chromium / native_client / nacl-gcc / f80d6b9ee7f94755c697ffb7194fb01dd0c537dd / . / mpfr-2.4.1 / cbrt.c

/* mpfr_cbrt -- cube root function. | |

Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. | |

Contributed by the Arenaire and Cacao projects, INRIA. | |

This file is part of the GNU MPFR Library. | |

The GNU MPFR Library is free software; you can redistribute it and/or modify | |

it under the terms of the GNU Lesser General Public License as published by | |

the Free Software Foundation; either version 2.1 of the License, or (at your | |

option) any later version. | |

The GNU MPFR Library 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 Lesser General Public | |

License for more details. | |

You should have received a copy of the GNU Lesser General Public License | |

along with the GNU MPFR Library; see the file COPYING.LIB. If not, write to | |

the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, | |

MA 02110-1301, USA. */ | |

#define MPFR_NEED_LONGLONG_H | |

#include "mpfr-impl.h" | |

/* The computation of y = x^(1/3) is done as follows: | |

Let x = sign * m * 2^(3*e) where m is an integer | |

with 2^(3n-3) <= m < 2^(3n) where n = PREC(y) | |

and m = s^3 + r where 0 <= r and m < (s+1)^3 | |

we want that s has n bits i.e. s >= 2^(n-1), or m >= 2^(3n-3) | |

i.e. m must have at least 3n-2 bits | |

then x^(1/3) = s * 2^e if r=0 | |

x^(1/3) = (s+1) * 2^e if round up | |

x^(1/3) = (s-1) * 2^e if round down | |

x^(1/3) = s * 2^e if nearest and r < 3/2*s^2+3/4*s+1/8 | |

(s+1) * 2^e otherwise | |

*/ | |

int | |

mpfr_cbrt (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) | |

{ | |

mpz_t m; | |

mp_exp_t e, r, sh; | |

mp_prec_t n, size_m, tmp; | |

int inexact, negative; | |

MPFR_SAVE_EXPO_DECL (expo); | |

/* special values */ | |

if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) | |

{ | |

if (MPFR_IS_NAN (x)) | |

{ | |

MPFR_SET_NAN (y); | |

MPFR_RET_NAN; | |

} | |

else if (MPFR_IS_INF (x)) | |

{ | |

MPFR_SET_INF (y); | |

MPFR_SET_SAME_SIGN (y, x); | |

MPFR_RET (0); | |

} | |

/* case 0: cbrt(+/- 0) = +/- 0 */ | |

else /* x is necessarily 0 */ | |

{ | |

MPFR_ASSERTD (MPFR_IS_ZERO (x)); | |

MPFR_SET_ZERO (y); | |

MPFR_SET_SAME_SIGN (y, x); | |

MPFR_RET (0); | |

} | |

} | |

/* General case */ | |

MPFR_SAVE_EXPO_MARK (expo); | |

mpz_init (m); | |

e = mpfr_get_z_exp (m, x); /* x = m * 2^e */ | |

if ((negative = MPFR_IS_NEG(x))) | |

mpz_neg (m, m); | |

r = e % 3; | |

if (r < 0) | |

r += 3; | |

/* x = (m*2^r) * 2^(e-r) = (m*2^r) * 2^(3*q) */ | |

MPFR_MPZ_SIZEINBASE2 (size_m, m); | |

n = MPFR_PREC (y) + (rnd_mode == GMP_RNDN); | |

/* we want 3*n-2 <= size_m + 3*sh + r <= 3*n | |

i.e. 3*sh + size_m + r <= 3*n */ | |

sh = (3 * (mp_exp_t) n - (mp_exp_t) size_m - r) / 3; | |

sh = 3 * sh + r; | |

if (sh >= 0) | |

{ | |

mpz_mul_2exp (m, m, sh); | |

e = e - sh; | |

} | |

else if (r > 0) | |

{ | |

mpz_mul_2exp (m, m, r); | |

e = e - r; | |

} | |

/* invariant: x = m*2^e, with e divisible by 3 */ | |

/* we reuse the variable m to store the cube root, since it is not needed | |

any more: we just need to know if the root is exact */ | |

inexact = mpz_root (m, m, 3) == 0; | |

MPFR_MPZ_SIZEINBASE2 (tmp, m); | |

sh = tmp - n; | |

if (sh > 0) /* we have to flush to 0 the last sh bits from m */ | |

{ | |

inexact = inexact || ((mp_exp_t) mpz_scan1 (m, 0) < sh); | |

mpz_div_2exp (m, m, sh); | |

e += 3 * sh; | |

} | |

if (inexact) | |

{ | |

if (negative) | |

rnd_mode = MPFR_INVERT_RND (rnd_mode); | |

if (rnd_mode == GMP_RNDU | |

|| (rnd_mode == GMP_RNDN && mpz_tstbit (m, 0))) | |

inexact = 1, mpz_add_ui (m, m, 1); | |

else | |

inexact = -1; | |

} | |

/* either inexact is not zero, and the conversion is exact, i.e. inexact | |

is not changed; or inexact=0, and inexact is set only when | |

rnd_mode=GMP_RNDN and bit (n+1) from m is 1 */ | |

inexact += mpfr_set_z (y, m, GMP_RNDN); | |

MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / 3); | |

if (negative) | |

{ | |

MPFR_CHANGE_SIGN (y); | |

inexact = -inexact; | |

} | |

mpz_clear (m); | |

MPFR_SAVE_EXPO_FREE (expo); | |

return mpfr_check_range (y, inexact, rnd_mode); | |

} |