Ben Murdoch | 4a90d5f | 2016-03-22 12:00:34 +0000 | [diff] [blame] | 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 |
| 3 | // found in the LICENSE file. |
| 4 | |
| 5 | (function(global, utils) { |
| 6 | "use strict"; |
| 7 | |
| 8 | %CheckIsBootstrapping(); |
| 9 | |
| 10 | // ------------------------------------------------------------------- |
| 11 | // Imports |
| 12 | |
| 13 | define kRandomBatchSize = 64; |
| 14 | // The first two slots are reserved to persist PRNG state. |
| 15 | define kRandomNumberStart = 2; |
| 16 | |
| 17 | var GlobalFloat64Array = global.Float64Array; |
| 18 | var GlobalMath = global.Math; |
| 19 | var GlobalObject = global.Object; |
| 20 | var InternalArray = utils.InternalArray; |
| 21 | var NaN = %GetRootNaN(); |
| 22 | var nextRandomIndex = kRandomBatchSize; |
| 23 | var randomNumbers = UNDEFINED; |
| 24 | var toStringTagSymbol = utils.ImportNow("to_string_tag_symbol"); |
| 25 | |
| 26 | //------------------------------------------------------------------- |
| 27 | |
| 28 | // ECMA 262 - 15.8.2.1 |
| 29 | function MathAbs(x) { |
| 30 | x = +x; |
| 31 | return (x > 0) ? x : 0 - x; |
| 32 | } |
| 33 | |
| 34 | // ECMA 262 - 15.8.2.2 |
| 35 | function MathAcosJS(x) { |
| 36 | return %_MathAcos(+x); |
| 37 | } |
| 38 | |
| 39 | // ECMA 262 - 15.8.2.3 |
| 40 | function MathAsinJS(x) { |
| 41 | return %_MathAsin(+x); |
| 42 | } |
| 43 | |
| 44 | // ECMA 262 - 15.8.2.4 |
| 45 | function MathAtanJS(x) { |
| 46 | return %_MathAtan(+x); |
| 47 | } |
| 48 | |
| 49 | // ECMA 262 - 15.8.2.5 |
| 50 | // The naming of y and x matches the spec, as does the order in which |
| 51 | // ToNumber (valueOf) is called. |
| 52 | function MathAtan2JS(y, x) { |
| 53 | y = +y; |
| 54 | x = +x; |
| 55 | return %_MathAtan2(y, x); |
| 56 | } |
| 57 | |
| 58 | // ECMA 262 - 15.8.2.6 |
| 59 | function MathCeil(x) { |
| 60 | return -%_MathFloor(-x); |
| 61 | } |
| 62 | |
| 63 | // ECMA 262 - 15.8.2.8 |
| 64 | function MathExp(x) { |
| 65 | return %MathExpRT(TO_NUMBER(x)); |
| 66 | } |
| 67 | |
| 68 | // ECMA 262 - 15.8.2.9 |
| 69 | function MathFloorJS(x) { |
| 70 | return %_MathFloor(+x); |
| 71 | } |
| 72 | |
| 73 | // ECMA 262 - 15.8.2.10 |
| 74 | function MathLog(x) { |
| 75 | return %_MathLogRT(TO_NUMBER(x)); |
| 76 | } |
| 77 | |
| 78 | // ECMA 262 - 15.8.2.11 |
| 79 | function MathMax(arg1, arg2) { // length == 2 |
| 80 | var length = %_ArgumentsLength(); |
| 81 | if (length == 2) { |
| 82 | arg1 = TO_NUMBER(arg1); |
| 83 | arg2 = TO_NUMBER(arg2); |
| 84 | if (arg2 > arg1) return arg2; |
| 85 | if (arg1 > arg2) return arg1; |
| 86 | if (arg1 == arg2) { |
| 87 | // Make sure -0 is considered less than +0. |
| 88 | return (arg1 === 0 && %_IsMinusZero(arg1)) ? arg2 : arg1; |
| 89 | } |
| 90 | // All comparisons failed, one of the arguments must be NaN. |
| 91 | return NaN; |
| 92 | } |
| 93 | var r = -INFINITY; |
| 94 | for (var i = 0; i < length; i++) { |
| 95 | var n = %_Arguments(i); |
| 96 | n = TO_NUMBER(n); |
| 97 | // Make sure +0 is considered greater than -0. |
| 98 | if (NUMBER_IS_NAN(n) || n > r || (r === 0 && n === 0 && %_IsMinusZero(r))) { |
| 99 | r = n; |
| 100 | } |
| 101 | } |
| 102 | return r; |
| 103 | } |
| 104 | |
| 105 | // ECMA 262 - 15.8.2.12 |
| 106 | function MathMin(arg1, arg2) { // length == 2 |
| 107 | var length = %_ArgumentsLength(); |
| 108 | if (length == 2) { |
| 109 | arg1 = TO_NUMBER(arg1); |
| 110 | arg2 = TO_NUMBER(arg2); |
| 111 | if (arg2 > arg1) return arg1; |
| 112 | if (arg1 > arg2) return arg2; |
| 113 | if (arg1 == arg2) { |
| 114 | // Make sure -0 is considered less than +0. |
| 115 | return (arg1 === 0 && %_IsMinusZero(arg1)) ? arg1 : arg2; |
| 116 | } |
| 117 | // All comparisons failed, one of the arguments must be NaN. |
| 118 | return NaN; |
| 119 | } |
| 120 | var r = INFINITY; |
| 121 | for (var i = 0; i < length; i++) { |
| 122 | var n = %_Arguments(i); |
| 123 | n = TO_NUMBER(n); |
| 124 | // Make sure -0 is considered less than +0. |
| 125 | if (NUMBER_IS_NAN(n) || n < r || (r === 0 && n === 0 && %_IsMinusZero(n))) { |
| 126 | r = n; |
| 127 | } |
| 128 | } |
| 129 | return r; |
| 130 | } |
| 131 | |
| 132 | // ECMA 262 - 15.8.2.13 |
| 133 | function MathPowJS(x, y) { |
| 134 | return %_MathPow(TO_NUMBER(x), TO_NUMBER(y)); |
| 135 | } |
| 136 | |
| 137 | // ECMA 262 - 15.8.2.14 |
| 138 | function MathRandom() { |
| 139 | if (nextRandomIndex >= kRandomBatchSize) { |
| 140 | randomNumbers = %GenerateRandomNumbers(randomNumbers); |
| 141 | nextRandomIndex = kRandomNumberStart; |
| 142 | } |
| 143 | return randomNumbers[nextRandomIndex++]; |
| 144 | } |
| 145 | |
| 146 | function MathRandomRaw() { |
| 147 | if (nextRandomIndex >= kRandomBatchSize) { |
| 148 | randomNumbers = %GenerateRandomNumbers(randomNumbers); |
| 149 | nextRandomIndex = kRandomNumberStart; |
| 150 | } |
| 151 | return %_DoubleLo(randomNumbers[nextRandomIndex++]) & 0x3FFFFFFF; |
| 152 | } |
| 153 | |
| 154 | // ECMA 262 - 15.8.2.15 |
| 155 | function MathRound(x) { |
| 156 | return %RoundNumber(TO_NUMBER(x)); |
| 157 | } |
| 158 | |
| 159 | // ECMA 262 - 15.8.2.17 |
| 160 | function MathSqrtJS(x) { |
| 161 | return %_MathSqrt(+x); |
| 162 | } |
| 163 | |
| 164 | // Non-standard extension. |
| 165 | function MathImul(x, y) { |
| 166 | return %NumberImul(TO_NUMBER(x), TO_NUMBER(y)); |
| 167 | } |
| 168 | |
| 169 | // ES6 draft 09-27-13, section 20.2.2.28. |
| 170 | function MathSign(x) { |
| 171 | x = +x; |
| 172 | if (x > 0) return 1; |
| 173 | if (x < 0) return -1; |
| 174 | // -0, 0 or NaN. |
| 175 | return x; |
| 176 | } |
| 177 | |
| 178 | // ES6 draft 09-27-13, section 20.2.2.34. |
| 179 | function MathTrunc(x) { |
| 180 | x = +x; |
| 181 | if (x > 0) return %_MathFloor(x); |
| 182 | if (x < 0) return -%_MathFloor(-x); |
| 183 | // -0, 0 or NaN. |
| 184 | return x; |
| 185 | } |
| 186 | |
| 187 | // ES6 draft 09-27-13, section 20.2.2.5. |
| 188 | function MathAsinh(x) { |
| 189 | x = TO_NUMBER(x); |
| 190 | // Idempotent for NaN, +/-0 and +/-Infinity. |
| 191 | if (x === 0 || !NUMBER_IS_FINITE(x)) return x; |
| 192 | if (x > 0) return MathLog(x + %_MathSqrt(x * x + 1)); |
| 193 | // This is to prevent numerical errors caused by large negative x. |
| 194 | return -MathLog(-x + %_MathSqrt(x * x + 1)); |
| 195 | } |
| 196 | |
| 197 | // ES6 draft 09-27-13, section 20.2.2.3. |
| 198 | function MathAcosh(x) { |
| 199 | x = TO_NUMBER(x); |
| 200 | if (x < 1) return NaN; |
| 201 | // Idempotent for NaN and +Infinity. |
| 202 | if (!NUMBER_IS_FINITE(x)) return x; |
| 203 | return MathLog(x + %_MathSqrt(x + 1) * %_MathSqrt(x - 1)); |
| 204 | } |
| 205 | |
| 206 | // ES6 draft 09-27-13, section 20.2.2.7. |
| 207 | function MathAtanh(x) { |
| 208 | x = TO_NUMBER(x); |
| 209 | // Idempotent for +/-0. |
| 210 | if (x === 0) return x; |
| 211 | // Returns NaN for NaN and +/- Infinity. |
| 212 | if (!NUMBER_IS_FINITE(x)) return NaN; |
| 213 | return 0.5 * MathLog((1 + x) / (1 - x)); |
| 214 | } |
| 215 | |
| 216 | // ES6 draft 09-27-13, section 20.2.2.17. |
| 217 | function MathHypot(x, y) { // Function length is 2. |
| 218 | // We may want to introduce fast paths for two arguments and when |
| 219 | // normalization to avoid overflow is not necessary. For now, we |
| 220 | // simply assume the general case. |
| 221 | var length = %_ArgumentsLength(); |
| 222 | var args = new InternalArray(length); |
| 223 | var max = 0; |
| 224 | for (var i = 0; i < length; i++) { |
| 225 | var n = %_Arguments(i); |
| 226 | n = TO_NUMBER(n); |
| 227 | if (n === INFINITY || n === -INFINITY) return INFINITY; |
| 228 | n = MathAbs(n); |
| 229 | if (n > max) max = n; |
| 230 | args[i] = n; |
| 231 | } |
| 232 | |
| 233 | // Kahan summation to avoid rounding errors. |
| 234 | // Normalize the numbers to the largest one to avoid overflow. |
| 235 | if (max === 0) max = 1; |
| 236 | var sum = 0; |
| 237 | var compensation = 0; |
| 238 | for (var i = 0; i < length; i++) { |
| 239 | var n = args[i] / max; |
| 240 | var summand = n * n - compensation; |
| 241 | var preliminary = sum + summand; |
| 242 | compensation = (preliminary - sum) - summand; |
| 243 | sum = preliminary; |
| 244 | } |
| 245 | return %_MathSqrt(sum) * max; |
| 246 | } |
| 247 | |
| 248 | // ES6 draft 09-27-13, section 20.2.2.16. |
| 249 | function MathFroundJS(x) { |
| 250 | return %MathFround(TO_NUMBER(x)); |
| 251 | } |
| 252 | |
| 253 | // ES6 draft 07-18-14, section 20.2.2.11 |
| 254 | function MathClz32JS(x) { |
| 255 | return %_MathClz32(x >>> 0); |
| 256 | } |
| 257 | |
| 258 | // ES6 draft 09-27-13, section 20.2.2.9. |
| 259 | // Cube root approximation, refer to: http://metamerist.com/cbrt/cbrt.htm |
| 260 | // Using initial approximation adapted from Kahan's cbrt and 4 iterations |
| 261 | // of Newton's method. |
| 262 | function MathCbrt(x) { |
| 263 | x = TO_NUMBER(x); |
| 264 | if (x == 0 || !NUMBER_IS_FINITE(x)) return x; |
| 265 | return x >= 0 ? CubeRoot(x) : -CubeRoot(-x); |
| 266 | } |
| 267 | |
| 268 | macro NEWTON_ITERATION_CBRT(x, approx) |
| 269 | (1.0 / 3.0) * (x / (approx * approx) + 2 * approx); |
| 270 | endmacro |
| 271 | |
| 272 | function CubeRoot(x) { |
| 273 | var approx_hi = MathFloorJS(%_DoubleHi(x) / 3) + 0x2A9F7893; |
| 274 | var approx = %_ConstructDouble(approx_hi | 0, 0); |
| 275 | approx = NEWTON_ITERATION_CBRT(x, approx); |
| 276 | approx = NEWTON_ITERATION_CBRT(x, approx); |
| 277 | approx = NEWTON_ITERATION_CBRT(x, approx); |
| 278 | return NEWTON_ITERATION_CBRT(x, approx); |
| 279 | } |
| 280 | |
| 281 | // ------------------------------------------------------------------- |
| 282 | |
| 283 | %AddNamedProperty(GlobalMath, toStringTagSymbol, "Math", READ_ONLY | DONT_ENUM); |
| 284 | |
| 285 | // Set up math constants. |
| 286 | utils.InstallConstants(GlobalMath, [ |
| 287 | // ECMA-262, section 15.8.1.1. |
| 288 | "E", 2.7182818284590452354, |
| 289 | // ECMA-262, section 15.8.1.2. |
| 290 | "LN10", 2.302585092994046, |
| 291 | // ECMA-262, section 15.8.1.3. |
| 292 | "LN2", 0.6931471805599453, |
| 293 | // ECMA-262, section 15.8.1.4. |
| 294 | "LOG2E", 1.4426950408889634, |
| 295 | "LOG10E", 0.4342944819032518, |
| 296 | "PI", 3.1415926535897932, |
| 297 | "SQRT1_2", 0.7071067811865476, |
| 298 | "SQRT2", 1.4142135623730951 |
| 299 | ]); |
| 300 | |
| 301 | // Set up non-enumerable functions of the Math object and |
| 302 | // set their names. |
| 303 | utils.InstallFunctions(GlobalMath, DONT_ENUM, [ |
| 304 | "random", MathRandom, |
| 305 | "abs", MathAbs, |
| 306 | "acos", MathAcosJS, |
| 307 | "asin", MathAsinJS, |
| 308 | "atan", MathAtanJS, |
| 309 | "ceil", MathCeil, |
| 310 | "exp", MathExp, |
| 311 | "floor", MathFloorJS, |
| 312 | "log", MathLog, |
| 313 | "round", MathRound, |
| 314 | "sqrt", MathSqrtJS, |
| 315 | "atan2", MathAtan2JS, |
| 316 | "pow", MathPowJS, |
| 317 | "max", MathMax, |
| 318 | "min", MathMin, |
| 319 | "imul", MathImul, |
| 320 | "sign", MathSign, |
| 321 | "trunc", MathTrunc, |
| 322 | "asinh", MathAsinh, |
| 323 | "acosh", MathAcosh, |
| 324 | "atanh", MathAtanh, |
| 325 | "hypot", MathHypot, |
| 326 | "fround", MathFroundJS, |
| 327 | "clz32", MathClz32JS, |
| 328 | "cbrt", MathCbrt |
| 329 | ]); |
| 330 | |
| 331 | %SetForceInlineFlag(MathAbs); |
| 332 | %SetForceInlineFlag(MathAcosJS); |
| 333 | %SetForceInlineFlag(MathAsinJS); |
| 334 | %SetForceInlineFlag(MathAtanJS); |
| 335 | %SetForceInlineFlag(MathAtan2JS); |
| 336 | %SetForceInlineFlag(MathCeil); |
| 337 | %SetForceInlineFlag(MathClz32JS); |
| 338 | %SetForceInlineFlag(MathFloorJS); |
| 339 | %SetForceInlineFlag(MathRandom); |
| 340 | %SetForceInlineFlag(MathSign); |
| 341 | %SetForceInlineFlag(MathSqrtJS); |
| 342 | %SetForceInlineFlag(MathTrunc); |
| 343 | |
| 344 | // ------------------------------------------------------------------- |
| 345 | // Exports |
| 346 | |
| 347 | utils.Export(function(to) { |
| 348 | to.MathAbs = MathAbs; |
| 349 | to.MathExp = MathExp; |
| 350 | to.MathFloor = MathFloorJS; |
| 351 | to.IntRandom = MathRandomRaw; |
| 352 | to.MathMax = MathMax; |
| 353 | to.MathMin = MathMin; |
| 354 | }); |
| 355 | |
| 356 | }) |