dlamch.f.html

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      DOUBLE PRECISION FUNCTION <a name="DLAMCH.1"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( CMACH )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          CMACH
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DLAMCH.14"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> determines double precision machine parameters.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  CMACH   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the value to be returned by <a name="DLAMCH.20"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>:
</span><span class="comment">*</span><span class="comment">          = 'E' or 'e',   <a name="DLAMCH.21"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := eps
</span><span class="comment">*</span><span class="comment">          = 'S' or 's ,   <a name="DLAMCH.22"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := sfmin
</span><span class="comment">*</span><span class="comment">          = 'B' or 'b',   <a name="DLAMCH.23"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := base
</span><span class="comment">*</span><span class="comment">          = 'P' or 'p',   <a name="DLAMCH.24"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := eps*base
</span><span class="comment">*</span><span class="comment">          = 'N' or 'n',   <a name="DLAMCH.25"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := t
</span><span class="comment">*</span><span class="comment">          = 'R' or 'r',   <a name="DLAMCH.26"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := rnd
</span><span class="comment">*</span><span class="comment">          = 'M' or 'm',   <a name="DLAMCH.27"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := emin
</span><span class="comment">*</span><span class="comment">          = 'U' or 'u',   <a name="DLAMCH.28"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := rmin
</span><span class="comment">*</span><span class="comment">          = 'L' or 'l',   <a name="DLAMCH.29"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := emax
</span><span class="comment">*</span><span class="comment">          = 'O' or 'o',   <a name="DLAMCH.30"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> := rmax
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          where
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          eps   = relative machine precision
</span><span class="comment">*</span><span class="comment">          sfmin = safe minimum, such that 1/sfmin does not overflow
</span><span class="comment">*</span><span class="comment">          base  = base of the machine
</span><span class="comment">*</span><span class="comment">          prec  = eps*base
</span><span class="comment">*</span><span class="comment">          t     = number of (base) digits in the mantissa
</span><span class="comment">*</span><span class="comment">          rnd   = 1.0 when rounding occurs in addition, 0.0 otherwise
</span><span class="comment">*</span><span class="comment">          emin  = minimum exponent before (gradual) underflow
</span><span class="comment">*</span><span class="comment">          rmin  = underflow threshold - base**(emin-1)
</span><span class="comment">*</span><span class="comment">          emax  = largest exponent before overflow
</span><span class="comment">*</span><span class="comment">          rmax  = overflow threshold  - (base**emax)*(1-eps)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            FIRST, LRND
      INTEGER            BETA, IMAX, IMIN, IT
      DOUBLE PRECISION   BASE, EMAX, EMIN, EPS, PREC, RMACH, RMAX, RMIN,
     $                   RND, SFMIN, SMALL, T
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.58"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.59"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="DLAMC2.62"></a><a href="dlamch.f.html#DLAMC2.316">DLAMC2</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Save statement ..
</span>      SAVE               FIRST, EPS, SFMIN, BASE, T, RND, EMIN, RMIN,
     $                   EMAX, RMAX, PREC
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Data statements ..
</span>      DATA               FIRST / .TRUE. /
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      IF( FIRST ) THEN
         CALL <a name="DLAMC2.74"></a><a href="dlamch.f.html#DLAMC2.316">DLAMC2</a>( BETA, IT, LRND, EPS, IMIN, RMIN, IMAX, RMAX )
         BASE = BETA
         T = IT
         IF( LRND ) THEN
            RND = ONE
            EPS = ( BASE**( 1-IT ) ) / 2
         ELSE
            RND = ZERO
            EPS = BASE**( 1-IT )
         END IF
         PREC = EPS*BASE
         EMIN = IMIN
         EMAX = IMAX
         SFMIN = RMIN
         SMALL = ONE / RMAX
         IF( SMALL.GE.SFMIN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Use SMALL plus a bit, to avoid the possibility of rounding
</span><span class="comment">*</span><span class="comment">           causing overflow when computing  1/sfmin.
</span><span class="comment">*</span><span class="comment">
</span>            SFMIN = SMALL*( ONE+EPS )
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.98"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'E'</span> ) ) THEN
         RMACH = EPS
      ELSE IF( <a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'S'</span> ) ) THEN
         RMACH = SFMIN
      ELSE IF( <a name="LSAME.102"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'B'</span> ) ) THEN
         RMACH = BASE
      ELSE IF( <a name="LSAME.104"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'P'</span> ) ) THEN
         RMACH = PREC
      ELSE IF( <a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'N'</span> ) ) THEN
         RMACH = T
      ELSE IF( <a name="LSAME.108"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'R'</span> ) ) THEN
         RMACH = RND
      ELSE IF( <a name="LSAME.110"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'M'</span> ) ) THEN
         RMACH = EMIN
      ELSE IF( <a name="LSAME.112"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'U'</span> ) ) THEN
         RMACH = RMIN
      ELSE IF( <a name="LSAME.114"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'L'</span> ) ) THEN
         RMACH = EMAX
      ELSE IF( <a name="LSAME.116"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( CMACH, <span class="string">'O'</span> ) ) THEN
         RMACH = RMAX
      END IF
<span class="comment">*</span><span class="comment">
</span>      <a name="DLAMCH.120"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a> = RMACH
      FIRST  = .FALSE.
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DLAMCH.124"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>
</span><span class="comment">*</span><span class="comment">
</span>      END
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">***********************************************************************
</span><span class="comment">*</span><span class="comment">
</span><a name="DLAMC1.130"></a>      SUBROUTINE <a name="DLAMC1.130"></a><a href="dlamch.f.html#DLAMC1.130">DLAMC1</a>( BETA, T, RND, IEEE1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      LOGICAL            IEEE1, RND
      INTEGER            BETA, T
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DLAMC1.144"></a><a href="dlamch.f.html#DLAMC1.130">DLAMC1</a> determines the machine parameters given by BETA, T, RND, and
</span><span class="comment">*</span><span class="comment">  IEEE1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  BETA    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The base of the machine.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  T       (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of ( BETA ) digits in the mantissa.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RND     (output) LOGICAL
</span><span class="comment">*</span><span class="comment">          Specifies whether proper rounding  ( RND = .TRUE. )  or
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