Subversion Repositories or1k_soc_on_altera_embedded_dev_kit

|

|       satanh.sa 3.3 12/19/90

|

|       The entry point satanh computes the inverse

|       hyperbolic tangent of

|       an input argument; satanhd does the same except for denormalized

|       input.

|

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

|               by address register a0.

|

|       Output: The value arctanh(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 satanh takes approximately 270 cycles.

|

|       Algorithm:

|

|       ATANH

|       1. If |X| >= 1, go to 3.

|

|       2. (|X| < 1) Calculate atanh(X) by

|               sgn := sign(X)

|               y := |X|

|               z := 2y/(1-y)

|               atanh(X) := sgn * (1/2) * logp1(z)

|               Exit.

|

|       3. If |X| > 1, go to 5.

|

|       4. (|X| = 1) Generate infinity with an appropriate sign and

|               divide-by-zero by

|               sgn := sign(X)

|               atan(X) := sgn / (+0).

|               Exit.

|

|       5. (|X| > 1) Generate an invalid operation by 0 * infinity.

|               Exit.

|

|               Copyright (C) Motorola, Inc. 1990

|                       All Rights Reserved

|

|       For details on the license for this file, please see the

|       file, README, in this same directory.

|satanh idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

        |xref   t_dz

        |xref   t_operr

        |xref   t_frcinx

        |xref   t_extdnrm

        |xref   slognp1

        .global satanhd

satanhd:

|--ATANH(X) = X FOR DENORMALIZED X

        bra             t_extdnrm

        .global satanh

satanh:

        movel           (%a0),%d0

        movew           4(%a0),%d0

        andil           #0x7FFFFFFF,%d0

        cmpil           #0x3FFF8000,%d0

        bges            ATANHBIG

|--THIS IS THE USUAL CASE, |X| < 1

|--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).

        fabsx           (%a0),%fp0      | ...Y = |X|

        fmovex          %fp0,%fp1

        fnegx           %fp1            | ...-Y

        faddx           %fp0,%fp0               | ...2Y

        fadds           #0x3F800000,%fp1        | ...1-Y

        fdivx           %fp1,%fp0               | ...2Y/(1-Y)

        movel           (%a0),%d0

        andil           #0x80000000,%d0

        oril            #0x3F000000,%d0 | ...SIGN(X)*HALF

        movel           %d0,-(%sp)

        fmovemx %fp0-%fp0,(%a0) | ...overwrite input

        movel           %d1,-(%sp)

        clrl            %d1

        bsr             slognp1         | ...LOG1P(Z)

        fmovel          (%sp)+,%fpcr

        fmuls           (%sp)+,%fp0

        bra             t_frcinx

ATANHBIG:

        fabsx           (%a0),%fp0      | ...|X|

        fcmps           #0x3F800000,%fp0

        fbgt            t_operr

        bra             t_dz

        |end