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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 | | | scosh.sa 3.1 12/10/90 | | The entry point sCosh computes the hyperbolic cosine of | an input argument; sCoshd does the same except for denormalized | input. | | Input: Double-extended number X in location pointed to | by address register a0. | | Output: The value cosh(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 sCOSH takes approximately 250 cycles. | | Algorithm: | | COSH | 1. If |X| > 16380 log2, go to 3. | | 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae | y = |X|, z = exp(Y), and | cosh(X) = (1/2)*( z + 1/z ). | Exit. | | 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. | | 4. (16380 log2 < |X| <= 16480 log2) | cosh(X) = sign(X) * exp(|X|)/2. | However, invoking exp(|X|) may cause premature overflow. | Thus, we calculate sinh(X) as follows: | Y := |X| | Fact := 2**(16380) | Y' := Y - 16381 log2 | cosh(X) := Fact * exp(Y'). | Exit. | | 5. (|X| > 16480 log2) sinh(X) must overflow. Return | Huge*Huge to generate overflow and an infinity with | the appropriate sign. Huge is the largest finite number in | extended format. 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 | | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | The copyright notice above does not evidence any | actual or intended publication of such source code. |SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package |section 8 |xref t_ovfl |xref t_frcinx |xref setox T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000 .global scoshd scoshd: |--COSH(X) = 1 FOR DENORMALIZED X fmoves #0x3F800000,%fp0 fmovel %d1,%FPCR fadds #0x00800000,%fp0 bra t_frcinx .global scosh scosh: fmovex (%a0),%fp0 | ...LOAD INPUT movel (%a0),%d0 movew 4(%a0),%d0 andil #0x7FFFFFFF,%d0 cmpil #0x400CB167,%d0 bgts COSHBIG |--THIS IS THE USUAL CASE, |X| < 16380 LOG2 |--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) ) fabsx %fp0 | ...|X| movel %d1,-(%sp) clrl %d1 fmovemx %fp0-%fp0,(%a0) |pass parameter to setox bsr setox | ...FP0 IS EXP(|X|) fmuls #0x3F000000,%fp0 | ...(1/2)EXP(|X|) movel (%sp)+,%d1 fmoves #0x3E800000,%fp1 | ...(1/4) fdivx %fp0,%fp1 | ...1/(2 EXP(|X|)) fmovel %d1,%FPCR faddx %fp1,%fp0 bra t_frcinx COSHBIG: cmpil #0x400CB2B3,%d0 bgts COSHHUGE fabsx %fp0 fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD) fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE movel %d1,-(%sp) clrl %d1 fmovemx %fp0-%fp0,(%a0) bsr setox fmovel (%sp)+,%fpcr fmulx TWO16380(%pc),%fp0 bra t_frcinx COSHHUGE: fmovel #0,%fpsr |clr N bit if set by source bclrb #7,(%a0) |always return positive value fmovemx (%a0),%fp0-%fp0 bra t_ovfl |end |