mirror of
https://github.com/vale981/arb
synced 2025-03-04 17:01:40 -05:00
more documentation and test code
This commit is contained in:
Fredrik Johansson
parent
32763c5a2e
commit
9a4b57ec91
6 changed files with 244 additions and 31 deletions
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@ -124,7 +124,7 @@ Computation of single Bernoulli numbers
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of the Bernoulli number `B_n`.
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This function computes the denominator `d` using von Staudt-Clausen
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theorem, numerically approximates `B_n` using :func:`bernoulli_fmprb_ui_zeta`,
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theorem, numerically approximates `B_n` using :func:`arb_bernoulli_ui_zeta`,
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and then rounds `d B_n` to the correct numerator.
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If the working precision is insufficient to determine the numerator,
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the function prints a warning message and retries with increased
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@ -137,7 +137,7 @@ Memory management
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Error bounding
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-------------------------------------------------------------------------------
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.. function:: long hypgeom_estimate_terms(const fmpr_t z, int r, long d)
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.. function:: long hypgeom_estimate_terms(const mag_t z, int r, long d)
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Computes an approximation of the largest `n` such
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that `|z|^n/(n!)^r = 2^{-d}`, giving a first-order estimate of the
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@ -154,7 +154,7 @@ Error bounding
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The function aborts if the computed value of `n` is greater
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than or equal to LONG_MAX / 2.
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.. function:: long hypgeom_bound(fmpr_t error, int r, long C, long D, long K, const fmpr_t TK, const fmpr_t z, long prec)
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.. function:: long hypgeom_bound(mag_t error, int r, long C, long D, long K, const mag_t TK, const mag_t z, long prec)
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Computes a truncation parameter sufficient to achieve *prec* bits
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of absolute accuracy, according to the strategy described above.
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@ -179,13 +179,29 @@ Error bounding
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Summation
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-------------------------------------------------------------------------------
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.. function:: void hypgeom_fmprb_sum(fmprb_t P, fmprb_t Q, const hypgeom_t hyp, const long n, long prec)
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.. function:: void fmprb_hypgeom_sum(fmprb_t P, fmprb_t Q, const hypgeom_t hyp, const long n, long prec)
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Computes `P, Q` such that `P / Q = \sum_{k=0}^{n-1} T(k)` where `T(k)`
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is defined by *hyp*,
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using binary splitting and a working precision of *prec* bits.
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.. function:: void hypgeom_fmprb_infsum(fmprb_t P, fmprb_t Q, hypgeom_t hyp, long tol, long prec)
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.. function:: void fmprb_hypgeom_infsum(fmprb_t P, fmprb_t Q, hypgeom_t hyp, long tol, long prec)
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Computes `P, Q` such that `P / Q = \sum_{k=0}^{\infty} T(k)` where `T(k)`
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is defined by *hyp*, using binary splitting and
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working precision of *prec* bits.
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The number of terms is chosen automatically to bound the
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truncation error by at most `2^{-\mathrm{tol}}`.
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The bound for the truncation error is included in the output
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as part of *P*.
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.. function:: void arb_hypgeom_sum(arb_t P, arb_t Q, const hypgeom_t hyp, const long n, long prec)
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Computes `P, Q` such that `P / Q = \sum_{k=0}^{n-1} T(k)` where `T(k)`
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is defined by *hyp*,
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using binary splitting and a working precision of *prec* bits.
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.. function:: void arb_hypgeom_infsum(arb_t P, arb_t Q, hypgeom_t hyp, long tol, long prec)
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Computes `P, Q` such that `P / Q = \sum_{k=0}^{\infty} T(k)` where `T(k)`
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is defined by *hyp*, using binary splitting and
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@ -40,10 +40,24 @@ Memory management
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.. function:: void mag_init_set(mag_t x, const mag_t y)
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Initializes *x* and sets it to the value of *y*.
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.. function:: void mag_swap(mag_t x, mag_t y)
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Swaps *x* and *y* efficiently.
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.. function:: void mag_set(mag_t x, const mag_t y)
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Sets *x* to the value of *y*.
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.. function:: mag_ptr _mag_vec_init(long n)
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Allocates a vector of length *n*. All entries are set to zero.
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.. function:: void _mag_vec_clear(mag_ptr v, long n)
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Clears a vector of length *n*.
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Special values
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-------------------------------------------------------------------------------
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@ -100,25 +114,57 @@ Arithmetic
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.. function:: void mag_mul_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t y)
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Sets `z` to `x \times 2^y`. This operation is exact.
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Sets *z* to `x \times 2^y`. This operation is exact.
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.. function:: void mag_mul(mag_t z, const mag_t x, const mag_t y)
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Sets `z` to an upper bound for `xy`.
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.. function:: void mag_mul_ui(mag_t z, const mag_t x, ulong y)
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.. function:: void mag_mul_fmpz(mag_t z, const mag_t x, const fmpz_t y)
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Sets *z* to an upper bound for `xy`.
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.. function:: void mag_add(mag_t z, const mag_t x, const mag_t y)
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Sets *z* to an upper bound for `x + y`.
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.. function:: void mag_addmul(mag_t z, const mag_t x, const mag_t y)
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Sets `z` to an upper bound for `z + xy`.
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Sets *z* to an upper bound for `z + xy`.
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.. function:: void mag_add_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t e)
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Sets `z` to an upper bound for `x + 2^e`.
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Sets *z* to an upper bound for `x + 2^e`.
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.. function:: void mag_div(mag_t z, const mag_t x, const mag_t y)
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Sets `z` to an upper bound for `x / y`.
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.. function:: void mag_div_ui(mag_t z, const mag_t x, ulong y)
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Fast versions
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.. function:: void mag_div_fmpz(mag_t z, const mag_t x, const fmpz_t y)
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Sets *z* to an upper bound for `x / y`.
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.. function:: void mag_mul_lower(mag_t z, const mag_t x, const mag_t y)
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.. function:: void mag_mul_ui_lower(mag_t z, const mag_t x, ulong y)
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.. function:: void mag_mul_fmpz_lower(mag_t z, const mag_t x, const fmpz_t y)
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Sets *z* to a lower bound for `xy`.
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.. function:: void mag_add_lower(mag_t z, const mag_t x, const mag_t y)
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Sets *z* to a lower bound for `x + y`.
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.. function:: void mag_pow_ui(mag_t z, const mag_t x, ulong e)
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Sets *z* to an upper bound for `x^e`.
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.. function:: void mag_pow_ui_lower(mag_t z, const mag_t x, ulong e)
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Sets *z* to a lower bound for `x^e`.
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Fast, unsafe versions
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-------------------------------------------------------------------------------
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The following methods assume that all inputs are finite and that all exponents
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@ -140,15 +186,15 @@ as they will be overwritten directly (thus leaking memory).
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.. function:: void mag_fast_mul(mag_t z, const mag_t x, const mag_t y)
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Sets `z` to an upper bound for `xy`.
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Sets *z* to an upper bound for `xy`.
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.. function:: void mag_fast_addmul(mag_t z, const mag_t x, const mag_t y)
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Sets `z` to an upper bound for `z + xy`.
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Sets *z* to an upper bound for `z + xy`.
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.. function:: void mag_fast_add_2exp_si(mag_t z, const mag_t x, long e)
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Sets `z` to an upper bound for `x + 2^e`.
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Sets *z* to an upper bound for `x + 2^e`.
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Input and output
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-------------------------------------------------------------------------------
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@ -172,15 +218,23 @@ Random generation
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Conversions
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-------------------------------------------------------------------------------
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.. function:: void mag_set_d(mag_t y, double x)
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.. function:: void mag_set_fmpr(mag_t y, const fmpr_t x)
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.. function:: void mag_set_ui(mag_t y, ulong x)
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.. function:: void mag_set_fmpz(mag_t y, const fmpz_t x)
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Sets *y* to an upper bound for `|x|`.
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.. function:: void mag_set_d_2exp_fmpz(mag_t z, double x, const fmpz_t y)
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.. function:: void mag_set_fmpz_2exp_fmpz(mag_t z, const fmpz_t x, const fmpz_t y)
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Sets *z* to an upper bound for `x \times 2^y`.
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.. function:: void mag_set_ui_2exp_si(mag_t z, ulong x, long y)
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.. function:: void mag_set_fmpr(mag_t y, const fmpr_t x)
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Sets *y* to an upper bound for *x*.
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Sets *z* to an upper bound for `|x| \times 2^y`.
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.. function:: void mag_get_fmpr(fmpr_t y, const mag_t x)
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@ -190,3 +244,34 @@ Conversions
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Sets *y* exactly to *x*. Assumes that no overflow occurs.
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.. function:: void mag_set_ui_lower(mag_t z, ulong x)
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.. function:: void mag_set_fmpz_lower(mag_t z, const fmpz_t x)
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Sets *y* to a lower bound for `|x|`.
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.. function:: void mag_set_fmpz_2exp_fmpz_lower(mag_t z, const fmpz_t x, const fmpz_t y)
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Sets *z* to a lower bound for `|x| \times 2^y`.
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Special functions
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-------------------------------------------------------------------------------
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.. function:: void mag_log1p(mag_t z, const mag_t x)
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Sets *z* to an upper bound for `\log(1+x)`. The bound is computed
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accurately for small *x*.
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.. function:: void mag_fac_ui(mag_t z, ulong n)
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Sets *z* to an upper bound for `n!`.
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.. function:: void mag_rfac_ui(mag_t z, ulong n)
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Sets *z* to an upper bound for `1/n!`.
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.. function:: void mag_bernoulli_div_fac_ui(mag_t z, ulong n)
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Sets *z* to an upper bound for `|B_n| / n!` where `B_n` denotes
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a Bernoulli number.
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@ -19,7 +19,7 @@ a correct error bound for the numerical approximation of `p(n)`.
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Optionally, hardware double arithmetic can be used for low-precision
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terms. This gives a significant speedup for small (e.g. `n < 10^6`).
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.. function:: void partitions_rademacher_bound(fmpr_t b, const fmpz_t n, ulong N)
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.. function:: void partitions_rademacher_bound(arf_t b, const fmpz_t n, ulong N)
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Sets `b` to an upper bound for
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@ -33,7 +33,7 @@ terms. This gives a significant speedup for small (e.g. `n < 10^6`).
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Hardy-Ramanujan-Rademacher formula when the series is taken up
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to the term `t(n,N)` inclusive.
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.. function:: partitions_hrr_sum_fmprb(fmprb_t x, const fmpz_t n, long N0, long N, int use_doubles)
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.. function:: partitions_hrr_sum_arb(arb_t x, const fmpz_t n, long N0, long N, int use_doubles)
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Evaluates the partial sum `\sum_{k=N_0}^N t(n,k)` of the
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Hardy-Ramanujan-Rademacher series.
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@ -57,7 +57,7 @@ terms. This gives a significant speedup for small (e.g. `n < 10^6`).
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has been selected with :func:`flint_set_num_threads()`, the computation
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time will be reduced by using two threads.
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See :func:`partitions_hrr_sum_fmprb` for an explanation of the
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See :func:`partitions_hrr_sum_arb` for an explanation of the
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*use_doubles* option.
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.. function:: void partitions_fmpz_ui(fmpz_t p, ulong n)
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@ -71,5 +71,5 @@ terms. This gives a significant speedup for small (e.g. `n < 10^6`).
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Computes the partition function `p(n)`, enabling the use of doubles
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internally. This significantly speeds up evaluation for small `n`
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(e.g. `n < 10^6`), but the error bounds are not certified
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(see remarks for :func:`partitions_hrr_sum_fmprb`).
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(see remarks for :func:`partitions_hrr_sum_arb`).
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14
mag.h
14
mag.h
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@ -288,7 +288,6 @@ mag_equal(const mag_t x, const mag_t y)
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void mag_mul(mag_t z, const mag_t x, const mag_t y);
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/* TODO: document */
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void mag_mul_lower(mag_t z, const mag_t x, const mag_t y);
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void mag_addmul(mag_t z, const mag_t x, const mag_t y);
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@ -297,7 +296,6 @@ void mag_add_2exp_fmpz(mag_t z, const mag_t x, const fmpz_t e);
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void mag_add(mag_t z, const mag_t x, const mag_t y);
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/* TODO: document */
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void mag_add_lower(mag_t z, const mag_t x, const mag_t y);
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void mag_div(mag_t z, const mag_t x, const mag_t y);
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@ -616,7 +614,6 @@ mag_cmp_2exp_si(const mag_t x, long e)
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return (fmpz_cmp_si(MAG_EXPREF(x), e) <= 0) ? -1 : 1;
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}
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/* TODO: document */
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static __inline__ mag_ptr
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_mag_vec_init(long n)
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{
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@ -638,7 +635,6 @@ _mag_vec_clear(mag_ptr v, long n)
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flint_free(v);
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}
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/* TODO: document/test */
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static __inline__ void mag_set_d(mag_t z, double x)
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{
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fmpz_t e;
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@ -651,23 +647,23 @@ static __inline__ void mag_set_d(mag_t z, double x)
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double mag_d_log_upper_bound(double x);
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double mag_d_log_lower_bound(double x);
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/* TODO: document */
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void mag_log1p(mag_t z, const mag_t x);
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/* TODO: document/test */
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/* TODO: test */
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void mag_pow_ui(mag_t z, const mag_t x, ulong e);
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void mag_pow_ui_lower(mag_t z, const mag_t x, ulong e);
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/* TODO: document/test */
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/* TODO: test */
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void mag_fac_ui(mag_t z, ulong n);
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void mag_rfac_ui(mag_t z, ulong n);
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/* TODO: document/test */
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/* TODO: test */
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void mag_bernoulli_div_fac_ui(mag_t z, ulong n);
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/* TODO: document/test */
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/* TODO: test */
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void mag_set_fmpz_2exp_fmpz_lower(mag_t z, const fmpz_t man, const fmpz_t exp);
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/* TODO: test functions below */
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static __inline__ void
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mag_set_ui(mag_t z, ulong x)
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{
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116
mag/test/t-set_d.c
Normal file
116
mag/test/t-set_d.c
Normal file
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@ -0,0 +1,116 @@
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/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2014 Fredrik Johansson
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******************************************************************************/
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#include "double_extras.h"
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#include "mag.h"
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/* XXX: d_randtest is not good enough */
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#define EXP_MINUS_32 2.3283064365386962891e-10
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#define EXP_MINUS_64 5.42101086242752217e-20
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double
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d_randtest2(flint_rand_t state)
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{
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mp_limb_t m1, m2;
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double t;
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if (FLINT_BITS == 64)
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{
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m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1));
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t = ((double) m1) * EXP_MINUS_64;
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}
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else
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{
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m1 = n_randtest(state) | (UWORD(1) << (FLINT_BITS - 1));
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m2 = n_randtest(state);
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t = ((double) m1) * EXP_MINUS_32 +
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((double) m2) * EXP_MINUS_64;
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}
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return t;
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}
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int main()
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{
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long iter;
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flint_rand_t state;
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printf("set_d....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 100000; iter++)
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{
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fmpr_t a, b, c;
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mag_t m;
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double x;
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fmpr_init(a);
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fmpr_init(b);
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fmpr_init(c);
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mag_init(m);
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x = d_randtest2(state);
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x = ldexp(x, 100 - n_randint(state, 200));
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if (n_randint(state, 100) == 0)
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x = 0.0;
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fmpr_set_d(a, x);
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mag_set_d(m, x);
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||||
mag_get_fmpr(b, m);
|
||||
|
||||
fmpr_set(c, a);
|
||||
fmpr_mul_ui(c, c, 1025, MAG_BITS, FMPR_RND_UP);
|
||||
fmpr_mul_2exp_si(c, c, -10);
|
||||
|
||||
MAG_CHECK_BITS(m)
|
||||
|
||||
if (!(fmpr_cmpabs(a, b) <= 0 && fmpr_cmpabs(b, c) <= 0))
|
||||
{
|
||||
printf("FAIL\n\n");
|
||||
printf("a = "); fmpr_print(a); printf("\n\n");
|
||||
printf("b = "); fmpr_print(b); printf("\n\n");
|
||||
printf("c = "); fmpr_print(c); printf("\n\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmpr_clear(a);
|
||||
fmpr_clear(b);
|
||||
fmpr_clear(c);
|
||||
mag_clear(m);
|
||||
}
|
||||
|
||||
flint_randclear(state);
|
||||
flint_cleanup();
|
||||
printf("PASS\n");
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
||||
Loading…
Add table
Reference in a new issue