LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
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Functions/Subroutines
slamchf77.f File Reference

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine slamc1 ( integer  BETA,
integer  T,
logical  RND,
logical  IEEE1 
)

SLAMC1

Purpose: 

 SLAMC1 determines the machine parameters given by BETA, T, RND, and
 IEEE1.
Parameters
[out]BETA
          The base of the machine.
[out]T
          The number of ( BETA ) digits in the mantissa.
[out]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.
[out]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.

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subroutine slamc2 ( integer  BETA,
integer  T,
logical  RND,
real  EPS,
integer  EMIN,
real  RMIN,
integer  EMAX,
real  RMAX 
)

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
[out]BETA
          The base of the machine.
[out]T
          The number of ( BETA ) digits in the mantissa.
[out]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.
[out]EPS
          The smallest positive number such that
             fl( 1.0 - EPS ) .LT. 1.0,
          where fl denotes the computed value.
[out]EMIN
          The minimum exponent before (gradual) underflow occurs.
[out]RMIN
          The smallest normalized number for the machine, given by
          BASE**( EMIN - 1 ), where  BASE  is the floating point value
          of BETA.
[out]EMAX
          The maximum exponent before overflow occurs.
[out]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.

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real function slamc3 ( real  A,
real  B 
)

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
[in]A
[in]B
          The values A and B.

Definition at line 646 of file slamchf77.f.

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subroutine slamc4 ( integer  EMIN,
real  START,
integer  BASE 
)

SLAMC4

Purpose: 

 SLAMC4 is a service routine for SLAMC2.
Parameters
[out]EMIN
          The minimum exponent before (gradual) underflow, computed by
          setting A = START and dividing by BASE until the previous A
          can not be recovered.
[in]START
          The starting point for determining EMIN.
[in]BASE
          The base of the machine.

Definition at line 693 of file slamchf77.f.

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subroutine slamc5 ( integer  BETA,
integer  P,
integer  EMIN,
logical  IEEE,
integer  EMAX,
real  RMAX 
)

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
[in]BETA
          The base of floating-point arithmetic.
[in]P
          The number of base BETA digits in the mantissa of a
          floating-point value.
[in]EMIN
          The minimum exponent before (gradual) underflow.
[in]IEEE
          A logical flag specifying whether or not the arithmetic
          system is thought to comply with the IEEE standard.
[out]EMAX
          The largest exponent before overflow
[out]RMAX
          The largest machine floating-point number.

Definition at line 801 of file slamchf77.f.

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real function slamch ( character  CMACH)

SLAMCHF77 deprecated

Purpose: 
 SLAMCH determines single precision machine parameters.
Parameters
[in]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.

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