slamc1()

subroutine slamc1	(	integer	beta,
		integer	t,
		logical	rnd,
		logical	ieee1
	)

Definition at line 131 of file slamch.f.

*
*  -- LAPACK auxiliary routine (version 2.1) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     October 31, 1992
*
*     .. Scalar Arguments ..
      LOGICAL            IEEE1, RND
      INTEGER            BETA, T
*     ..
*
*  Purpose
*  =======
*
*  SLAMC1 determines the machine parameters given by BETA, T, RND, and
*  IEEE1.
*
*  Arguments
*  =========
*
*  BETA    (output) INTEGER
*          The base of the machine.
*
*  T       (output) INTEGER
*          The number of ( BETA ) digits in the mantissa.
*
*  RND     (output) LOGICAL
*          Specifies whether proper rounding  ( RND = .TRUE. )  or
*          chopping  ( RND = .FALSE. )  occurs in addition. This may not
*          be a reliable guide to the way in which the machine performs
*          its arithmetic.
*
*  IEEE1   (output) LOGICAL
*          Specifies whether rounding appears to be done in the IEEE
*          'round to nearest' style.
*
*  Further Details
*  ===============
*
*  The routine is based on the routine  ENVRON  by Malcolm and
*  incorporates suggestions by Gentleman and Marovich. See
*
*     Malcolm M. A. (1972) Algorithms to reveal properties of
*        floating-point arithmetic. Comms. of the ACM, 15, 949-951.
*
*     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.
*
* =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            FIRST, LIEEE1, LRND
      INTEGER            LBETA, LT
      REAL               A, B, C, F, ONE, QTR, SAVEC, T1, T2
*     ..
*     .. External Functions ..
      REAL               SLAMC3
      EXTERNAL           slamc3
*     ..
*     .. Save statement ..
      SAVE               first, lieee1, lbeta, lrnd, lt
*     ..
*     .. Data statements ..
      DATA               first / .true. /
*     ..
*     .. Executable Statements ..
*
      IF( first ) THEN
         first = .false.
         one = 1
*
*        LBETA,  LIEEE1,  LT and  LRND  are the  local values  of  BETA,
*        IEEE1, T and RND.
*
*        Throughout this routine  we use the function  SLAMC3  to ensure
*        that relevant values are  stored and not held in registers,  or
*        are not affected by optimizers.
*
*        Compute  a = 2.0**m  with the  smallest positive integer m such
*        that
*
*           fl( a + 1.0 ) = a.
*
         a = 1
         c = 1
*
*+       WHILE( C.EQ.ONE )LOOP
   10    CONTINUE
         IF( c.EQ.one ) THEN
            a = 2*a
            c = slamc3( a, one )
            c = slamc3( c, -a )
            GO TO 10
         END IF
*+       END WHILE
*
*        Now compute  b = 2.0**m  with the smallest positive integer m
*        such that
*
*           fl( a + b ) .gt. a.
*
         b = 1
         c = slamc3( a, b )
*
*+       WHILE( C.EQ.A )LOOP
   20    CONTINUE
         IF( c.EQ.a ) THEN
            b = 2*b
            c = slamc3( a, b )
            GO TO 20
         END IF
*+       END WHILE
*
*        Now compute the base.  a and c  are neighbouring floating point
*        numbers  in the  interval  ( beta**t, beta**( t + 1 ) )  and so
*        their difference is beta. Adding 0.25 to c is to ensure that it
*        is truncated to beta and not ( beta - 1 ).
*
         qtr = one / 4
         savec = c
         c = slamc3( c, -a )
         lbeta = c + qtr
*
*        Now determine whether rounding or chopping occurs,  by adding a
*        bit  less  than  beta/2  and a  bit  more  than  beta/2  to  a.
*
         b = lbeta
         f = slamc3( b / 2, -b / 100 )
         c = slamc3( f, a )
         IF( c.EQ.a ) THEN
            lrnd = .true.
         ELSE
            lrnd = .false.
         END IF
         f = slamc3( b / 2, b / 100 )
         c = slamc3( f, a )
         IF( ( lrnd ) .AND. ( c.EQ.a ) )
     $      lrnd = .false.
*
*        Try and decide whether rounding is done in the  IEEE  'round to
*        nearest' style. B/2 is half a unit in the last place of the two
*        numbers A and SAVEC. Furthermore, A is even, i.e. has last  bit
*        zero, and SAVEC is odd. Thus adding B/2 to A should not  change
*        A, but adding B/2 to SAVEC should change SAVEC.
*
         t1 = slamc3( b / 2, a )
         t2 = slamc3( b / 2, savec )
         lieee1 = ( t1.EQ.a ) .AND. ( t2.GT.savec ) .AND. lrnd
*
*        Now find  the  mantissa, t.  It should  be the  integer part of
*        log to the base beta of a,  however it is safer to determine  t
*        by powering.  So we find t as the smallest positive integer for
*        which
*
*           fl( beta**t + 1.0 ) = 1.0.
*
         lt = 0
         a = 1
         c = 1
*
*+       WHILE( C.EQ.ONE )LOOP
   30    CONTINUE
         IF( c.EQ.one ) THEN
            lt = lt + 1
            a = a*lbeta
            c = slamc3( a, one )
            c = slamc3( c, -a )
            GO TO 30
         END IF
*+       END WHILE
*
      END IF
*
      beta = lbeta
      t = lt
      rnd = lrnd
      ieee1 = lieee1
      RETURN
*
*     End of SLAMC1
*