1| 2| scosh.sa 3.1 12/10/90 3| 4| The entry point sCosh computes the hyperbolic cosine of 5| an input argument; sCoshd 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 cosh(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 sCOSH takes approximately 250 cycles. 19| 20| Algorithm: 21| 22| COSH 23| 1. If |X| > 16380 log2, go to 3. 24| 25| 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae 26| y = |X|, z = exp(Y), and 27| cosh(X) = (1/2)*( z + 1/z ). 28| Exit. 29| 30| 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. 31| 32| 4. (16380 log2 < |X| <= 16480 log2) 33| cosh(X) = sign(X) * exp(|X|)/2. 34| However, invoking exp(|X|) may cause premature overflow. 35| Thus, we calculate sinh(X) as follows: 36| Y := |X| 37| Fact := 2**(16380) 38| Y' := Y - 16381 log2 39| cosh(X) := Fact * exp(Y'). 40| Exit. 41| 42| 5. (|X| > 16480 log2) sinh(X) must overflow. Return 43| Huge*Huge to generate overflow and an infinity with 44| the appropriate sign. Huge is the largest finite number in 45| extended format. Exit. 46| 47| 48 49| Copyright (C) Motorola, Inc. 1990 50| All Rights Reserved 51| 52| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 53| The copyright notice above does not evidence any 54| actual or intended publication of such source code. 55 56|SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package 57 58 |section 8 59 60 |xref t_ovfl 61 |xref t_frcinx 62 |xref setox 63 64T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD 65T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL 66 67TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000 68 69 .global scoshd 70scoshd: 71|--COSH(X) = 1 FOR DENORMALIZED X 72 73 fmoves #0x3F800000,%fp0 74 75 fmovel %d1,%FPCR 76 fadds #0x00800000,%fp0 77 bra t_frcinx 78 79 .global scosh 80scosh: 81 fmovex (%a0),%fp0 | ...LOAD INPUT 82 83 movel (%a0),%d0 84 movew 4(%a0),%d0 85 andil #0x7FFFFFFF,%d0 86 cmpil #0x400CB167,%d0 87 bgts COSHBIG 88 89|--THIS IS THE USUAL CASE, |X| < 16380 LOG2 90|--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) ) 91 92 fabsx %fp0 | ...|X| 93 94 movel %d1,-(%sp) 95 clrl %d1 96 fmovemx %fp0-%fp0,(%a0) |pass parameter to setox 97 bsr setox | ...FP0 IS EXP(|X|) 98 fmuls #0x3F000000,%fp0 | ...(1/2)EXP(|X|) 99 movel (%sp)+,%d1 100 101 fmoves #0x3E800000,%fp1 | ...(1/4) 102 fdivx %fp0,%fp1 | ...1/(2 EXP(|X|)) 103 104 fmovel %d1,%FPCR 105 faddx %fp1,%fp0 106 107 bra t_frcinx 108 109COSHBIG: 110 cmpil #0x400CB2B3,%d0 111 bgts COSHHUGE 112 113 fabsx %fp0 114 fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD) 115 fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE 116 117 movel %d1,-(%sp) 118 clrl %d1 119 fmovemx %fp0-%fp0,(%a0) 120 bsr setox 121 fmovel (%sp)+,%fpcr 122 123 fmulx TWO16380(%pc),%fp0 124 bra t_frcinx 125 126COSHHUGE: 127 fmovel #0,%fpsr |clr N bit if set by source 128 bclrb #7,(%a0) |always return positive value 129 fmovemx (%a0),%fp0-%fp0 130 bra t_ovfl 131 132 |end 133