1 | ; $Id: cos.asm 98103 2023-01-17 14:15:46Z vboxsync $
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2 | ;; @file
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3 | ; IPRT - No-CRT cos - AMD64 & X86.
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4 | ;
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5 |
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6 | ;
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7 | ; Copyright (C) 2006-2023 Oracle and/or its affiliates.
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8 | ;
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9 | ; This file is part of VirtualBox base platform packages, as
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10 | ; available from https://www.virtualbox.org.
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11 | ;
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12 | ; This program is free software; you can redistribute it and/or
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13 | ; modify it under the terms of the GNU General Public License
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14 | ; as published by the Free Software Foundation, in version 3 of the
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15 | ; License.
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16 | ;
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17 | ; This program is distributed in the hope that it will be useful, but
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18 | ; WITHOUT ANY WARRANTY; without even the implied warranty of
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19 | ; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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20 | ; General Public License for more details.
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21 | ;
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22 | ; You should have received a copy of the GNU General Public License
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23 | ; along with this program; if not, see <https://www.gnu.org/licenses>.
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24 | ;
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25 | ; The contents of this file may alternatively be used under the terms
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26 | ; of the Common Development and Distribution License Version 1.0
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27 | ; (CDDL), a copy of it is provided in the "COPYING.CDDL" file included
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28 | ; in the VirtualBox distribution, in which case the provisions of the
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29 | ; CDDL are applicable instead of those of the GPL.
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30 | ;
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31 | ; You may elect to license modified versions of this file under the
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32 | ; terms and conditions of either the GPL or the CDDL or both.
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33 | ;
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34 | ; SPDX-License-Identifier: GPL-3.0-only OR CDDL-1.0
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35 | ;
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36 |
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37 |
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38 | %define RT_ASM_WITH_SEH64
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39 | %include "iprt/asmdefs.mac"
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40 | %include "iprt/x86.mac"
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41 |
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42 |
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43 | BEGINCODE
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44 |
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45 | ;;
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46 | ; Compute the cosine of rd, measured in radians.
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47 | ;
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48 | ; @returns st(0) / xmm0
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49 | ; @param rd [rbp + xCB*2] / xmm0
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50 | ;
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51 | RT_NOCRT_BEGINPROC cos
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52 | push xBP
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53 | SEH64_PUSH_xBP
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54 | mov xBP, xSP
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55 | SEH64_SET_FRAME_xBP 0
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56 | sub xSP, 20h
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57 | SEH64_ALLOCATE_STACK 20h
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58 | SEH64_END_PROLOGUE
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59 |
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60 | %ifdef RT_OS_WINDOWS
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61 | ;
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62 | ; Make sure we use full precision and not the windows default of 53 bits.
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63 | ;
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64 | ;; @todo not sure if this makes any difference...
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65 | fnstcw [xBP - 20h]
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66 | mov ax, [xBP - 20h]
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67 | or ax, X86_FCW_PC_64 ; includes both bits, so no need to clear the mask.
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68 | mov [xBP - 1ch], ax
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69 | fldcw [xBP - 1ch]
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70 | %endif
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71 |
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72 | ;
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73 | ; Load the input into st0.
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74 | ;
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75 | %ifdef RT_ARCH_AMD64
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76 | movsd [xBP - 10h], xmm0
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77 | fld qword [xBP - 10h]
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78 | %else
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79 | fld qword [xBP + xCB*2]
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80 | %endif
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81 |
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82 | ;
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83 | ; The FCOS instruction has a very narrow range (-3pi/8 to 3pi/8) where it
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84 | ; works reliably, so outside that we'll use the FSIN instruction instead
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85 | ; as it has a larger good range (-5pi/4 to 1pi/4 for cosine).
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86 | ; Input conversion follows: cos(x) = sin(x + pi/2)
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87 | ;
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88 | ; We examin the input and weed out non-finit numbers first.
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89 | ;
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90 |
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91 | ; We only do the range check on normal finite numbers.
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92 | fxam
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93 | fnstsw ax
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94 | and ax, X86_FSW_C3 | X86_FSW_C2 | X86_FSW_C0
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95 | cmp ax, X86_FSW_C2 ; Normal finite number (excluding zero)
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96 | je .finite
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97 | cmp ax, X86_FSW_C3 ; Zero
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98 | je .zero
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99 | cmp ax, X86_FSW_C3 | X86_FSW_C2 ; Denormals - treat them as zero.
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100 | je .zero
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101 | cmp ax, X86_FSW_C0 ; NaN - must handle it special,
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102 | je .nan
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103 |
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104 | ; Pass infinities and unsupported inputs to fcos, assuming it does the right thing.
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105 | ; We also jump here if we get a finite number in the "good" range, see below.
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106 | .do_fcos:
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107 | fcos
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108 | jmp .return_val
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109 |
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110 | ;
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111 | ; Finite number.
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112 | ;
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113 | ; First check if it's a very tiny number where we can simply return 1.
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114 | ; Next check if it's in the range where FCOS is reasonable, otherwise
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115 | ; go to FSIN to do the work.
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116 | ;
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117 | .finite:
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118 | fld st0
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119 | fabs
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120 | fld qword [.s_r64TinyCosTo1 xWrtRIP]
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121 | fcomip st1
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122 | ja .zero_extra_pop
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123 |
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124 | .not_that_tiny_input:
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125 | fld qword [.s_r64FCosOkay xWrtRIP]
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126 | fcomip st1
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127 | ffreep st0 ; pop fabs(input)
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128 | ja .do_fcos ; jmp if fabs(input) < .s_r64FCosOkay
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129 |
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130 | ;
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131 | ; If we have a positive number we subtract 3pi/2, for negative we add pi/2.
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132 | ; We still have the FXAM result in AX.
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133 | ;
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134 | .outside_fcos_range:
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135 | test ax, X86_FSW_C1 ; The sign bit.
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136 | jnz .adjust_negative_to_sine
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137 |
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138 | ; Calc -3pi/2 using FPU-internal pi constant.
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139 | fldpi
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140 | fadd st0, st0 ; st0=2pi
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141 | fldpi
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142 | fdiv qword [.s_r64Two xWrtRIP] ; st1=2pi; st0=pi/2
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143 | fsubp st1, st0 ; st0=3pi/2
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144 | fchs ; st0=-3pi/2
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145 | jmp .make_sine_adjustment
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146 |
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147 | .adjust_negative_to_sine:
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148 | ; Calc +pi/2.
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149 | fldpi
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150 | fdiv qword [.s_r64Two xWrtRIP] ; st1=2pi; st0=pi/2
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151 |
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152 | .make_sine_adjustment:
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153 | faddp st1, st0
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154 |
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155 | ;
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156 | ; Call internal sine worker to calculate st0=sin(st0)
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157 | ;
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158 | .do_sine:
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159 | mov ecx, 1 ; double
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160 | extern NAME(rtNoCrtMathSinCore)
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161 | call NAME(rtNoCrtMathSinCore)
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162 |
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163 | ;
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164 | ; Return st0.
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165 | ;
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166 | .return_val:
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167 | %ifdef RT_ARCH_AMD64
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168 | fstp qword [xBP - 10h]
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169 | movsd xmm0, [xBP - 10h]
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170 | %endif
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171 | %ifdef RT_OS_WINDOWS
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172 | fldcw [xBP - 20h] ; restore original
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173 | %endif
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174 | .return:
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175 | leave
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176 | ret
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177 |
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178 | ;
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179 | ; cos(+/-0) = +1.0
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180 | ;
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181 | .zero_extra_pop:
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182 | ffreep st0
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183 | .zero:
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184 | ffreep st0
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185 | fld1
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186 | jmp .return_val
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187 |
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188 | ;
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189 | ; Input is NaN, output it unmodified as far as we can (FLD changes SNaN
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190 | ; to QNaN when masked).
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191 | ;
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192 | .nan:
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193 | %ifdef RT_ARCH_AMD64
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194 | ffreep st0
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195 | %endif
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196 | jmp .return
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197 |
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198 | ;
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199 | ; Local constants.
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200 | ;
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201 | ALIGNCODE(8)
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202 | ; About 2**-27. When fabs(input) is below this limit we can consider cos(input) ~= 1.0.
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203 | .s_r64TinyCosTo1:
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204 | dq 7.4505806e-9
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205 |
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206 | ; The absolute limit for the range which FCOS is expected to produce reasonable results.
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207 | .s_r64FCosOkay:
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208 | dq 1.1780972450961724644225 ; 3*pi/8
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209 |
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210 | .s_r64Two:
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211 | dq 2.0
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212 | ENDPROC RT_NOCRT(cos)
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213 |
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