
result = compute_unsigned_magic_info(shifted_D, num_bits - pre_shift);
assert(result.increment == 0 && result.pre_shift == 0); //expect no increment or pre_shift in this path
result.pre_shift = pre_shift;
}
return result;
}
struct magics_info compute_signed_magic_info(signed_type D) {
// D must not be zero and must not be a power of 2 (or its negative)
assert(D != 0 && (D & -D) != D && (D & -D) != -D);
// Our result
struct magics_info result;
// Bits in an signed_type
const unsigned SINT_BITS = sizeof(signed_type) * CHAR_BIT;
// Absolute value of D (we know D is not the most negative value since that's a power of 2)
const unsigned_type 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 unsigned_type initial_power_of_2 = (unsigned_type)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 unsigned_type tmp = initial_power_of_2 + (D < 0);
const unsigned_type abs_test_numer = tmp - 1 - tmp % abs_d;
// Initialize our quotients and remainders (q1, r1, q2, r2 in Warren)
unsigned_type quotient1 = initial_power_of_2 / abs_test_numer, remainder1 = initial_power_of_2 % abs_test_numer;
unsigned_type quotient2 = initial_power_of_2 / abs_d, remainder2 = initial_power_of_2 % abs_d;
unsigned_type delta;
// Begin our loop
do {
// Update the exponent
exponent++;
// Update quotient1 and remainder1
quotient1 *= 2;
remainder1 *= 2;
if (remainder1 >= abs_test_numer) {
quotient1 += 1;
remainder1 -= abs_test_numer;
}
// Update quotient2 and remainder2
quotient2 *= 2;
remainder2 *= 2;
if (remainder2 >= abs_d) {
quotient2 += 1;
remainder2 -= abs_d;
}
// Keep going as long as (2**exponent) / abs_d <= delta
delta = abs_d - remainder2;
} while (quotient1 < delta || (quotient1 == delta && remainder1 == 0));
result.multiplier = quotient2 + 1;
if (D < 0) result.multiplier = -result.multiplier;
result.shift = exponent - SINT_BITS;
return result;
}

117
src/divideByConstantCodegen.h
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/*
Copyright (c) 2018 tevador
This file is part of RandomX.
RandomX is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
RandomX is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with RandomX. If not, see<http://www.gnu.org/licenses/>.
*/
#pragma once
#include <stdint.h>
#if defined(__cplusplus)
extern "C" {
#endif
typedef uint64_t unsigned_type;
typedef int64_t signed_type;
/* Computes "magic info" for performing signed division by a fixed integer D.
The type 'signed_type' 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 magics_info {
signed_type multiplier; // the "magic number" multiplier
unsigned shift; // shift for the dividend after multiplying
};
struct magics_info compute_signed_magic_info(signed_type D);
/* Computes "magic info" for performing unsigned division by a fixed positive integer D.
The type 'unsigned_type' 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 unsigned_type; if this is not known then pass
(sizeof(unsigned_type) * CHAR_BIT) 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")
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 magicu_info {
unsigned_type 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 magicu_info compute_unsigned_magic_info(unsigned_type D, unsigned num_bits);
#if defined(__cplusplus)
}
#endif