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stb/stb_divide.h

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// stb_divide.h - v0.91 - public domain - Sean Barrett, Feb 2010
// Three kinds of divide/modulus of signed integers.
//
// HISTORY
//
// v0.91 2010-02-27 Fix euclidean division by INT_MIN for non-truncating C
// Check result with 64-bit math to catch such cases
// v0.90 2010-02-24 First public release
//
// USAGE
//
// In *ONE* source file, put:
//
// #define STB_DIVIDE_IMPLEMENTATION
// // #define C_INTEGER_DIVISION_TRUNCATES // see Note 1
// // #define C_INTEGER_DIVISION_FLOORS // see Note 2
// #include "stb_divide.h"
//
// Other source files should just include stb_divide.h
//
// Note 1: On platforms/compilers that you know signed C division
// truncates, you can #define C_INTEGER_DIVISION_TRUNCATES.
//
// Note 2: On platforms/compilers that you know signed C division
// floors (rounds to negative infinity), you can #define
// C_INTEGER_DIVISION_FLOORS.
//
// You can #define STB_DIVIDE_TEST in which case the implementation
// will generate a main() and compiling the result will create a
// program that tests the implementation. Run it with no arguments
// and any output indicates an error; run it with any argument and
// it will also print the test results. Define STB_DIVIDE_TEST_64
// to a 64-bit integer type to avoid overflows in the result-checking
// which give false negatives.
//
// ABOUT
//
// This file provides three different consistent divide/mod pairs
// implemented on top of arbitrary C/C++ division, including correct
// handling of overflow of intermediate calculations:
//
// trunc: a/b truncates to 0, a%b has same sign as a
// floor: a/b truncates to -inf, a%b has same sign as b
// eucl: a/b truncates to sign(b)*inf, a%b is non-negative
//
// Not necessarily optimal; I tried to keep it generally efficient,
// but there may be better ways.
//
// Briefly, for those who are not familiar with the problem, we note
// the reason these divides exist and are interesting:
//
// 'trunc' is easy to implement in hardware (strip the signs,
// compute, reapply the signs), thus is commonly defined
// by many languages (including C99)
//
// 'floor' is simple to define and better behaved than trunc;
// for example it divides integers into fixed-size buckets
// without an extra-wide bucket at 0, and for a fixed
// divisor N there are only |N| possible moduli.
//
// 'eucl' guarantees fixed-sized buckets *and* a non-negative
// modulus and defines division to be whatever is needed
// to achieve that result.
//
// See "The Euclidean definition of the functions div and mod"
// by Raymond Boute (1992), or "Division and Modulus for Computer
// Scientists" by Daan Leijen (2001)
//
// We assume of the built-in C division:
// (a) modulus is the remainder for the corresponding division
// (b) a/b truncates if a and b are the same sign
//
// Property (a) requires (a/b)*b + (a%b)==a, and is required by C.
// Property (b) seems to be true of all hardware but is *not* satisfied
// by the euclidean division operator we define, so it's possibly not
// always true. If any such platform turns up, we can add more cases.
// (Possibly only stb_div_trunc currently relies on property (b).)
//
// LICENSE
//
// This software is dual-licensed to the public domain and under the following
// license: you are granted a perpetual, irrevocable license to copy, modify,
// publish, and distribute this file as you see fit.
#ifndef INCLUDE_STB_DIVIDE_H
#define INCLUDE_STB_DIVIDE_H
#ifdef __cplusplus
extern "C" {
#endif
extern int stb_div_trunc(int value_to_be_divided, int value_to_divide_by);
extern int stb_div_floor(int value_to_be_divided, int value_to_divide_by);
extern int stb_div_eucl (int value_to_be_divided, int value_to_divide_by);
extern int stb_mod_trunc(int value_to_be_divided, int value_to_divide_by);
extern int stb_mod_floor(int value_to_be_divided, int value_to_divide_by);
extern int stb_mod_eucl (int value_to_be_divided, int value_to_divide_by);
#ifdef __cplusplus
}
#endif
#ifdef STB_DIVIDE_IMPLEMENTATION
#if defined(__STDC_VERSION) && __STDC_VERSION__ >= 19901
#ifndef C_INTEGER_DIVISION_TRUNCATES
#define C_INTEGER_DIVISION_TRUNCATES
#endif
#endif
#ifndef INT_MIN
#include <limits.h> // if you have no limits.h, #define INT_MIN yourself
#endif
// the following macros are designed to allow testing
// other platforms by simulating them
#ifndef STB_DIVIDE_TEST_FLOOR
#define stb__div(a,b) ((a)/(b))
#define stb__mod(a,b) ((a)%(b))
#else
// implement floor-style divide on trunc platform
#ifndef C_INTEGER_DIVISION_TRUNCATES
#error "floor test requires truncating division"
#endif
#undef C_INTEGER_DIVISION_TRUNCATES
int stb__div(int v1, int v2)
{
int q = v1/v2, r = v1%v2;
if ((r > 0 && v2 < 0) || (r < 0 && v2 > 0))
return q-1;
else
return q;
}
int stb__mod(int v1, int v2)
{
int r = v1%v2;
if ((r > 0 && v2 < 0) || (r < 0 && v2 > 0))
return r+v2;
else
return r;
}
#endif
int stb_div_trunc(int v1, int v2)
{
#ifdef C_INTEGER_DIVISION_TRUNCATES
return v1/v2;
#else
if (v1 >= 0 && v2 <= 0)
return -stb__div(-v1,v2); // both negative to avoid overflow
if (v1 <= 0 && v2 >= 0)
if (v1 != INT_MIN)
return -stb__div(v1,-v2); // both negative to avoid overflow
else
return -stb__div(v1+v2,-v2)-1; // push v1 away from wrap point
else
return v1/v2; // same sign, so expect truncation
#endif
}
int stb_div_floor(int v1, int v2)
{
#ifdef C_INTEGER_DIVISION_FLOORS
return v1/v2;
#else
if (v1 >= 0 && v2 < 0)
if ((-v1)+v2+1 < 0) // check if increasing v1's magnitude overflows
return -stb__div(-v1+v2+1,v2); // nope, so just compute it
else
return -stb__div(-v1,v2) + ((-v1)%v2 ? -1 : 0);
if (v1 < 0 && v2 >= 0)
if (v1 != INT_MIN)
if (v1-v2+1 < 0) // check if increasing v1's magnitude overflows
return -stb__div(v1-v2+1,-v2); // nope, so just compute it
else
return -stb__div(-v1,v2) + (stb__mod(v1,-v2) ? -1 : 0);
else // it must be possible to compute -(v1+v2) without overflowing
return -stb__div(-(v1+v2),v2) + (stb__mod(-(v1+v2),v2) ? -2 : -1);
else
return v1/v2; // same sign, so expect truncation
#endif
}
int stb_div_eucl(int v1, int v2)
{
int q,r;
#ifdef C_INTEGER_DIVISION_TRUNCATES
q = v1/v2;
r = v1%v2;
#else
// handle every quadrant separately, since we can't rely on q and r flor
if (v1 >= 0)
if (v2 >= 0)
return stb__div(v1,v2);
else if (v2 != INT_MIN)
q = -stb__div(v1,-v2), r = stb__mod(v1,-v2);
else
q = 0, r = v1;
else if (v1 != INT_MIN)
if (v2 >= 0)
q = -stb__div(-v1,v2), r = -stb__mod(-v1,v2);
else if (v2 != INT_MIN)
q = stb__div(-v1,-v2), r = -stb__mod(-v1,-v2);
else // if v2 is INT_MIN, then we can't use -v2, but we can't divide by v2
q = 1, r = v1-q*v2;
else // if v1 is INT_MIN, we have to move away from overflow place
if (v2 >= 0)
q = -stb__div(-(v1+v2),v2)-1, r = -stb__mod(-(v1+v2),v2);
else
q = stb__div(-(v1-v2),-v2)+1, r = -stb__mod(-(v1-v2),-v2);
#endif
if (r >= 0)
return q;
else
return q + (v2 > 0 ? -1 : 1);
}
int stb_mod_trunc(int v1, int v2)
{
#ifdef C_INTEGER_DIVISION_TRUNCATES
return v1%v2;
#else
if (v1 >= 0) { // modulus result should always be positive
int r = stb__mod(v1,v2);
if (r >= 0)
return r;
else
return r + (v2 > 0 ? v2 : -v2);
} else { // modulus result should always be negative
int r = stb__mod(v1,v2);
if (r <= 0)
return r;
else
return r - (v2 > 0 ? v2 : -v2);
}
#endif
}
int stb_mod_floor(int v1, int v2)
{
#ifdef C_INTEGER_DIVISION_FLOORS
return v1%v2;
#else
if (v2 >= 0) { // result should always be positive
int r = stb__mod(v1,v2);
if (r >= 0)
return r;
else
return r + v2;
} else { // result should always be negative
int r = stb__mod(v1,v2);
if (r <= 0)
return r;
else
return r + v2;
}
#endif
}
int stb_mod_eucl(int v1, int v2)
{
int r = stb__mod(v1,v2);
if (r >= 0)
return r;
else
return r + (v2 > 0 ? v2 : -v2); // abs()
}
#ifdef STB_DIVIDE_TEST
#include <stdio.h>
#include <math.h>
#include <limits.h>
int show=0;
void stbdiv_check(int q, int r, int a, int b, char *type, int dir)
{
if ((dir > 0 && r < 0) || (dir < 0 && r > 0))
fprintf(stderr, "FAILED: %s(%d,%d) remainder %d in wrong direction\n", type,a,b,r);
else
if (b != INT_MIN) // can't compute abs(), but if b==INT_MIN all remainders are valid
if (r <= -abs(b) || r >= abs(b))
fprintf(stderr, "FAILED: %s(%d,%d) remainder %d out of range\n", type,a,b,r);
#ifdef STB_DIVIDE_TEST_64
{
STB_DIVIDE_TEST_64 q64 = q, r64=r, a64=a, b64=b;
if (q64*b64+r64 != a64)
fprintf(stderr, "FAILED: %s(%d,%d) remainder %d doesn't match quotient %d\n", type,a,b,r,q);
}
#else
if (q*b+r != a)
fprintf(stderr, "FAILED: %s(%d,%d) remainder %d doesn't match quotient %d\n", type,a,b,r,q);
#endif
}
void test(int a, int b)
{
int q,r;
if (show) printf("(%+11d,%+d) | ", a,b);
q = stb_div_trunc(a,b), r = stb_mod_trunc(a,b);
if (show) printf("(%+11d,%+2d) ", q,r); stbdiv_check(q,r,a,b, "trunc",a);
q = stb_div_floor(a,b), r = stb_mod_floor(a,b);
if (show) printf("(%+11d,%+2d) ", q,r); stbdiv_check(q,r,a,b, "floor",b);
q = stb_div_eucl (a,b), r = stb_mod_eucl (a,b);
if (show) printf("(%+11d,%+2d)\n", q,r); stbdiv_check(q,r,a,b, "euclidean",1);
}
void testh(int a, int b)
{
int q,r;
if (show) printf("(%08x,%08x) |\n", a,b);
q = stb_div_trunc(a,b), r = stb_mod_trunc(a,b); stbdiv_check(q,r,a,b, "trunc",a);
if (show) printf(" (%08x,%08x)", q,r);
q = stb_div_floor(a,b), r = stb_mod_floor(a,b); stbdiv_check(q,r,a,b, "floor",b);
if (show) printf(" (%08x,%08x)", q,r);
q = stb_div_eucl (a,b), r = stb_mod_eucl (a,b); stbdiv_check(q,r,a,b, "euclidean",1);
if (show) printf(" (%08x,%08x)\n ", q,r);
}
int main(int argc, char **argv)
{
if (argc > 1) show=1;
test(8,3);
test(8,-3);
test(-8,3);
test(-8,-3);
test(1,2);
test(1,-2);
test(-1,2);
test(-1,-2);
test(8,4);
test(8,-4);
test(-8,4);
test(-8,-4);
test(INT_MAX,1);
test(INT_MIN,1);
test(INT_MIN+1,1);
test(INT_MAX,-1);
//test(INT_MIN,-1); // this traps in MSVC, so we leave it untested
test(INT_MIN+1,-1);
test(INT_MIN,-2);
test(INT_MIN+1,2);
test(INT_MIN+1,-2);
test(INT_MAX,2);
test(INT_MAX,-2);
test(INT_MIN+1,2);
test(INT_MIN+1,-2);
test(INT_MIN,2);
test(INT_MIN,-2);
test(INT_MIN,7);
test(INT_MIN,-7);
test(INT_MIN+1,4);
test(INT_MIN+1,-4);
testh(-7, INT_MIN);
testh(-1, INT_MIN);
testh(1, INT_MIN);
testh(7, INT_MIN);
testh(INT_MAX-1, INT_MIN);
testh(INT_MAX, INT_MIN);
testh(INT_MIN, INT_MIN);
testh(INT_MIN+1, INT_MIN);
testh(INT_MAX-1, INT_MAX);
testh(INT_MAX , INT_MAX);
testh(INT_MIN , INT_MAX);
testh(INT_MIN+1, INT_MAX);
return 0;
}
#endif // STB_DIVIDE_TEST
#endif // STB_DIVIDE_IMPLEMENTATION
#endif // INCLUDE_STB_DIVIDE_H
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