source: rtems/c/src/lib/libcpu/m68k/m68040/fpsp/ssinh.s @ 010e7582

//
//      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//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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