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path: root/arch/m68k/fpsp040/sasin.S
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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 ``` ``````| | 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 | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | The copyright notice above does not evidence any | actual or intended publication of such source code.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 ``````