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path: root/arch/m68k/fpsp040/ssinh.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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 ``` ``````| | ssinh.sa 3.1 12/10/90 | | The entry point sSinh computes the hyperbolic sine of | an input argument; sSinhd does the same except for denormalized | input. | | Input: Double-extended number X in location pointed to | by address register a0. | | Output: The value sinh(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 sSINH takes approximately 280 cycles. | | Algorithm: | | SINH | 1. If |X| > 16380 log2, go to 3. | | 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae | y = |X|, sgn = sign(X), and z = expm1(Y), | sinh(X) = sgn*(1/2)*( z + z/(1+z) ). | Exit. | | 3. If |X| > 16480 log2, go to 5. | | 4. (16380 log2 < |X| <= 16480 log2) | sinh(X) = sign(X) * exp(|X|)/2. | However, invoking exp(|X|) may cause premature overflow. | Thus, we calculate sinh(X) as follows: | Y := |X| | sgn := sign(X) | sgnFact := sgn * 2**(16380) | Y' := Y - 16381 log2 | sinh(X) := sgnFact * exp(Y'). | Exit. | | 5. (|X| > 16480 log2) sinh(X) must overflow. Return | sign(X)*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 | | Copyright (C) Motorola, Inc. 1990 | All Rights Reserved | | THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA | The copyright notice above does not evidence any | actual or intended publication of such source code. |SSINH idnt 2,1 | Motorola 040 Floating Point Software Package |section 8 T1: .long 0x40C62D38,0xD3D64634 | ... 16381 LOG2 LEAD T2: .long 0x3D6F90AE,0xB1E75CC7 | ... 16381 LOG2 TRAIL |xref t_frcinx |xref t_ovfl |xref t_extdnrm |xref setox |xref setoxm1 .global ssinhd ssinhd: |--SINH(X) = X FOR DENORMALIZED X bra t_extdnrm .global ssinh ssinh: fmovex (%a0),%fp0 | ...LOAD INPUT movel (%a0),%d0 movew 4(%a0),%d0 movel %d0,%a1 | save a copy of original (compacted) operand andl #0x7FFFFFFF,%d0 cmpl #0x400CB167,%d0 bgts SINHBIG |--THIS IS THE USUAL CASE, |X| < 16380 LOG2 |--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) ) fabsx %fp0 | ...Y = |X| moveml %a1/%d1,-(%sp) fmovemx %fp0-%fp0,(%a0) clrl %d1 bsr setoxm1 | ...FP0 IS Z = EXPM1(Y) fmovel #0,%fpcr moveml (%sp)+,%a1/%d1 fmovex %fp0,%fp1 fadds #0x3F800000,%fp1 | ...1+Z fmovex %fp0,-(%sp) fdivx %fp1,%fp0 | ...Z/(1+Z) movel %a1,%d0 andl #0x80000000,%d0 orl #0x3F000000,%d0 faddx (%sp)+,%fp0 movel %d0,-(%sp) fmovel %d1,%fpcr fmuls (%sp)+,%fp0 |last fp inst - possible exceptions set bra t_frcinx SINHBIG: cmpl #0x400CB2B3,%d0 bgt t_ovfl fabsx %fp0 fsubd T1(%pc),%fp0 | ...(|X|-16381LOG2_LEAD) movel #0,-(%sp) movel #0x80000000,-(%sp) movel %a1,%d0 andl #0x80000000,%d0 orl #0x7FFB0000,%d0 movel %d0,-(%sp) | ...EXTENDED FMT fsubd T2(%pc),%fp0 | ...|X| - 16381 LOG2, ACCURATE movel %d1,-(%sp) clrl %d1 fmovemx %fp0-%fp0,(%a0) bsr setox fmovel (%sp)+,%fpcr fmulx (%sp)+,%fp0 |possible exception bra t_frcinx |end ``````