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LAPACK
3.5.0
LAPACK: Linear Algebra PACKage
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Go to the source code of this file.
Functions/Subroutines | |
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 |
subroutine dlamc1 | ( | integer | BETA, |
integer | T, | ||
logical | RND, | ||
logical | IEEE1 | ||
) |
DLAMC1
Purpose:
DLAMC1 determines the machine parameters given by BETA, T, RND, and IEEE1.
[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. |
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.
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.
[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.
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.
[in] | A | |
[in] | B | The values A and B. |
Definition at line 642 of file dlamchf77.f.
subroutine dlamc4 | ( | integer | EMIN, |
double precision | START, | ||
integer | BASE | ||
) |
DLAMC4
Purpose:
DLAMC4 is a service routine for DLAMC2.
[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.
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.
[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.
DOUBLE PRECISION function dlamch | ( | character | CMACH | ) |
DLAMCHF77 deprecated
DLAMCHF77 determines double precision machine 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) |
Definition at line 64 of file dlamchf77.f.