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document vector functions
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Fredrik Johansson
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3 changed files with 186 additions and 2 deletions
2
acb.h
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acb.h
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@ -721,14 +721,12 @@ void acb_root_newton(acb_t r, const acb_t a, long m, long index, long prec);
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void acb_root(acb_t r, const acb_t a, long m, long index, long prec);
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*/
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/* TODO: document */
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ACB_INLINE int
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acb_is_finite(const acb_t x)
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{
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return arb_is_finite(acb_realref(x)) && arb_is_finite(acb_imagref(x));
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}
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/* TODO: document */
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ACB_INLINE void
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acb_indeterminate(acb_t x)
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{
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@ -82,6 +82,10 @@ Basic manipulation
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Returns nonzero iff *z* is exactly 1.
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.. function:: int acb_is_finite(const acb_t z)
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Returns nonzero iff *z* certainly is finite.
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.. function:: int acb_is_exact(const acb_t z)
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Returns nonzero iff *z* is exact.
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@ -245,6 +249,12 @@ Precision and comparisons
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and imaginary parts of *x*, i.e. the minimum precision sufficient
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to represent *x* exactly.
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.. function:: void acb_indeterminate(acb_t x)
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Sets *x* to
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`[\operatorname{NaN} \pm \infty] + [\operatorname{NaN} \pm \infty]i`,
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representing an indeterminate result.
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.. function:: void acb_trim(acb_t y, const acb_t x)
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Sets *y* to a a copy of *x* with both the real and imaginary
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@ -665,3 +675,93 @@ Arithmetic-geometric mean
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arithmetic-geometric mean at the point *z* truncated to length *len*, i.e.
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`M(z+x) \in \mathbb{C}[[x]]`.
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Vector functions
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-------------------------------------------------------------------------------
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.. function:: void _acb_vec_zero(acb_ptr A, long n)
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Sets all entries in *vec* to zero.
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.. function:: int _acb_vec_is_zero(acb_srcptr vec, long len)
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Returns nonzero iff all entries in *x* are zero.
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.. function:: int _acb_vec_is_real(acb_srcptr v, long len)
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Returns nonzero iff all entries in *x* have zero imaginary part.
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.. function:: void _acb_vec_set(acb_ptr res, acb_srcptr vec, long len)
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Sets *res* to a copy of *vec*.
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.. function:: void _acb_vec_set_round(acb_ptr res, acb_srcptr vec, long len, long prec)
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Sets *res* to a copy of *vec*, rounding each entry to *prec* bits.
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.. function:: void _acb_vec_neg(acb_ptr res, acb_srcptr vec, long len)
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.. function:: void _acb_vec_add(acb_ptr res, acb_srcptr vec1, acb_srcptr vec2, long len, long prec)
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.. function:: void _acb_vec_sub(acb_ptr res, acb_srcptr vec1, acb_srcptr vec2, long len, long prec)
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.. function:: void _acb_vec_scalar_submul(acb_ptr res, acb_srcptr vec, long len, const acb_t c, long prec)
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.. function:: void _acb_vec_scalar_addmul(acb_ptr res, acb_srcptr vec, long len, const acb_t c, long prec)
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.. function:: void _acb_vec_scalar_mul(acb_ptr res, acb_srcptr vec, long len, const acb_t c, long prec)
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.. function:: void _acb_vec_scalar_mul_ui(acb_ptr res, acb_srcptr vec, long len, ulong c, long prec)
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.. function:: void _acb_vec_scalar_mul_2exp_si(acb_ptr res, acb_srcptr vec, long len, long c)
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.. function:: void _acb_vec_scalar_mul_onei(acb_ptr res, acb_srcptr vec, long len)
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.. function:: void _acb_vec_scalar_div_ui(acb_ptr res, acb_srcptr vec, long len, ulong c, long prec)
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.. function:: void _acb_vec_scalar_div(acb_ptr res, acb_srcptr vec, long len, const acb_t c, long prec)
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.. function:: void _acb_vec_scalar_mul_arb(acb_ptr res, acb_srcptr vec, long len, const arb_t c, long prec)
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.. function:: void _acb_vec_scalar_div_arb(acb_ptr res, acb_srcptr vec, long len, const arb_t c, long prec)
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.. function:: void _acb_vec_scalar_mul_fmpz(acb_ptr res, acb_srcptr vec, long len, const fmpz_t c, long prec)
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.. function:: void _acb_vec_scalar_div_fmpz(acb_ptr res, acb_srcptr vec, long len, const fmpz_t c, long prec)
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Performs the respective scalar operation elementwise.
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.. function:: long _acb_vec_bits(acb_srcptr vec, long len)
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Returns the maximum of :func:`arb_bits` for all entries in *vec*.
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.. function:: void _acb_vec_set_powers(acb_ptr xs, const acb_t x, long len, long prec)
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Sets *xs* to the powers `1, x, x^2, \ldots, x^{len-1}`.
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.. function:: void _acb_vec_add_error_arf_vec(acb_ptr res, arf_srcptr err, long len)
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.. function:: void _acb_vec_add_error_mag_vec(acb_ptr res, mag_srcptr err, long len)
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Adds the magnitude of each entry in *err* to the radius of the
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corresponding entry in *res*.
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.. function:: void _acb_vec_indeterminate(acb_ptr vec, long len)
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Applies :func:`acb_indeterminate` elementwise.
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.. function:: void _acb_vec_trim(acb_ptr res, acb_srcptr vec, long len)
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Applies :func:`acb_trim` elementwise.
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.. function:: int _acb_vec_get_unique_fmpz_vec(fmpz * res, acb_srcptr vec, long len)
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Calls :func:`acb_get_unique_fmpz` elementwise and returns nonzero if
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all entries can be rounded uniquely to integers. If any entry in *vec*
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cannot be rounded uniquely to an integer, returns zero.
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.. function:: void _acb_vec_sort_pretty(acb_ptr vec, long len)
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Sorts the vector of complex numbers based on the real and imaginary parts.
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This is intended to reveal structure when printing a set of complex numbers,
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not to apply an order relation in a rigorous way.
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@ -1344,3 +1344,89 @@ Internals for computing elementary functions
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is applied repeatedly instead of integrating a differential
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equation for the arctangent, as this appears to be more efficient.
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Vector functions
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-------------------------------------------------------------------------------
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.. function:: void _arb_vec_zero(arb_ptr vec, long n)
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Sets all entries in *vec* to zero.
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.. function:: int _arb_vec_is_zero(arb_srcptr vec, long len)
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Returns nonzero iff all entries in *x* are zero.
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.. function:: int _arb_vec_is_finite(arb_srcptr x, long len)
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Returns nonzero iff all entries in *x* certainly are finite.
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.. function:: void _arb_vec_set(arb_ptr res, arb_srcptr vec, long len)
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Sets *res* to a copy of *vec*.
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.. function:: void _arb_vec_set_round(arb_ptr res, arb_srcptr vec, long len, long prec)
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Sets *res* to a copy of *vec*, rounding each entry to *prec* bits.
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.. function:: void _arb_vec_swap(arb_ptr vec1, arb_ptr vec2, long len)
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Swaps the entries of *vec1* and *vec2*.
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.. function:: void _arb_vec_neg(arb_ptr B, arb_srcptr A, long n)
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.. function:: void _arb_vec_sub(arb_ptr C, arb_srcptr A, arb_srcptr B, long n, long prec)
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.. function:: void _arb_vec_add(arb_ptr C, arb_srcptr A, arb_srcptr B, long n, long prec)
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.. function:: void _arb_vec_scalar_mul(arb_ptr res, arb_srcptr vec, long len, const arb_t c, long prec)
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.. function:: void _arb_vec_scalar_div(arb_ptr res, arb_srcptr vec, long len, const arb_t c, long prec)
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.. function:: void _arb_vec_scalar_mul_fmpz(arb_ptr res, arb_srcptr vec, long len, const fmpz_t c, long prec)
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.. function:: void _arb_vec_scalar_mul_2exp_si(arb_ptr res, arb_srcptr src, long len, long c)
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.. function:: void _arb_vec_scalar_addmul(arb_ptr res, arb_srcptr vec, long len, const arb_t c, long prec)
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Performs the respective scalar operation elementwise.
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.. function:: void _arb_vec_dot(arb_t res, arb_srcptr vec1, arb_srcptr vec2, long len2, long prec)
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Sets *res* to the dot product of *vec1* and *vec2*.
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.. function:: void _arb_vec_norm(arb_t res, arb_srcptr vec, long len, long prec)
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Sets *res* to the dot product of *vec* with itself.
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.. function:: void _arb_vec_get_mag(mag_t bound, arb_srcptr vec, long len, long prec)
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Sets *bound* to an upper bound for the entries in *vec*.
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.. function:: long _arb_vec_bits(arb_srcptr x, long len)
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Returns the maximum of :func:`arb_bits` for all entries in *vec*.
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.. function:: void _arb_vec_set_powers(arb_ptr xs, const arb_t x, long len, long prec)
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Sets *xs* to the powers `1, x, x^2, \ldots, x^{len-1}`.
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.. function:: void _arb_vec_add_error_arf_vec(arb_ptr res, arf_srcptr err, long len)
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.. function:: void _arb_vec_add_error_mag_vec(arb_ptr res, mag_srcptr err, long len)
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Adds the magnitude of each entry in *err* to the radius of the
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corresponding entry in *res*.
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.. function:: void _arb_vec_indeterminate(arb_ptr vec, long len)
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Applies :func:`arb_indeterminate` elementwise.
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.. function:: void _arb_vec_trim(arb_ptr res, arb_srcptr vec, long len)
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Applies :func:`arb_trim` elementwise.
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.. function:: int _arb_vec_get_unique_fmpz_vec(fmpz * res, arb_srcptr vec, long len)
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Calls :func:`arb_get_unique_fmpz` elementwise and returns nonzero if
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all entries can be rounded uniquely to integers. If any entry in *vec*
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cannot be rounded uniquely to an integer, returns zero.
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