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|
|       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|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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