LAPACK  3.5.0
LAPACK: Linear Algebra PACKage
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dlamchf77.f File Reference

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Functions/Subroutines

double precision function dlamch (CMACH)
 DLAMCHF77 deprecated More...
 
subroutine dlamc1 (BETA, T, RND, IEEE1)
 DLAMC1 More...
 
subroutine dlamc2 (BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX)
 DLAMC2 More...
 
double precision function dlamc3 (A, B)
 DLAMC3 More...
 
subroutine dlamc4 (EMIN, START, BASE)
 DLAMC4 More...
 
subroutine dlamc5 (BETA, P, EMIN, IEEE, EMAX, RMAX)
 DLAMC5 More...
 

Function/Subroutine Documentation

subroutine dlamc1 ( integer  BETA,
integer  T,
logical  RND,
logical  IEEE1 
)

DLAMC1

Purpose: 

 DLAMC1 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 206 of file dlamchf77.f.

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subroutine dlamc2 ( integer  BETA,
integer  T,
logical  RND,
double precision  EPS,
integer  EMIN,
double precision  RMIN,
integer  EMAX,
double precision  RMAX 
)

DLAMC2

Purpose: 

 DLAMC2 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 419 of file dlamchf77.f.

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double precision function dlamc3 ( double precision  A,
double precision  B 
)

DLAMC3

Purpose: 

 DLAMC3  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 642 of file dlamchf77.f.

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subroutine dlamc4 ( integer  EMIN,
double precision  START,
integer  BASE 
)

DLAMC4

Purpose: 

 DLAMC4 is a service routine for DLAMC2.
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 689 of file dlamchf77.f.

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subroutine dlamc5 ( integer  BETA,
integer  P,
integer  EMIN,
logical  IEEE,
integer  EMAX,
double precision  RMAX 
)

DLAMC5

Purpose: 

 DLAMC5 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 796 of file dlamchf77.f.

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double precision function dlamch ( character  CMACH)

DLAMCHF77 deprecated

Purpose: 
 DLAMCHF77 determines double precision machine parameters.
Parameters
[in]CMACH
          Specifies the value to be returned by DLAMCH:
          = 'E' or 'e',   DLAMCH := eps
          = 'S' or 's ,   DLAMCH := sfmin
          = 'B' or 'b',   DLAMCH := base
          = 'P' or 'p',   DLAMCH := eps*base
          = 'N' or 'n',   DLAMCH := t
          = 'R' or 'r',   DLAMCH := rnd
          = 'M' or 'm',   DLAMCH := emin
          = 'U' or 'u',   DLAMCH := rmin
          = 'L' or 'l',   DLAMCH := emax
          = 'O' or 'o',   DLAMCH := 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 64 of file dlamchf77.f.

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