sasin.s
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- /* sasin.s - Motorola 68040 FP arc-sine 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
- sasinsa 3.3 12/19/90
- Description: The entry point sAsin computes the inverse sine of
- an input argument| sAsind does the same except for denormalized
- input.
- Input: Double-extended number X in location pointed to
- by address register a0.
- Output: The value arcsin(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 sASIN takes approximately 310 cycles.
- Algorithm:
- ASIN
- 1. If |X| >= 1, go to 3.
- 2. (|X| < 1) Calculate asin(X) by
- z := sqrt( [1-X][1+X] )
- asin(X) = atan( x / z ).
- Exit.
- 3. If |X| > 1, go to 5.
- 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. 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- THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.
- SASIN idnt 2,1 Motorola 040 Floating Point Software Package
- section 8
- NOMANUAL
- */
- PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
- | xref __x_t_operr
- | xref __x_t_frcinx
- | xref __x_t_extdnrm
- | xref __x_satan
- .text
- .globl __x_sasind
- __x_sasind:
- |--ASIN(X) = X FOR DENORMALIZED X
- jra __x_t_extdnrm
- .globl __x_sasin
- __x_sasin:
- fmovex a0@,fp0 |...lOAD INPUT
- movel a0@,d0
- movew a0@(4),d0
- andil #0x7FFFFFFF,d0
- cmpil #0x3FFF8000,d0
- jge asinbig
- |--THIS IS THE USUAL CASE, |X| < 1
- |--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
- .long 0xf23c4480,0x3f800000 /* fmoves &0x3F800000,fp1 */
- fsubx fp0,fp1 |...1-X
- fmovemx fp2-fp2,a7@-
- .long 0xf23c4500,0x3f800000 /* fmoves &0x3F800000,fp2 */
- faddx fp0,fp2 |...1+X
- fmulx fp2,fp1 |...(1+X)(1-X)
- fmovemx a7@+,fp2-fp2
- fsqrtx fp1 |...SQRT([1-X][1+X])
- fdivx fp1,fp0 |...X/SQRT([1-X][1+X])
- fmovemx fp0-fp0,a0@
- bsrl __x_satan
- jra __x_t_frcinx
- asinbig:
- fabsx fp0,fp0 |...|X|
- .long 0xf23c4438,0x3f800000 /* fcmps &0x3F800000,fp0 */
- fbgtl __x_t_operr | cause an operr exception
- |--|X| = 1, ASIN(X) = +- PI/2.
- fmovex PIBY2,fp0
- movel a0@,d0
- andil #0x80000000,d0 |...SIGN BIT OF X
- oril #0x3F800000,d0 |...+-1 IN SGL FORMAT
- movel d0,a7@- |...push SIGN(X) IN SGL-FMT
- fmovel d1,fpcr
- fmuls a7@+,fp0
- jra __x_t_frcinx
- | end