1 | #include "fpsp-namespace.h" |
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2 | // |
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3 | // |
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4 | // scosh.sa 3.1 12/10/90 |
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5 | // |
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6 | // The entry point sCosh computes the hyperbolic cosine of |
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7 | // an input argument; sCoshd does the same except for denormalized |
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8 | // input. |
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9 | // |
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10 | // Input: Double-extended number X in location pointed to |
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11 | // by address register a0. |
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12 | // |
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13 | // Output: The value cosh(X) returned in floating-point register Fp0. |
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14 | // |
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15 | // Accuracy and Monotonicity: The returned result is within 3 ulps in |
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16 | // 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the |
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17 | // result is subsequently rounded to double precision. The |
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18 | // result is provably monotonic in double precision. |
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19 | // |
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20 | // Speed: The program sCOSH takes approximately 250 cycles. |
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21 | // |
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22 | // Algorithm: |
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23 | // |
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24 | // COSH |
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25 | // 1. If |X| > 16380 log2, go to 3. |
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26 | // |
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27 | // 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae |
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28 | // y = |X|, z = exp(Y), and |
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29 | // cosh(X) = (1/2)*( z + 1/z ). |
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30 | // Exit. |
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31 | // |
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32 | // 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. |
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33 | // |
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34 | // 4. (16380 log2 < |X| <= 16480 log2) |
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35 | // cosh(X) = sign(X) * exp(|X|)/2. |
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36 | // However, invoking exp(|X|) may cause premature overflow. |
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37 | // Thus, we calculate sinh(X) as follows: |
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38 | // Y := |X| |
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39 | // Fact := 2**(16380) |
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40 | // Y' := Y - 16381 log2 |
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41 | // cosh(X) := Fact * exp(Y'). |
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42 | // Exit. |
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43 | // |
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44 | // 5. (|X| > 16480 log2) sinh(X) must overflow. Return |
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45 | // Huge*Huge to generate overflow and an infinity with |
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46 | // the appropriate sign. Huge is the largest finite number in |
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47 | // extended format. Exit. |
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48 | // |
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49 | // |
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50 | |
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51 | // Copyright (C) Motorola, Inc. 1990 |
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52 | // All Rights Reserved |
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53 | // |
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54 | // THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA |
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55 | // The copyright notice above does not evidence any |
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56 | // actual or intended publication of such source code. |
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57 | |
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58 | //SCOSH idnt 2,1 | Motorola 040 Floating Point Software Package |
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59 | |
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60 | |section 8 |
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61 | |
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62 | |xref t_ovfl |
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63 | |xref t_frcinx |
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64 | |xref setox |
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65 | |
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66 | T1: .long 0x40C62D38,0xD3D64634 // ... 16381 LOG2 LEAD |
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67 | T2: .long 0x3D6F90AE,0xB1E75CC7 // ... 16381 LOG2 TRAIL |
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68 | |
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69 | TWO16380: .long 0x7FFB0000,0x80000000,0x00000000,0x00000000 |
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70 | |
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71 | .global scoshd |
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72 | scoshd: |
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73 | //--COSH(X) = 1 FOR DENORMALIZED X |
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74 | |
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75 | fmoves #0x3F800000,%fp0 |
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76 | |
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77 | fmovel %d1,%FPCR |
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78 | fadds #0x00800000,%fp0 |
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79 | bra t_frcinx |
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80 | |
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81 | .global scosh |
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82 | scosh: |
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83 | fmovex (%a0),%fp0 // ...LOAD INPUT |
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84 | |
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85 | movel (%a0),%d0 |
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86 | movew 4(%a0),%d0 |
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87 | andil #0x7FFFFFFF,%d0 |
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88 | cmpil #0x400CB167,%d0 |
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89 | bgts COSHBIG |
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90 | |
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91 | //--THIS IS THE USUAL CASE, |X| < 16380 LOG2 |
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92 | //--COSH(X) = (1/2) * ( EXP(X) + 1/EXP(X) ) |
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93 | |
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94 | fabsx %fp0 // ...|X| |
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95 | |
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96 | movel %d1,-(%sp) |
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97 | clrl %d1 |
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98 | fmovemx %fp0-%fp0,(%a0) //pass parameter to setox |
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99 | bsr setox // ...FP0 IS EXP(|X|) |
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100 | fmuls #0x3F000000,%fp0 // ...(1/2)EXP(|X|) |
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101 | movel (%sp)+,%d1 |
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102 | |
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103 | fmoves #0x3E800000,%fp1 // ...(1/4) |
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104 | fdivx %fp0,%fp1 // ...1/(2 EXP(|X|)) |
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105 | |
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106 | fmovel %d1,%FPCR |
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107 | faddx %fp1,%fp0 |
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108 | |
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109 | bra t_frcinx |
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110 | |
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111 | COSHBIG: |
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112 | cmpil #0x400CB2B3,%d0 |
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113 | bgts COSHHUGE |
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114 | |
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115 | fabsx %fp0 |
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116 | fsubd T1(%pc),%fp0 // ...(|X|-16381LOG2_LEAD) |
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117 | fsubd T2(%pc),%fp0 // ...|X| - 16381 LOG2, ACCURATE |
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118 | |
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119 | movel %d1,-(%sp) |
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120 | clrl %d1 |
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121 | fmovemx %fp0-%fp0,(%a0) |
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122 | bsr setox |
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123 | fmovel (%sp)+,%fpcr |
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124 | |
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125 | fmulx TWO16380(%pc),%fp0 |
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126 | bra t_frcinx |
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127 | |
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128 | COSHHUGE: |
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129 | fmovel #0,%fpsr //clr N bit if set by source |
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130 | bclrb #7,(%a0) //always return positive value |
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131 | fmovemx (%a0),%fp0-%fp0 |
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132 | bra t_ovfl |
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133 | |
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134 | |end |
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