satanh.s
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上传日期:2007-01-17
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- /* satanh.s - Motorola 68040 FP hyperbolic arc-tangent routines (EXC) */
- /* Copyright 1991-1993 Wind River Systems, Inc. */
- .data
- .globl _copyright_wind_river
- .long _copyright_wind_river
- /*
- modification history
- --------------------
- 01f,14jun95,tpr changed fbxx to fbxxl.
- 01e,21jul93,kdl added .text (SPR #2372).
- 01d,23aug92,jcf changed bxxx to jxx.
- 01c,26may92,rrr the tree shuffle
- 01b,10jan92,kdl added modification history; general cleanup.
- 01a,15aug91,kdl original version, from Motorola FPSP v2.0.
- */
- /*
- DESCRIPTION
- __x_satanhsa 3.3 12/19/90
- The entry point __x_satanh computes the inverse
- hyperbolic tangent of
- an input argument; __x_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 __x_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
- THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
- The copyright notice above does not evidence any
- actual or intended publication of such source code.
- __x_satanh IDNT 2,1 Motorola 040 Floating Point Software Package
- section 8
- NOMANUAL
- */
- | xref __x_t_dz
- | xref __x_t_operr
- | xref __x_t_frcinx
- | xref __x_t_extdnrm
- | xref __x_slognp1
- .text
- .globl __x_satanhd
- __x_satanhd:
- |--ATANH(X) = X FOR DENORMALIZED X
- jra __x_t_extdnrm
- .globl __x_satanh
- __x_satanh:
- movel a0@,d0
- movew a0@(4),d0
- andil #0x7FFFFFFF,d0
- cmpil #0x3FFF8000,d0
- jge 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
- .long 0xf23c44a2,0x3f800000 /* fadds &0x3F800000,fp1 */
- fdivx fp1,fp0 |...2Y/(1-Y)
- movel a0@,d0
- andil #0x80000000,d0
- oril #0x3F000000,d0 |...SIGN(X)*HALF
- movel d0,a7@-
- fmovemx fp0-fp0,a0@ |...overwrite input
- movel d1,a7@-
- clrl d1
- bsrl __x_slognp1 |...lOG1P(Z)
- fmovel a7@+,fpcr
- fmuls a7@+,fp0
- jra __x_t_frcinx
- ATANHBIG:
- fabsx a0@,fp0 |...|X|
- .long 0xf23c4438,0x3f800000 /* fcmps &0x3F800000,fp0 */
- fbgtl __x_t_operr
- jra __x_t_dz
- | end