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//

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

//

//      ssinh.sa 3.1 12/10/90

//

//       The entry point sSinh computes the hyperbolic sine of

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

//       input.

//

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

//              by address register a0.

//

//       Output: The value sinh(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 sSINH takes approximately 280 cycles.

//

//       Algorithm:

//

//       SINH

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

//

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

//               y = |X|, sgn = sign(X), and z = expm1(Y),

//               sinh(X) = sgn*(1/2)*( z + z/(1+z) ).

//          Exit.

//

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

//

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

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

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

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

//             Y       := |X|

//             sgn     := sign(X)

//             sgnFact := sgn * 2**(16380)

//             Y'      := Y - 16381 log2

//             sinh(X) := sgnFact * exp(Y').

//          Exit.

//

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

//          sign(X)*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//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.

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

        |section        8

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

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

        |xref   t_frcinx

        |xref   t_ovfl

        |xref   t_extdnrm

        |xref   setox

        |xref   setoxm1

        .global ssinhd

ssinhd:

//--SINH(X) = X FOR DENORMALIZED X

        bra     t_extdnrm

        .global ssinh

ssinh:

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

        movel   (%a0),%d0

        movew   4(%a0),%d0

        movel   %d0,%a1         // save a copy of original (compacted) operand

        andl    #0x7FFFFFFF,%d0

        cmpl    #0x400CB167,%d0

        bgts    SINHBIG

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

//--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )

        fabsx   %fp0            // ...Y = |X|

        moveml  %a1/%d1,-(%sp)

        fmovemx %fp0-%fp0,(%a0)

        clrl    %d1

        bsr     setoxm1         // ...FP0 IS Z = EXPM1(Y)

        fmovel  #0,%fpcr

        moveml  (%sp)+,%a1/%d1

        fmovex  %fp0,%fp1

        fadds   #0x3F800000,%fp1        // ...1+Z

        fmovex  %fp0,-(%sp)

        fdivx   %fp1,%fp0               // ...Z/(1+Z)

        movel   %a1,%d0

        andl    #0x80000000,%d0

        orl     #0x3F000000,%d0

        faddx   (%sp)+,%fp0

        movel   %d0,-(%sp)

        fmovel  %d1,%fpcr

        fmuls   (%sp)+,%fp0     //last fp inst - possible exceptions set

        bra     t_frcinx

SINHBIG:

        cmpl    #0x400CB2B3,%d0

        bgt     t_ovfl

        fabsx   %fp0

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

        movel   #0,-(%sp)

        movel   #0x80000000,-(%sp)

        movel   %a1,%d0

        andl    #0x80000000,%d0

        orl     #0x7FFB0000,%d0

        movel   %d0,-(%sp)      // ...EXTENDED FMT

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

        movel   %d1,-(%sp)

        clrl    %d1

        fmovemx %fp0-%fp0,(%a0)

        bsr     setox

        fmovel  (%sp)+,%fpcr

        fmulx   (%sp)+,%fp0     //possible exception

        bra     t_frcinx

        |end