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//

//      $Id: scosh.S,v 1.2 2001-09-27 12:01:22 chris Exp $

//

//      scosh.sa 3.1 12/10/90

//

//      The entry point sCosh computes the hyperbolic cosine of

//      an input argument; sCoshd does the same except for denormalized

//      input.

//

//      Input: Double-extended number X in location pointed to

//              by address register a0.

//

//      Output: The value cosh(X) returned in floating-point register Fp0.

//

//      Accuracy and Monotonicity: The returned result is within 3 ulps in

//              64 significant bit, i.e. within 0.5001 ulp to 53 bits if the

//              result is subsequently rounded to double precision. The

//              result is provably monotonic in double precision.

//

//      Speed: The program sCOSH takes approximately 250 cycles.

//

//      Algorithm:

//

//      COSH

//      1. If |X| > 16380 log2, go to 3.

//

//      2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae

//              y = |X|, z = exp(Y), and

//              cosh(X) = (1/2)*( z + 1/z ).

//              Exit.

//

//      3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5.

//

//      4. (16380 log2 < |X| <= 16480 log2)

//              cosh(X) = sign(X) * exp(|X|)/2.

//              However, invoking exp(|X|) may cause premature overflow.

//              Thus, we calculate sinh(X) as follows:

//              Y       := |X|

//              Fact    :=      2**(16380)

//              Y'      := Y - 16381 log2

//              cosh(X) := Fact * exp(Y').

//              Exit.

//

//      5. (|X| > 16480 log2) sinh(X) must overflow. Return

//              Huge*Huge to generate overflow and an infinity with

//              the appropriate sign. Huge is the largest finite number in

//              extended format. Exit.

//

//

//              Copyright (C) Motorola, Inc. 1990

//                      All Rights Reserved

//

//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA

//      The copyright notice above does not evidence any

//      actual or intended publication of such source code.

//SCOSH idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

        |xref   t_ovfl

        |xref   t_frcinx

        |xref   setox

T1:     .long 0x40C62D38,0xD3D64634 // ... 16381 LOG2 LEAD

T2:     .long 0x3D6F90AE,0xB1E75CC7 // ... 16381 LOG2 TRAIL

TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000

        .global scoshd

scoshd:

//--COSH(X) = 1 FOR DENORMALIZED X

        fmoves          #0x3F800000,%fp0

        fmovel          %d1,%FPCR

        fadds           #0x00800000,%fp0

        bra             t_frcinx

        .global scosh

scosh:

        fmovex          (%a0),%fp0      // ...LOAD INPUT

        movel           (%a0),%d0

        movew           4(%a0),%d0

        andil           #0x7FFFFFFF,%d0

        cmpil           #0x400CB167,%d0

        bgts            COSHBIG

//--THIS IS THE USUAL CASE, |X| < 16380 LOG2

//--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) )

        fabsx           %fp0            // ...|X|

        movel           %d1,-(%sp)

        clrl            %d1

        fmovemx %fp0-%fp0,(%a0) //pass parameter to setox

        bsr             setox           // ...FP0 IS EXP(|X|)

        fmuls           #0x3F000000,%fp0        // ...(1/2)EXP(|X|)

        movel           (%sp)+,%d1

        fmoves          #0x3E800000,%fp1        // ...(1/4)

        fdivx           %fp0,%fp1               // ...1/(2 EXP(|X|))

        fmovel          %d1,%FPCR

        faddx           %fp1,%fp0

        bra             t_frcinx

COSHBIG:

        cmpil           #0x400CB2B3,%d0

        bgts            COSHHUGE

        fabsx           %fp0

        fsubd           T1(%pc),%fp0            // ...(|X|-16381LOG2_LEAD)

        fsubd           T2(%pc),%fp0            // ...|X| - 16381 LOG2, ACCURATE

        movel           %d1,-(%sp)

        clrl            %d1

        fmovemx %fp0-%fp0,(%a0)

        bsr             setox

        fmovel          (%sp)+,%fpcr

        fmulx           TWO16380(%pc),%fp0

        bra             t_frcinx

COSHHUGE:

        fmovel          #0,%fpsr                //clr N bit if set by source

        bclrb           #7,(%a0)                //always return positive value

        fmovemx (%a0),%fp0-%fp0

        bra             t_ovfl

        |end