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

/* __gmpfr_isqrt && __gmpfr_cuberoot -- Integer square root and cube root | |

Copyright 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. */ | |

#include "mpfr-impl.h" | |

/* returns floor(sqrt(n)) */ | |

unsigned long | |

__gmpfr_isqrt (unsigned long n) | |

{ | |

unsigned long i, s; | |

/* First find an approximation to floor(sqrt(n)) of the form 2^k. */ | |

i = n; | |

s = 1; | |

while (i >= 2) | |

{ | |

i >>= 2; | |

s <<= 1; | |

} | |

do | |

{ | |

s = (s + n / s) / 2; | |

} | |

while (!(s*s <= n && (s*s > s*(s+2) || n <= s*(s+2)))); | |

/* Short explanation: As mathematically s*(s+2) < 2*ULONG_MAX, | |

the condition s*s > s*(s+2) is evaluated as true when s*(s+2) | |

"overflows" but not s*s. This implies that mathematically, one | |

has s*s <= n <= s*(s+2). If s*s "overflows", this means that n | |

is "large" and the inequality n <= s*(s+2) cannot be satisfied. */ | |

return s; | |

} | |

/* returns floor(n^(1/3)) */ | |

unsigned long | |

__gmpfr_cuberoot (unsigned long n) | |

{ | |

unsigned long i, s; | |

/* First find an approximation to floor(cbrt(n)) of the form 2^k. */ | |

i = n; | |

s = 1; | |

while (i >= 4) | |

{ | |

i >>= 3; | |

s <<= 1; | |

} | |

/* Improve the approximation (this is necessary if n is large, so that | |

mathematically (s+1)*(s+1)*(s+1) isn't much larger than ULONG_MAX). */ | |

if (n >= 256) | |

{ | |

s = (2 * s + n / (s * s)) / 3; | |

s = (2 * s + n / (s * s)) / 3; | |

s = (2 * s + n / (s * s)) / 3; | |

} | |

do | |

{ | |

s = (2 * s + n / (s * s)) / 3; | |

} | |

while (!(s*s*s <= n && (s*s*s > (s+1)*(s+1)*(s+1) || | |

n < (s+1)*(s+1)*(s+1)))); | |

return s; | |

} |