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1 // Copyright 2012 the V8 project authors. All rights reserved. | 1 // Copyright 2012 the V8 project authors. All rights reserved. |
2 // Use of this source code is governed by a BSD-style license that can be | 2 // Use of this source code is governed by a BSD-style license that can be |
3 // found in the LICENSE file. | 3 // found in the LICENSE file. |
4 | 4 |
5 (function(global, utils) { | 5 (function(global, utils) { |
6 "use strict"; | 6 "use strict"; |
7 | 7 |
8 %CheckIsBootstrapping(); | 8 %CheckIsBootstrapping(); |
9 | 9 |
10 // ------------------------------------------------------------------- | 10 // ------------------------------------------------------------------- |
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81 | 81 |
82 // ES6 draft 09-27-13, section 20.2.2.3. | 82 // ES6 draft 09-27-13, section 20.2.2.3. |
83 function MathAcosh(x) { | 83 function MathAcosh(x) { |
84 x = TO_NUMBER(x); | 84 x = TO_NUMBER(x); |
85 if (x < 1) return NaN; | 85 if (x < 1) return NaN; |
86 // Idempotent for NaN and +Infinity. | 86 // Idempotent for NaN and +Infinity. |
87 if (!NUMBER_IS_FINITE(x)) return x; | 87 if (!NUMBER_IS_FINITE(x)) return x; |
88 return %math_log(x + %math_sqrt(x + 1) * %math_sqrt(x - 1)); | 88 return %math_log(x + %math_sqrt(x + 1) * %math_sqrt(x - 1)); |
89 } | 89 } |
90 | 90 |
91 // ES6 draft 09-27-13, section 20.2.2.7. | |
92 function MathAtanh(x) { | |
93 x = TO_NUMBER(x); | |
94 // Idempotent for +/-0. | |
95 if (x === 0) return x; | |
96 // Returns NaN for NaN and +/- Infinity. | |
97 if (!NUMBER_IS_FINITE(x)) return NaN; | |
98 return 0.5 * %math_log((1 + x) / (1 - x)); | |
99 } | |
100 | |
101 // ES6 draft 09-27-13, section 20.2.2.17. | 91 // ES6 draft 09-27-13, section 20.2.2.17. |
102 function MathHypot(x, y) { // Function length is 2. | 92 function MathHypot(x, y) { // Function length is 2. |
103 // We may want to introduce fast paths for two arguments and when | 93 // We may want to introduce fast paths for two arguments and when |
104 // normalization to avoid overflow is not necessary. For now, we | 94 // normalization to avoid overflow is not necessary. For now, we |
105 // simply assume the general case. | 95 // simply assume the general case. |
106 var length = arguments.length; | 96 var length = arguments.length; |
107 var max = 0; | 97 var max = 0; |
108 for (var i = 0; i < length; i++) { | 98 for (var i = 0; i < length; i++) { |
109 var n = MathAbs(arguments[i]); | 99 var n = MathAbs(arguments[i]); |
110 if (n > max) max = n; | 100 if (n > max) max = n; |
111 arguments[i] = n; | 101 arguments[i] = n; |
112 } | 102 } |
113 if (max === INFINITY) return INFINITY; | 103 if (max === INFINITY) return INFINITY; |
114 | 104 |
115 // Kahan summation to avoid rounding errors. | 105 // Kahan summation to avoid rounding errors. |
116 // Normalize the numbers to the largest one to avoid overflow. | 106 // Normalize the numbers to the largest one to avoid overflow. |
117 if (max === 0) max = 1; | 107 if (max === 0) max = 1; |
118 var sum = 0; | 108 var sum = 0; |
119 var compensation = 0; | 109 var compensation = 0; |
120 for (var i = 0; i < length; i++) { | 110 for (var i = 0; i < length; i++) { |
121 var n = arguments[i] / max; | 111 var n = arguments[i] / max; |
122 var summand = n * n - compensation; | 112 var summand = n * n - compensation; |
123 var preliminary = sum + summand; | 113 var preliminary = sum + summand; |
124 compensation = (preliminary - sum) - summand; | 114 compensation = (preliminary - sum) - summand; |
125 sum = preliminary; | 115 sum = preliminary; |
126 } | 116 } |
127 return %math_sqrt(sum) * max; | 117 return %math_sqrt(sum) * max; |
128 } | 118 } |
129 | 119 |
130 // ES6 draft 09-27-13, section 20.2.2.9. | |
131 // Cube root approximation, refer to: http://metamerist.com/cbrt/cbrt.htm | |
132 // Using initial approximation adapted from Kahan's cbrt and 4 iterations | |
133 // of Newton's method. | |
134 function MathCbrt(x) { | |
135 x = TO_NUMBER(x); | |
136 if (x == 0 || !NUMBER_IS_FINITE(x)) return x; | |
137 return x >= 0 ? CubeRoot(x) : -CubeRoot(-x); | |
138 } | |
139 | |
140 macro NEWTON_ITERATION_CBRT(x, approx) | |
141 (1.0 / 3.0) * (x / (approx * approx) + 2 * approx); | |
142 endmacro | |
143 | |
144 function CubeRoot(x) { | |
145 var approx_hi = %math_floor(%_DoubleHi(x) / 3) + 0x2A9F7893; | |
146 var approx = %_ConstructDouble(approx_hi | 0, 0); | |
147 approx = NEWTON_ITERATION_CBRT(x, approx); | |
148 approx = NEWTON_ITERATION_CBRT(x, approx); | |
149 approx = NEWTON_ITERATION_CBRT(x, approx); | |
150 return NEWTON_ITERATION_CBRT(x, approx); | |
151 } | |
152 | |
153 // ------------------------------------------------------------------- | 120 // ------------------------------------------------------------------- |
154 | 121 |
155 %InstallToContext([ | 122 %InstallToContext([ |
156 "math_pow", MathPowJS, | 123 "math_pow", MathPowJS, |
157 ]); | 124 ]); |
158 | 125 |
159 %AddNamedProperty(GlobalMath, toStringTagSymbol, "Math", READ_ONLY | DONT_ENUM); | 126 %AddNamedProperty(GlobalMath, toStringTagSymbol, "Math", READ_ONLY | DONT_ENUM); |
160 | 127 |
161 // Set up math constants. | 128 // Set up math constants. |
162 utils.InstallConstants(GlobalMath, [ | 129 utils.InstallConstants(GlobalMath, [ |
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176 | 143 |
177 // Set up non-enumerable functions of the Math object and | 144 // Set up non-enumerable functions of the Math object and |
178 // set their names. | 145 // set their names. |
179 utils.InstallFunctions(GlobalMath, DONT_ENUM, [ | 146 utils.InstallFunctions(GlobalMath, DONT_ENUM, [ |
180 "random", MathRandom, | 147 "random", MathRandom, |
181 "abs", MathAbs, | 148 "abs", MathAbs, |
182 "pow", MathPowJS, | 149 "pow", MathPowJS, |
183 "sign", MathSign, | 150 "sign", MathSign, |
184 "asinh", MathAsinh, | 151 "asinh", MathAsinh, |
185 "acosh", MathAcosh, | 152 "acosh", MathAcosh, |
186 "atanh", MathAtanh, | |
187 "hypot", MathHypot, | 153 "hypot", MathHypot, |
188 "cbrt", MathCbrt | |
189 ]); | 154 ]); |
190 | 155 |
191 %SetForceInlineFlag(MathAbs); | 156 %SetForceInlineFlag(MathAbs); |
192 %SetForceInlineFlag(MathRandom); | 157 %SetForceInlineFlag(MathRandom); |
193 %SetForceInlineFlag(MathSign); | 158 %SetForceInlineFlag(MathSign); |
194 | 159 |
195 // ------------------------------------------------------------------- | 160 // ------------------------------------------------------------------- |
196 // Exports | 161 // Exports |
197 | 162 |
198 utils.Export(function(to) { | 163 utils.Export(function(to) { |
199 to.MathAbs = MathAbs; | 164 to.MathAbs = MathAbs; |
200 to.IntRandom = MathRandomRaw; | 165 to.IntRandom = MathRandomRaw; |
201 }); | 166 }); |
202 | 167 |
203 }) | 168 }) |
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