Dlamchf77.f -
double precision function dlamch (CMACH)
DLAMCHF77 deprecated subroutine dlamc1 (BETA, T, RND, IEEE1)
DLAMC1 subroutine dlamc2 (BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX)
DLAMC2 double precision function dlamc3 (A, B)
DLAMC3 subroutine dlamc4 (EMIN, START, BASE)
DLAMC4 subroutine dlamc5 (BETA, P, EMIN, IEEE, EMAX, RMAX)
DLAMC5
DLAMC1 Purpose:
DLAMC1 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 206 of file dlamchf77.f.
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:
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 419 of file dlamchf77.f.
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:
A
B
The values A and B.
Definition at line 642 of file dlamchf77.f.
DLAMC4 Purpose:
DLAMC4 is a service routine for DLAMC2.
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 689 of file dlamchf77.f.
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:
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 796 of file dlamchf77.f.
DLAMCHF77 deprecated
Purpose:
DLAMCHF77 determines double precision machine parameters.
Parameters:
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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