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

/* mpfr_root -- kth root. | |

Copyright 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/k) is done as follows: | |

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

with 2^(k*(n-1)) <= m < 2^(k*n) where n = PREC(y) | |

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

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

i.e. m must have at least k*(n-1)+1 bits | |

then, not taking into account the sign, the result will be | |

x^(1/k) = s * 2^e or (s+1) * 2^e according to the rounding mode. | |

*/ | |

int | |

mpfr_root (mpfr_ptr y, mpfr_srcptr x, unsigned long k, 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); | |

if (MPFR_UNLIKELY (k <= 1)) | |

{ | |

if (k < 1) /* k==0 => y=x^(1/0)=x^(+Inf) */ | |

#if 0 | |

/* For 0 <= x < 1 => +0. | |

For x = 1 => 1. | |

For x > 1, => +Inf. | |

For x < 0 => NaN. | |

*/ | |

{ | |

if (MPFR_IS_NEG (x) && !MPFR_IS_ZERO (x)) | |

{ | |

MPFR_SET_NAN (y); | |

MPFR_RET_NAN; | |

} | |

inexact = mpfr_cmp (x, __gmpfr_one); | |

if (inexact == 0) | |

return mpfr_set_ui (y, 1, rnd_mode); /* 1 may be Out of Range */ | |

else if (inexact < 0) | |

return mpfr_set_ui (y, 0, rnd_mode); /* 0+ */ | |

else | |

{ | |

mpfr_set_inf (y, 1); | |

return 0; | |

} | |

} | |

#endif | |

{ | |

MPFR_SET_NAN (y); | |

MPFR_RET_NAN; | |

} | |

else /* y =x^(1/1)=x */ | |

return mpfr_set (y, x, rnd_mode); | |

} | |

/* Singular values */ | |

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

{ | |

if (MPFR_IS_NAN (x)) | |

{ | |

MPFR_SET_NAN (y); /* NaN^(1/k) = NaN */ | |

MPFR_RET_NAN; | |

} | |

else if (MPFR_IS_INF (x)) /* +Inf^(1/k) = +Inf | |

-Inf^(1/k) = -Inf if k odd | |

-Inf^(1/k) = NaN if k even */ | |

{ | |

if (MPFR_IS_NEG(x) && (k % 2 == 0)) | |

{ | |

MPFR_SET_NAN (y); | |

MPFR_RET_NAN; | |

} | |

MPFR_SET_INF (y); | |

MPFR_SET_SAME_SIGN (y, x); | |

MPFR_RET (0); | |

} | |

else /* x is necessarily 0: (+0)^(1/k) = +0 | |

(-0)^(1/k) = -0 */ | |

{ | |

MPFR_ASSERTD (MPFR_IS_ZERO (x)); | |

MPFR_SET_ZERO (y); | |

MPFR_SET_SAME_SIGN (y, x); | |

MPFR_RET (0); | |

} | |

} | |

/* Returns NAN for x < 0 and k even */ | |

else if (MPFR_IS_NEG (x) && (k % 2 == 0)) | |

{ | |

MPFR_SET_NAN (y); | |

MPFR_RET_NAN; | |

} | |

/* 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 % (mp_exp_t) k; | |

if (r < 0) | |

r += k; /* now r = e (mod k) with 0 <= e < r */ | |

/* x = (m*2^r) * 2^(e-r) where e-r is a multiple of k */ | |

MPFR_MPZ_SIZEINBASE2 (size_m, m); | |

/* for rounding to nearest, we want the round bit to be in the root */ | |

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

/* we now multiply m by 2^(r+k*sh) so that root(m,k) will give | |

exactly n bits: we want k*(n-1)+1 <= size_m + k*sh + r <= k*n | |

i.e. sh = floor ((kn-size_m-r)/k) */ | |

if ((mp_exp_t) size_m + r > k * (mp_exp_t) n) | |

sh = 0; /* we already have too many bits */ | |

else | |

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

sh = k * 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 k */ | |

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

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

inexact = mpz_root (m, m, k) == 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 += k * 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 / (mp_exp_t) k); | |

if (negative) | |

{ | |

MPFR_CHANGE_SIGN (y); | |

inexact = -inexact; | |

} | |

mpz_clear (m); | |

MPFR_SAVE_EXPO_FREE (expo); | |

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

} |