1* $NetBSD: sacos.sa,v 1.3 1994/10/26 07:49:27 cgd Exp $ 2 3* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP 4* M68000 Hi-Performance Microprocessor Division 5* M68040 Software Package 6* 7* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc. 8* All rights reserved. 9* 10* THE SOFTWARE is provided on an "AS IS" basis and without warranty. 11* To the maximum extent permitted by applicable law, 12* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, 13* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A 14* PARTICULAR PURPOSE and any warranty against infringement with 15* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF) 16* and any accompanying written materials. 17* 18* To the maximum extent permitted by applicable law, 19* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER 20* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS 21* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR 22* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE 23* SOFTWARE. Motorola assumes no responsibility for the maintenance 24* and support of the SOFTWARE. 25* 26* You are hereby granted a copyright license to use, modify, and 27* distribute the SOFTWARE so long as this entire notice is retained 28* without alteration in any modified and/or redistributed versions, 29* and that such modified versions are clearly identified as such. 30* No licenses are granted by implication, estoppel or otherwise 31* under any patents or trademarks of Motorola, Inc. 32 33* 34* sacos.sa 3.3 12/19/90 35* 36* Description: The entry point sAcos computes the inverse cosine of 37* an input argument; sAcosd does the same except for denormalized 38* input. 39* 40* Input: Double-extended number X in location pointed to 41* by address register a0. 42* 43* Output: The value arccos(X) returned in floating-point register Fp0. 44* 45* Accuracy and Monotonicity: The returned result is within 3 ulps in 46* 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 47* result is subsequently rounded to double precision. The 48* result is provably monotonic in double precision. 49* 50* Speed: The program sCOS takes approximately 310 cycles. 51* 52* Algorithm: 53* 54* ACOS 55* 1. If |X| >= 1, go to 3. 56* 57* 2. (|X| < 1) Calculate acos(X) by 58* z := (1-X) / (1+X) 59* acos(X) = 2 * atan( sqrt(z) ). 60* Exit. 61* 62* 3. If |X| > 1, go to 5. 63* 64* 4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. Exit. 65* 66* 5. (|X| > 1) Generate an invalid operation by 0 * infinity. 67* Exit. 68* 69 70SACOS IDNT 2,1 Motorola 040 Floating Point Software Package 71 72 section 8 73 74PI DC.L $40000000,$C90FDAA2,$2168C235,$00000000 75PIBY2 DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000 76 77 xref t_operr 78 xref t_frcinx 79 xref satan 80 81 xdef sacosd 82sacosd: 83*--ACOS(X) = PI/2 FOR DENORMALIZED X 84 fmove.l d1,fpcr ...load user's rounding mode/precision 85 FMOVE.X PIBY2,FP0 86 bra t_frcinx 87 88 xdef sacos 89sacos: 90 FMOVE.X (a0),FP0 ...LOAD INPUT 91 92 move.l (a0),d0 ...pack exponent with upper 16 fraction 93 move.w 4(a0),d0 94 ANDI.L #$7FFFFFFF,D0 95 CMPI.L #$3FFF8000,D0 96 BGE.B ACOSBIG 97 98*--THIS IS THE USUAL CASE, |X| < 1 99*--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) ) 100 101 FMOVE.S #:3F800000,FP1 102 FADD.X FP0,FP1 ...1+X 103 FNEG.X FP0 ... -X 104 FADD.S #:3F800000,FP0 ...1-X 105 FDIV.X FP1,FP0 ...(1-X)/(1+X) 106 FSQRT.X FP0 ...SQRT((1-X)/(1+X)) 107 fmovem.x fp0,(a0) ...overwrite input 108 move.l d1,-(sp) ;save original users fpcr 109 clr.l d1 110 bsr satan ...ATAN(SQRT([1-X]/[1+X])) 111 fMOVE.L (sp)+,fpcr ;restore users exceptions 112 FADD.X FP0,FP0 ...2 * ATAN( STUFF ) 113 bra t_frcinx 114 115ACOSBIG: 116 FABS.X FP0 117 FCMP.S #:3F800000,FP0 118 fbgt t_operr ;cause an operr exception 119 120*--|X| = 1, ACOS(X) = 0 OR PI 121 move.l (a0),d0 ...pack exponent with upper 16 fraction 122 move.w 4(a0),d0 123 TST.L D0 ;D0 has original exponent+fraction 124 BGT.B ACOSP1 125 126*--X = -1 127*Returns PI and inexact exception 128 FMOVE.X PI,FP0 129 FMOVE.L d1,FPCR 130 FADD.S #:00800000,FP0 ;cause an inexact exception to be put 131* ;into the 040 - will not trap until next 132* ;fp inst. 133 bra t_frcinx 134 135ACOSP1: 136 FMOVE.L d1,FPCR 137 FMOVE.S #:00000000,FP0 138 rts ;Facos of +1 is exact 139 140 end 141