diff options
Diffstat (limited to 'numpy/linalg/dlamch.c')
| -rw-r--r-- | numpy/linalg/dlamch.c | 951 |
1 files changed, 951 insertions, 0 deletions
diff --git a/numpy/linalg/dlamch.c b/numpy/linalg/dlamch.c new file mode 100644 index 000000000..dda3f36e2 --- /dev/null +++ b/numpy/linalg/dlamch.c @@ -0,0 +1,951 @@ +#include <stdio.h> +#include "f2c.h" + +/* If config.h is available, we only need dlamc3 */ +#ifndef HAVE_CONFIG +doublereal dlamch_(char *cmach) +{ +/* -- LAPACK auxiliary routine (version 3.0) -- + Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., + Courant Institute, Argonne National Lab, and Rice University + October 31, 1992 + + + 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) + + ===================================================================== +*/ +/* >>Start of File<< + Initialized data */ + static logical first = TRUE_; + /* System generated locals */ + integer i__1; + doublereal ret_val; + /* Builtin functions */ + double pow_di(doublereal *, integer *); + /* Local variables */ + static doublereal base; + static integer beta; + static doublereal emin, prec, emax; + static integer imin, imax; + static logical lrnd; + static doublereal rmin, rmax, t, rmach; + extern logical lsame_(char *, char *); + static doublereal small, sfmin; + extern /* Subroutine */ int dlamc2_(integer *, integer *, logical *, + doublereal *, integer *, doublereal *, integer *, doublereal *); + static integer it; + static doublereal rnd, eps; + + + + if (first) { + first = FALSE_; + dlamc2_(&beta, &it, &lrnd, &eps, &imin, &rmin, &imax, &rmax); + base = (doublereal) beta; + t = (doublereal) it; + if (lrnd) { + rnd = 1.; + i__1 = 1 - it; + eps = pow_di(&base, &i__1) / 2; + } else { + rnd = 0.; + i__1 = 1 - it; + eps = pow_di(&base, &i__1); + } + prec = eps * base; + emin = (doublereal) imin; + emax = (doublereal) imax; + sfmin = rmin; + small = 1. / rmax; + if (small >= sfmin) { + +/* Use SMALL plus a bit, to avoid the possibility of rou +nding + causing overflow when computing 1/sfmin. */ + + sfmin = small * (eps + 1.); + } + } + + if (lsame_(cmach, "E")) { + rmach = eps; + } else if (lsame_(cmach, "S")) { + rmach = sfmin; + } else if (lsame_(cmach, "B")) { + rmach = base; + } else if (lsame_(cmach, "P")) { + rmach = prec; + } else if (lsame_(cmach, "N")) { + rmach = t; + } else if (lsame_(cmach, "R")) { + rmach = rnd; + } else if (lsame_(cmach, "M")) { + rmach = emin; + } else if (lsame_(cmach, "U")) { + rmach = rmin; + } else if (lsame_(cmach, "L")) { + rmach = emax; + } else if (lsame_(cmach, "O")) { + rmach = rmax; + } + + ret_val = rmach; + return ret_val; + +/* End of DLAMCH */ + +} /* dlamch_ */ + + +/* Subroutine */ int dlamc1_(integer *beta, integer *t, logical *rnd, logical + *ieee1) +{ +/* -- LAPACK auxiliary routine (version 3.0) -- + Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., + Courant Institute, Argonne National Lab, and Rice University + October 31, 1992 + + + Purpose + ======= + + DLAMC1 determines the machine parameters given by BETA, T, RND, and + IEEE1. + + Arguments + ========= + + BETA (output) INTEGER + The base of the machine. + + T (output) INTEGER + The number of ( BETA ) digits in the mantissa. + + RND (output) LOGICAL + 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) LOGICAL + 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. + + ===================================================================== +*/ + /* Initialized data */ + static logical first = TRUE_; + /* System generated locals */ + doublereal d__1, d__2; + /* Local variables */ + static logical lrnd; + static doublereal a, b, c, f; + static integer lbeta; + static doublereal savec; + extern doublereal dlamc3_(doublereal *, doublereal *); + static logical lieee1; + static doublereal t1, t2; + static integer lt; + static doublereal one, qtr; + + + + if (first) { + first = FALSE_; + one = 1.; + +/* LBETA, LIEEE1, LT and LRND are the local values of BE +TA, + IEEE1, T and RND. + + Throughout this routine we use the function DLAMC3 to ens +ure + that relevant values are stored and not held in registers, + or + are not affected by optimizers. + + Compute a = 2.0**m with the smallest positive integer m s +uch + that + + fl( a + 1.0 ) = a. */ + + a = 1.; + c = 1.; + +/* + WHILE( C.EQ.ONE )LOOP */ +L10: + if (c == one) { + a *= 2; + c = dlamc3_(&a, &one); + d__1 = -a; + c = dlamc3_(&c, &d__1); + goto L10; + } +/* + END WHILE + + Now compute b = 2.0**m with the smallest positive integer +m + such that + + fl( a + b ) .gt. a. */ + + b = 1.; + c = dlamc3_(&a, &b); + +/* + WHILE( C.EQ.A )LOOP */ +L20: + if (c == a) { + b *= 2; + c = dlamc3_(&a, &b); + goto L20; + } +/* + END WHILE + + Now compute the base. a and c are neighbouring floating po +int + numbers in the interval ( beta**t, beta**( t + 1 ) ) and + so + their difference is beta. Adding 0.25 to c is to ensure that + it + is truncated to beta and not ( beta - 1 ). */ + + qtr = one / 4; + savec = c; + d__1 = -a; + c = dlamc3_(&c, &d__1); + lbeta = (integer) (c + qtr); + +/* Now determine whether rounding or chopping occurs, by addin +g a + bit less than beta/2 and a bit more than beta/2 to + a. */ + + b = (doublereal) lbeta; + d__1 = b / 2; + d__2 = -b / 100; + f = dlamc3_(&d__1, &d__2); + c = dlamc3_(&f, &a); + if (c == a) { + lrnd = TRUE_; + } else { + lrnd = FALSE_; + } + d__1 = b / 2; + d__2 = b / 100; + f = dlamc3_(&d__1, &d__2); + c = dlamc3_(&f, &a); + if (lrnd && c == a) { + lrnd = FALSE_; + } + +/* Try and decide whether rounding is done in the IEEE 'round + to + nearest' style. B/2 is half a unit in the last place of the +two + numbers A and SAVEC. Furthermore, A is even, i.e. has last +bit + zero, and SAVEC is odd. Thus adding B/2 to A should not cha +nge + A, but adding B/2 to SAVEC should change SAVEC. */ + + d__1 = b / 2; + t1 = dlamc3_(&d__1, &a); + d__1 = b / 2; + t2 = dlamc3_(&d__1, &savec); + lieee1 = t1 == a && t2 > savec && lrnd; + +/* Now find the mantissa, t. It should be the integer part + of + log to the base beta of a, however it is safer to determine + t + by powering. So we find t as the smallest positive integer +for + which + + fl( beta**t + 1.0 ) = 1.0. */ + + lt = 0; + a = 1.; + c = 1.; + +/* + WHILE( C.EQ.ONE )LOOP */ +L30: + if (c == one) { + ++lt; + a *= lbeta; + c = dlamc3_(&a, &one); + d__1 = -a; + c = dlamc3_(&c, &d__1); + goto L30; + } +/* + END WHILE */ + + } + + *beta = lbeta; + *t = lt; + *rnd = lrnd; + *ieee1 = lieee1; + return 0; + +/* End of DLAMC1 */ + +} /* dlamc1_ */ + + +/* Subroutine */ int dlamc2_(integer *beta, integer *t, logical *rnd, + doublereal *eps, integer *emin, doublereal *rmin, integer *emax, + doublereal *rmax) +{ +/* -- LAPACK auxiliary routine (version 3.0) -- + Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., + Courant Institute, Argonne National Lab, and Rice University + October 31, 1992 + + + Purpose + ======= + + DLAMC2 determines the machine parameters specified in its argument + list. + + Arguments + ========= + + BETA (output) INTEGER + The base of the machine. + + T (output) INTEGER + The number of ( BETA ) digits in the mantissa. + + RND (output) LOGICAL + 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) INTEGER + 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) INTEGER + 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. + + ===================================================================== +*/ + + /* Initialized data */ + static logical first = TRUE_; + static logical iwarn = FALSE_; + /* System generated locals */ + integer i__1; + doublereal d__1, d__2, d__3, d__4, d__5; + /* Builtin functions */ + double pow_di(doublereal *, integer *); + /* Local variables */ + static logical ieee; + static doublereal half; + static logical lrnd; + static doublereal leps, zero, a, b, c; + static integer i, lbeta; + static doublereal rbase; + static integer lemin, lemax, gnmin; + static doublereal small; + static integer gpmin; + static doublereal third, lrmin, lrmax, sixth; + extern /* Subroutine */ int dlamc1_(integer *, integer *, logical *, + logical *); + extern doublereal dlamc3_(doublereal *, doublereal *); + static logical lieee1; + extern /* Subroutine */ int dlamc4_(integer *, doublereal *, integer *), + dlamc5_(integer *, integer *, integer *, logical *, integer *, + doublereal *); + static integer lt, ngnmin, ngpmin; + static doublereal one, two; + + + + if (first) { + first = FALSE_; + zero = 0.; + one = 1.; + two = 2.; + +/* LBETA, LT, LRND, LEPS, LEMIN and LRMIN are the local values + of + BETA, T, RND, EPS, EMIN and RMIN. + + Throughout this routine we use the function DLAMC3 to ens +ure + that relevant values are stored and not held in registers, + or + are not affected by optimizers. + + DLAMC1 returns the parameters LBETA, LT, LRND and LIEEE1. +*/ + + dlamc1_(&lbeta, <, &lrnd, &lieee1); + +/* Start to find EPS. */ + + b = (doublereal) lbeta; + i__1 = -lt; + a = pow_di(&b, &i__1); + leps = a; + +/* Try some tricks to see whether or not this is the correct E +PS. */ + + b = two / 3; + half = one / 2; + d__1 = -half; + sixth = dlamc3_(&b, &d__1); + third = dlamc3_(&sixth, &sixth); + d__1 = -half; + b = dlamc3_(&third, &d__1); + b = dlamc3_(&b, &sixth); + b = abs(b); + if (b < leps) { + b = leps; + } + + leps = 1.; + +/* + WHILE( ( LEPS.GT.B ).AND.( B.GT.ZERO ) )LOOP */ +L10: + if (leps > b && b > zero) { + leps = b; + d__1 = half * leps; +/* Computing 5th power */ + d__3 = two, d__4 = d__3, d__3 *= d__3; +/* Computing 2nd power */ + d__5 = leps; + d__2 = d__4 * (d__3 * d__3) * (d__5 * d__5); + c = dlamc3_(&d__1, &d__2); + d__1 = -c; + c = dlamc3_(&half, &d__1); + b = dlamc3_(&half, &c); + d__1 = -b; + c = dlamc3_(&half, &d__1); + b = dlamc3_(&half, &c); + goto L10; + } +/* + END WHILE */ + + if (a < leps) { + leps = a; + } + +/* Computation of EPS complete. + + Now find EMIN. Let A = + or - 1, and + or - (1 + BASE**(-3 +)). + Keep dividing A by BETA until (gradual) underflow occurs. T +his + is detected when we cannot recover the previous A. */ + + rbase = one / lbeta; + small = one; + for (i = 1; i <= 3; ++i) { + d__1 = small * rbase; + small = dlamc3_(&d__1, &zero); +/* L20: */ + } + a = dlamc3_(&one, &small); + dlamc4_(&ngpmin, &one, &lbeta); + d__1 = -one; + dlamc4_(&ngnmin, &d__1, &lbeta); + dlamc4_(&gpmin, &a, &lbeta); + d__1 = -a; + dlamc4_(&gnmin, &d__1, &lbeta); + ieee = FALSE_; + + if (ngpmin == ngnmin && gpmin == gnmin) { + if (ngpmin == gpmin) { + lemin = ngpmin; +/* ( Non twos-complement machines, no gradual under +flow; + e.g., VAX ) */ + } else if (gpmin - ngpmin == 3) { + lemin = ngpmin - 1 + lt; + ieee = TRUE_; +/* ( Non twos-complement machines, with gradual und +erflow; + e.g., IEEE standard followers ) */ + } else { + lemin = min(ngpmin,gpmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } + + } else if (ngpmin == gpmin && ngnmin == gnmin) { + if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1) { + lemin = max(ngpmin,ngnmin); +/* ( Twos-complement machines, no gradual underflow +; + e.g., CYBER 205 ) */ + } else { + lemin = min(ngpmin,ngnmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } + + } else if ((i__1 = ngpmin - ngnmin, abs(i__1)) == 1 && gpmin == gnmin) + { + if (gpmin - min(ngpmin,ngnmin) == 3) { + lemin = max(ngpmin,ngnmin) - 1 + lt; +/* ( Twos-complement machines with gradual underflo +w; + no known machine ) */ + } else { + lemin = min(ngpmin,ngnmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } + + } else { +/* Computing MIN */ + i__1 = min(ngpmin,ngnmin), i__1 = min(i__1,gpmin); + lemin = min(i__1,gnmin); +/* ( A guess; no known machine ) */ + iwarn = TRUE_; + } +/* ** + Comment out this if block if EMIN is ok */ + if (iwarn) { + first = TRUE_; + printf("\n\n WARNING. The value EMIN may be incorrect:- "); + printf("EMIN = %8i\n",lemin); + printf("If, after inspection, the value EMIN looks acceptable"); + printf("please comment out \n the IF block as marked within the"); + printf("code of routine DLAMC2, \n otherwise supply EMIN"); + printf("explicitly.\n"); + } +/* ** + + Assume IEEE arithmetic if we found denormalised numbers abo +ve, + or if arithmetic seems to round in the IEEE style, determi +ned + in routine DLAMC1. A true IEEE machine should have both thi +ngs + true; however, faulty machines may have one or the other. */ + + ieee = ieee || lieee1; + +/* Compute RMIN by successive division by BETA. We could comp +ute + RMIN as BASE**( EMIN - 1 ), but some machines underflow dur +ing + this computation. */ + + lrmin = 1.; + i__1 = 1 - lemin; + for (i = 1; i <= 1-lemin; ++i) { + d__1 = lrmin * rbase; + lrmin = dlamc3_(&d__1, &zero); +/* L30: */ + } + +/* Finally, call DLAMC5 to compute EMAX and RMAX. */ + + dlamc5_(&lbeta, <, &lemin, &ieee, &lemax, &lrmax); + } + + *beta = lbeta; + *t = lt; + *rnd = lrnd; + *eps = leps; + *emin = lemin; + *rmin = lrmin; + *emax = lemax; + *rmax = lrmax; + + return 0; + + +/* End of DLAMC2 */ + +} /* dlamc2_ */ +#endif + + +doublereal dlamc3_(doublereal *a, doublereal *b) +{ +/* -- LAPACK auxiliary routine (version 3.0) -- + Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., + Courant Institute, Argonne National Lab, and Rice University + October 31, 1992 + + + 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. + + ===================================================================== +*/ +/* >>Start of File<< + System generated locals */ + doublereal ret_val; + + + + ret_val = *a + *b; + + return ret_val; + +/* End of DLAMC3 */ + +} /* dlamc3_ */ + + +#ifndef HAVE_CONFIG +/* Subroutine */ int dlamc4_(integer *emin, doublereal *start, integer *base) +{ +/* -- 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 + + + 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) INTEGER + The base of the machine. + + ===================================================================== +*/ + /* System generated locals */ + integer i__1; + doublereal d__1; + /* Local variables */ + static doublereal zero, a; + static integer i; + static doublereal rbase, b1, b2, c1, c2, d1, d2; + extern doublereal dlamc3_(doublereal *, doublereal *); + static doublereal one; + + + + a = *start; + one = 1.; + rbase = one / *base; + zero = 0.; + *emin = 1; + d__1 = a * rbase; + b1 = dlamc3_(&d__1, &zero); + c1 = a; + c2 = a; + d1 = a; + d2 = a; +/* + WHILE( ( C1.EQ.A ).AND.( C2.EQ.A ).AND. + $ ( D1.EQ.A ).AND.( D2.EQ.A ) )LOOP */ +L10: + if (c1 == a && c2 == a && d1 == a && d2 == a) { + --(*emin); + a = b1; + d__1 = a / *base; + b1 = dlamc3_(&d__1, &zero); + d__1 = b1 * *base; + c1 = dlamc3_(&d__1, &zero); + d1 = zero; + i__1 = *base; + for (i = 1; i <= *base; ++i) { + d1 += b1; +/* L20: */ + } + d__1 = a * rbase; + b2 = dlamc3_(&d__1, &zero); + d__1 = b2 / rbase; + c2 = dlamc3_(&d__1, &zero); + d2 = zero; + i__1 = *base; + for (i = 1; i <= *base; ++i) { + d2 += b2; +/* L30: */ + } + goto L10; + } +/* + END WHILE */ + + return 0; + +/* End of DLAMC4 */ + +} /* dlamc4_ */ + + +/* Subroutine */ int dlamc5_(integer *beta, integer *p, integer *emin, + logical *ieee, integer *emax, doublereal *rmax) +{ +/* -- LAPACK auxiliary routine (version 3.0) -- + Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., + Courant Institute, Argonne National Lab, and Rice University + October 31, 1992 + + + 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) INTEGER + The base of floating-point arithmetic. + + P (input) INTEGER + The number of base BETA digits in the mantissa of a + floating-point value. + + EMIN (input) INTEGER + The minimum exponent before (gradual) underflow. + + IEEE (input) LOGICAL + A logical flag specifying whether or not the arithmetic + system is thought to comply with the IEEE standard. + + EMAX (output) INTEGER + 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). */ + /* Table of constant values */ + static doublereal c_b5 = 0.; + + /* System generated locals */ + integer i__1; + doublereal d__1; + /* Local variables */ + static integer lexp; + static doublereal oldy; + static integer uexp, i; + static doublereal y, z; + static integer nbits; + extern doublereal dlamc3_(doublereal *, doublereal *); + static doublereal recbas; + static integer exbits, expsum, try__; + + + + lexp = 1; + exbits = 1; +L10: + try__ = lexp << 1; + if (try__ <= -(*emin)) { + lexp = try__; + ++exbits; + goto L10; + } + if (lexp == -(*emin)) { + uexp = lexp; + } else { + uexp = try__; + ++exbits; + } + +/* Now -LEXP is less than or equal to EMIN, and -UEXP is greater + than or equal to EMIN. EXBITS is the number of bits needed to + store the exponent. */ + + if (uexp + *emin > -lexp - *emin) { + expsum = lexp << 1; + } else { + expsum = uexp << 1; + } + +/* EXPSUM is the exponent range, approximately equal to + EMAX - EMIN + 1 . */ + + *emax = expsum + *emin - 1; + nbits = exbits + 1 + *p; + +/* NBITS is the total number of bits needed to store a + floating-point number. */ + + if (nbits % 2 == 1 && *beta == 2) { + +/* Either there are an odd number of bits used to store a + floating-point number, which is unlikely, or some bits are + + not used in the representation of numbers, which is possible +, + (e.g. Cray machines) or the mantissa has an implicit bit, + (e.g. IEEE machines, Dec Vax machines), which is perhaps the + + most likely. We have to assume the last alternative. + If this is true, then we need to reduce EMAX by one because + + there must be some way of representing zero in an implicit-b +it + system. On machines like Cray, we are reducing EMAX by one + + unnecessarily. */ + + --(*emax); + } + + if (*ieee) { + +/* Assume we are on an IEEE machine which reserves one exponent + + for infinity and NaN. */ + + --(*emax); + } + +/* Now create RMAX, the largest machine number, which should + be equal to (1.0 - BETA**(-P)) * BETA**EMAX . + + First compute 1.0 - BETA**(-P), being careful that the + result is less than 1.0 . */ + + recbas = 1. / *beta; + z = *beta - 1.; + y = 0.; + i__1 = *p; + for (i = 1; i <= *p; ++i) { + z *= recbas; + if (y < 1.) { + oldy = y; + } + y = dlamc3_(&y, &z); +/* L20: */ + } + if (y >= 1.) { + y = oldy; + } + +/* Now multiply by BETA**EMAX to get RMAX. */ + + i__1 = *emax; + for (i = 1; i <= *emax; ++i) { + d__1 = y * *beta; + y = dlamc3_(&d__1, &c_b5); +/* L30: */ + } + + *rmax = y; + return 0; + +/* End of DLAMC5 */ + +} /* dlamc5_ */ +#endif |