SLAMC1 determines the machine parameters given by BETA, T, RND, and


 IEEE1.

BETA

          The base of the machine.

T

          The number of ( BETA ) digits in the mantissa.

RND

          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

          Specifies whether rounding appears to be done in the IEEE


          'round to nearest' style.

LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..

April 2012

  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.

 SLAMC2 determines the machine parameters specified in its argument


 list.

LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..

April 2012

BETA

          The base of the machine.

T

          The number of ( BETA ) digits in the mantissa.

RND

          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.

EPS

          The smallest positive number such that


             fl( 1.0 - EPS ) .LT. 1.0,


          where fl denotes the computed value.

EMIN

          The minimum exponent before (gradual) underflow occurs.

RMIN

          The smallest normalized number for the machine, given by


          BASE**( EMIN - 1 ), where  BASE  is the floating point value


          of BETA.

EMAX

          The maximum exponent before overflow occurs.

RMAX

          The largest positive number for the machine, given by


          BASE**EMAX * ( 1 - EPS ), where  BASE  is the floating point


          value of BETA.

  The computation of  EPS  is based on a routine PARANOIA by


  W. Kahan of the University of California at Berkeley.

 SLAMC3  is intended to force  A  and  B  to be stored prior to doing


 the addition of  A  and  B ,  for use in situations where optimizers


 might hold one of these in a register.

A
B

          The values A and B.

 SLAMC4 is a service routine for SLAMC2.

EMIN

          The minimum exponent before (gradual) underflow, computed by


          setting A = START and dividing by BASE until the previous A


          can not be recovered.

START

          The starting point for determining EMIN.

BASE

          The base of the machine.

 SLAMC5 attempts to compute RMAX, the largest machine floating-point


 number, without overflow.  It assumes that EMAX + abs(EMIN) 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,


 EMAX = 28718).  It will also fail if the value supplied for EMIN is


 too large (i.e. too close to zero), probably with overflow.

BETA

          The base of floating-point arithmetic.

P

          The number of base BETA digits in the mantissa of a


          floating-point value.

EMIN

          The minimum exponent before (gradual) underflow.

IEEE

          A logical flag specifying whether or not the arithmetic


          system is thought to comply with the IEEE standard.

EMAX

          The largest exponent before overflow

RMAX

          The largest machine floating-point number.

 SLAMCH determines single precision machine parameters.

CMACH

          Specifies the value to be returned by SLAMCH:


          = 'E' or 'e',   SLAMCH := eps


          = 'S' or 's ,   SLAMCH := sfmin


          = 'B' or 'b',   SLAMCH := base


          = 'P' or 'p',   SLAMCH := eps*base


          = 'N' or 'n',   SLAMCH := t


          = 'R' or 'r',   SLAMCH := rnd


          = 'M' or 'm',   SLAMCH := emin


          = 'U' or 'u',   SLAMCH := rmin


          = 'L' or 'l',   SLAMCH := emax


          = 'O' or 'o',   SLAMCH := rmax


          where


          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)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

April 2012