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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 | |
REAL function | slamch (CMACH) |
SLAMCHF77 deprecated | |
subroutine | slamc1 (BETA, T, RND, IEEE1) |
SLAMC1 | |
subroutine | slamc2 (BETA, T, RND, EPS, EMIN, RMIN, EMAX, RMAX) |
SLAMC2 | |
REAL function | slamc3 (A, B) |
SLAMC3 | |
subroutine | slamc4 (EMIN, START, BASE) |
SLAMC4 | |
subroutine | slamc5 (BETA, P, EMIN, IEEE, EMAX, RMAX) |
SLAMC5 |
subroutine slamc1 | ( | integer | BETA, |
integer | T, | ||
logical | RND, | ||
logical | IEEE1 | ||
) |
SLAMC1
Purpose:
SLAMC1 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 210 of file slamchf77.f.
subroutine slamc2 | ( | integer | BETA, |
integer | T, | ||
logical | RND, | ||
real | EPS, | ||
integer | EMIN, | ||
real | RMIN, | ||
integer | EMAX, | ||
real | RMAX | ||
) |
SLAMC2
Purpose:
SLAMC2 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 423 of file slamchf77.f.
REAL function slamc3 | ( | real | A, |
real | B | ||
) |
SLAMC3
Purpose:
SLAMC3 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 646 of file slamchf77.f.
subroutine slamc4 | ( | integer | EMIN, |
real | START, | ||
integer | BASE | ||
) |
SLAMC4
Purpose:
SLAMC4 is a service routine for SLAMC2.
[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 693 of file slamchf77.f.
subroutine slamc5 | ( | integer | BETA, |
integer | P, | ||
integer | EMIN, | ||
logical | IEEE, | ||
integer | EMAX, | ||
real | RMAX | ||
) |
SLAMC5
Purpose:
SLAMC5 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 801 of file slamchf77.f.
REAL function slamch | ( | character | CMACH | ) |
SLAMCHF77 deprecated
SLAMCH determines single precision machine parameters.
[in] | CMACH | Specifies the value to be returned by SLAMCH: = 'E' or 'e', SLAMCH := eps = 'S' or 's , SLAMCH := sfmin = 'B' or 'b', SLAMCH := base = 'P' or 'p', SLAMCH := eps*base = 'N' or 'n', SLAMCH := t = 'R' or 'r', SLAMCH := rnd = 'M' or 'm', SLAMCH := emin = 'U' or 'u', SLAMCH := rmin = 'L' or 'l', SLAMCH := emax = 'O' or 'o', SLAMCH := 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 68 of file slamchf77.f.