l_sacos.s
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- /* l_sacos.s - Motorola 68040 FP arc-cosine routines (LIB) */
- /* 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,09jan92,kdl added modification history; general cleanup.
- 01a,15aug91,kdl original version, from Motorola FPSP v2.0.
- */
- /*
- DESCRIPTION
- sacossa 3.3 12/19/90
- Description: The entry point sAcos computes the inverse cosine of
- an input argument| sAcosd does the same except for denormalized
- input.
- Input: Double-extended number X in location pointed to
- by address register a0.
- Output: The value arccos(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 sCOS takes approximately 310 cycles.
- Algorithm:
- ACOS
- 1. If |X| >= 1, go to 3.
- 2. (|X| < 1) Calculate acos(X) by
- z := (1-X) / (1+X)
- acos(X) = 2 * atan( sqrt(z) ).
- Exit.
- 3. If |X| > 1, go to 5.
- 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. 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- THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
- SACOS idnt 2,1 Motorola 040 Floating Point Software Package
- section 8
- NOMANUAL
- */
- PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
- PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
- | xref __l_t_operr
- | xref __l_t_frcinx
- | xref __l_satan
- .text
- .globl __l_sacosd
- __l_sacosd:
- |--ACOS(X) = PI/2 FOR DENORMALIZED X
- fmovel d1,fpcr /* |...load user's rounding mode/precision */
- fmovex PIBY2,fp0
- jra __l_t_frcinx
- .globl __l_sacos
- __l_sacos:
- fmovex a0@,fp0 |...lOAD INPUT
- movel a0@,d0 |...pack exponent with upper 16 fraction
- movew a0@(4),d0
- andil #0x7FFFFFFF,d0
- cmpil #0x3FFF8000,d0
- jge ACOSBIG
- |--THIS IS THE USUAL CASE, |X| < 1
- |--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
- /* fmoves &0x3F800000,fp1 */ .long 0xf23c4480,0x3f800000
- faddx fp0,fp1 |...1+X
- fnegx fp0 |... -X
- /* fadds &0x3F800000,fp0 */ .long 0xf23c4422,0x3f800000
- fdivx fp1,fp0 |...(1-X)/(1+X)
- fsqrtx fp0 |...SQRT((1-X)/(1+X))
- fmovemx fp0-fp0,a0@ |...overwrite input
- movel d1,a7@- | save original users fpcr
- clrl d1
- bsrl __l_satan |...ATAN(SQRT([1-X]/[1+X]))
- fmovel a7@+,fpcr | restore users exceptions
- faddx fp0,fp0 |...2 * ATAN( STUFF )
- jra __l_t_frcinx
- ACOSBIG:
- fabsx fp0,fp0
- /* fcmps &0x3F800000,fp0 */ .long 0xf23c4438,0x3f800000
- fbgtl __l_t_operr | cause an operr exception
- |--|X| = 1, ACOS(X) = 0 OR PI
- movel a0@,d0 |...pack exponent with upper 16 fraction
- movew a0@(4),d0
- cmpl #0,d0 | D0 has original exponent+fraction
- jgt ACOSP1
- |--X = -1
- |Returns PI and inexact exception
- fmovex PI,fp0
- fmovel d1,fpcr
- /* fadds &0x00800000,fp0 */ .long 0xf23c4422,0x00800000
- | cause an inexact exception to be put
- | | into the 040 - will not trap until next
- | | fp inst.
- jra __l_t_frcinx
- ACOSP1:
- fmovel d1,fpcr
- /* fmoves &0x00000000,fp0 */ .long 0xf23c4400,0x00000000
- rts | Facos of +1 is exact
- | end