1| 2| sasin.sa 3.3 12/19/90 3| 4| Description: The entry point sAsin computes the inverse sine of 5| an input argument; sAsind does the same except for denormalized 6| input. 7| 8| Input: Double-extended number X in location pointed to 9| by address register a0. 10| 11| Output: The value arcsin(X) returned in floating-point register Fp0. 12| 13| Accuracy and Monotonicity: The returned result is within 3 ulps in 14| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 15| result is subsequently rounded to double precision. The 16| result is provably monotonic in double precision. 17| 18| Speed: The program sASIN takes approximately 310 cycles. 19| 20| Algorithm: 21| 22| ASIN 23| 1. If |X| >= 1, go to 3. 24| 25| 2. (|X| < 1) Calculate asin(X) by 26| z := sqrt( [1-X][1+X] ) 27| asin(X) = atan( x / z ). 28| Exit. 29| 30| 3. If |X| > 1, go to 5. 31| 32| 4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit. 33| 34| 5. (|X| > 1) Generate an invalid operation by 0 * infinity. 35| Exit. 36| 37 38| Copyright (C) Motorola, Inc. 1990 39| All Rights Reserved 40| 41| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 42| The copyright notice above does not evidence any 43| actual or intended publication of such source code. 44 45|SASIN idnt 2,1 | Motorola 040 Floating Point Software Package 46 47 |section 8 48 49PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000 50 51 |xref t_operr 52 |xref t_frcinx 53 |xref t_extdnrm 54 |xref satan 55 56 .global sasind 57sasind: 58|--ASIN(X) = X FOR DENORMALIZED X 59 60 bra t_extdnrm 61 62 .global sasin 63sasin: 64 fmovex (%a0),%fp0 | ...LOAD INPUT 65 66 movel (%a0),%d0 67 movew 4(%a0),%d0 68 andil #0x7FFFFFFF,%d0 69 cmpil #0x3FFF8000,%d0 70 bges asinbig 71 72|--THIS IS THE USUAL CASE, |X| < 1 73|--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) ) 74 75 fmoves #0x3F800000,%fp1 76 fsubx %fp0,%fp1 | ...1-X 77 fmovemx %fp2-%fp2,-(%a7) 78 fmoves #0x3F800000,%fp2 79 faddx %fp0,%fp2 | ...1+X 80 fmulx %fp2,%fp1 | ...(1+X)(1-X) 81 fmovemx (%a7)+,%fp2-%fp2 82 fsqrtx %fp1 | ...SQRT([1-X][1+X]) 83 fdivx %fp1,%fp0 | ...X/SQRT([1-X][1+X]) 84 fmovemx %fp0-%fp0,(%a0) 85 bsr satan 86 bra t_frcinx 87 88asinbig: 89 fabsx %fp0 | ...|X| 90 fcmps #0x3F800000,%fp0 91 fbgt t_operr |cause an operr exception 92 93|--|X| = 1, ASIN(X) = +- PI/2. 94 95 fmovex PIBY2,%fp0 96 movel (%a0),%d0 97 andil #0x80000000,%d0 | ...SIGN BIT OF X 98 oril #0x3F800000,%d0 | ...+-1 IN SGL FORMAT 99 movel %d0,-(%sp) | ...push SIGN(X) IN SGL-FMT 100 fmovel %d1,%FPCR 101 fmuls (%sp)+,%fp0 102 bra t_frcinx 103 104 |end 105