X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fnumeric.cpp;h=e4124f7c4b52c4bbac569edb7b187d08d0812a6b;hp=149f049c2723bbded17d6299ff2a5ecb9d4e4185;hb=857ca8ca24fbfe26d4c0c624aa6c3f2296c419f8;hpb=956eeb82c513a723e864edefa857133282cf692b diff --git a/ginac/numeric.cpp b/ginac/numeric.cpp index 149f049c..e4124f7c 100644 --- a/ginac/numeric.cpp +++ b/ginac/numeric.cpp @@ -146,7 +146,7 @@ numeric::numeric(int i) : basic(TINFO_numeric) { debugmsg("numeric constructor from int",LOGLEVEL_CONSTRUCT); // Not the whole int-range is available if we don't cast to long - // first. This is due to the behaviour of the cl_I-ctor, which + // first. This is due to the behaviour of the cl_I-ctor, which // emphasizes efficiency: value = new cl_I((long) i); calchash(); @@ -159,7 +159,7 @@ numeric::numeric(unsigned int i) : basic(TINFO_numeric) { debugmsg("numeric constructor from uint",LOGLEVEL_CONSTRUCT); // Not the whole uint-range is available if we don't cast to ulong - // first. This is due to the behaviour of the cl_I-ctor, which + // first. This is due to the behaviour of the cl_I-ctor, which // emphasizes efficiency: value = new cl_I((unsigned long)i); calchash(); @@ -231,7 +231,7 @@ numeric::numeric(const char *s) : basic(TINFO_numeric) /** Ctor from CLN types. This is for the initiated user or internal use * only. */ -numeric::numeric(cl_N const & z) : basic(TINFO_numeric) +numeric::numeric(const cl_N & z) : basic(TINFO_numeric) { debugmsg("numeric constructor from cl_N", LOGLEVEL_CONSTRUCT); value = new cl_N(z); @@ -261,13 +261,13 @@ numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_l case 'N': // Ordinary number case 'R': // Integer-decoded real number s >> re.sign >> re.mantissa >> re.exponent; - *value = re.sign * re.mantissa * expt(cl_float(2.0, cl_default_float_format), re.exponent); + *value = re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent); break; case 'C': // Integer-decoded complex number s >> re.sign >> re.mantissa >> re.exponent; s >> im.sign >> im.mantissa >> im.exponent; - *value = complex(re.sign * re.mantissa * expt(cl_float(2.0, cl_default_float_format), re.exponent), - im.sign * im.mantissa * expt(cl_float(2.0, cl_default_float_format), im.exponent)); + *value = ::complex(re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent), + im.sign * im.mantissa * ::expt(cl_float(2.0, cl_default_float_format), im.exponent)); break; default: // Ordinary number s.putback(c); @@ -286,13 +286,13 @@ numeric::numeric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_l switch (c) { case 'R': // Integer-decoded real number f >> re.sign >> re.mantissa >> re.exponent; - *value = re.sign * re.mantissa * expt(cl_float(2.0, cl_default_float_format), re.exponent); + *value = re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent); break; case 'C': // Integer-decoded complex number f >> re.sign >> re.mantissa >> re.exponent; f >> im.sign >> im.mantissa >> im.exponent; - *value = complex(re.sign * re.mantissa * expt(cl_float(2.0, cl_default_float_format), re.exponent), - im.sign * im.mantissa * expt(cl_float(2.0, cl_default_float_format), im.exponent)); + *value = ::complex(re.sign * re.mantissa * ::expt(cl_float(2.0, cl_default_float_format), re.exponent), + im.sign * im.mantissa * ::expt(cl_float(2.0, cl_default_float_format), im.exponent)); break; default: // Ordinary number f.putback(c); @@ -319,18 +319,18 @@ void numeric::archive(archive_node &n) const #ifdef HAVE_SSTREAM // Write number as string ostringstream s; - if (is_crational()) + if (this->is_crational()) s << *value; else { // Non-rational numbers are written in an integer-decoded format // to preserve the precision - if (is_real()) { + if (this->is_real()) { cl_idecoded_float re = integer_decode_float(The(cl_F)(*value)); s << "R"; s << re.sign << " " << re.mantissa << " " << re.exponent; } else { - cl_idecoded_float re = integer_decode_float(The(cl_F)(realpart(*value))); - cl_idecoded_float im = integer_decode_float(The(cl_F)(imagpart(*value))); + cl_idecoded_float re = integer_decode_float(The(cl_F)(::realpart(*value))); + cl_idecoded_float im = integer_decode_float(The(cl_F)(::imagpart(*value))); s << "C"; s << re.sign << " " << re.mantissa << " " << re.exponent << " "; s << im.sign << " " << im.mantissa << " " << im.exponent; @@ -341,18 +341,18 @@ void numeric::archive(archive_node &n) const // Write number as string char buf[1024]; ostrstream f(buf, 1024); - if (is_crational()) + if (this->is_crational()) f << *value << ends; else { // Non-rational numbers are written in an integer-decoded format // to preserve the precision - if (is_real()) { + if (this->is_real()) { cl_idecoded_float re = integer_decode_float(The(cl_F)(*value)); f << "R"; f << re.sign << " " << re.mantissa << " " << re.exponent << ends; } else { - cl_idecoded_float re = integer_decode_float(The(cl_F)(realpart(*value))); - cl_idecoded_float im = integer_decode_float(The(cl_F)(imagpart(*value))); + cl_idecoded_float re = integer_decode_float(The(cl_F)(::realpart(*value))); + cl_idecoded_float im = integer_decode_float(The(cl_F)(::imagpart(*value))); f << "C"; f << re.sign << " " << re.mantissa << " " << re.exponent << " "; f << im.sign << " " << im.mantissa << " " << im.exponent << ends; @@ -381,48 +381,48 @@ void numeric::print(ostream & os, unsigned upper_precedence) const // together with the other routines and produces something compatible to // ginsh input. debugmsg("numeric print", LOGLEVEL_PRINT); - if (is_real()) { + if (this->is_real()) { // case 1, real: x or -x - if ((precedence<=upper_precedence) && (!is_pos_integer())) { + if ((precedence<=upper_precedence) && (!this->is_pos_integer())) { os << "(" << *value << ")"; } else { os << *value; } } else { // case 2, imaginary: y*I or -y*I - if (realpart(*value) == 0) { - if ((precedence<=upper_precedence) && (imagpart(*value) < 0)) { - if (imagpart(*value) == -1) { + if (::realpart(*value) == 0) { + if ((precedence<=upper_precedence) && (::imagpart(*value) < 0)) { + if (::imagpart(*value) == -1) { os << "(-I)"; } else { - os << "(" << imagpart(*value) << "*I)"; + os << "(" << ::imagpart(*value) << "*I)"; } } else { - if (imagpart(*value) == 1) { + if (::imagpart(*value) == 1) { os << "I"; } else { - if (imagpart (*value) == -1) { + if (::imagpart (*value) == -1) { os << "-I"; } else { - os << imagpart(*value) << "*I"; + os << ::imagpart(*value) << "*I"; } } } } else { // case 3, complex: x+y*I or x-y*I or -x+y*I or -x-y*I if (precedence <= upper_precedence) os << "("; - os << realpart(*value); - if (imagpart(*value) < 0) { - if (imagpart(*value) == -1) { + os << ::realpart(*value); + if (::imagpart(*value) < 0) { + if (::imagpart(*value) == -1) { os << "-I"; } else { - os << imagpart(*value) << "*I"; + os << ::imagpart(*value) << "*I"; } } else { - if (imagpart(*value) == 1) { + if (::imagpart(*value) == 1) { os << "+I"; } else { - os << "+" << imagpart(*value) << "*I"; + os << "+" << ::imagpart(*value) << "*I"; } } if (precedence <= upper_precedence) os << ")"; @@ -438,6 +438,8 @@ void numeric::printraw(ostream & os) const debugmsg("numeric printraw", LOGLEVEL_PRINT); os << "numeric(" << *value << ")"; } + + void numeric::printtree(ostream & os, unsigned indent) const { debugmsg("numeric printtree", LOGLEVEL_PRINT); @@ -447,12 +449,13 @@ void numeric::printtree(ostream & os, unsigned indent) const << ", flags=" << flags << endl; } + void numeric::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const { debugmsg("numeric print csrc", LOGLEVEL_PRINT); ios::fmtflags oldflags = os.flags(); os.setf(ios::scientific); - if (is_rational() && !is_integer()) { + if (this->is_rational() && !this->is_integer()) { if (compare(_num0()) > 0) { os << "("; if (type == csrc_types::ctype_cl_N) @@ -481,6 +484,7 @@ void numeric::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) os.flags(oldflags); } + bool numeric::info(unsigned inf) const { switch (inf) { @@ -507,11 +511,11 @@ bool numeric::info(unsigned inf) const case info_flags::negative: return is_negative(); case info_flags::nonnegative: - return compare(_num0())>=0; + return !is_negative(); case info_flags::posint: return is_pos_integer(); case info_flags::negint: - return is_integer() && (compare(_num0())<0); + return is_integer() && is_negative(); case info_flags::nonnegint: return is_nonneg_integer(); case info_flags::even: @@ -524,6 +528,34 @@ bool numeric::info(unsigned inf) const return false; } +/** Disassemble real part and imaginary part to scan for the occurrence of a + * single number. Also handles the imaginary unit. It ignores the sign on + * both this and the argument, which may lead to what might appear as funny + * results: (2+I).has(-2) -> true. But this is consistent, since we also + * would like to have (-2+I).has(2) -> true and we want to think about the + * sign as a multiplicative factor. */ +bool numeric::has(const ex & other) const +{ + if (!is_exactly_of_type(*other.bp, numeric)) + return false; + const numeric & o = static_cast(const_cast(*other.bp)); + if (this->is_equal(o) || this->is_equal(-o)) + return true; + if (o.imag().is_zero()) // e.g. scan for 3 in -3*I + return (this->real().is_equal(o) || this->imag().is_equal(o) || + this->real().is_equal(-o) || this->imag().is_equal(-o)); + else { + if (o.is_equal(I)) // e.g scan for I in 42*I + return !this->is_real(); + if (o.real().is_zero()) // e.g. scan for 2*I in 2*I+1 + return (this->real().has(o*I) || this->imag().has(o*I) || + this->real().has(-o*I) || this->imag().has(-o*I)); + } + return false; +} + + +/** Evaluation of numbers doesn't do anything at all. */ ex numeric::eval(int level) const { // Warning: if this is ever gonna do something, the ex ctors from all kinds @@ -531,6 +563,7 @@ ex numeric::eval(int level) const return this->hold(); } + /** Cast numeric into a floating-point object. For example exact numeric(1) is * returned as a 1.0000000000000000000000 and so on according to how Digits is * currently set. @@ -540,11 +573,20 @@ ex numeric::eval(int level) const ex numeric::evalf(int level) const { // level can safely be discarded for numeric objects. - return numeric(cl_float(1.0, cl_default_float_format) * (*value)); // -> CLN + return numeric(::cl_float(1.0, ::cl_default_float_format) * (*value)); // -> CLN } // protected +/** Implementation of ex::diff() for a numeric. It always returns 0. + * + * @see ex::diff */ +ex numeric::derivative(const symbol & s) const +{ + return _ex0(); +} + + int numeric::compare_same_type(const basic & other) const { GINAC_ASSERT(is_exactly_of_type(other, numeric)); @@ -557,12 +599,23 @@ int numeric::compare_same_type(const basic & other) const return compare(o); } + bool numeric::is_equal_same_type(const basic & other) const { GINAC_ASSERT(is_exactly_of_type(other,numeric)); const numeric *o = static_cast(&other); - return is_equal(*o); + return this->is_equal(*o); +} + +unsigned numeric::calchash(void) const +{ + return (hashvalue=cl_equal_hashcode(*value) | 0x80000000U); + /* + cout << *value << "->" << hashvalue << endl; + hashvalue=HASHVALUE_NUMERIC+1000U; + return HASHVALUE_NUMERIC+1000U; + */ } /* @@ -634,8 +687,14 @@ numeric numeric::power(const numeric & other) const static const numeric * _num1p=&_num1(); if (&other==_num1p) return *this; - if (::zerop(*value) && other.is_real() && ::minusp(realpart(*other.value))) - throw (std::overflow_error("division by zero")); + if (::zerop(*value)) { + if (::zerop(*other.value)) + throw (std::domain_error("numeric::eval(): pow(0,0) is undefined")); + else if (other.is_real() && !::plusp(::realpart(*other.value))) + throw (std::overflow_error("numeric::eval(): division by zero")); + else + return _num0(); + } return numeric(::expt(*value,*other.value)); } @@ -682,8 +741,14 @@ const numeric & numeric::power_dyn(const numeric & other) const static const numeric * _num1p=&_num1(); if (&other==_num1p) return *this; - if (::zerop(*value) && other.is_real() && ::minusp(realpart(*other.value))) - throw (std::overflow_error("division by zero")); + if (::zerop(*value)) { + if (::zerop(*other.value)) + throw (std::domain_error("numeric::eval(): pow(0,0) is undefined")); + else if (other.is_real() && !::plusp(::realpart(*other.value))) + throw (std::overflow_error("numeric::eval(): division by zero")); + else + return _num0(); + } return static_cast((new numeric(::expt(*value,*other.value)))-> setflag(status_flags::dynallocated)); } @@ -725,15 +790,15 @@ const numeric & numeric::operator=(const char * s) * @see numeric::compare(const numeric & other) */ int numeric::csgn(void) const { - if (is_zero()) + if (this->is_zero()) return 0; - if (!::zerop(realpart(*value))) { - if (::plusp(realpart(*value))) + if (!::zerop(::realpart(*value))) { + if (::plusp(::realpart(*value))) return 1; else return -1; } else { - if (::plusp(imagpart(*value))) + if (::plusp(::imagpart(*value))) return 1; else return -1; @@ -750,16 +815,16 @@ int numeric::csgn(void) const int numeric::compare(const numeric & other) const { // Comparing two real numbers? - if (is_real() && other.is_real()) + if (this->is_real() && other.is_real()) // Yes, just compare them return ::cl_compare(The(cl_R)(*value), The(cl_R)(*other.value)); else { // No, first compare real parts - cl_signean real_cmp = ::cl_compare(realpart(*value), realpart(*other.value)); + cl_signean real_cmp = ::cl_compare(::realpart(*value), ::realpart(*other.value)); if (real_cmp) return real_cmp; - return ::cl_compare(imagpart(*value), imagpart(*other.value)); + return ::cl_compare(::imagpart(*value), ::imagpart(*other.value)); } } @@ -777,7 +842,7 @@ bool numeric::is_zero(void) const /** True if object is not complex and greater than zero. */ bool numeric::is_positive(void) const { - if (is_real()) + if (this->is_real()) return ::plusp(The(cl_R)(*value)); // -> CLN return false; } @@ -785,7 +850,7 @@ bool numeric::is_positive(void) const /** True if object is not complex and less than zero. */ bool numeric::is_negative(void) const { - if (is_real()) + if (this->is_real()) return ::minusp(The(cl_R)(*value)); // -> CLN return false; } @@ -799,25 +864,25 @@ bool numeric::is_integer(void) const /** True if object is an exact integer greater than zero. */ bool numeric::is_pos_integer(void) const { - return (is_integer() && ::plusp(The(cl_I)(*value))); // -> CLN + return (this->is_integer() && ::plusp(The(cl_I)(*value))); // -> CLN } /** True if object is an exact integer greater or equal zero. */ bool numeric::is_nonneg_integer(void) const { - return (is_integer() && !::minusp(The(cl_I)(*value))); // -> CLN + return (this->is_integer() && !::minusp(The(cl_I)(*value))); // -> CLN } /** True if object is an exact even integer. */ bool numeric::is_even(void) const { - return (is_integer() && ::evenp(The(cl_I)(*value))); // -> CLN + return (this->is_integer() && ::evenp(The(cl_I)(*value))); // -> CLN } /** True if object is an exact odd integer. */ bool numeric::is_odd(void) const { - return (is_integer() && ::oddp(The(cl_I)(*value))); // -> CLN + return (this->is_integer() && ::oddp(The(cl_I)(*value))); // -> CLN } /** Probabilistic primality test. @@ -825,7 +890,7 @@ bool numeric::is_odd(void) const * @return true if object is exact integer and prime. */ bool numeric::is_prime(void) const { - return (is_integer() && ::isprobprime(The(cl_I)(*value))); // -> CLN + return (this->is_integer() && ::isprobprime(The(cl_I)(*value))); // -> CLN } /** True if object is an exact rational number, may even be complex @@ -857,9 +922,9 @@ bool numeric::is_cinteger(void) const { if (::instanceof(*value, cl_I_ring)) return true; - else if (!is_real()) { // complex case, handle n+m*I - if (::instanceof(realpart(*value), cl_I_ring) && - ::instanceof(imagpart(*value), cl_I_ring)) + else if (!this->is_real()) { // complex case, handle n+m*I + if (::instanceof(::realpart(*value), cl_I_ring) && + ::instanceof(::imagpart(*value), cl_I_ring)) return true; } return false; @@ -871,9 +936,9 @@ bool numeric::is_crational(void) const { if (::instanceof(*value, cl_RA_ring)) return true; - else if (!is_real()) { // complex case, handle Q(i): - if (::instanceof(realpart(*value), cl_RA_ring) && - ::instanceof(imagpart(*value), cl_RA_ring)) + else if (!this->is_real()) { // complex case, handle Q(i): + if (::instanceof(::realpart(*value), cl_RA_ring) && + ::instanceof(::imagpart(*value), cl_RA_ring)) return true; } return false; @@ -884,8 +949,8 @@ bool numeric::is_crational(void) const * @exception invalid_argument (complex inequality) */ bool numeric::operator<(const numeric & other) const { - if (is_real() && other.is_real()) - return (bool)(The(cl_R)(*value) < The(cl_R)(*other.value)); // -> CLN + if (this->is_real() && other.is_real()) + return (The(cl_R)(*value) < The(cl_R)(*other.value)); // -> CLN throw (std::invalid_argument("numeric::operator<(): complex inequality")); return false; // make compiler shut up } @@ -895,8 +960,8 @@ bool numeric::operator<(const numeric & other) const * @exception invalid_argument (complex inequality) */ bool numeric::operator<=(const numeric & other) const { - if (is_real() && other.is_real()) - return (bool)(The(cl_R)(*value) <= The(cl_R)(*other.value)); // -> CLN + if (this->is_real() && other.is_real()) + return (The(cl_R)(*value) <= The(cl_R)(*other.value)); // -> CLN throw (std::invalid_argument("numeric::operator<=(): complex inequality")); return false; // make compiler shut up } @@ -906,8 +971,8 @@ bool numeric::operator<=(const numeric & other) const * @exception invalid_argument (complex inequality) */ bool numeric::operator>(const numeric & other) const { - if (is_real() && other.is_real()) - return (bool)(The(cl_R)(*value) > The(cl_R)(*other.value)); // -> CLN + if (this->is_real() && other.is_real()) + return (The(cl_R)(*value) > The(cl_R)(*other.value)); // -> CLN throw (std::invalid_argument("numeric::operator>(): complex inequality")); return false; // make compiler shut up } @@ -917,8 +982,8 @@ bool numeric::operator>(const numeric & other) const * @exception invalid_argument (complex inequality) */ bool numeric::operator>=(const numeric & other) const { - if (is_real() && other.is_real()) - return (bool)(The(cl_R)(*value) >= The(cl_R)(*other.value)); // -> CLN + if (this->is_real() && other.is_real()) + return (The(cl_R)(*value) >= The(cl_R)(*other.value)); // -> CLN throw (std::invalid_argument("numeric::operator>=(): complex inequality")); return false; // make compiler shut up } @@ -928,7 +993,7 @@ bool numeric::operator>=(const numeric & other) const * You may also consider checking the range first. */ int numeric::to_int(void) const { - GINAC_ASSERT(is_integer()); + GINAC_ASSERT(this->is_integer()); return ::cl_I_to_int(The(cl_I)(*value)); // -> CLN } @@ -937,7 +1002,7 @@ int numeric::to_int(void) const * You may also consider checking the range first. */ long numeric::to_long(void) const { - GINAC_ASSERT(is_integer()); + GINAC_ASSERT(this->is_integer()); return ::cl_I_to_long(The(cl_I)(*value)); // -> CLN } @@ -945,8 +1010,8 @@ long numeric::to_long(void) const * if the number is really not complex before calling this method. */ double numeric::to_double(void) const { - GINAC_ASSERT(is_real()); - return ::cl_double_approx(realpart(*value)); // -> CLN + GINAC_ASSERT(this->is_real()); + return ::cl_double_approx(::realpart(*value)); // -> CLN } /** Real part of a number. */ @@ -980,25 +1045,25 @@ inline cl_heap_ratio* TheRatio (const cl_N& obj) * cases. */ numeric numeric::numer(void) const { - if (is_integer()) { + if (this->is_integer()) { return numeric(*this); } #ifdef SANE_LINKER else if (::instanceof(*value, cl_RA_ring)) { return numeric(::numerator(The(cl_RA)(*value))); } - else if (!is_real()) { // complex case, handle Q(i): + else if (!this->is_real()) { // complex case, handle Q(i): cl_R r = ::realpart(*value); cl_R i = ::imagpart(*value); if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_I_ring)) return numeric(*this); if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_RA_ring)) - return numeric(complex(r*::denominator(The(cl_RA)(i)), ::numerator(The(cl_RA)(i)))); + return numeric(::complex(r*::denominator(The(cl_RA)(i)), ::numerator(The(cl_RA)(i)))); if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_I_ring)) - return numeric(complex(::numerator(The(cl_RA)(r)), i*::denominator(The(cl_RA)(r)))); + return numeric(::complex(::numerator(The(cl_RA)(r)), i*::denominator(The(cl_RA)(r)))); if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_RA_ring)) { - cl_I s = lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i))); - return numeric(complex(::numerator(The(cl_RA)(r))*(exquo(s,::denominator(The(cl_RA)(r)))), + cl_I s = ::lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i))); + return numeric(::complex(::numerator(The(cl_RA)(r))*(exquo(s,::denominator(The(cl_RA)(r)))), ::numerator(The(cl_RA)(i))*(exquo(s,::denominator(The(cl_RA)(i)))))); } } @@ -1006,18 +1071,18 @@ numeric numeric::numer(void) const else if (instanceof(*value, cl_RA_ring)) { return numeric(TheRatio(*value)->numerator); } - else if (!is_real()) { // complex case, handle Q(i): - cl_R r = realpart(*value); - cl_R i = imagpart(*value); + else if (!this->is_real()) { // complex case, handle Q(i): + cl_R r = ::realpart(*value); + cl_R i = ::imagpart(*value); if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring)) return numeric(*this); if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring)) - return numeric(complex(r*TheRatio(i)->denominator, TheRatio(i)->numerator)); + return numeric(::complex(r*TheRatio(i)->denominator, TheRatio(i)->numerator)); if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring)) - return numeric(complex(TheRatio(r)->numerator, i*TheRatio(r)->denominator)); + return numeric(::complex(TheRatio(r)->numerator, i*TheRatio(r)->denominator)); if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring)) { - cl_I s = lcm(TheRatio(r)->denominator, TheRatio(i)->denominator); - return numeric(complex(TheRatio(r)->numerator*(exquo(s,TheRatio(r)->denominator)), + cl_I s = ::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator); + return numeric(::complex(TheRatio(r)->numerator*(exquo(s,TheRatio(r)->denominator)), TheRatio(i)->numerator*(exquo(s,TheRatio(i)->denominator)))); } } @@ -1031,16 +1096,16 @@ numeric numeric::numer(void) const * (i.e denom(4/3+5/6*I) == 6), one in all other cases. */ numeric numeric::denom(void) const { - if (is_integer()) { + if (this->is_integer()) { return _num1(); } #ifdef SANE_LINKER if (instanceof(*value, cl_RA_ring)) { return numeric(::denominator(The(cl_RA)(*value))); } - if (!is_real()) { // complex case, handle Q(i): - cl_R r = realpart(*value); - cl_R i = imagpart(*value); + if (!this->is_real()) { // complex case, handle Q(i): + cl_R r = ::realpart(*value); + cl_R i = ::imagpart(*value); if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_I_ring)) return _num1(); if (::instanceof(r, cl_I_ring) && ::instanceof(i, cl_RA_ring)) @@ -1048,15 +1113,15 @@ numeric numeric::denom(void) const if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_I_ring)) return numeric(::denominator(The(cl_RA)(r))); if (::instanceof(r, cl_RA_ring) && ::instanceof(i, cl_RA_ring)) - return numeric(lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i)))); + return numeric(::lcm(::denominator(The(cl_RA)(r)), ::denominator(The(cl_RA)(i)))); } #else if (instanceof(*value, cl_RA_ring)) { return numeric(TheRatio(*value)->denominator); } - if (!is_real()) { // complex case, handle Q(i): - cl_R r = realpart(*value); - cl_R i = imagpart(*value); + if (!this->is_real()) { // complex case, handle Q(i): + cl_R r = ::realpart(*value); + cl_R i = ::imagpart(*value); if (instanceof(r, cl_I_ring) && instanceof(i, cl_I_ring)) return _num1(); if (instanceof(r, cl_I_ring) && instanceof(i, cl_RA_ring)) @@ -1064,7 +1129,7 @@ numeric numeric::denom(void) const if (instanceof(r, cl_RA_ring) && instanceof(i, cl_I_ring)) return numeric(TheRatio(r)->denominator); if (instanceof(r, cl_RA_ring) && instanceof(i, cl_RA_ring)) - return numeric(lcm(TheRatio(r)->denominator, TheRatio(i)->denominator)); + return numeric(::lcm(TheRatio(r)->denominator, TheRatio(i)->denominator)); } #endif // def SANE_LINKER // at least one float encountered @@ -1079,7 +1144,7 @@ numeric numeric::denom(void) const * in two's complement if it is an integer, 0 otherwise. */ int numeric::int_length(void) const { - if (is_integer()) + if (this->is_integer()) return ::integer_length(The(cl_I)(*value)); // -> CLN else return 0; @@ -1102,7 +1167,7 @@ const numeric some_numeric; const type_info & typeid_numeric=typeid(some_numeric); /** Imaginary unit. This is not a constant but a numeric since we are * natively handing complex numbers anyways. */ -const numeric I = numeric(complex(cl_I(0),cl_I(1))); +const numeric I = numeric(::complex(cl_I(0),cl_I(1))); /** Exponential function. @@ -1195,7 +1260,7 @@ const numeric atan(const numeric & x) const numeric atan(const numeric & y, const numeric & x) { if (x.is_real() && y.is_real()) - return ::atan(realpart(*x.value), realpart(*y.value)); // -> CLN + return ::atan(::realpart(*x.value), ::realpart(*y.value)); // -> CLN else throw (std::invalid_argument("numeric::atan(): complex argument")); } @@ -1265,7 +1330,7 @@ const numeric zeta(const numeric & x) // being an exact zero for CLN, which can be tested and then we can just // pass the number casted to an int: if (x.is_real()) { - int aux = (int)(::cl_double_approx(realpart(*x.value))); + int aux = (int)(::cl_double_approx(::realpart(*x.value))); if (zerop(*x.value-aux)) return ::cl_zeta(aux); // -> CLN } @@ -1378,9 +1443,11 @@ const numeric bernoulli(const numeric & nn) return _num0(); // Until somebody has the Blues and comes up with a much better idea and // codes it (preferably in CLN) we make this a remembering function which - // computes its results using the formula + // computes its results using the defining formula // B(nn) == - 1/(nn+1) * sum_{k=0}^{nn-1}(binomial(nn+1,k)*B(k)) // whith B(0) == 1. + // Be warned, though: the Bernoulli numbers are probably computationally + // very expensive anyhow and you shouldn't expect miracles to happen. static vector results; static int highest_result = -1; int n = nn.sub(_num2()).div(_num2()).to_int(); @@ -1412,23 +1479,50 @@ const numeric bernoulli(const numeric & nn) * @exception range_error (argument must be an integer) */ const numeric fibonacci(const numeric & n) { - if (!n.is_integer()) { + if (!n.is_integer()) throw (std::range_error("numeric::fibonacci(): argument must be integer")); - } - // For positive arguments compute the nearest integer to - // ((1+sqrt(5))/2)^n/sqrt(5). For negative arguments, apply an additional - // sign. Note that we are falling back to longs, but this should suffice - // for all times. - int sig = 1; - const long nn = ::abs(n.to_double()); - if (n.is_negative() && n.is_even()) - sig =-1; + // The following addition formula holds: + // F(n+m) = F(m-1)*F(n) + F(m)*F(n+1) for m >= 1, n >= 0. + // (Proof: For fixed m, the LHS and the RHS satisfy the same recurrence + // w.r.t. n, and the initial values (n=0, n=1) agree. Hence all values + // agree.) + // Replace m by m+1: + // F(n+m+1) = F(m)*F(n) + F(m+1)*F(n+1) for m >= 0, n >= 0 + // Now put in m = n, to get + // F(2n) = (F(n+1)-F(n))*F(n) + F(n)*F(n+1) = F(n)*(2*F(n+1) - F(n)) + // F(2n+1) = F(n)^2 + F(n+1)^2 + // hence + // F(2n+2) = F(n+1)*(2*F(n) + F(n+1)) + if (n.is_zero()) + return _num0(); + if (n.is_negative()) + if (n.is_even()) + return -fibonacci(-n); + else + return fibonacci(-n); - // Need a precision of ((1+sqrt(5))/2)^-n. - cl_float_format_t prec = ::cl_float_format((int)(0.208987641*nn+5)); - cl_R sqrt5 = ::sqrt(::cl_float(5,prec)); - cl_R phi = (1+sqrt5)/2; - return numeric(::round1(::expt(phi,nn)/sqrt5)*sig); + cl_I u(0); + cl_I v(1); + cl_I m = The(cl_I)(*n.value) >> 1L; // floor(n/2); + for (uintL bit=::integer_length(m); bit>0; --bit) { + // Since a squaring is cheaper than a multiplication, better use + // three squarings instead of one multiplication and two squarings. + cl_I u2 = ::square(u); + cl_I v2 = ::square(v); + if (::logbitp(bit-1, m)) { + v = ::square(u + v) - u2; + u = u2 + v2; + } else { + u = v2 - ::square(v - u); + v = u2 + v2; + } + } + if (n.is_even()) + // Here we don't use the squaring formula because one multiplication + // is cheaper than two squarings. + return u * ((v << 1) - u); + else + return ::square(u) + ::square(v); } @@ -1461,7 +1555,6 @@ numeric mod(const numeric & a, const numeric & b) * @return a mod b in the range [-iquo(abs(m)-1,2), iquo(abs(m),2)]. */ numeric smod(const numeric & a, const numeric & b) { - // FIXME: Should this become a member function? if (a.is_integer() && b.is_integer()) { cl_I b2 = The(cl_I)(ceiling1(The(cl_I)(*b.value) / 2)) - 1; return ::mod(The(cl_I)(*a.value) + b2, The(cl_I)(*b.value)) - b2; @@ -1593,21 +1686,21 @@ numeric lcm(const numeric & a, const numeric & b) /** Floating point evaluation of Archimedes' constant Pi. */ ex PiEvalf(void) { - return numeric(cl_pi(cl_default_float_format)); // -> CLN + return numeric(::cl_pi(cl_default_float_format)); // -> CLN } /** Floating point evaluation of Euler's constant Gamma. */ ex EulerGammaEvalf(void) { - return numeric(cl_eulerconst(cl_default_float_format)); // -> CLN + return numeric(::cl_eulerconst(cl_default_float_format)); // -> CLN } /** Floating point evaluation of Catalan's constant. */ ex CatalanEvalf(void) { - return numeric(cl_catalanconst(cl_default_float_format)); // -> CLN + return numeric(::cl_catalanconst(cl_default_float_format)); // -> CLN } @@ -1619,14 +1712,14 @@ _numeric_digits::_numeric_digits() { assert(!too_late); too_late = true; - cl_default_float_format = cl_float_format(17); + cl_default_float_format = ::cl_float_format(17); } _numeric_digits& _numeric_digits::operator=(long prec) { digits=prec; - cl_default_float_format = cl_float_format(prec); + cl_default_float_format = ::cl_float_format(prec); return *this; } @@ -1659,15 +1752,6 @@ ostream& operator<<(ostream& os, const _numeric_digits & e) bool _numeric_digits::too_late = false; -////////// -// utility functions -////////// - -const numeric &ex_to_numeric(const ex &e) -{ - return static_cast(*e.bp); -} - /** Accuracy in decimal digits. Only object of this type! Can be set using * assignment from C++ unsigned ints and evaluated like any built-in type. */ _numeric_digits Digits;