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authorLinus Torvalds <torvalds@ppc970.osdl.org>2005-04-16 15:20:36 -0700
committerLinus Torvalds <torvalds@ppc970.osdl.org>2005-04-16 15:20:36 -0700
commit1da177e4c3f41524e886b7f1b8a0c1fc7321cac2 (patch)
tree0bba044c4ce775e45a88a51686b5d9f90697ea9d /arch/m68k/fpsp040/sasin.S
downloadconfigs-1da177e4c3f41524e886b7f1b8a0c1fc7321cac2.tar.gz
Linux-2.6.12-rc2v2.6.12-rc2
Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
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+|
+| sasin.sa 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+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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
+
+PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
+
+ |xref t_operr
+ |xref t_frcinx
+ |xref t_extdnrm
+ |xref satan
+
+ .global sasind
+sasind:
+|--ASIN(X) = X FOR DENORMALIZED X
+
+ bra t_extdnrm
+
+ .global sasin
+sasin:
+ fmovex (%a0),%fp0 | ...LOAD INPUT
+
+ movel (%a0),%d0
+ movew 4(%a0),%d0
+ andil #0x7FFFFFFF,%d0
+ cmpil #0x3FFF8000,%d0
+ bges asinbig
+
+|--THIS IS THE USUAL CASE, |X| < 1
+|--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
+
+ fmoves #0x3F800000,%fp1
+ fsubx %fp0,%fp1 | ...1-X
+ fmovemx %fp2-%fp2,-(%a7)
+ 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)
+ bsr satan
+ bra t_frcinx
+
+asinbig:
+ fabsx %fp0 | ...|X|
+ fcmps #0x3F800000,%fp0
+ fbgt 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,-(%sp) | ...push SIGN(X) IN SGL-FMT
+ fmovel %d1,%FPCR
+ fmuls (%sp)+,%fp0
+ bra t_frcinx
+
+ |end