SuperLU
5.0
|
Determines double precision machine parameters. More...
Macros | |
#define | TRUE_ (1) |
#define | FALSE_ (0) |
#define | abs(x) ((x) >= 0 ? (x) : -(x)) |
#define | min(a, b) ((a) <= (b) ? (a) : (b)) |
#define | max(a, b) ((a) >= (b) ? (a) : (b)) |
Functions | |
double | dlamch_ (char *cmach) |
int | dlamc1_ (int *beta, int *t, int *rnd, int *ieee1) |
int | dlamc2_ (int *beta, int *t, int *rnd, double *eps, int *emin, double *rmin, int *emax, double *rmax) |
double | dlamc3_ (double *a, double *b) |
int | dlamc4_ (int *emin, double *start, int *base) |
int | dlamc5_ (int *beta, int *p, int *emin, int *ieee, int *emax, double *rmax) |
double | pow_di (double *ap, int *bp) |
– LAPACK auxiliary routine (version 2.0) – Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University October 31, 1992
#define abs | ( | x | ) | ((x) >= 0 ? (x) : -(x)) |
#define FALSE_ (0) |
#define max | ( | a, | |
b | |||
) | ((a) >= (b) ? (a) : (b)) |
#define min | ( | a, | |
b | |||
) | ((a) <= (b) ? (a) : (b)) |
#define TRUE_ (1) |
int dlamc1_ | ( | int * | beta, |
int * | t, | ||
int * | rnd, | ||
int * | ieee1 | ||
) |
Purpose
DLAMC1 determines the machine parameters given by BETA, T, RND, and IEEE1.
Arguments
BETA (output) INT The base of the machine.
T (output) INT The number of ( BETA ) digits in the mantissa.
RND (output) INT 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 (output) INT Specifies whether rounding appears to be done in the IEEE 'round to nearest' style.
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.
int dlamc2_ | ( | int * | beta, |
int * | t, | ||
int * | rnd, | ||
double * | eps, | ||
int * | emin, | ||
double * | rmin, | ||
int * | emax, | ||
double * | rmax | ||
) |
Purpose
DLAMC2 determines the machine parameters specified in its argument list.
Arguments
BETA (output) INT The base of the machine.
T (output) INT The number of ( BETA ) digits in the mantissa.
RND (output) INT 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 (output) DOUBLE PRECISION The smallest positive number such that
fl( 1.0 - EPS ) .LT. 1.0,
where fl denotes the computed value.
EMIN (output) INT The minimum exponent before (gradual) underflow occurs.
RMIN (output) DOUBLE PRECISION The smallest normalized number for the machine, given by BASE**( EMIN - 1 ), where BASE is the floating point value
of BETA.
EMAX (output) INT The maximum exponent before overflow occurs.
RMAX (output) DOUBLE PRECISION 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.
double dlamc3_ | ( | double * | a, |
double * | b | ||
) |
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.
Arguments
A, B (input) DOUBLE PRECISION The values A and B.
int dlamc4_ | ( | int * | emin, |
double * | start, | ||
int * | base | ||
) |
Purpose
DLAMC4 is a service routine for DLAMC2.
Arguments
EMIN (output) 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 (input) DOUBLE PRECISION The starting point for determining EMIN.
BASE (input) INT The base of the machine.
int dlamc5_ | ( | int * | beta, |
int * | p, | ||
int * | emin, | ||
int * | ieee, | ||
int * | emax, | ||
double * | rmax | ||
) |
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.
Arguments
BETA (input) INT The base of floating-point arithmetic.
P (input) INT The number of base BETA digits in the mantissa of a floating-point value.
EMIN (input) INT The minimum exponent before (gradual) underflow.
IEEE (input) INT A int flag specifying whether or not the arithmetic system is thought to comply with the IEEE standard.
EMAX (output) INT The largest exponent before overflow
RMAX (output) DOUBLE PRECISION The largest machine floating-point number.
First compute LEXP and UEXP, two powers of 2 that bound abs(EMIN). We then assume that EMAX + abs(EMIN) will sum approximately to the bound that is closest to abs(EMIN). (EMAX is the exponent of the required number RMAX).
double dlamch_ | ( | char * | cmach | ) |
Purpose
DLAMCH determines double precision machine parameters.
Arguments
CMACH (input) CHARACTER*1 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)
double pow_di | ( | double * | ap, |
int * | bp | ||
) |