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|
|       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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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