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<meta content="text/html;charset=UTF-8" http-equiv="Content-Type">
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<title>SuperLU: SRC/slamch.c File Reference</title>
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<link href="doxygen.css" rel="stylesheet" type="text/css">
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Main Page
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Data Structures
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Files
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SRC/slamch.c File ReferenceDetermines single precision machine parameters and other service routines. More...
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#include <stdio.h>
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#include "slu_Cnames.h"
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Defines
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#define TRUE_ (1)
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#define FALSE_ (0)
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#define min(a, b) ((a) <= (b) ? (a) : (b))
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#define max(a, b) ((a) >= (b) ? (a) : (b))
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#define abs(x) ((x) >= 0 ? (x) : -(x))
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#define dabs(x) (double)abs(x)
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Functions
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float slamch_ (char *cmach)
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int slamc1_ (int *beta, int *t, int *rnd, int *ieee1)
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int slamc2_ (int *beta, int *t, int *rnd, float *eps, int *emin, float *rmin, int *emax, float *rmax)
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double slamc3_ (float *a, float *b)
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int slamc4_ (int *emin, float *start, int *base)
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int slamc5_ (int *beta, int *p, int *emin, int *ieee, int *emax, float *rmax)
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double pow_ri (float *ap, int *bp)
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Detailed Description
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-- LAPACK auxiliary routine (version 2.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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October 31, 1992
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Define Documentation
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#define abs
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(
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x
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)
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((x) >= 0 ? (x) : -(x))
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#define dabs
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(
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x
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)
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(double)abs(x)
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#define FALSE_ (0)
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#define max
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(
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a,
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b
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)
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((a) >= (b) ? (a) : (b))
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#define min
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(
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a,
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b
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)
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((a) <= (b) ? (a) : (b))
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#define TRUE_ (1)
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Function Documentation
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double pow_ri
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(
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float *
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ap,
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int *
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bp
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)
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int slamc1_
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(
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int *
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beta,
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int *
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t,
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int *
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rnd,
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int *
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ieee1
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)
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Purpose
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=======
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SLAMC1 determines the machine parameters given by BETA, T, RND, and
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IEEE1.
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Arguments
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=========
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BETA (output) INT
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The base of the machine.
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T (output) INT
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The number of ( BETA ) digits in the mantissa.
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RND (output) INT
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Specifies whether proper rounding ( RND = .TRUE. ) or
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chopping ( RND = .FALSE. ) occurs in addition. This may not
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be a reliable guide to the way in which the machine performs
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its arithmetic.
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IEEE1 (output) INT
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Specifies whether rounding appears to be done in the IEEE
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'round to nearest' style.
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Further Details
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===============
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The routine is based on the routine ENVRON by Malcolm and
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incorporates suggestions by Gentleman and Marovich. See
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Malcolm M. A. (1972) Algorithms to reveal properties of
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floating-point arithmetic. Comms. of the ACM, 15, 949-951.
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Gentleman W. M. and Marovich S. B. (1974) More on algorithms
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that reveal properties of floating point arithmetic units.
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Comms. of the ACM, 17, 276-277.
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=====================================================================
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int slamc2_
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(
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int *
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beta,
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int *
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t,
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int *
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rnd,
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float *
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eps,
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int *
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emin,
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float *
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rmin,
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int *
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emax,
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float *
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rmax
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)
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Purpose
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=======
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SLAMC2 determines the machine parameters specified in its argument
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list.
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Arguments
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=========
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BETA (output) INT
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The base of the machine.
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T (output) INT
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The number of ( BETA ) digits in the mantissa.
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RND (output) INT
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Specifies whether proper rounding ( RND = .TRUE. ) or
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chopping ( RND = .FALSE. ) occurs in addition. This may not
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be a reliable guide to the way in which the machine performs
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its arithmetic.
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EPS (output) FLOAT
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The smallest positive number such that
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fl( 1.0 - EPS ) .LT. 1.0,
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where fl denotes the computed value.
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EMIN (output) INT
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The minimum exponent before (gradual) underflow occurs.
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RMIN (output) FLOAT
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The smallest normalized number for the machine, given by
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BASE**( EMIN - 1 ), where BASE is the floating point value
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of BETA.
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7d535a |
EMAX (output) INT
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7d535a |
The maximum exponent before overflow occurs.
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7d535a |
RMAX (output) FLOAT
|
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7d535a |
The largest positive number for the machine, given by
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7d535a |
BASE**EMAX * ( 1 - EPS ), where BASE is the floating point
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7d535a |
value of BETA.
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7d535a |
Further Details
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===============
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The computation of EPS is based on a routine PARANOIA by
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W. Kahan of the University of California at Berkeley.
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=====================================================================
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double slamc3_
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(
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7d535a |
float *
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a,
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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float *
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7d535a |
b
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7d535a |
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7d535a |
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7d535a |
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)
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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Purpose
|
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7d535a |
=======
|
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7d535a |
SLAMC3 is intended to force A and B to be stored prior to doing
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7d535a |
the addition of A and B , for use in situations where optimizers
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7d535a |
might hold one of these in a register.
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7d535a |
Arguments
|
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7d535a |
=========
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7d535a |
A, B (input) FLOAT
|
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7d535a |
The values A and B.
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7d535a |
=====================================================================
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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int slamc4_
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(
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7d535a |
int *
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7d535a |
emin,
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7d535a |
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7d535a |
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7d535a |
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7d535a |
|
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7d535a |
float *
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kusano |
7d535a |
start,
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7d535a |
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kusano |
7d535a |
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7d535a |
|
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7d535a |
|
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7d535a |
int *
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7d535a |
base
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kusano |
7d535a |
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kusano |
7d535a |
|
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7d535a |
|
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7d535a |
)
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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kusano |
7d535a |
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kusano |
7d535a |
|
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kusano |
7d535a |
|
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7d535a |
Purpose
|
|
kusano |
7d535a |
=======
|
|
kusano |
7d535a |
SLAMC4 is a service routine for SLAMC2.
|
|
kusano |
7d535a |
Arguments
|
|
kusano |
7d535a |
=========
|
|
kusano |
7d535a |
EMIN (output) EMIN
|
|
kusano |
7d535a |
The minimum exponent before (gradual) underflow, computed by
|
|
kusano |
7d535a |
setting A = START and dividing by BASE until the previous A
|
|
kusano |
7d535a |
can not be recovered.
|
|
kusano |
7d535a |
START (input) FLOAT
|
|
kusano |
7d535a |
The starting point for determining EMIN.
|
|
kusano |
7d535a |
BASE (input) INT
|
|
kusano |
7d535a |
The base of the machine.
|
|
kusano |
7d535a |
=====================================================================
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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7d535a |
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kusano |
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|
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int slamc5_
|
|
kusano |
7d535a |
(
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7d535a |
int *
|
|
kusano |
7d535a |
beta,
|
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7d535a |
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7d535a |
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7d535a |
|
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7d535a |
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7d535a |
int *
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kusano |
7d535a |
p,
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7d535a |
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kusano |
7d535a |
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7d535a |
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7d535a |
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7d535a |
int *
|
|
kusano |
7d535a |
emin,
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kusano |
7d535a |
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kusano |
7d535a |
|
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7d535a |
|
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7d535a |
|
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7d535a |
int *
|
|
kusano |
7d535a |
ieee,
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7d535a |
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7d535a |
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7d535a |
|
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7d535a |
|
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kusano |
7d535a |
int *
|
|
kusano |
7d535a |
emax,
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7d535a |
|
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kusano |
7d535a |
|
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kusano |
7d535a |
|
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kusano |
7d535a |
|
|
kusano |
7d535a |
float *
|
|
kusano |
7d535a |
rmax
|
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kusano |
7d535a |
|
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kusano |
7d535a |
|
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kusano |
7d535a |
|
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kusano |
7d535a |
)
|
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7d535a |
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kusano |
7d535a |
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kusano |
7d535a |
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7d535a |
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kusano |
7d535a |
|
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kusano |
7d535a |
|
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kusano |
7d535a |
|
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kusano |
7d535a |
|
|
kusano |
7d535a |
Purpose
|
|
kusano |
7d535a |
=======
|
|
kusano |
7d535a |
SLAMC5 attempts to compute RMAX, the largest machine floating-point
|
|
kusano |
7d535a |
number, without overflow. It assumes that EMAX + abs(EMIN) sum
|
|
kusano |
7d535a |
approximately to a power of 2. It will fail on machines where this
|
|
kusano |
7d535a |
assumption does not hold, for example, the Cyber 205 (EMIN = -28625,
|
|
kusano |
7d535a |
EMAX = 28718). It will also fail if the value supplied for EMIN is
|
|
kusano |
7d535a |
too large (i.e. too close to zero), probably with overflow.
|
|
kusano |
7d535a |
Arguments
|
|
kusano |
7d535a |
=========
|
|
kusano |
7d535a |
BETA (input) INT
|
|
kusano |
7d535a |
The base of floating-point arithmetic.
|
|
kusano |
7d535a |
P (input) INT
|
|
kusano |
7d535a |
The number of base BETA digits in the mantissa of a
|
|
kusano |
7d535a |
floating-point value.
|
|
kusano |
7d535a |
EMIN (input) INT
|
|
kusano |
7d535a |
The minimum exponent before (gradual) underflow.
|
|
kusano |
7d535a |
IEEE (input) INT
|
|
kusano |
7d535a |
A logical flag specifying whether or not the arithmetic
|
|
kusano |
7d535a |
system is thought to comply with the IEEE standard.
|
|
kusano |
7d535a |
EMAX (output) INT
|
|
kusano |
7d535a |
The largest exponent before overflow
|
|
kusano |
7d535a |
RMAX (output) FLOAT
|
|
kusano |
7d535a |
The largest machine floating-point number.
|
|
kusano |
7d535a |
=====================================================================
|
|
kusano |
7d535a |
First compute LEXP and UEXP, two powers of 2 that bound
|
|
kusano |
7d535a |
abs(EMIN). We then assume that EMAX + abs(EMIN) will sum
|
|
kusano |
7d535a |
approximately to the bound that is closest to abs(EMIN).
|
|
kusano |
7d535a |
(EMAX is the exponent of the required number RMAX).
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
float slamch_
|
|
kusano |
7d535a |
(
|
|
kusano |
7d535a |
char *
|
|
kusano |
7d535a |
cmach
|
|
kusano |
7d535a |
)
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
Purpose
|
|
kusano |
7d535a |
=======
|
|
kusano |
7d535a |
SLAMCH determines single precision machine parameters.
|
|
kusano |
7d535a |
Arguments
|
|
kusano |
7d535a |
=========
|
|
kusano |
7d535a |
CMACH (input) CHARACTER*1
|
|
kusano |
7d535a |
Specifies the value to be returned by SLAMCH:
|
|
kusano |
7d535a |
= 'E' or 'e', SLAMCH := eps
|
|
kusano |
7d535a |
= 'S' or 's , SLAMCH := sfmin
|
|
kusano |
7d535a |
= 'B' or 'b', SLAMCH := base
|
|
kusano |
7d535a |
= 'P' or 'p', SLAMCH := eps*base
|
|
kusano |
7d535a |
= 'N' or 'n', SLAMCH := t
|
|
kusano |
7d535a |
= 'R' or 'r', SLAMCH := rnd
|
|
kusano |
7d535a |
= 'M' or 'm', SLAMCH := emin
|
|
kusano |
7d535a |
= 'U' or 'u', SLAMCH := rmin
|
|
kusano |
7d535a |
= 'L' or 'l', SLAMCH := emax
|
|
kusano |
7d535a |
= 'O' or 'o', SLAMCH := rmax
|
|
kusano |
7d535a |
where
|
|
kusano |
7d535a |
eps = relative machine precision
|
|
kusano |
7d535a |
sfmin = safe minimum, such that 1/sfmin does not overflow
|
|
kusano |
7d535a |
base = base of the machine
|
|
kusano |
7d535a |
prec = eps*base
|
|
kusano |
7d535a |
t = number of (base) digits in the mantissa
|
|
kusano |
7d535a |
rnd = 1.0 when rounding occurs in addition, 0.0 otherwise
|
|
kusano |
7d535a |
emin = minimum exponent before (gradual) underflow
|
|
kusano |
7d535a |
rmin = underflow threshold - base**(emin-1)
|
|
kusano |
7d535a |
emax = largest exponent before overflow
|
|
kusano |
7d535a |
rmax = overflow threshold - (base**emax)*(1-eps)
|
|
kusano |
7d535a |
=====================================================================
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
<address style="text-align: right;"><small>Generated on Mon Nov 22 10:23:48 2010 for SuperLU by </small></address>
|
|
kusano |
7d535a |
|
|
kusano |
7d535a |
 1.5.5
|
|
kusano |
7d535a |
|
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kusano |
7d535a |
|