 
      SUBROUTINE XSLEGF(DNU1,NUDIFF,MU1,MU2,THETA,ID,PQA,IPQA)
C***BEGIN PROLOGUE   XSLEGF
C***DATE WRITTEN   820728   (YYMMDD)
C***REVISION DATE  871015   (YYMMDD)
C***CATEGORY NO.  C3a2,C9
C***KEYWORDS  LEGENDRE FUNCTIONS
C***AUTHOR  SMITH, JOHN M. (NBS AND GEORGE MASON UNIVERSITY)
C***PURPOSE  TO COMPUTE THE VALUES OF LEGENDRE FUNCTIONS
C***DESCRIPTION
C
C   XSLEGF: Extended-range Single-precision Legendre Functions
C
C   A feature of the XSLEGF subroutine for Legendre functions is
C the use of extended-range arithmetic, a software extension of
C ordinary floating-point arithmetic that greatly increases the
C exponent range of the representable numbers. This avoids the
C need for scaling the solutions to lie within the exponent range
C of the most restrictive manufacturer's hardware. The increased
C exponent range is achieved by allocating an integer storage
C location together with each floating-point storage location.
C
C   The interpretation of the pair (X,I) where X is floating-point
C and I is integer is X*(IR**I) where IR is the internal radix of
C the computer arithmetic.
C
C   This subroutine computes one of the following vectors:
C
C 1. Legendre function of the first kind of negative order, either
C    a. P(-MU1,NU,X), P(-MU1-1,NU,X), ..., P(-MU2,NU,X) or
C    b. P(-MU,NU1,X), P(-MU,NU1+1,X), ..., P(-MU,NU2,X)
C 2. Legendre function of the second kind, either
C    a. Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X) or
C    b. Q(MU,NU1,X), Q(MU,NU1+1,X), ..., Q(MU,NU2,X)
C 3. Legendre function of the first kind of positive order, either
C    a. P(MU1,NU,X), P(MU1+1,NU,X), ..., P(MU2,NU,X) or
C    b. P(MU,NU1,X), P(MU,NU1+1,X), ..., P(MU,NU2,X)
C 4. Normalized Legendre polynomials, either
C    a. PN(MU1,NU,X), PN(MU1+1,NU,X), ..., PN(MU2,NU,X) or
C    b. PN(MU,NU1,X), PN(MU,NU1+1,X), ..., PN(MU,NU2,X)
C
C where X = COS(THETA).
C
C   The input values to XSLEGF are DNU1, NUDIFF, MU1, MU2, THETA,
C and ID. These must satisfy
C
C    DNU1 is REAL and greater than or equal to -0.5;
C    NUDIFF is INTEGER and non-negative;
C    MU1 is INTEGER and non-negative;
C    MU2 is INTEGER and greater than or equal to MU1;
C    THETA is REAL and in the half-open interval (0,PI/2];
C    ID is INTEGER and equal to 1, 2, 3 or 4;
C
C and  additionally either NUDIFF = 0 or MU2 = MU1.
C
C   If ID=1 and NUDIFF=0, a vector of type 1a above is computed
C with NU=DNU1.
C
C   If ID=1 and MU1=MU2, a vector of type 1b above is computed
C with NU1=DNU1, NU2=DNU1+NUDIFF and MU=MU1.
C
C   If ID=2 and NUDIFF=0, a vector of type 2a above is computed
C with NU=DNU1.
C
C   If ID=2 and MU1=MU2, a vector of type 2b above is computed
C with NU1=DNU1, NU2=DNU1+NUDIFF and MU=MU1.
C
C   If ID=3 and NUDIFF=0, a vector of type 3a above is computed
C with NU=DNU1.
C
C   If ID=3 and MU1=MU2, a vector of type 3b above is computed
C with NU1=DNU1, NU2=DNU1+NUDIFF and MU=MU1.
C
C   If ID=4 and NUDIFF=0, a vector of type 4a above is computed
C with NU=DNU1.
C
C   If ID=4 and MU1=MU2, a vector of type 4b above is computed
C with NU1=DNU1, NU2=DNU1+NUDIFF and MU=MU1.
C
C   In each case the vector of computed Legendre function values
C is returned in the extended-range vector (PQA(I),IPQA(I)). The
C length of this vector is either MU2-MU1+1 or NUDIFF+1.
C
C Where possible, XSLEGF returns IPQA(I) as zero. In this case the
C value of the Legendre function is contained entirely in PQA(I),
C so it can be used in subsequent computations without further
C consideration of extended-range arithmetic. If IPQA(I) is nonzero,
C then the value of the Legendre function is not representable in
C floating-point because of underflow or overflow. The program that
C calls XSLEGF must test IPQA(I) to ensure correct usage.
C
C***REFERENCES  OLVER AND SMITH,J.COMPUT.PHYSICS,51(1983),N0.3,502-518.
C***ROUTINES CALLED  XERROR, XSPMU, XSPMUP, XSPNRM, XSPQNU, XSQMU, XSQNU,
C                    XSRED, XSSET
C***END PROLOGUE  XSLEGF
 
 
