sdk/lib/crt/arith64.c

// SPDX-License-Identifier: Unlicense

// GCC 32/64-bit integer arithmetic support for 32-bit systems that can't link
// to libgcc.

// Function prototypes and descriptions are taken from
// https://gcc.gnu.org/onlinedocs/gccint/Integer-library-routines.html.

// This file may be #include'd by another file, so we try not to pollute the
// namespace and we don't import any headers.

// All functions must be resolvable by the linker and therefore can't be inline
// or static, even if they're #included into the file where they'll be used.

// For best performance we try to avoid branching. This makes the code a little
// weird in places.

// See https://github.com/glitchub/arith64 for more information.
// This software is released as-is into the public domain, as described at
// https://unlicense.org. Do whatever you like with it.

// Changes for CHERIoT:
// - Add prototypes for all exported functions.
// - Mark the functions as libcall and no-builtin.
// - Add asm labels so that the compiler doesn't need to know the C++ type encodings for builtins.
// - Use standard integer types.
// - Add SPDX tags for license from the upstream repository (commit 426b7578ecfb5ce7c841e738613cff2a261214eb)
// - Add the implementation of __multi3() 
//
// This file is *not* formatted, to make it easier to track changes from upstream (if there are any).

#include "cdefs.h"
#include <stdint.h>
#include <compartment-macros.h>

#define arith64_u64 uint64_t
#define arith64_s64 int64_t
#define arith64_u32 uint32_t
#define arith64_s32 int32_t

arith64_s64 __cheri_libcall __ashldi3(arith64_s64 a, int b) __asm__("__ashldi3");
arith64_s64 __cheri_libcall __absvdi2(arith64_s64 a) __asm__("__absvdi2");
arith64_s64 __cheri_libcall __ashldi3(arith64_s64 a, int b) __asm__("__ashldi3");
arith64_s64 __cheri_libcall __ashrdi3(arith64_s64 a, int b) __asm__("__ashrdi3");
int __cheri_libcall __clzsi2(arith64_u32 a) __asm__("__clzsi2");
int __cheri_libcall __clzdi2(arith64_u64 a) __asm__("__clzdi2");
int __cheri_libcall __ctzsi2(arith64_u32 a) __asm__("__ctzsi2");
int __cheri_libcall __ctzdi2(arith64_u64 a) __asm__("__ctzdi2");
arith64_u64 __cheri_libcall __divmoddi4(arith64_u64 a, arith64_u64 b, arith64_u64 *c) __asm__("__divmoddi4");
arith64_s64 __cheri_libcall __divdi3(arith64_s64 a, arith64_s64 b) __asm__("__divdi3");
int __cheri_libcall __ffsdi2(arith64_u64 a) __asm__("__ffsdi2");
arith64_u64 __cheri_libcall __lshrdi3(arith64_u64 a, int b) __asm__("__lshrdi3");
arith64_s64 __cheri_libcall __moddi3(arith64_s64 a, arith64_s64 b) __asm__("__moddi3");
int __cheri_libcall __popcountsi2(arith64_u32 a) __asm__("__popcountsi2");
int __cheri_libcall __popcountdi2(arith64_u64 a) __asm__("__popcountdi2");
arith64_u64 __cheri_libcall __udivdi3(arith64_u64 a, arith64_u64 b) __asm__("__udivdi3");
arith64_u64 __cheri_libcall __umoddi3(arith64_u64 a, arith64_u64 b) __asm__("__umoddi3");
arith64_s64 __cheri_libcall __multi3(arith64_s64 a, arith64_s64 b) __asm__("__multi3");

typedef union
{
    arith64_u64 u64;
    arith64_s64 s64;
    struct
    {
#if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
        arith64_u32 hi; arith64_u32 lo;
#else
        arith64_u32 lo; arith64_u32 hi;
#endif
    } u32;
    struct
    {
#if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
        arith64_s32 hi; arith64_s32 lo;
#else
        arith64_s32 lo; arith64_s32 hi;
#endif
    } s32;
} arith64_word;

// extract hi and lo 32-bit words from 64-bit value
#define arith64_hi(n) (arith64_word){.u64=n}.u32.hi
#define arith64_lo(n) (arith64_word){.u64=n}.u32.lo

// Negate a if b is negative, via invert and increment.
#define arith64_neg(a, b) (((a) ^ ((((arith64_s64)(b)) >= 0) - 1)) + (((arith64_s64)(b)) < 0))
#define arith64_abs(a) arith64_neg(a, a)

// Return the absolute value of a.
// Note LLINT_MIN cannot be negated.
[[clang::no_builtin]] arith64_s64 __absvdi2(arith64_s64 a)
{
    return arith64_abs(a);
}

// Return the result of shifting a left by b bits.
[[clang::no_builtin]] arith64_s64 __ashldi3(arith64_s64 a, int b)
{
    arith64_word w = {.s64 = a};

    b &= 63;

    if (b >= 32)
    {
        w.u32.hi = w.u32.lo << (b - 32);
        w.u32.lo = 0;
    } else if (b)
    {
        w.u32.hi = (w.u32.lo >> (32 - b)) | (w.u32.hi << b);
        w.u32.lo <<= b;
    }
    return w.s64;
}

// Return the result of arithmetically shifting a right by b bits.
[[clang::no_builtin]] arith64_s64 __ashrdi3(arith64_s64 a, int b)
{
    arith64_word w = {.s64 = a};

    b &= 63;

    if (b >= 32)
    {
        w.s32.lo = w.s32.hi >> (b - 32);
        w.s32.hi >>= 31; // 0xFFFFFFFF or 0
    } else if (b)
    {
        w.u32.lo = (w.u32.hi << (32 - b)) | (w.u32.lo >> b);
        w.s32.hi >>= b;
    }
    return w.s64;
}

// These functions return the number of leading 0-bits in a, starting at the
// most significant bit position. If a is zero, the result is undefined.
[[clang::no_builtin]] int __clzsi2(arith64_u32 a)
{
    int b, n = 0;
    b = !(a & 0xffff0000) << 4; n += b; a <<= b;
    b = !(a & 0xff000000) << 3; n += b; a <<= b;
    b = !(a & 0xf0000000) << 2; n += b; a <<= b;
    b = !(a & 0xc0000000) << 1; n += b; a <<= b;
    return n + !(a & 0x80000000);
}

[[clang::no_builtin]] int __clzdi2(arith64_u64 a)
{
    int b, n = 0;
    b = !(a & 0xffffffff00000000ULL) << 5; n += b; a <<= b;
    b = !(a & 0xffff000000000000ULL) << 4; n += b; a <<= b;
    b = !(a & 0xff00000000000000ULL) << 3; n += b; a <<= b;
    b = !(a & 0xf000000000000000ULL) << 2; n += b; a <<= b;
    b = !(a & 0xc000000000000000ULL) << 1; n += b; a <<= b;
    return n + !(a & 0x8000000000000000ULL);
}

// These functions return the number of trailing 0-bits in a, starting at the
// least significant bit position. If a is zero, the result is undefined.
[[clang::no_builtin]] int __ctzsi2(arith64_u32 a)
{
    int b, n = 0;
    b = !(a & 0x0000ffff) << 4; n += b; a >>= b;
    b = !(a & 0x000000ff) << 3; n += b; a >>= b;
    b = !(a & 0x0000000f) << 2; n += b; a >>= b;
    b = !(a & 0x00000003) << 1; n += b; a >>= b;
    return n + !(a & 0x00000001);
}

[[clang::no_builtin]] int __ctzdi2(arith64_u64 a)
{
    int b, n = 0;
    b = !(a & 0x00000000ffffffffULL) << 5; n += b; a >>= b;
    b = !(a & 0x000000000000ffffULL) << 4; n += b; a >>= b;
    b = !(a & 0x00000000000000ffULL) << 3; n += b; a >>= b;
    b = !(a & 0x000000000000000fULL) << 2; n += b; a >>= b;
    b = !(a & 0x0000000000000003ULL) << 1; n += b; a >>= b;
    return n + !(a & 0x0000000000000001ULL);
}

// Calculate both the quotient and remainder of the unsigned division of a and
// b. The return value is the quotient, and the remainder is placed in variable
// pointed to by c (if it's not NULL).
[[clang::no_builtin]] arith64_u64 __divmoddi4(arith64_u64 a, arith64_u64 b, arith64_u64 *c)
{
    if (b > a)                                  // divisor > numerator?
    {
        if (c) *c = a;                          // remainder = numerator
        return 0;                               // quotient = 0
    }
    if (!arith64_hi(b))                         // divisor is 32-bit
    {
        if (b == 0)                             // divide by 0
        {
            volatile char x = 0; x = 1 / x;     // force an exception
        }
        if (b == 1)                             // divide by 1
        {
            if (c) *c = 0;                      // remainder = 0
            return a;                           // quotient = numerator
        }
        if (!arith64_hi(a))                     // numerator is also 32-bit
        {
            if (c)                              // use generic 32-bit operators
                *c = arith64_lo(a) % arith64_lo(b);
            return arith64_lo(a) / arith64_lo(b);
        }
    }

    // let's do long division
    char bits = __clzdi2(b) - __clzdi2(a) + 1;  // number of bits to iterate (a and b are non-zero)
    arith64_u64 rem = a >> bits;                   // init remainder
    a <<= 64 - bits;                            // shift numerator to the high bit
    arith64_u64 wrap = 0;                          // start with wrap = 0
    while (bits-- > 0)                          // for each bit
    {
        rem = (rem << 1) | (a >> 63);           // shift numerator MSB to remainder LSB
        a = (a << 1) | (wrap & 1);              // shift out the numerator, shift in wrap
        wrap = ((arith64_s64)(b - rem - 1) >> 63);  // wrap = (b > rem) ? 0 : 0xffffffffffffffff (via sign extension)
        rem -= b & wrap;                        // if (wrap) rem -= b
    }
    if (c) *c = rem;                            // maybe set remainder
    return (a << 1) | (wrap & 1);               // return the quotient
}

// Return the quotient of the signed division of a and b.
[[clang::no_builtin]] arith64_s64 __divdi3(arith64_s64 a, arith64_s64 b)
{
    arith64_u64 q = __divmoddi4(arith64_abs(a), arith64_abs(b), (void *)0);
    return arith64_neg(q, a^b); // negate q if a and b signs are different
}

// Return the index of the least significant 1-bit in a, or the value zero if a
// is zero. The least significant bit is index one.
[[clang::no_builtin]] int __ffsdi2(arith64_u64 a)
{
    return a ? __ctzdi2(a) + 1 : 0;
}

// Return the result of logically shifting a right by b bits.
[[clang::no_builtin]] arith64_u64 __lshrdi3(arith64_u64 a, int b)
{
    arith64_word w = {.u64 = a};

    b &= 63;

    if (b >= 32)
    {
        w.u32.lo = w.u32.hi >> (b - 32);
        w.u32.hi = 0;
    } else if (b)
    {
        w.u32.lo = (w.u32.hi << (32 - b)) | (w.u32.lo >> b);
        w.u32.hi >>= b;
    }
    return w.u64;
}

// Return the remainder of the signed division of a and b.
[[clang::no_builtin]] arith64_s64 __moddi3(arith64_s64 a, arith64_s64 b)
{
    arith64_u64 r;
    __divmoddi4(arith64_abs(a), arith64_abs(b), &r);
    return arith64_neg(r, a); // negate remainder if numerator is negative
}

// Return the number of bits set in a.
[[clang::no_builtin]] int __popcountsi2(arith64_u32 a)
{
    // collect sums into two low bytes
    a = a - ((a >> 1) & 0x55555555);
    a = ((a >> 2) & 0x33333333) + (a & 0x33333333);
    a = (a + (a >> 4)) & 0x0F0F0F0F;
    a = (a + (a >> 16));
    // add the bytes, return bottom 6 bits
    return (a + (a >> 8)) & 63;
}

// Return the number of bits set in a.
[[clang::no_builtin]] int __popcountdi2(arith64_u64 a)
{
    // collect sums into two low bytes
    a = a - ((a >> 1) & 0x5555555555555555ULL);
    a = ((a >> 2) & 0x3333333333333333ULL) + (a & 0x3333333333333333ULL);
    a = (a + (a >> 4)) & 0x0F0F0F0F0F0F0F0FULL;
    a = (a + (a >> 32));
    a = (a + (a >> 16));
    // add the bytes, return bottom 7 bits
    return (a + (a >> 8)) & 127;
}

// Return the quotient of the unsigned division of a and b.
[[clang::no_builtin]] arith64_u64 __udivdi3(arith64_u64 a, arith64_u64 b)
{
    return __divmoddi4(a, b, (void *)0);
}

// Return the remainder of the unsigned division of a and b.
[[clang::no_builtin]] arith64_u64 __umoddi3(arith64_u64 a, arith64_u64 b)
{
    arith64_u64 r;
    __divmoddi4(a, b, &r);
    return r;
}

// Return the product of a and b
[[clang::no_builtin]] arith64_s64 __multi3(arith64_s64 a, arith64_s64 b)
{
    return a * b;
}