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<h1>SRC/dlamch.c File Reference</h1>Determines double precision machine parameters. <a href="#_details">More...</a>
<p>
<code>#include &lt;stdio.h&gt;</code><br>
<code>#include &quot;<a class="el" href="slu__Cnames_8h-source.html">slu_Cnames.h</a>&quot;</code><br>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Defines</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">#define&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#ca1e6c3771fa0306e1dad2b11d22a8e5">TRUE_</a>&nbsp;&nbsp;&nbsp;(1)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">#define&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#d4986ecbba005b963f63a85f7c8c281d">FALSE_</a>&nbsp;&nbsp;&nbsp;(0)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">#define&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#3aa069ac3980707dae1e0530f50d59e4">abs</a>(x)&nbsp;&nbsp;&nbsp;((x) &gt;= 0 ? (x) : -(x))</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">#define&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#c6afabdc09a49a433ee19d8a9486056d">min</a>(a, b)&nbsp;&nbsp;&nbsp;((a) &lt;= (b) ? (a) : (b))</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">#define&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#ffe776513b24d84b39af8ab0930fef7f">max</a>(a, b)&nbsp;&nbsp;&nbsp;((a) &gt;= (b) ? (a) : (b))</td></tr>
 
<tr><td colspan="2"><br><h2>Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#8f8bef103c45d87276d6508164f5883c">dlamch_</a> (char *cmach)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#eaa4a6b78a27d38535ca1a7dc010c92e">dlamc1_</a> (int *beta, int *t, int *rnd, int *ieee1)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#a05275111d3110333608138f59f3f8c3">dlamc2_</a> (int *beta, int *t, int *rnd, double *eps, int *emin, double *rmin, int *emax, double *rmax)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#35cd4981c9a7d3c46226a75f68720dad">dlamc3_</a> (double *a, double *b)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#141c735fa5fb73f28150470ee91da0f9">dlamc4_</a> (int *emin, double *start, int *base)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#0309c617fb0124d2d3ca73dfbdda9fa9">dlamc5_</a> (int *beta, int *p, int *emin, int *ieee, int *emax, double *rmax)</td></tr>
 
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="dlamch_8c.html#9537f19743fcaaac6231895afa9f9e4d">pow_di</a> (double *ap, int *bp)</td></tr>
 
</table>
<hr><a name="_details"></a><h2>Detailed Description</h2>
<pre>
       -- LAPACK auxiliary routine (version 2.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       October 31, 1992   
 </pre> <hr><h2>Define Documentation</h2>
<a class="anchor" name="3aa069ac3980707dae1e0530f50d59e4"></a><!-- doxytag: member="dlamch.c::abs" ref="3aa069ac3980707dae1e0530f50d59e4" args="(x)" -->
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          <td class="memname">#define abs          </td>
          <td>(</td>
          <td class="paramtype">x&nbsp;</td>
          <td class="paramname">          </td>
          <td>&nbsp;)&nbsp;</td>
          <td width="100%">&nbsp;&nbsp;&nbsp;((x) &gt;= 0 ? (x) : -(x))</td>
        </tr>
      </table>
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<div class="memdoc">
 
<p>
 
</div>
</div><p>
<a class="anchor" name="d4986ecbba005b963f63a85f7c8c281d"></a><!-- doxytag: member="dlamch.c::FALSE_" ref="d4986ecbba005b963f63a85f7c8c281d" args="" -->
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          <td class="memname">#define FALSE_&nbsp;&nbsp;&nbsp;(0)          </td>
        </tr>
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<p>
 
</div>
</div><p>
<a class="anchor" name="ffe776513b24d84b39af8ab0930fef7f"></a><!-- doxytag: member="dlamch.c::max" ref="ffe776513b24d84b39af8ab0930fef7f" args="(a, b)" -->
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          <td class="memname">#define max          </td>
          <td>(</td>
          <td class="paramtype">a,         <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">b&nbsp;</td>
          <td class="paramname">          </td>
          <td>&nbsp;)&nbsp;</td>
          <td width="100%">&nbsp;&nbsp;&nbsp;((a) &gt;= (b) ? (a) : (b))</td>
        </tr>
      </table>
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<p>
 
</div>
</div><p>
<a class="anchor" name="c6afabdc09a49a433ee19d8a9486056d"></a><!-- doxytag: member="dlamch.c::min" ref="c6afabdc09a49a433ee19d8a9486056d" args="(a, b)" -->
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          <td class="memname">#define min          </td>
          <td>(</td>
          <td class="paramtype">a,         <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">b&nbsp;</td>
          <td class="paramname">          </td>
          <td>&nbsp;)&nbsp;</td>
          <td width="100%">&nbsp;&nbsp;&nbsp;((a) &lt;= (b) ? (a) : (b))</td>
        </tr>
      </table>
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<p>
 
</div>
</div><p>
<a class="anchor" name="ca1e6c3771fa0306e1dad2b11d22a8e5"></a><!-- doxytag: member="dlamch.c::TRUE_" ref="ca1e6c3771fa0306e1dad2b11d22a8e5" args="" -->
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          <td class="memname">#define TRUE_&nbsp;&nbsp;&nbsp;(1)          </td>
        </tr>
      </table>
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<p>
 
</div>
</div><p>
<hr><h2>Function Documentation</h2>
<a class="anchor" name="eaa4a6b78a27d38535ca1a7dc010c92e"></a><!-- doxytag: member="dlamch.c::dlamc1_" ref="eaa4a6b78a27d38535ca1a7dc010c92e" args="(int *beta, int *t, int *rnd, int *ieee1)" -->
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          <td class="memname">int dlamc1_           </td>
          <td>(</td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>beta</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>t</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>rnd</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>ieee1</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td width="100%"></td>
        </tr>
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<p>
<pre>
 Purpose   
    =======</pre><p>
<pre>    DLAMC1 determines the machine parameters given by BETA, T, RND, and   
    IEEE1.</pre><p>
<pre>    Arguments   
    =========</pre><p>
<pre>    BETA    (output) INT   
            The base of the machine.</pre><p>
<pre>    T       (output) INT   
            The number of ( BETA ) digits in the mantissa.</pre><p>
<pre>    RND     (output) INT   
            Specifies whether proper rounding  ( RND = .TRUE. )  or   
            chopping  ( RND = .FALSE. )  occurs in addition. This may not</pre><p>
<pre>            be a reliable guide to the way in which the machine performs</pre><p>
<pre>            its arithmetic.</pre><p>
<pre>    IEEE1   (output) INT   
            Specifies whether rounding appears to be done in the IEEE   
            'round to nearest' style.</pre><p>
<pre>    Further Details   
    ===============</pre><p>
<pre>    The routine is based on the routine  ENVRON  by Malcolm and   
    incorporates suggestions by Gentleman and Marovich. See</pre><p>
<pre>       Malcolm M. A. (1972) Algorithms to reveal properties of   
          floating-point arithmetic. Comms. of the ACM, 15, 949-951.</pre><p>
<pre>       Gentleman W. M. and Marovich S. B. (1974) More on algorithms   
          that reveal properties of floating point arithmetic units.   
          Comms. of the ACM, 17, 276-277.</pre><p>
<pre>   ===================================================================== 
</pre> 
</div>
</div><p>
<a class="anchor" name="a05275111d3110333608138f59f3f8c3"></a><!-- doxytag: member="dlamch.c::dlamc2_" ref="a05275111d3110333608138f59f3f8c3" args="(int *beta, int *t, int *rnd, double *eps, int *emin, double *rmin, int *emax, double *rmax)" -->
<div class="memitem">
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          <td class="memname">int dlamc2_           </td>
          <td>(</td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>beta</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>t</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>rnd</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>eps</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>emin</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>rmin</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>emax</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>rmax</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td width="100%"></td>
        </tr>
      </table>
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<p>
<pre>
    Purpose   
    =======</pre><p>
<pre>    DLAMC2 determines the machine parameters specified in its argument   
    list.</pre><p>
<pre>    Arguments   
    =========</pre><p>
<pre>    BETA    (output) INT   
            The base of the machine.</pre><p>
<pre>    T       (output) INT   
            The number of ( BETA ) digits in the mantissa.</pre><p>
<pre>    RND     (output) INT   
            Specifies whether proper rounding  ( RND = .TRUE. )  or   
            chopping  ( RND = .FALSE. )  occurs in addition. This may not</pre><p>
<pre>            be a reliable guide to the way in which the machine performs</pre><p>
<pre>            its arithmetic.</pre><p>
<pre>    EPS     (output) DOUBLE PRECISION   
            The smallest positive number such that</pre><p>
<pre>               fl( 1.0 - EPS ) .LT. 1.0,</pre><p>
<pre>            where fl denotes the computed value.</pre><p>
<pre>    EMIN    (output) INT   
            The minimum exponent before (gradual) underflow occurs.</pre><p>
<pre>    RMIN    (output) DOUBLE PRECISION   
            The smallest normalized number for the machine, given by   
            BASE**( EMIN - 1 ), where  BASE  is the floating point value</pre><p>
<pre>            of BETA.</pre><p>
<pre>    EMAX    (output) INT   
            The maximum exponent before overflow occurs.</pre><p>
<pre>    RMAX    (output) DOUBLE PRECISION   
            The largest positive number for the machine, given by   
            BASE**EMAX * ( 1 - EPS ), where  BASE  is the floating point</pre><p>
<pre>            value of BETA.</pre><p>
<pre>    Further Details   
    ===============</pre><p>
<pre>    The computation of  EPS  is based on a routine PARANOIA by   
    W. Kahan of the University of California at Berkeley.</pre><p>
<pre>   ===================================================================== 
</pre> 
</div>
</div><p>
<a class="anchor" name="35cd4981c9a7d3c46226a75f68720dad"></a><!-- doxytag: member="dlamch.c::dlamc3_" ref="35cd4981c9a7d3c46226a75f68720dad" args="(double *a, double *b)" -->
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          <td class="memname">double dlamc3_           </td>
          <td>(</td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>a</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>b</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td width="100%"></td>
        </tr>
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<p>
<pre>
    Purpose   
    =======</pre><p>
<pre>    DLAMC3  is intended to force  A  and  B  to be stored prior to doing</pre><p>
<pre>    the addition of  A  and  B ,  for use in situations where optimizers</pre><p>
<pre>    might hold one of these in a register.</pre><p>
<pre>    Arguments   
    =========</pre><p>
<pre>    A, B    (input) DOUBLE PRECISION   
            The values A and B.</pre><p>
<pre>   ===================================================================== 
</pre> 
</div>
</div><p>
<a class="anchor" name="141c735fa5fb73f28150470ee91da0f9"></a><!-- doxytag: member="dlamch.c::dlamc4_" ref="141c735fa5fb73f28150470ee91da0f9" args="(int *emin, double *start, int *base)" -->
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          <td class="memname">int dlamc4_           </td>
          <td>(</td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>emin</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>start</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>base</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td width="100%"></td>
        </tr>
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<p>
<pre>
    Purpose   
    =======</pre><p>
<pre>    DLAMC4 is a service routine for DLAMC2.</pre><p>
<pre>    Arguments   
    =========</pre><p>
<pre>    EMIN    (output) EMIN   
            The minimum exponent before (gradual) underflow, computed by</pre><p>
<pre>            setting A = START and dividing by BASE until the previous A   
            can not be recovered.</pre><p>
<pre>    START   (input) DOUBLE PRECISION   
            The starting point for determining EMIN.</pre><p>
<pre>    BASE    (input) INT   
            The base of the machine.</pre><p>
<pre>   ===================================================================== 
</pre> 
</div>
</div><p>
<a class="anchor" name="0309c617fb0124d2d3ca73dfbdda9fa9"></a><!-- doxytag: member="dlamch.c::dlamc5_" ref="0309c617fb0124d2d3ca73dfbdda9fa9" args="(int *beta, int *p, int *emin, int *ieee, int *emax, double *rmax)" -->
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          <td class="memname">int dlamc5_           </td>
          <td>(</td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>beta</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>p</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>emin</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>ieee</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int *&nbsp;</td>
          <td class="paramname"> <em>emax</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">double *&nbsp;</td>
          <td class="paramname"> <em>rmax</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td width="100%"></td>
        </tr>
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<p>
<pre>
    Purpose   
    =======</pre><p>
<pre>    DLAMC5 attempts to compute RMAX, the largest machine floating-point   
    number, without overflow.  It assumes that EMAX + <a class="el" href="slamch_8c.html#3aa069ac3980707dae1e0530f50d59e4">abs(EMIN)</a> sum   
    approximately to a power of 2.  It will fail on machines where this   
    assumption does not hold, for example, the Cyber 205 (EMIN = -28625,</pre><p>
<pre>    EMAX = 28718).  It will also fail if the value supplied for EMIN is   
    too large (i.e. too close to zero), probably with overflow.</pre><p>
<pre>    Arguments   
    =========</pre><p>
<pre>    BETA    (input) INT   
            The base of floating-point arithmetic.</pre><p>
<pre>    P       (input) INT   
            The number of base BETA digits in the mantissa of a   
            floating-point value.</pre><p>
<pre>    EMIN    (input) INT   
            The minimum exponent before (gradual) underflow.</pre><p>
<pre>    IEEE    (input) INT   
            A int flag specifying whether or not the arithmetic   
            system is thought to comply with the IEEE standard.</pre><p>
<pre>    EMAX    (output) INT   
            The largest exponent before overflow</pre><p>
<pre>    RMAX    (output) DOUBLE PRECISION   
            The largest machine floating-point number.</pre><p>
<pre>   =====================================================================</pre><p>
<pre>       First compute LEXP and UEXP, two powers of 2 that bound   
       <a class="el" href="slamch_8c.html#3aa069ac3980707dae1e0530f50d59e4">abs(EMIN)</a>. We then assume that EMAX + <a class="el" href="slamch_8c.html#3aa069ac3980707dae1e0530f50d59e4">abs(EMIN)</a> will sum   
       approximately to the bound that is closest to <a class="el" href="slamch_8c.html#3aa069ac3980707dae1e0530f50d59e4">abs(EMIN)</a>.   
       (EMAX is the exponent of the required number RMAX).
</pre> 
</div>
</div><p>
<a class="anchor" name="8f8bef103c45d87276d6508164f5883c"></a><!-- doxytag: member="dlamch.c::dlamch_" ref="8f8bef103c45d87276d6508164f5883c" args="(char *cmach)" -->
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          <td class="memname">double dlamch_           </td>
          <td>(</td>
          <td class="paramtype">char *&nbsp;</td>
          <td class="paramname"> <em>cmach</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td width="100%"></td>
        </tr>
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<pre>
    Purpose   
    =======</pre><p>
<pre>    DLAMCH determines double precision machine parameters.</pre><p>
<pre>    Arguments   
    =========</pre><p>
<pre>    CMACH   (input) CHARACTER*1   
            Specifies the value to be returned by DLAMCH:   
            = 'E' or 'e',   DLAMCH := eps   
            = 'S' or 's ,   DLAMCH := sfmin   
            = 'B' or 'b',   DLAMCH := base   
            = 'P' or 'p',   DLAMCH := eps*base   
            = 'N' or 'n',   DLAMCH := t   
            = 'R' or 'r',   DLAMCH := rnd   
            = 'M' or 'm',   DLAMCH := emin   
            = 'U' or 'u',   DLAMCH := rmin   
            = 'L' or 'l',   DLAMCH := emax   
            = 'O' or 'o',   DLAMCH := rmax</pre><p>
<pre>            where</pre><p>
<pre>            eps   = relative machine precision   
            sfmin = safe minimum, such that 1/sfmin does not overflow   
            base  = base of the machine   
            prec  = eps*base   
            t     = number of (base) digits in the mantissa   
            rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise   
            emin  = minimum exponent before (gradual) underflow   
            rmin  = underflow threshold - base**(emin-1)   
            emax  = largest exponent before overflow   
            rmax  = overflow threshold  - (base**emax)*(1-eps)</pre><p>
<pre>   ===================================================================== 
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          <td class="memname">double pow_di           </td>
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<hr size="1"><address style="text-align: right;"><small>Generated on Mon Nov 22 10:23:47 2010 for SuperLU by&nbsp;
<a href="http://www.doxygen.org/index.html">
<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.5 </small></address>
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