slamchf77.f(3)

NAME
slamchf77.f -

SYNOPSIS

  Functions/Subroutines

real function slamch (CMACH)
SLAMCHF77 deprecated
subroutine slamc1 (BETA, T, RND, IEEE1)
SLAMC1
subroutine slamc2 (BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX)
SLAMC2
real function slamc3 (A, B)
SLAMC3
subroutine slamc4 (EMIN, START, BASE)
SLAMC4
subroutine slamc5 (BETA, P, EMIN, IEEE, EMAX, RMAX)
SLAMC5

Function/Subroutine Documentation

  subroutine slamc1 (integerBETA, integerT, logicalRND, logicalIEEE1)

SLAMC1 Purpose:

 SLAMC1 determines the machine parameters given by BETA, T, RND, and
 IEEE1.

Parameters:
    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.

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

Date:
    April 2012

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.

Definition at line 210 of file slamchf77.f.

  subroutine slamc2 (integerBETA, integerT, logicalRND, realEPS, integerEMIN, realRMIN, integerEMAX, realRMAX)

SLAMC2 Purpose:

 SLAMC2 determines the machine parameters specified in its argument
 list.

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

Date:
    April 2012

Parameters:
    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.

Further Details

  The computation of  EPS  is based on a routine PARANOIA by
  W. Kahan of the University of California at Berkeley.

Definition at line 423 of file slamchf77.f.

  real function slamc3 (realA, realB)

SLAMC3 Purpose:

 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.

Parameters:
    A
    B

              The values A and B.

Definition at line 646 of file slamchf77.f.

  subroutine slamc4 (integerEMIN, realSTART, integerBASE)

SLAMC4 Purpose:

 SLAMC4 is a service routine for SLAMC2.

Parameters:
    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.

Definition at line 693 of file slamchf77.f.

  subroutine slamc5 (integerBETA, integerP, integerEMIN, logicalIEEE, integerEMAX, realRMAX)

SLAMC5 Purpose:

 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.

Parameters:
    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.

Definition at line 801 of file slamchf77.f.

  real function slamch (characterCMACH)

SLAMCHF77 deprecated

Purpose:

     SLAMCH determines single precision machine parameters.

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)

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    April 2012

Definition at line 68 of file slamchf77.f.

Author

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