Mercurial > octave
view liboctave/util/oct-inttypes.cc @ 31556:9978ef12aea3 stable
avoid overflow due to abs(min_val) in signed int64 multiplication (bug #63416)
* oct-inttypes.cc (octave_int_arith_base<int64_t, true>::mul_internal):
Avoid calling abs on min_val.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Sat, 26 Nov 2022 17:08:30 -0500 |
parents | e7fc6251b698 |
children | 597f3ee61a48 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 2004-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave 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. // // Octave 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 Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include "fpucw-wrappers.h" #include "lo-error.h" #include "oct-inttypes.h" template <typename T> const octave_int<T> octave_int<T>::s_zero (static_cast<T> (0)); template <typename T> const octave_int<T> octave_int<T>::s_one (static_cast<T> (1)); // Define type names. #define DEFINE_OCTAVE_INT_TYPENAME(TYPE, TYPENAME) \ template <> \ OCTAVE_API const char * \ octave_int<TYPE>::type_name (void) { return TYPENAME; } DEFINE_OCTAVE_INT_TYPENAME (int8_t, "int8") DEFINE_OCTAVE_INT_TYPENAME (int16_t, "int16") DEFINE_OCTAVE_INT_TYPENAME (int32_t, "int32") DEFINE_OCTAVE_INT_TYPENAME (int64_t, "int64") DEFINE_OCTAVE_INT_TYPENAME (uint8_t, "uint8") DEFINE_OCTAVE_INT_TYPENAME (uint16_t, "uint16") DEFINE_OCTAVE_INT_TYPENAME (uint32_t, "uint32") DEFINE_OCTAVE_INT_TYPENAME (uint64_t, "uint64") template <class T> template <class S> T octave_int_base<T>::convert_real (const S& value) { // Compute proper thresholds. static const S thmin = compute_threshold (static_cast<S> (min_val ()), min_val ()); static const S thmax = compute_threshold (static_cast<S> (max_val ()), max_val ()); if (octave::math::isnan (value)) return static_cast<T> (0); else if (value < thmin) return min_val (); else if (value > thmax) return max_val (); else { S rvalue = octave::math::round (value); return static_cast<T> (rvalue); } } #define INSTANTIATE_CONVERT_REAL_1(T, S) \ template \ OCTAVE_API \ T \ octave_int_base<T>::convert_real (const S&) #define INSTANTIATE_CONVERT_REAL(S) \ INSTANTIATE_CONVERT_REAL_1 (int8_t, S); \ INSTANTIATE_CONVERT_REAL_1 (uint8_t, S); \ INSTANTIATE_CONVERT_REAL_1 (int16_t, S); \ INSTANTIATE_CONVERT_REAL_1 (uint16_t, S); \ INSTANTIATE_CONVERT_REAL_1 (int32_t, S); \ INSTANTIATE_CONVERT_REAL_1 (uint32_t, S); \ INSTANTIATE_CONVERT_REAL_1 (int64_t, S); \ INSTANTIATE_CONVERT_REAL_1 (uint64_t, S) INSTANTIATE_CONVERT_REAL (double); INSTANTIATE_CONVERT_REAL (float); #if defined (OCTAVE_INT_USE_LONG_DOUBLE) INSTANTIATE_CONVERT_REAL (long double); #endif #if defined (OCTAVE_INT_USE_LONG_DOUBLE) # if defined (OCTAVE_ENSURE_LONG_DOUBLE_OPERATIONS_ARE_NOT_TRUNCATED) # define DEFINE_OCTAVE_LONG_DOUBLE_CMP_OP_TEMPLATES(T) \ template <typename xop> \ bool \ octave_int_cmp_op::external_mop (double x, T y) \ { \ unsigned int oldcw = octave_begin_long_double_rounding (); \ \ bool retval = xop::op (static_cast<long double> (x), \ static_cast<long double> (y)); \ \ octave_end_long_double_rounding (oldcw); \ \ return retval; \ } \ \ template <typename xop> \ bool \ octave_int_cmp_op::external_mop (T x, double y) \ { \ unsigned int oldcw = octave_begin_long_double_rounding (); \ \ bool retval = xop::op (static_cast<long double> (x), \ static_cast<long double> (y)); \ \ octave_end_long_double_rounding (oldcw); \ \ return retval; \ } DEFINE_OCTAVE_LONG_DOUBLE_CMP_OP_TEMPLATES (int64_t) DEFINE_OCTAVE_LONG_DOUBLE_CMP_OP_TEMPLATES (uint64_t) # define INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP(OP, T) \ template OCTAVE_API bool \ octave_int_cmp_op::external_mop<octave_int_cmp_op::OP> (double, T); \ \ template OCTAVE_API bool \ octave_int_cmp_op::external_mop<octave_int_cmp_op::OP> (T, double) # define INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OPS(T) \ INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (lt, T); \ INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (le, T); \ INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (gt, T); \ INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (ge, T); \ INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (eq, T); \ INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (ne, T) INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OPS (int64_t); INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OPS (uint64_t); uint64_t octave_external_uint64_uint64_mul (uint64_t x, uint64_t y) { unsigned int oldcw = octave_begin_long_double_rounding (); uint64_t retval = octave_int_arith_base<uint64_t, false>::mul_internal (x, y); octave_end_long_double_rounding (oldcw); return retval; } int64_t octave_external_int64_int64_mul (int64_t x, int64_t y) { unsigned int oldcw = octave_begin_long_double_rounding (); int64_t retval = octave_int_arith_base<int64_t, true>::mul_internal (x, y); octave_end_long_double_rounding (oldcw); return retval; } // Note that if we return long double it is apparently possible for // truncation to happen at the point of storing the result in retval, // which can happen after we end long double rounding. Attempt to avoid // that problem by storing the full precision temporary value in the // integer value before we end the long double rounding mode. // Similarly, the conversion from the 64-bit integer type to long double // must also occur in long double rounding mode. # define DEFINE_OCTAVE_LONG_DOUBLE_OP(T, OP, NAME) \ T \ external_double_ ## T ## _ ## NAME (double x, T y) \ { \ unsigned int oldcw = octave_begin_long_double_rounding (); \ \ T retval = T (x OP static_cast<long double> (y.value ())); \ \ octave_end_long_double_rounding (oldcw); \ \ return retval; \ } \ \ T \ external_ ## T ## _double_ ## NAME (T x, double y) \ { \ unsigned int oldcw = octave_begin_long_double_rounding (); \ \ T retval = T (static_cast<long double> (x.value ()) OP y); \ \ octave_end_long_double_rounding (oldcw); \ \ return retval; \ } # define DEFINE_OCTAVE_LONG_DOUBLE_OPS(T) \ DEFINE_OCTAVE_LONG_DOUBLE_OP (T, +, add); \ DEFINE_OCTAVE_LONG_DOUBLE_OP (T, -, sub); \ DEFINE_OCTAVE_LONG_DOUBLE_OP (T, *, mul); \ DEFINE_OCTAVE_LONG_DOUBLE_OP (T, /, div) DEFINE_OCTAVE_LONG_DOUBLE_OPS (octave_int64); DEFINE_OCTAVE_LONG_DOUBLE_OPS (octave_uint64); # endif #else // Define comparison operators template <typename xop> bool octave_int_cmp_op::emulate_mop (uint64_t x, double y) { // The following cast changes the value to 2^64 (which is outside the range // of `uint64_t`). Take care to handle this correctly (e.g., don't cast back // to `uint64_t`)! static const double xxup = static_cast<double> (std::numeric_limits<uint64_t>::max ()); // This converts to the nearest double. Unless there's an equality, the // result is clear. double xx = x; if (xx != y) return xop::op (xx, y); else { // If equality occurred we compare as integers. if (xx == xxup) return xop::gtval; else return xop::op (x, static_cast<uint64_t> (xx)); } } template <typename xop> bool octave_int_cmp_op::emulate_mop (int64_t x, double y) { // The following cast changes the value to 2^63 (which is outside the range // of `int64_t`). Take care to handle this correctly (e.g., don't cast back // to `int64_t`)! The same applies to the lower limit on systems using one's // complement. static const double xxup = static_cast<double> (std::numeric_limits<int64_t>::max ()); static const double xxlo = static_cast<double> (std::numeric_limits<int64_t>::min ()); // This converts to the nearest double. Unless there's an equality, the // result is clear. double xx = x; if (xx != y) return xop::op (xx, y); else { // If equality occurred we compare as integers. if (xx == xxup) return xop::gtval; else if (xx == xxlo) return xop::ltval; else return xop::op (x, static_cast<int64_t> (xx)); } } // We define double-int operations by reverting the operator // A trait class reverting the operator template <typename xop> class rev_op { public: typedef xop op; }; #define DEFINE_REVERTED_OPERATOR(OP1, OP2) \ template <> \ class rev_op<octave_int_cmp_op::OP1> \ { \ public: \ typedef octave_int_cmp_op::OP2 op; \ } DEFINE_REVERTED_OPERATOR (lt, gt); DEFINE_REVERTED_OPERATOR (gt, lt); DEFINE_REVERTED_OPERATOR (le, ge); DEFINE_REVERTED_OPERATOR (ge, le); template <typename xop> bool octave_int_cmp_op::emulate_mop (double x, uint64_t y) { typedef typename rev_op<xop>::op rop; return mop<rop> (y, x); } template <typename xop> bool octave_int_cmp_op::emulate_mop (double x, int64_t y) { typedef typename rev_op<xop>::op rop; return mop<rop> (y, x); } // Define handlers for (u)int64 multiplication. template <> uint64_t octave_int_arith_base<uint64_t, false>::mul_internal (uint64_t x, uint64_t y) { // Get upper words uint64_t ux = x >> 32; uint64_t uy = y >> 32; uint64_t res; if (ux) { if (uy) goto overflow; else { uint64_t ly = static_cast<uint32_t> (y); uint64_t uxly = ux*ly; if (uxly >> 32) goto overflow; uxly <<= 32; // never overflows uint64_t lx = static_cast<uint32_t> (x); uint64_t lxly = lx*ly; res = add (uxly, lxly); } } else if (uy) { uint64_t lx = static_cast<uint32_t> (x); uint64_t uylx = uy*lx; if (uylx >> 32) goto overflow; uylx <<= 32; // never overflows uint64_t ly = static_cast<uint32_t> (y); uint64_t lylx = ly*lx; res = add (uylx, lylx); } else { uint64_t lx = static_cast<uint32_t> (x); uint64_t ly = static_cast<uint32_t> (y); res = lx*ly; } return res; overflow: return max_val (); } template <> int64_t octave_int_arith_base<int64_t, true>::mul_internal (int64_t x, int64_t y) { // The signed case is far worse. The problem is that even if neither // integer fits into signed 32-bit range, the result may still be OK. // Uh oh. // Essentially, what we do is compute sign, multiply absolute values // (as above) and impose the sign. // But first, avoid overflow in computation of abs (min_val ()). if (x == min_val ()) return y == 0 ? 0 : (y < 0 ? max_val () : min_val ()); if (y == min_val ()) return x == 0 ? 0 : (x < 0 ? max_val () : min_val ()); uint64_t usx = octave_int_abs (x); uint64_t usy = octave_int_abs (y); bool positive = (x < 0) == (y < 0); // Get upper words uint64_t ux = usx >> 32; uint64_t uy = usy >> 32; uint64_t res; if (ux) { if (uy) goto overflow; else { uint64_t ly = static_cast<uint32_t> (usy); uint64_t uxly = ux*ly; if (uxly >> 32) goto overflow; uxly <<= 32; // never overflows uint64_t lx = static_cast<uint32_t> (usx); uint64_t lxly = lx*ly; res = uxly + lxly; if (res < uxly) goto overflow; } } else if (uy) { uint64_t lx = static_cast<uint32_t> (usx); uint64_t uylx = uy*lx; if (uylx >> 32) goto overflow; uylx <<= 32; // never overflows uint64_t ly = static_cast<uint32_t> (usy); uint64_t lylx = ly*lx; res = uylx + lylx; if (res < uylx) goto overflow; } else { uint64_t lx = static_cast<uint32_t> (usx); uint64_t ly = static_cast<uint32_t> (usy); res = lx*ly; } if (positive) { if (res > static_cast<uint64_t> (max_val ())) return max_val (); else return static_cast<int64_t> (res); } else { if (res > static_cast<uint64_t> (min_val ())) return min_val (); else return -static_cast<int64_t> (res); } overflow: return positive ? max_val () : min_val (); } template <> OCTAVE_API octave_uint64 operator + (const octave_uint64& x, const double& y) { return (y < 0) ? x - octave_uint64 (-y) : x + octave_uint64 (y); } template <> OCTAVE_API octave_uint64 operator + (const double& x, const octave_uint64& y) { return y + x; } template <> OCTAVE_API octave_int64 operator + (const octave_int64& x, const double& y) { // The following cast changes the value to 2^63 (which is outside the range // of `int64_t`). if (fabs (y) < static_cast<double> (octave_int64::max ())) return x + octave_int64 (y); else { // If the number is within the int64 range (the most common case, // probably), the above will work as expected. If not, it's more // complicated - as long as y is within _twice_ the signed range, the // result may still be an integer. An instance of such an operation is // 3*2^62 + (1+intmin ('int64')) that should yield int64 (2^62) + 1. // So what we do is to try to convert y/2 and add it twice. Note that // if y/2 overflows, the result must overflow as well, and that y/2 // cannot be a fractional number. octave_int64 y2 (y / 2); return (x + y2) + y2; } } template <> OCTAVE_API octave_int64 operator + (const double& x, const octave_int64& y) { return y + x; } template <> OCTAVE_API octave_uint64 operator - (const octave_uint64& x, const double& y) { return x + (-y); } template <> OCTAVE_API octave_uint64 operator - (const double& x, const octave_uint64& y) { // The following cast changes the value to 2^64 (which is outside the range // of `uint64_t`). if (x < static_cast<double> (octave_uint64::max ())) return octave_uint64 (x) - y; else { // Again a trick to get the corner cases right. Things like // 3^2^63 - intmax ('uint64') should produce the correct result, i.e. // int64 (2^63) + 1. const double p2_64 = std::pow (2.0, 64); if (y.bool_value ()) { const uint64_t p2_64my = (~y.value ()) + 1; // Equals 2^64 - y return octave_uint64 (x - p2_64) + octave_uint64 (p2_64my); } else return octave_uint64 (p2_64); } } template <> OCTAVE_API octave_int64 operator - (const octave_int64& x, const double& y) { return x + (-y); } template <> OCTAVE_API octave_int64 operator - (const double& x, const octave_int64& y) { static const bool twosc = (std::numeric_limits<int64_t>::min () < -std::numeric_limits<int64_t>::max ()); // In case of symmetric integers (not two's complement), this will probably // be eliminated at compile time. if (twosc && y.value () == std::numeric_limits<int64_t>::min ()) return octave_int64 (x + std::pow (2.0, 63)); else return x + (-y); } // NOTE: // Emulated mixed multiplications are tricky due to possible precision loss. // Here, after sorting out common cases for speed, we follow the strategy // of converting the double number into the form sign * 64-bit integer * // 2^exponent, multiply the 64-bit integers to get a 128-bit number, split that // number into 32-bit words and form 4 double-valued summands (none of which // loses precision), then convert these into integers and sum them. Though it // is not immediately obvious, this should work even w.r.t. rounding (none of // the summands lose precision). // Multiplies two unsigned 64-bit ints to get a 128-bit number represented // as four 32-bit words. static void umul128 (uint64_t x, uint64_t y, uint32_t w[4]) { uint64_t lx = static_cast<uint32_t> (x); uint64_t ux = x >> 32; uint64_t ly = static_cast<uint32_t> (y); uint64_t uy = y >> 32; uint64_t a = lx * ly; w[0] = a; a >>= 32; uint64_t uxly = ux*ly; uint64_t uylx = uy*lx; a += static_cast<uint32_t> (uxly); uxly >>= 32; a += static_cast<uint32_t> (uylx); uylx >>= 32; w[1] = a; a >>= 32; uint64_t uxuy = ux * uy; a += uxly; a += uylx; a += uxuy; w[2] = a; a >>= 32; w[3] = a; } // Splits a double into bool sign, unsigned 64-bit mantissa and int exponent static void dblesplit (double x, bool& sign, uint64_t& mtis, int& exp) { sign = x < 0; x = fabs (x); x = octave::math::frexp (x, &exp); exp -= 52; mtis = static_cast<uint64_t> (ldexp (x, 52)); } // Gets a double number from a // 32-bit unsigned integer mantissa, exponent, and sign. static double dbleget (bool sign, uint32_t mtis, int exp) { double x = ldexp (static_cast<double> (mtis), exp); return sign ? -x : x; } template <> OCTAVE_API octave_uint64 operator * (const octave_uint64& x, const double& y) { // The following cast changes the value to 2^64 (which is outside the range // of `uint64_t`). if (y >= 0 && y < static_cast<double> (octave_uint64::max ()) && y == octave::math::fix (y)) return x * octave_uint64 (static_cast<uint64_t> (y)); else if (y == 0.5) return x / octave_uint64 (static_cast<uint64_t> (2)); else if (y < 0 || octave::math::isnan (y) || octave::math::isinf (y)) return octave_uint64 (x.value () * y); else { bool sign; uint64_t my; int e; dblesplit (y, sign, my, e); uint32_t w[4]; umul128 (x.value (), my, w); octave_uint64 res = octave_uint64::s_zero; for (short i = 0; i < 4; i++) { res += octave_uint64 (dbleget (sign, w[i], e)); e += 32; } return res; } } template <> OCTAVE_API octave_uint64 operator * (const double& x, const octave_uint64& y) { return y * x; } template <> OCTAVE_API octave_int64 operator * (const octave_int64& x, const double& y) { // The following cast changes the value to 2^63 (which is outside the range // of `int64_t`). if (fabs (y) < static_cast<double> (octave_int64::max ()) && y == octave::math::fix (y)) return x * octave_int64 (static_cast<int64_t> (y)); else if (fabs (y) == 0.5) return x / octave_int64 (static_cast<uint64_t> (4*y)); else if (octave::math::isnan (y) || octave::math::isinf (y)) return octave_int64 (x.value () * y); else { bool sign; uint64_t my; int e; dblesplit (y, sign, my, e); uint32_t w[4]; sign = (sign != (x.value () < 0)); umul128 (octave_int_abs (x.value ()), my, w); octave_int64 res = octave_int64::s_zero; for (short i = 0; i < 4; i++) { res += octave_int64 (dbleget (sign, w[i], e)); e += 32; } return res; } } template <> OCTAVE_API octave_int64 operator * (const double& x, const octave_int64& y) { return y * x; } template <> OCTAVE_API octave_uint64 operator / (const double& x, const octave_uint64& y) { return octave_uint64 (x / static_cast<double> (y)); } template <> OCTAVE_API octave_int64 operator / (const double& x, const octave_int64& y) { return octave_int64 (x / static_cast<double> (y)); } template <> OCTAVE_API octave_uint64 operator / (const octave_uint64& x, const double& y) { // The following cast changes the value to 2^64 (which is outside the range // of `uint64_t`). if (y >= 0 && y < static_cast<double> (octave_uint64::max ()) && y == octave::math::fix (y)) return x / octave_uint64 (y); else return x * (1.0/y); } template <> OCTAVE_API octave_int64 operator / (const octave_int64& x, const double& y) { // The following cast changes the value to 2^63 (which is outside the range // of `int64_t`). if (fabs (y) < static_cast<double> (octave_int64::max ()) && y == octave::math::fix (y)) return x / octave_int64 (y); else return x * (1.0/y); } #define INSTANTIATE_INT64_DOUBLE_CMP_OP0(OP, T1, T2) \ template OCTAVE_API bool \ octave_int_cmp_op::emulate_mop<octave_int_cmp_op::OP> (T1 x, T2 y) #define INSTANTIATE_INT64_DOUBLE_CMP_OP(OP) \ INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, double, int64_t); \ INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, double, uint64_t); \ INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, int64_t, double); \ INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, uint64_t, double) INSTANTIATE_INT64_DOUBLE_CMP_OP (lt); INSTANTIATE_INT64_DOUBLE_CMP_OP (le); INSTANTIATE_INT64_DOUBLE_CMP_OP (gt); INSTANTIATE_INT64_DOUBLE_CMP_OP (ge); INSTANTIATE_INT64_DOUBLE_CMP_OP (eq); INSTANTIATE_INT64_DOUBLE_CMP_OP (ne); #endif template <typename T> octave_int<T> pow (const octave_int<T>& a, const octave_int<T>& b) { octave_int<T> retval; const octave_int<T> zero = octave_int<T>::s_zero; const octave_int<T> one = octave_int<T>::s_one; if (b == zero || a == one) retval = one; else if (b < zero) { if (a == -one) retval = (b.value () % 2) ? a : one; else retval = zero; } else { octave_int<T> a_val = a; T b_val = b; // no need to do saturation on b retval = a; b_val -= 1; while (b_val != 0) { if (b_val & 1) retval = retval * a_val; b_val = b_val >> 1; if (b_val) a_val = a_val * a_val; } } return retval; } template <typename T> octave_int<T> pow (const double& a, const octave_int<T>& b) { return octave_int<T> (std::pow (a, b.double_value ())); } template <typename T> octave_int<T> pow (const octave_int<T>& a, const double& b) { return ((b >= 0 && b < std::numeric_limits<T>::digits && b == octave::math::fix (b)) ? pow (a, octave_int<T> (static_cast<T> (b))) : octave_int<T> (std::pow (a.double_value (), b))); } template <typename T> octave_int<T> pow (const float& a, const octave_int<T>& b) { return octave_int<T> (std::pow (a, b.float_value ())); } template <typename T> octave_int<T> pow (const octave_int<T>& a, const float& b) { return ((b >= 0 && b < std::numeric_limits<T>::digits && b == octave::math::fix (b)) ? pow (a, octave_int<T> (static_cast<T> (b))) : octave_int<T> (std::pow (a.double_value (), static_cast<double> (b)))); } // FIXME: Do we really need a differently named single-precision function // integer power function here instead of an overloaded one? template <typename T> octave_int<T> powf (const float& a, const octave_int<T>& b) { return octave_int<T> (pow (a, b.float_value ())); } template <typename T> octave_int<T> powf (const octave_int<T>& a, const float& b) { return ((b >= 0 && b < std::numeric_limits<T>::digits && b == octave::math::fix (b)) ? pow (a, octave_int<T> (static_cast<T> (b))) : octave_int<T> (std::pow (a.double_value (), static_cast<double> (b)))); } #define INSTANTIATE_INTTYPE(T) \ template class OCTAVE_CLASS_TEMPLATE_INSTANTIATION_API octave_int<T>; \ \ template OCTAVE_API octave_int<T> \ pow (const octave_int<T>&, const octave_int<T>&); \ \ template OCTAVE_API octave_int<T> \ pow (const double&, const octave_int<T>&); \ \ template OCTAVE_API octave_int<T> \ pow (const octave_int<T>&, const double&); \ \ template OCTAVE_API octave_int<T> \ pow (const float&, const octave_int<T>&); \ \ template OCTAVE_API octave_int<T> \ pow (const octave_int<T>&, const float&); \ \ template OCTAVE_API octave_int<T> \ powf (const float&, const octave_int<T>&); \ \ template OCTAVE_API octave_int<T> \ powf (const octave_int<T>&, const float&); \ \ template OCTAVE_API octave_int<T> \ bitshift (const octave_int<T>&, int, const octave_int<T>&); INSTANTIATE_INTTYPE (int8_t); INSTANTIATE_INTTYPE (int16_t); INSTANTIATE_INTTYPE (int32_t); INSTANTIATE_INTTYPE (int64_t); INSTANTIATE_INTTYPE (uint8_t); INSTANTIATE_INTTYPE (uint16_t); INSTANTIATE_INTTYPE (uint32_t); INSTANTIATE_INTTYPE (uint64_t); /* %!assert (intmax ("int64") / intmin ("int64"), int64 (-1)) %!assert (intmin ("int64") / int64 (-1), intmax ("int64")) %!assert (int64 (2^63), intmax ("int64")) %!assert (uint64 (2^64), intmax ("uint64")) %!test %! a = 1.9*2^61; b = uint64 (a); b++; assert (b > a); %!test %! a = -1.9*2^61; b = int64 (a); b++; assert (b > a); %!test %! a = int64 (-2^60) + 2; assert (1.25*a == (5*a)/4); %!test %! a = uint64 (2^61) + 2; assert (1.25*a == (5*a)/4); %!assert (int32 (2^31+0.5), intmax ("int32")) %!assert (int32 (-2^31-0.5), intmin ("int32")) %!assert ((int64 (2^62)+1)^1, int64 (2^62)+1) %!assert ((int64 (2^30)+1)^2, int64 (2^60+2^31) + 1) %!assert <54382> (uint8 (char (128)), uint8 (128)) %!assert <54382> (uint8 (char (255)), uint8 (255)) %!assert <54382> (int8 (char (128)), int8 (128)) %!assert <54382> (int8 (char (255)), int8 (255)) %!assert <54382> (uint16 (char (128)), uint16 (128)) %!assert <54382> (uint16 (char (255)), uint16 (255)) %!assert <54382> (int16 (char (128)), int16 (128)) %!assert <54382> (int16 (char (255)), int16 (255)) %!assert <54382> (uint32 (char (128)), uint32 (128)) %!assert <54382> (uint32 (char (255)), uint32 (255)) %!assert <54382> (int32 (char (128)), int32 (128)) %!assert <54382> (int32 (char (255)), int32 (255)) %!assert <54382> (uint64 (char (128)), uint64 (128)) %!assert <54382> (uint64 (char (255)), uint64 (255)) %!assert <54382> (int64 (char (128)), int64 (128)) %!assert <54382> (int64 (char (255)), int64 (255)) */