1* $NetBSD: scosh.sa,v 1.2 1994/10/26 07:49:39 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* scosh.sa 3.1 12/10/90 35* 36* The entry point sCosh computes the hyperbolic cosine of 37* an input argument; sCoshd 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 cosh(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 sCOSH takes approximately 250 cycles. 51* 52* Algorithm: 53* 54* COSH 55* 1. If |X| > 16380 log2, go to 3. 56* 57* 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae 58* y = |X|, z = exp(Y), and 59* cosh(X) = (1/2)*( z + 1/z ). 60* Exit. 61* 62* 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. 63* 64* 4. (16380 log2 < |X| <= 16480 log2) 65* cosh(X) = sign(X) * exp(|X|)/2. 66* However, invoking exp(|X|) may cause premature overflow. 67* Thus, we calculate sinh(X) as follows: 68* Y := |X| 69* Fact := 2**(16380) 70* Y' := Y - 16381 log2 71* cosh(X) := Fact * exp(Y'). 72* Exit. 73* 74* 5. (|X| > 16480 log2) sinh(X) must overflow. Return 75* Huge*Huge to generate overflow and an infinity with 76* the appropriate sign. Huge is the largest finite number in 77* extended format. Exit. 78* 79 80SCOSH IDNT 2,1 Motorola 040 Floating Point Software Package 81 82 section 8 83 84 xref t_ovfl 85 xref t_frcinx 86 xref setox 87 88T1 DC.L $40C62D38,$D3D64634 ... 16381 LOG2 LEAD 89T2 DC.L $3D6F90AE,$B1E75CC7 ... 16381 LOG2 TRAIL 90 91TWO16380 DC.L $7FFB0000,$80000000,$00000000,$00000000 92 93 xdef scoshd 94scoshd: 95*--COSH(X) = 1 FOR DENORMALIZED X 96 97 FMOVE.S #:3F800000,FP0 98 99 FMOVE.L d1,FPCR 100 FADD.S #:00800000,FP0 101 bra t_frcinx 102 103 xdef scosh 104scosh: 105 FMOVE.X (a0),FP0 ...LOAD INPUT 106 107 move.l (a0),d0 108 move.w 4(a0),d0 109 ANDI.L #$7FFFFFFF,d0 110 CMPI.L #$400CB167,d0 111 BGT.B COSHBIG 112 113*--THIS IS THE USUAL CASE, |X| < 16380 LOG2 114*--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) ) 115 116 FABS.X FP0 ...|X| 117 118 move.l d1,-(sp) 119 clr.l d1 120 fmovem.x fp0,(a0) ;pass parameter to setox 121 bsr setox ...FP0 IS EXP(|X|) 122 FMUL.S #:3F000000,FP0 ...(1/2)EXP(|X|) 123 move.l (sp)+,d1 124 125 FMOVE.S #:3E800000,FP1 ...(1/4) 126 FDIV.X FP0,FP1 ...1/(2 EXP(|X|)) 127 128 FMOVE.L d1,FPCR 129 FADD.X fp1,FP0 130 131 bra t_frcinx 132 133COSHBIG: 134 CMPI.L #$400CB2B3,d0 135 BGT.B COSHHUGE 136 137 FABS.X FP0 138 FSUB.D T1(pc),FP0 ...(|X|-16381LOG2_LEAD) 139 FSUB.D T2(pc),FP0 ...|X| - 16381 LOG2, ACCURATE 140 141 move.l d1,-(sp) 142 clr.l d1 143 fmovem.x fp0,(a0) 144 bsr setox 145 fmove.l (sp)+,fpcr 146 147 FMUL.X TWO16380(pc),FP0 148 bra t_frcinx 149 150COSHHUGE: 151 fmove.l #0,fpsr ;clr N bit if set by source 152 bclr.b #7,(a0) ;always return positive value 153 fmovem.x (a0),fp0 154 bra t_ovfl 155 156 end 157