SoftFloat.cs 87 KB

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  1. using ChocolArm64.State;
  2. using System;
  3. using System.Diagnostics;
  4. using System.Runtime.CompilerServices;
  5. namespace ChocolArm64.Instructions
  6. {
  7. static class SoftFloat
  8. {
  9. static SoftFloat()
  10. {
  11. RecipEstimateTable = BuildRecipEstimateTable();
  12. RecipSqrtEstimateTable = BuildRecipSqrtEstimateTable();
  13. }
  14. internal static readonly byte[] RecipEstimateTable;
  15. internal static readonly byte[] RecipSqrtEstimateTable;
  16. private static byte[] BuildRecipEstimateTable()
  17. {
  18. byte[] tbl = new byte[256];
  19. for (int idx = 0; idx < 256; idx++)
  20. {
  21. uint src = (uint)idx + 256u;
  22. Debug.Assert(256u <= src && src < 512u);
  23. src = (src << 1) + 1u;
  24. uint aux = (1u << 19) / src;
  25. uint dst = (aux + 1u) >> 1;
  26. Debug.Assert(256u <= dst && dst < 512u);
  27. tbl[idx] = (byte)(dst - 256u);
  28. }
  29. return tbl;
  30. }
  31. private static byte[] BuildRecipSqrtEstimateTable()
  32. {
  33. byte[] tbl = new byte[384];
  34. for (int idx = 0; idx < 384; idx++)
  35. {
  36. uint src = (uint)idx + 128u;
  37. Debug.Assert(128u <= src && src < 512u);
  38. if (src < 256u)
  39. {
  40. src = (src << 1) + 1u;
  41. }
  42. else
  43. {
  44. src = (src >> 1) << 1;
  45. src = (src + 1u) << 1;
  46. }
  47. uint aux = 512u;
  48. while (src * (aux + 1u) * (aux + 1u) < (1u << 28))
  49. {
  50. aux = aux + 1u;
  51. }
  52. uint dst = (aux + 1u) >> 1;
  53. Debug.Assert(256u <= dst && dst < 512u);
  54. tbl[idx] = (byte)(dst - 256u);
  55. }
  56. return tbl;
  57. }
  58. }
  59. static class SoftFloat16_32
  60. {
  61. public static float FPConvert(ushort valueBits, CpuThreadState state)
  62. {
  63. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat16_32.FPConvert: state.Fpcr = 0x{state.CFpcr:X8}");
  64. double real = valueBits.FPUnpackCv(out FpType type, out bool sign, state);
  65. float result;
  66. if (type == FpType.SNaN || type == FpType.QNaN)
  67. {
  68. if (state.GetFpcrFlag(Fpcr.Dn))
  69. {
  70. result = FPDefaultNaN();
  71. }
  72. else
  73. {
  74. result = FPConvertNaN(valueBits);
  75. }
  76. if (type == FpType.SNaN)
  77. {
  78. FPProcessException(FpExc.InvalidOp, state);
  79. }
  80. }
  81. else if (type == FpType.Infinity)
  82. {
  83. result = FPInfinity(sign);
  84. }
  85. else if (type == FpType.Zero)
  86. {
  87. result = FPZero(sign);
  88. }
  89. else
  90. {
  91. result = FPRoundCv(real, state);
  92. }
  93. return result;
  94. }
  95. private static float FPDefaultNaN()
  96. {
  97. return -float.NaN;
  98. }
  99. private static float FPInfinity(bool sign)
  100. {
  101. return sign ? float.NegativeInfinity : float.PositiveInfinity;
  102. }
  103. private static float FPZero(bool sign)
  104. {
  105. return sign ? -0f : +0f;
  106. }
  107. private static float FPMaxNormal(bool sign)
  108. {
  109. return sign ? float.MinValue : float.MaxValue;
  110. }
  111. private static double FPUnpackCv(
  112. this ushort valueBits,
  113. out FpType type,
  114. out bool sign,
  115. CpuThreadState state)
  116. {
  117. sign = (~(uint)valueBits & 0x8000u) == 0u;
  118. uint exp16 = ((uint)valueBits & 0x7C00u) >> 10;
  119. uint frac16 = (uint)valueBits & 0x03FFu;
  120. double real;
  121. if (exp16 == 0u)
  122. {
  123. if (frac16 == 0u)
  124. {
  125. type = FpType.Zero;
  126. real = 0d;
  127. }
  128. else
  129. {
  130. type = FpType.Nonzero; // Subnormal.
  131. real = Math.Pow(2d, -14) * ((double)frac16 * Math.Pow(2d, -10));
  132. }
  133. }
  134. else if (exp16 == 0x1Fu && !state.GetFpcrFlag(Fpcr.Ahp))
  135. {
  136. if (frac16 == 0u)
  137. {
  138. type = FpType.Infinity;
  139. real = Math.Pow(2d, 1000);
  140. }
  141. else
  142. {
  143. type = (~frac16 & 0x0200u) == 0u ? FpType.QNaN : FpType.SNaN;
  144. real = 0d;
  145. }
  146. }
  147. else
  148. {
  149. type = FpType.Nonzero; // Normal.
  150. real = Math.Pow(2d, (int)exp16 - 15) * (1d + (double)frac16 * Math.Pow(2d, -10));
  151. }
  152. return sign ? -real : real;
  153. }
  154. private static float FPRoundCv(double real, CpuThreadState state)
  155. {
  156. const int minimumExp = -126;
  157. const int e = 8;
  158. const int f = 23;
  159. bool sign;
  160. double mantissa;
  161. if (real < 0d)
  162. {
  163. sign = true;
  164. mantissa = -real;
  165. }
  166. else
  167. {
  168. sign = false;
  169. mantissa = real;
  170. }
  171. int exponent = 0;
  172. while (mantissa < 1d)
  173. {
  174. mantissa *= 2d;
  175. exponent--;
  176. }
  177. while (mantissa >= 2d)
  178. {
  179. mantissa /= 2d;
  180. exponent++;
  181. }
  182. if (state.GetFpcrFlag(Fpcr.Fz) && exponent < minimumExp)
  183. {
  184. state.SetFpsrFlag(Fpsr.Ufc);
  185. return FPZero(sign);
  186. }
  187. uint biasedExp = (uint)Math.Max(exponent - minimumExp + 1, 0);
  188. if (biasedExp == 0u)
  189. {
  190. mantissa /= Math.Pow(2d, minimumExp - exponent);
  191. }
  192. uint intMant = (uint)Math.Floor(mantissa * Math.Pow(2d, f));
  193. double error = mantissa * Math.Pow(2d, f) - (double)intMant;
  194. if (biasedExp == 0u && (error != 0d || state.GetFpcrFlag(Fpcr.Ufe)))
  195. {
  196. FPProcessException(FpExc.Underflow, state);
  197. }
  198. bool overflowToInf;
  199. bool roundUp;
  200. switch (state.FPRoundingMode())
  201. {
  202. default:
  203. case RoundMode.ToNearest:
  204. roundUp = (error > 0.5d || (error == 0.5d && (intMant & 1u) == 1u));
  205. overflowToInf = true;
  206. break;
  207. case RoundMode.TowardsPlusInfinity:
  208. roundUp = (error != 0d && !sign);
  209. overflowToInf = !sign;
  210. break;
  211. case RoundMode.TowardsMinusInfinity:
  212. roundUp = (error != 0d && sign);
  213. overflowToInf = sign;
  214. break;
  215. case RoundMode.TowardsZero:
  216. roundUp = false;
  217. overflowToInf = false;
  218. break;
  219. }
  220. if (roundUp)
  221. {
  222. intMant++;
  223. if (intMant == 1u << f)
  224. {
  225. biasedExp = 1u;
  226. }
  227. if (intMant == 1u << (f + 1))
  228. {
  229. biasedExp++;
  230. intMant >>= 1;
  231. }
  232. }
  233. float result;
  234. if (biasedExp >= (1u << e) - 1u)
  235. {
  236. result = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign);
  237. FPProcessException(FpExc.Overflow, state);
  238. error = 1d;
  239. }
  240. else
  241. {
  242. result = BitConverter.Int32BitsToSingle(
  243. (int)((sign ? 1u : 0u) << 31 | (biasedExp & 0xFFu) << 23 | (intMant & 0x007FFFFFu)));
  244. }
  245. if (error != 0d)
  246. {
  247. FPProcessException(FpExc.Inexact, state);
  248. }
  249. return result;
  250. }
  251. private static float FPConvertNaN(ushort valueBits)
  252. {
  253. return BitConverter.Int32BitsToSingle(
  254. (int)(((uint)valueBits & 0x8000u) << 16 | 0x7FC00000u | ((uint)valueBits & 0x01FFu) << 13));
  255. }
  256. private static void FPProcessException(FpExc exc, CpuThreadState state)
  257. {
  258. int enable = (int)exc + 8;
  259. if ((state.CFpcr & (1 << enable)) != 0)
  260. {
  261. throw new NotImplementedException("Floating-point trap handling.");
  262. }
  263. else
  264. {
  265. state.CFpsr |= 1 << (int)exc;
  266. }
  267. }
  268. }
  269. static class SoftFloat32_16
  270. {
  271. public static ushort FPConvert(float value, CpuThreadState state)
  272. {
  273. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32_16.FPConvert: state.Fpcr = 0x{state.CFpcr:X8}");
  274. double real = value.FPUnpackCv(out FpType type, out bool sign, out uint valueBits, state);
  275. bool altHp = state.GetFpcrFlag(Fpcr.Ahp);
  276. ushort resultBits;
  277. if (type == FpType.SNaN || type == FpType.QNaN)
  278. {
  279. if (altHp)
  280. {
  281. resultBits = FPZero(sign);
  282. }
  283. else if (state.GetFpcrFlag(Fpcr.Dn))
  284. {
  285. resultBits = FPDefaultNaN();
  286. }
  287. else
  288. {
  289. resultBits = FPConvertNaN(valueBits);
  290. }
  291. if (type == FpType.SNaN || altHp)
  292. {
  293. FPProcessException(FpExc.InvalidOp, state);
  294. }
  295. }
  296. else if (type == FpType.Infinity)
  297. {
  298. if (altHp)
  299. {
  300. resultBits = (ushort)((sign ? 1u : 0u) << 15 | 0x7FFFu);
  301. FPProcessException(FpExc.InvalidOp, state);
  302. }
  303. else
  304. {
  305. resultBits = FPInfinity(sign);
  306. }
  307. }
  308. else if (type == FpType.Zero)
  309. {
  310. resultBits = FPZero(sign);
  311. }
  312. else
  313. {
  314. resultBits = FPRoundCv(real, state);
  315. }
  316. return resultBits;
  317. }
  318. private static ushort FPDefaultNaN()
  319. {
  320. return (ushort)0x7E00u;
  321. }
  322. private static ushort FPInfinity(bool sign)
  323. {
  324. return sign ? (ushort)0xFC00u : (ushort)0x7C00u;
  325. }
  326. private static ushort FPZero(bool sign)
  327. {
  328. return sign ? (ushort)0x8000u : (ushort)0x0000u;
  329. }
  330. private static ushort FPMaxNormal(bool sign)
  331. {
  332. return sign ? (ushort)0xFBFFu : (ushort)0x7BFFu;
  333. }
  334. private static double FPUnpackCv(
  335. this float value,
  336. out FpType type,
  337. out bool sign,
  338. out uint valueBits,
  339. CpuThreadState state)
  340. {
  341. valueBits = (uint)BitConverter.SingleToInt32Bits(value);
  342. sign = (~valueBits & 0x80000000u) == 0u;
  343. uint exp32 = (valueBits & 0x7F800000u) >> 23;
  344. uint frac32 = valueBits & 0x007FFFFFu;
  345. double real;
  346. if (exp32 == 0u)
  347. {
  348. if (frac32 == 0u || state.GetFpcrFlag(Fpcr.Fz))
  349. {
  350. type = FpType.Zero;
  351. real = 0d;
  352. if (frac32 != 0u)
  353. {
  354. FPProcessException(FpExc.InputDenorm, state);
  355. }
  356. }
  357. else
  358. {
  359. type = FpType.Nonzero; // Subnormal.
  360. real = Math.Pow(2d, -126) * ((double)frac32 * Math.Pow(2d, -23));
  361. }
  362. }
  363. else if (exp32 == 0xFFu)
  364. {
  365. if (frac32 == 0u)
  366. {
  367. type = FpType.Infinity;
  368. real = Math.Pow(2d, 1000);
  369. }
  370. else
  371. {
  372. type = (~frac32 & 0x00400000u) == 0u ? FpType.QNaN : FpType.SNaN;
  373. real = 0d;
  374. }
  375. }
  376. else
  377. {
  378. type = FpType.Nonzero; // Normal.
  379. real = Math.Pow(2d, (int)exp32 - 127) * (1d + (double)frac32 * Math.Pow(2d, -23));
  380. }
  381. return sign ? -real : real;
  382. }
  383. private static ushort FPRoundCv(double real, CpuThreadState state)
  384. {
  385. const int minimumExp = -14;
  386. const int e = 5;
  387. const int f = 10;
  388. bool sign;
  389. double mantissa;
  390. if (real < 0d)
  391. {
  392. sign = true;
  393. mantissa = -real;
  394. }
  395. else
  396. {
  397. sign = false;
  398. mantissa = real;
  399. }
  400. int exponent = 0;
  401. while (mantissa < 1d)
  402. {
  403. mantissa *= 2d;
  404. exponent--;
  405. }
  406. while (mantissa >= 2d)
  407. {
  408. mantissa /= 2d;
  409. exponent++;
  410. }
  411. uint biasedExp = (uint)Math.Max(exponent - minimumExp + 1, 0);
  412. if (biasedExp == 0u)
  413. {
  414. mantissa /= Math.Pow(2d, minimumExp - exponent);
  415. }
  416. uint intMant = (uint)Math.Floor(mantissa * Math.Pow(2d, f));
  417. double error = mantissa * Math.Pow(2d, f) - (double)intMant;
  418. if (biasedExp == 0u && (error != 0d || state.GetFpcrFlag(Fpcr.Ufe)))
  419. {
  420. FPProcessException(FpExc.Underflow, state);
  421. }
  422. bool overflowToInf;
  423. bool roundUp;
  424. switch (state.FPRoundingMode())
  425. {
  426. default:
  427. case RoundMode.ToNearest:
  428. roundUp = (error > 0.5d || (error == 0.5d && (intMant & 1u) == 1u));
  429. overflowToInf = true;
  430. break;
  431. case RoundMode.TowardsPlusInfinity:
  432. roundUp = (error != 0d && !sign);
  433. overflowToInf = !sign;
  434. break;
  435. case RoundMode.TowardsMinusInfinity:
  436. roundUp = (error != 0d && sign);
  437. overflowToInf = sign;
  438. break;
  439. case RoundMode.TowardsZero:
  440. roundUp = false;
  441. overflowToInf = false;
  442. break;
  443. }
  444. if (roundUp)
  445. {
  446. intMant++;
  447. if (intMant == 1u << f)
  448. {
  449. biasedExp = 1u;
  450. }
  451. if (intMant == 1u << (f + 1))
  452. {
  453. biasedExp++;
  454. intMant >>= 1;
  455. }
  456. }
  457. ushort resultBits;
  458. if (!state.GetFpcrFlag(Fpcr.Ahp))
  459. {
  460. if (biasedExp >= (1u << e) - 1u)
  461. {
  462. resultBits = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign);
  463. FPProcessException(FpExc.Overflow, state);
  464. error = 1d;
  465. }
  466. else
  467. {
  468. resultBits = (ushort)((sign ? 1u : 0u) << 15 | (biasedExp & 0x1Fu) << 10 | (intMant & 0x03FFu));
  469. }
  470. }
  471. else
  472. {
  473. if (biasedExp >= 1u << e)
  474. {
  475. resultBits = (ushort)((sign ? 1u : 0u) << 15 | 0x7FFFu);
  476. FPProcessException(FpExc.InvalidOp, state);
  477. error = 0d;
  478. }
  479. else
  480. {
  481. resultBits = (ushort)((sign ? 1u : 0u) << 15 | (biasedExp & 0x1Fu) << 10 | (intMant & 0x03FFu));
  482. }
  483. }
  484. if (error != 0d)
  485. {
  486. FPProcessException(FpExc.Inexact, state);
  487. }
  488. return resultBits;
  489. }
  490. private static ushort FPConvertNaN(uint valueBits)
  491. {
  492. return (ushort)((valueBits & 0x80000000u) >> 16 | 0x7E00u | (valueBits & 0x003FE000u) >> 13);
  493. }
  494. private static void FPProcessException(FpExc exc, CpuThreadState state)
  495. {
  496. int enable = (int)exc + 8;
  497. if ((state.CFpcr & (1 << enable)) != 0)
  498. {
  499. throw new NotImplementedException("Floating-point trap handling.");
  500. }
  501. else
  502. {
  503. state.CFpsr |= 1 << (int)exc;
  504. }
  505. }
  506. }
  507. static class SoftFloat32
  508. {
  509. public static float FPAdd(float value1, float value2, CpuThreadState state)
  510. {
  511. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPAdd: state.Fpcr = 0x{state.CFpcr:X8}");
  512. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  513. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  514. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  515. if (!done)
  516. {
  517. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  518. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  519. if (inf1 && inf2 && sign1 == !sign2)
  520. {
  521. result = FPDefaultNaN();
  522. FPProcessException(FpExc.InvalidOp, state);
  523. }
  524. else if ((inf1 && !sign1) || (inf2 && !sign2))
  525. {
  526. result = FPInfinity(false);
  527. }
  528. else if ((inf1 && sign1) || (inf2 && sign2))
  529. {
  530. result = FPInfinity(true);
  531. }
  532. else if (zero1 && zero2 && sign1 == sign2)
  533. {
  534. result = FPZero(sign1);
  535. }
  536. else
  537. {
  538. result = value1 + value2;
  539. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  540. {
  541. state.SetFpsrFlag(Fpsr.Ufc);
  542. result = FPZero(result < 0f);
  543. }
  544. }
  545. }
  546. return result;
  547. }
  548. public static int FPCompare(float value1, float value2, bool signalNaNs, CpuThreadState state)
  549. {
  550. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPCompare: state.Fpcr = 0x{state.CFpcr:X8}");
  551. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out _, state);
  552. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out _, state);
  553. int result;
  554. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  555. {
  556. result = 0b0011;
  557. if (type1 == FpType.SNaN || type2 == FpType.SNaN || signalNaNs)
  558. {
  559. FPProcessException(FpExc.InvalidOp, state);
  560. }
  561. }
  562. else
  563. {
  564. if (value1 == value2)
  565. {
  566. result = 0b0110;
  567. }
  568. else if (value1 < value2)
  569. {
  570. result = 0b1000;
  571. }
  572. else
  573. {
  574. result = 0b0010;
  575. }
  576. }
  577. return result;
  578. }
  579. public static float FPCompareEQ(float value1, float value2, CpuThreadState state)
  580. {
  581. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPCompareEQ: state.Fpcr = 0x{state.CFpcr:X8}");
  582. value1 = value1.FPUnpack(out FpType type1, out _, out _, state);
  583. value2 = value2.FPUnpack(out FpType type2, out _, out _, state);
  584. float result;
  585. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  586. {
  587. result = ZerosOrOnes(false);
  588. if (type1 == FpType.SNaN || type2 == FpType.SNaN)
  589. {
  590. FPProcessException(FpExc.InvalidOp, state);
  591. }
  592. }
  593. else
  594. {
  595. result = ZerosOrOnes(value1 == value2);
  596. }
  597. return result;
  598. }
  599. public static float FPCompareGE(float value1, float value2, CpuThreadState state)
  600. {
  601. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPCompareGE: state.Fpcr = 0x{state.CFpcr:X8}");
  602. value1 = value1.FPUnpack(out FpType type1, out _, out _, state);
  603. value2 = value2.FPUnpack(out FpType type2, out _, out _, state);
  604. float result;
  605. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  606. {
  607. result = ZerosOrOnes(false);
  608. FPProcessException(FpExc.InvalidOp, state);
  609. }
  610. else
  611. {
  612. result = ZerosOrOnes(value1 >= value2);
  613. }
  614. return result;
  615. }
  616. public static float FPCompareGT(float value1, float value2, CpuThreadState state)
  617. {
  618. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPCompareGT: state.Fpcr = 0x{state.CFpcr:X8}");
  619. value1 = value1.FPUnpack(out FpType type1, out _, out _, state);
  620. value2 = value2.FPUnpack(out FpType type2, out _, out _, state);
  621. float result;
  622. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  623. {
  624. result = ZerosOrOnes(false);
  625. FPProcessException(FpExc.InvalidOp, state);
  626. }
  627. else
  628. {
  629. result = ZerosOrOnes(value1 > value2);
  630. }
  631. return result;
  632. }
  633. [MethodImpl(MethodImplOptions.AggressiveInlining)]
  634. public static float FPCompareLE(float value1, float value2, CpuThreadState state)
  635. {
  636. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPCompareLE: state.Fpcr = 0x{state.CFpcr:X8}");
  637. return FPCompareGE(value2, value1, state);
  638. }
  639. [MethodImpl(MethodImplOptions.AggressiveInlining)]
  640. public static float FPCompareLT(float value1, float value2, CpuThreadState state)
  641. {
  642. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPCompareLT: state.Fpcr = 0x{state.CFpcr:X8}");
  643. return FPCompareGT(value2, value1, state);
  644. }
  645. public static float FPDiv(float value1, float value2, CpuThreadState state)
  646. {
  647. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPDiv: state.Fpcr = 0x{state.CFpcr:X8}");
  648. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  649. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  650. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  651. if (!done)
  652. {
  653. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  654. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  655. if ((inf1 && inf2) || (zero1 && zero2))
  656. {
  657. result = FPDefaultNaN();
  658. FPProcessException(FpExc.InvalidOp, state);
  659. }
  660. else if (inf1 || zero2)
  661. {
  662. result = FPInfinity(sign1 ^ sign2);
  663. if (!inf1)
  664. {
  665. FPProcessException(FpExc.DivideByZero, state);
  666. }
  667. }
  668. else if (zero1 || inf2)
  669. {
  670. result = FPZero(sign1 ^ sign2);
  671. }
  672. else
  673. {
  674. result = value1 / value2;
  675. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  676. {
  677. state.SetFpsrFlag(Fpsr.Ufc);
  678. result = FPZero(result < 0f);
  679. }
  680. }
  681. }
  682. return result;
  683. }
  684. public static float FPMax(float value1, float value2, CpuThreadState state)
  685. {
  686. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMax: state.Fpcr = 0x{state.CFpcr:X8}");
  687. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  688. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  689. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  690. if (!done)
  691. {
  692. if (value1 > value2)
  693. {
  694. if (type1 == FpType.Infinity)
  695. {
  696. result = FPInfinity(sign1);
  697. }
  698. else if (type1 == FpType.Zero)
  699. {
  700. result = FPZero(sign1 && sign2);
  701. }
  702. else
  703. {
  704. result = value1;
  705. }
  706. }
  707. else
  708. {
  709. if (type2 == FpType.Infinity)
  710. {
  711. result = FPInfinity(sign2);
  712. }
  713. else if (type2 == FpType.Zero)
  714. {
  715. result = FPZero(sign1 && sign2);
  716. }
  717. else
  718. {
  719. result = value2;
  720. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  721. {
  722. state.SetFpsrFlag(Fpsr.Ufc);
  723. result = FPZero(result < 0f);
  724. }
  725. }
  726. }
  727. }
  728. return result;
  729. }
  730. public static float FPMaxNum(float value1, float value2, CpuThreadState state)
  731. {
  732. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMaxNum: state.Fpcr = 0x{state.CFpcr:X8}");
  733. value1.FPUnpack(out FpType type1, out _, out _, state);
  734. value2.FPUnpack(out FpType type2, out _, out _, state);
  735. if (type1 == FpType.QNaN && type2 != FpType.QNaN)
  736. {
  737. value1 = FPInfinity(true);
  738. }
  739. else if (type1 != FpType.QNaN && type2 == FpType.QNaN)
  740. {
  741. value2 = FPInfinity(true);
  742. }
  743. return FPMax(value1, value2, state);
  744. }
  745. public static float FPMin(float value1, float value2, CpuThreadState state)
  746. {
  747. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMin: state.Fpcr = 0x{state.CFpcr:X8}");
  748. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  749. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  750. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  751. if (!done)
  752. {
  753. if (value1 < value2)
  754. {
  755. if (type1 == FpType.Infinity)
  756. {
  757. result = FPInfinity(sign1);
  758. }
  759. else if (type1 == FpType.Zero)
  760. {
  761. result = FPZero(sign1 || sign2);
  762. }
  763. else
  764. {
  765. result = value1;
  766. }
  767. }
  768. else
  769. {
  770. if (type2 == FpType.Infinity)
  771. {
  772. result = FPInfinity(sign2);
  773. }
  774. else if (type2 == FpType.Zero)
  775. {
  776. result = FPZero(sign1 || sign2);
  777. }
  778. else
  779. {
  780. result = value2;
  781. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  782. {
  783. state.SetFpsrFlag(Fpsr.Ufc);
  784. result = FPZero(result < 0f);
  785. }
  786. }
  787. }
  788. }
  789. return result;
  790. }
  791. public static float FPMinNum(float value1, float value2, CpuThreadState state)
  792. {
  793. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMinNum: state.Fpcr = 0x{state.CFpcr:X8}");
  794. value1.FPUnpack(out FpType type1, out _, out _, state);
  795. value2.FPUnpack(out FpType type2, out _, out _, state);
  796. if (type1 == FpType.QNaN && type2 != FpType.QNaN)
  797. {
  798. value1 = FPInfinity(false);
  799. }
  800. else if (type1 != FpType.QNaN && type2 == FpType.QNaN)
  801. {
  802. value2 = FPInfinity(false);
  803. }
  804. return FPMin(value1, value2, state);
  805. }
  806. public static float FPMul(float value1, float value2, CpuThreadState state)
  807. {
  808. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMul: state.Fpcr = 0x{state.CFpcr:X8}");
  809. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  810. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  811. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  812. if (!done)
  813. {
  814. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  815. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  816. if ((inf1 && zero2) || (zero1 && inf2))
  817. {
  818. result = FPDefaultNaN();
  819. FPProcessException(FpExc.InvalidOp, state);
  820. }
  821. else if (inf1 || inf2)
  822. {
  823. result = FPInfinity(sign1 ^ sign2);
  824. }
  825. else if (zero1 || zero2)
  826. {
  827. result = FPZero(sign1 ^ sign2);
  828. }
  829. else
  830. {
  831. result = value1 * value2;
  832. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  833. {
  834. state.SetFpsrFlag(Fpsr.Ufc);
  835. result = FPZero(result < 0f);
  836. }
  837. }
  838. }
  839. return result;
  840. }
  841. public static float FPMulAdd(
  842. float valueA,
  843. float value1,
  844. float value2,
  845. CpuThreadState state)
  846. {
  847. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMulAdd: state.Fpcr = 0x{state.CFpcr:X8}");
  848. valueA = valueA.FPUnpack(out FpType typeA, out bool signA, out uint addend, state);
  849. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  850. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  851. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  852. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  853. float result = FPProcessNaNs3(typeA, type1, type2, addend, op1, op2, out bool done, state);
  854. if (typeA == FpType.QNaN && ((inf1 && zero2) || (zero1 && inf2)))
  855. {
  856. result = FPDefaultNaN();
  857. FPProcessException(FpExc.InvalidOp, state);
  858. }
  859. if (!done)
  860. {
  861. bool infA = typeA == FpType.Infinity; bool zeroA = typeA == FpType.Zero;
  862. bool signP = sign1 ^ sign2;
  863. bool infP = inf1 || inf2;
  864. bool zeroP = zero1 || zero2;
  865. if ((inf1 && zero2) || (zero1 && inf2) || (infA && infP && signA != signP))
  866. {
  867. result = FPDefaultNaN();
  868. FPProcessException(FpExc.InvalidOp, state);
  869. }
  870. else if ((infA && !signA) || (infP && !signP))
  871. {
  872. result = FPInfinity(false);
  873. }
  874. else if ((infA && signA) || (infP && signP))
  875. {
  876. result = FPInfinity(true);
  877. }
  878. else if (zeroA && zeroP && signA == signP)
  879. {
  880. result = FPZero(signA);
  881. }
  882. else
  883. {
  884. // TODO: When available, use: T MathF.FusedMultiplyAdd(T, T, T);
  885. // https://github.com/dotnet/corefx/issues/31903
  886. result = valueA + (value1 * value2);
  887. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  888. {
  889. state.SetFpsrFlag(Fpsr.Ufc);
  890. result = FPZero(result < 0f);
  891. }
  892. }
  893. }
  894. return result;
  895. }
  896. [MethodImpl(MethodImplOptions.AggressiveInlining)]
  897. public static float FPMulSub(
  898. float valueA,
  899. float value1,
  900. float value2,
  901. CpuThreadState state)
  902. {
  903. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMulSub: state.Fpcr = 0x{state.CFpcr:X8}");
  904. value1 = value1.FPNeg();
  905. return FPMulAdd(valueA, value1, value2, state);
  906. }
  907. public static float FPMulX(float value1, float value2, CpuThreadState state)
  908. {
  909. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPMulX: state.Fpcr = 0x{state.CFpcr:X8}");
  910. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  911. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  912. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  913. if (!done)
  914. {
  915. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  916. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  917. if ((inf1 && zero2) || (zero1 && inf2))
  918. {
  919. result = FPTwo(sign1 ^ sign2);
  920. }
  921. else if (inf1 || inf2)
  922. {
  923. result = FPInfinity(sign1 ^ sign2);
  924. }
  925. else if (zero1 || zero2)
  926. {
  927. result = FPZero(sign1 ^ sign2);
  928. }
  929. else
  930. {
  931. result = value1 * value2;
  932. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  933. {
  934. state.SetFpsrFlag(Fpsr.Ufc);
  935. result = FPZero(result < 0f);
  936. }
  937. }
  938. }
  939. return result;
  940. }
  941. public static float FPRecipEstimate(float value, CpuThreadState state)
  942. {
  943. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPRecipEstimate: state.Fpcr = 0x{state.CFpcr:X8}");
  944. value.FPUnpack(out FpType type, out bool sign, out uint op, state);
  945. float result;
  946. if (type == FpType.SNaN || type == FpType.QNaN)
  947. {
  948. result = FPProcessNaN(type, op, state);
  949. }
  950. else if (type == FpType.Infinity)
  951. {
  952. result = FPZero(sign);
  953. }
  954. else if (type == FpType.Zero)
  955. {
  956. result = FPInfinity(sign);
  957. FPProcessException(FpExc.DivideByZero, state);
  958. }
  959. else if (MathF.Abs(value) < MathF.Pow(2f, -128))
  960. {
  961. bool overflowToInf;
  962. switch (state.FPRoundingMode())
  963. {
  964. default:
  965. case RoundMode.ToNearest: overflowToInf = true; break;
  966. case RoundMode.TowardsPlusInfinity: overflowToInf = !sign; break;
  967. case RoundMode.TowardsMinusInfinity: overflowToInf = sign; break;
  968. case RoundMode.TowardsZero: overflowToInf = false; break;
  969. }
  970. result = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign);
  971. FPProcessException(FpExc.Overflow, state);
  972. FPProcessException(FpExc.Inexact, state);
  973. }
  974. else if (state.GetFpcrFlag(Fpcr.Fz) && (MathF.Abs(value) >= MathF.Pow(2f, 126)))
  975. {
  976. result = FPZero(sign);
  977. state.SetFpsrFlag(Fpsr.Ufc);
  978. }
  979. else
  980. {
  981. ulong fraction = (ulong)(op & 0x007FFFFFu) << 29;
  982. uint exp = (op & 0x7F800000u) >> 23;
  983. if (exp == 0u)
  984. {
  985. if ((fraction & 0x0008000000000000ul) == 0ul)
  986. {
  987. fraction = (fraction & 0x0003FFFFFFFFFFFFul) << 2;
  988. exp -= 1u;
  989. }
  990. else
  991. {
  992. fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1;
  993. }
  994. }
  995. uint scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44);
  996. uint resultExp = 253u - exp;
  997. uint estimate = (uint)SoftFloat.RecipEstimateTable[scaled - 256u] + 256u;
  998. fraction = (ulong)(estimate & 0xFFu) << 44;
  999. if (resultExp == 0u)
  1000. {
  1001. fraction = ((fraction & 0x000FFFFFFFFFFFFEul) | 0x0010000000000000ul) >> 1;
  1002. }
  1003. else if (resultExp + 1u == 0u)
  1004. {
  1005. fraction = ((fraction & 0x000FFFFFFFFFFFFCul) | 0x0010000000000000ul) >> 2;
  1006. resultExp = 0u;
  1007. }
  1008. result = BitConverter.Int32BitsToSingle(
  1009. (int)((sign ? 1u : 0u) << 31 | (resultExp & 0xFFu) << 23 | (uint)(fraction >> 29) & 0x007FFFFFu));
  1010. }
  1011. return result;
  1012. }
  1013. public static float FPRecipStepFused(float value1, float value2, CpuThreadState state)
  1014. {
  1015. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPRecipStepFused: state.Fpcr = 0x{state.CFpcr:X8}");
  1016. value1 = value1.FPNeg();
  1017. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  1018. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  1019. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1020. if (!done)
  1021. {
  1022. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1023. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1024. if ((inf1 && zero2) || (zero1 && inf2))
  1025. {
  1026. result = FPTwo(false);
  1027. }
  1028. else if (inf1 || inf2)
  1029. {
  1030. result = FPInfinity(sign1 ^ sign2);
  1031. }
  1032. else
  1033. {
  1034. // TODO: When available, use: T MathF.FusedMultiplyAdd(T, T, T);
  1035. // https://github.com/dotnet/corefx/issues/31903
  1036. result = 2f + (value1 * value2);
  1037. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  1038. {
  1039. state.SetFpsrFlag(Fpsr.Ufc);
  1040. result = FPZero(result < 0f);
  1041. }
  1042. }
  1043. }
  1044. return result;
  1045. }
  1046. public static float FPRecpX(float value, CpuThreadState state)
  1047. {
  1048. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPRecpX: state.Fpcr = 0x{state.CFpcr:X8}");
  1049. value.FPUnpack(out FpType type, out bool sign, out uint op, state);
  1050. float result;
  1051. if (type == FpType.SNaN || type == FpType.QNaN)
  1052. {
  1053. result = FPProcessNaN(type, op, state);
  1054. }
  1055. else
  1056. {
  1057. uint notExp = (~op >> 23) & 0xFFu;
  1058. uint maxExp = 0xFEu;
  1059. result = BitConverter.Int32BitsToSingle(
  1060. (int)((sign ? 1u : 0u) << 31 | (notExp == 0xFFu ? maxExp : notExp) << 23));
  1061. }
  1062. return result;
  1063. }
  1064. public static float FPRSqrtEstimate(float value, CpuThreadState state)
  1065. {
  1066. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPRSqrtEstimate: state.Fpcr = 0x{state.CFpcr:X8}");
  1067. value.FPUnpack(out FpType type, out bool sign, out uint op, state);
  1068. float result;
  1069. if (type == FpType.SNaN || type == FpType.QNaN)
  1070. {
  1071. result = FPProcessNaN(type, op, state);
  1072. }
  1073. else if (type == FpType.Zero)
  1074. {
  1075. result = FPInfinity(sign);
  1076. FPProcessException(FpExc.DivideByZero, state);
  1077. }
  1078. else if (sign)
  1079. {
  1080. result = FPDefaultNaN();
  1081. FPProcessException(FpExc.InvalidOp, state);
  1082. }
  1083. else if (type == FpType.Infinity)
  1084. {
  1085. result = FPZero(false);
  1086. }
  1087. else
  1088. {
  1089. ulong fraction = (ulong)(op & 0x007FFFFFu) << 29;
  1090. uint exp = (op & 0x7F800000u) >> 23;
  1091. if (exp == 0u)
  1092. {
  1093. while ((fraction & 0x0008000000000000ul) == 0ul)
  1094. {
  1095. fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1;
  1096. exp -= 1u;
  1097. }
  1098. fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1;
  1099. }
  1100. uint scaled;
  1101. if ((exp & 1u) == 0u)
  1102. {
  1103. scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44);
  1104. }
  1105. else
  1106. {
  1107. scaled = (uint)(((fraction & 0x000FE00000000000ul) | 0x0010000000000000ul) >> 45);
  1108. }
  1109. uint resultExp = (380u - exp) >> 1;
  1110. uint estimate = (uint)SoftFloat.RecipSqrtEstimateTable[scaled - 128u] + 256u;
  1111. result = BitConverter.Int32BitsToSingle((int)((resultExp & 0xFFu) << 23 | (estimate & 0xFFu) << 15));
  1112. }
  1113. return result;
  1114. }
  1115. public static float FPRSqrtStepFused(float value1, float value2, CpuThreadState state)
  1116. {
  1117. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPRSqrtStepFused: state.Fpcr = 0x{state.CFpcr:X8}");
  1118. value1 = value1.FPNeg();
  1119. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  1120. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  1121. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1122. if (!done)
  1123. {
  1124. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1125. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1126. if ((inf1 && zero2) || (zero1 && inf2))
  1127. {
  1128. result = FPOnePointFive(false);
  1129. }
  1130. else if (inf1 || inf2)
  1131. {
  1132. result = FPInfinity(sign1 ^ sign2);
  1133. }
  1134. else
  1135. {
  1136. // TODO: When available, use: T MathF.FusedMultiplyAdd(T, T, T);
  1137. // https://github.com/dotnet/corefx/issues/31903
  1138. result = (3f + (value1 * value2)) / 2f;
  1139. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  1140. {
  1141. state.SetFpsrFlag(Fpsr.Ufc);
  1142. result = FPZero(result < 0f);
  1143. }
  1144. }
  1145. }
  1146. return result;
  1147. }
  1148. public static float FPSqrt(float value, CpuThreadState state)
  1149. {
  1150. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPSqrt: state.Fpcr = 0x{state.CFpcr:X8}");
  1151. value = value.FPUnpack(out FpType type, out bool sign, out uint op, state);
  1152. float result;
  1153. if (type == FpType.SNaN || type == FpType.QNaN)
  1154. {
  1155. result = FPProcessNaN(type, op, state);
  1156. }
  1157. else if (type == FpType.Zero)
  1158. {
  1159. result = FPZero(sign);
  1160. }
  1161. else if (type == FpType.Infinity && !sign)
  1162. {
  1163. result = FPInfinity(sign);
  1164. }
  1165. else if (sign)
  1166. {
  1167. result = FPDefaultNaN();
  1168. FPProcessException(FpExc.InvalidOp, state);
  1169. }
  1170. else
  1171. {
  1172. result = MathF.Sqrt(value);
  1173. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  1174. {
  1175. state.SetFpsrFlag(Fpsr.Ufc);
  1176. result = FPZero(result < 0f);
  1177. }
  1178. }
  1179. return result;
  1180. }
  1181. public static float FPSub(float value1, float value2, CpuThreadState state)
  1182. {
  1183. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat32.FPSub: state.Fpcr = 0x{state.CFpcr:X8}");
  1184. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out uint op1, state);
  1185. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out uint op2, state);
  1186. float result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1187. if (!done)
  1188. {
  1189. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1190. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1191. if (inf1 && inf2 && sign1 == sign2)
  1192. {
  1193. result = FPDefaultNaN();
  1194. FPProcessException(FpExc.InvalidOp, state);
  1195. }
  1196. else if ((inf1 && !sign1) || (inf2 && sign2))
  1197. {
  1198. result = FPInfinity(false);
  1199. }
  1200. else if ((inf1 && sign1) || (inf2 && !sign2))
  1201. {
  1202. result = FPInfinity(true);
  1203. }
  1204. else if (zero1 && zero2 && sign1 == !sign2)
  1205. {
  1206. result = FPZero(sign1);
  1207. }
  1208. else
  1209. {
  1210. result = value1 - value2;
  1211. if (state.GetFpcrFlag(Fpcr.Fz) && float.IsSubnormal(result))
  1212. {
  1213. state.SetFpsrFlag(Fpsr.Ufc);
  1214. result = FPZero(result < 0f);
  1215. }
  1216. }
  1217. }
  1218. return result;
  1219. }
  1220. private static float FPDefaultNaN()
  1221. {
  1222. return -float.NaN;
  1223. }
  1224. private static float FPInfinity(bool sign)
  1225. {
  1226. return sign ? float.NegativeInfinity : float.PositiveInfinity;
  1227. }
  1228. private static float FPZero(bool sign)
  1229. {
  1230. return sign ? -0f : +0f;
  1231. }
  1232. private static float FPMaxNormal(bool sign)
  1233. {
  1234. return sign ? float.MinValue : float.MaxValue;
  1235. }
  1236. private static float FPTwo(bool sign)
  1237. {
  1238. return sign ? -2f : +2f;
  1239. }
  1240. private static float FPOnePointFive(bool sign)
  1241. {
  1242. return sign ? -1.5f : +1.5f;
  1243. }
  1244. private static float FPNeg(this float value)
  1245. {
  1246. return -value;
  1247. }
  1248. private static float ZerosOrOnes(bool ones)
  1249. {
  1250. return BitConverter.Int32BitsToSingle(ones ? -1 : 0);
  1251. }
  1252. private static float FPUnpack(
  1253. this float value,
  1254. out FpType type,
  1255. out bool sign,
  1256. out uint valueBits,
  1257. CpuThreadState state)
  1258. {
  1259. valueBits = (uint)BitConverter.SingleToInt32Bits(value);
  1260. sign = (~valueBits & 0x80000000u) == 0u;
  1261. if ((valueBits & 0x7F800000u) == 0u)
  1262. {
  1263. if ((valueBits & 0x007FFFFFu) == 0u || state.GetFpcrFlag(Fpcr.Fz))
  1264. {
  1265. type = FpType.Zero;
  1266. value = FPZero(sign);
  1267. if ((valueBits & 0x007FFFFFu) != 0u)
  1268. {
  1269. FPProcessException(FpExc.InputDenorm, state);
  1270. }
  1271. }
  1272. else
  1273. {
  1274. type = FpType.Nonzero;
  1275. }
  1276. }
  1277. else if ((~valueBits & 0x7F800000u) == 0u)
  1278. {
  1279. if ((valueBits & 0x007FFFFFu) == 0u)
  1280. {
  1281. type = FpType.Infinity;
  1282. }
  1283. else
  1284. {
  1285. type = (~valueBits & 0x00400000u) == 0u ? FpType.QNaN : FpType.SNaN;
  1286. value = FPZero(sign);
  1287. }
  1288. }
  1289. else
  1290. {
  1291. type = FpType.Nonzero;
  1292. }
  1293. return value;
  1294. }
  1295. private static float FPProcessNaNs(
  1296. FpType type1,
  1297. FpType type2,
  1298. uint op1,
  1299. uint op2,
  1300. out bool done,
  1301. CpuThreadState state)
  1302. {
  1303. done = true;
  1304. if (type1 == FpType.SNaN)
  1305. {
  1306. return FPProcessNaN(type1, op1, state);
  1307. }
  1308. else if (type2 == FpType.SNaN)
  1309. {
  1310. return FPProcessNaN(type2, op2, state);
  1311. }
  1312. else if (type1 == FpType.QNaN)
  1313. {
  1314. return FPProcessNaN(type1, op1, state);
  1315. }
  1316. else if (type2 == FpType.QNaN)
  1317. {
  1318. return FPProcessNaN(type2, op2, state);
  1319. }
  1320. done = false;
  1321. return FPZero(false);
  1322. }
  1323. private static float FPProcessNaNs3(
  1324. FpType type1,
  1325. FpType type2,
  1326. FpType type3,
  1327. uint op1,
  1328. uint op2,
  1329. uint op3,
  1330. out bool done,
  1331. CpuThreadState state)
  1332. {
  1333. done = true;
  1334. if (type1 == FpType.SNaN)
  1335. {
  1336. return FPProcessNaN(type1, op1, state);
  1337. }
  1338. else if (type2 == FpType.SNaN)
  1339. {
  1340. return FPProcessNaN(type2, op2, state);
  1341. }
  1342. else if (type3 == FpType.SNaN)
  1343. {
  1344. return FPProcessNaN(type3, op3, state);
  1345. }
  1346. else if (type1 == FpType.QNaN)
  1347. {
  1348. return FPProcessNaN(type1, op1, state);
  1349. }
  1350. else if (type2 == FpType.QNaN)
  1351. {
  1352. return FPProcessNaN(type2, op2, state);
  1353. }
  1354. else if (type3 == FpType.QNaN)
  1355. {
  1356. return FPProcessNaN(type3, op3, state);
  1357. }
  1358. done = false;
  1359. return FPZero(false);
  1360. }
  1361. private static float FPProcessNaN(FpType type, uint op, CpuThreadState state)
  1362. {
  1363. if (type == FpType.SNaN)
  1364. {
  1365. op |= 1u << 22;
  1366. FPProcessException(FpExc.InvalidOp, state);
  1367. }
  1368. if (state.GetFpcrFlag(Fpcr.Dn))
  1369. {
  1370. return FPDefaultNaN();
  1371. }
  1372. return BitConverter.Int32BitsToSingle((int)op);
  1373. }
  1374. private static void FPProcessException(FpExc exc, CpuThreadState state)
  1375. {
  1376. int enable = (int)exc + 8;
  1377. if ((state.CFpcr & (1 << enable)) != 0)
  1378. {
  1379. throw new NotImplementedException("Floating-point trap handling.");
  1380. }
  1381. else
  1382. {
  1383. state.CFpsr |= 1 << (int)exc;
  1384. }
  1385. }
  1386. }
  1387. static class SoftFloat64
  1388. {
  1389. public static double FPAdd(double value1, double value2, CpuThreadState state)
  1390. {
  1391. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPAdd: state.Fpcr = 0x{state.CFpcr:X8}");
  1392. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1393. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1394. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1395. if (!done)
  1396. {
  1397. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1398. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1399. if (inf1 && inf2 && sign1 == !sign2)
  1400. {
  1401. result = FPDefaultNaN();
  1402. FPProcessException(FpExc.InvalidOp, state);
  1403. }
  1404. else if ((inf1 && !sign1) || (inf2 && !sign2))
  1405. {
  1406. result = FPInfinity(false);
  1407. }
  1408. else if ((inf1 && sign1) || (inf2 && sign2))
  1409. {
  1410. result = FPInfinity(true);
  1411. }
  1412. else if (zero1 && zero2 && sign1 == sign2)
  1413. {
  1414. result = FPZero(sign1);
  1415. }
  1416. else
  1417. {
  1418. result = value1 + value2;
  1419. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1420. {
  1421. state.SetFpsrFlag(Fpsr.Ufc);
  1422. result = FPZero(result < 0d);
  1423. }
  1424. }
  1425. }
  1426. return result;
  1427. }
  1428. public static int FPCompare(double value1, double value2, bool signalNaNs, CpuThreadState state)
  1429. {
  1430. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPCompare: state.Fpcr = 0x{state.CFpcr:X8}");
  1431. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out _, state);
  1432. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out _, state);
  1433. int result;
  1434. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  1435. {
  1436. result = 0b0011;
  1437. if (type1 == FpType.SNaN || type2 == FpType.SNaN || signalNaNs)
  1438. {
  1439. FPProcessException(FpExc.InvalidOp, state);
  1440. }
  1441. }
  1442. else
  1443. {
  1444. if (value1 == value2)
  1445. {
  1446. result = 0b0110;
  1447. }
  1448. else if (value1 < value2)
  1449. {
  1450. result = 0b1000;
  1451. }
  1452. else
  1453. {
  1454. result = 0b0010;
  1455. }
  1456. }
  1457. return result;
  1458. }
  1459. public static double FPCompareEQ(double value1, double value2, CpuThreadState state)
  1460. {
  1461. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPCompareEQ: state.Fpcr = 0x{state.CFpcr:X8}");
  1462. value1 = value1.FPUnpack(out FpType type1, out _, out _, state);
  1463. value2 = value2.FPUnpack(out FpType type2, out _, out _, state);
  1464. double result;
  1465. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  1466. {
  1467. result = ZerosOrOnes(false);
  1468. if (type1 == FpType.SNaN || type2 == FpType.SNaN)
  1469. {
  1470. FPProcessException(FpExc.InvalidOp, state);
  1471. }
  1472. }
  1473. else
  1474. {
  1475. result = ZerosOrOnes(value1 == value2);
  1476. }
  1477. return result;
  1478. }
  1479. public static double FPCompareGE(double value1, double value2, CpuThreadState state)
  1480. {
  1481. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPCompareGE: state.Fpcr = 0x{state.CFpcr:X8}");
  1482. value1 = value1.FPUnpack(out FpType type1, out _, out _, state);
  1483. value2 = value2.FPUnpack(out FpType type2, out _, out _, state);
  1484. double result;
  1485. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  1486. {
  1487. result = ZerosOrOnes(false);
  1488. FPProcessException(FpExc.InvalidOp, state);
  1489. }
  1490. else
  1491. {
  1492. result = ZerosOrOnes(value1 >= value2);
  1493. }
  1494. return result;
  1495. }
  1496. public static double FPCompareGT(double value1, double value2, CpuThreadState state)
  1497. {
  1498. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPCompareGT: state.Fpcr = 0x{state.CFpcr:X8}");
  1499. value1 = value1.FPUnpack(out FpType type1, out _, out _, state);
  1500. value2 = value2.FPUnpack(out FpType type2, out _, out _, state);
  1501. double result;
  1502. if (type1 == FpType.SNaN || type1 == FpType.QNaN || type2 == FpType.SNaN || type2 == FpType.QNaN)
  1503. {
  1504. result = ZerosOrOnes(false);
  1505. FPProcessException(FpExc.InvalidOp, state);
  1506. }
  1507. else
  1508. {
  1509. result = ZerosOrOnes(value1 > value2);
  1510. }
  1511. return result;
  1512. }
  1513. [MethodImpl(MethodImplOptions.AggressiveInlining)]
  1514. public static double FPCompareLE(double value1, double value2, CpuThreadState state)
  1515. {
  1516. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPCompareLE: state.Fpcr = 0x{state.CFpcr:X8}");
  1517. return FPCompareGE(value2, value1, state);
  1518. }
  1519. [MethodImpl(MethodImplOptions.AggressiveInlining)]
  1520. public static double FPCompareLT(double value1, double value2, CpuThreadState state)
  1521. {
  1522. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPCompareLT: state.Fpcr = 0x{state.CFpcr:X8}");
  1523. return FPCompareGT(value2, value1, state);
  1524. }
  1525. public static double FPDiv(double value1, double value2, CpuThreadState state)
  1526. {
  1527. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPDiv: state.Fpcr = 0x{state.CFpcr:X8}");
  1528. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1529. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1530. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1531. if (!done)
  1532. {
  1533. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1534. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1535. if ((inf1 && inf2) || (zero1 && zero2))
  1536. {
  1537. result = FPDefaultNaN();
  1538. FPProcessException(FpExc.InvalidOp, state);
  1539. }
  1540. else if (inf1 || zero2)
  1541. {
  1542. result = FPInfinity(sign1 ^ sign2);
  1543. if (!inf1)
  1544. {
  1545. FPProcessException(FpExc.DivideByZero, state);
  1546. }
  1547. }
  1548. else if (zero1 || inf2)
  1549. {
  1550. result = FPZero(sign1 ^ sign2);
  1551. }
  1552. else
  1553. {
  1554. result = value1 / value2;
  1555. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1556. {
  1557. state.SetFpsrFlag(Fpsr.Ufc);
  1558. result = FPZero(result < 0d);
  1559. }
  1560. }
  1561. }
  1562. return result;
  1563. }
  1564. public static double FPMax(double value1, double value2, CpuThreadState state)
  1565. {
  1566. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMax: state.Fpcr = 0x{state.CFpcr:X8}");
  1567. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1568. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1569. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1570. if (!done)
  1571. {
  1572. if (value1 > value2)
  1573. {
  1574. if (type1 == FpType.Infinity)
  1575. {
  1576. result = FPInfinity(sign1);
  1577. }
  1578. else if (type1 == FpType.Zero)
  1579. {
  1580. result = FPZero(sign1 && sign2);
  1581. }
  1582. else
  1583. {
  1584. result = value1;
  1585. }
  1586. }
  1587. else
  1588. {
  1589. if (type2 == FpType.Infinity)
  1590. {
  1591. result = FPInfinity(sign2);
  1592. }
  1593. else if (type2 == FpType.Zero)
  1594. {
  1595. result = FPZero(sign1 && sign2);
  1596. }
  1597. else
  1598. {
  1599. result = value2;
  1600. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1601. {
  1602. state.SetFpsrFlag(Fpsr.Ufc);
  1603. result = FPZero(result < 0d);
  1604. }
  1605. }
  1606. }
  1607. }
  1608. return result;
  1609. }
  1610. public static double FPMaxNum(double value1, double value2, CpuThreadState state)
  1611. {
  1612. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMaxNum: state.Fpcr = 0x{state.CFpcr:X8}");
  1613. value1.FPUnpack(out FpType type1, out _, out _, state);
  1614. value2.FPUnpack(out FpType type2, out _, out _, state);
  1615. if (type1 == FpType.QNaN && type2 != FpType.QNaN)
  1616. {
  1617. value1 = FPInfinity(true);
  1618. }
  1619. else if (type1 != FpType.QNaN && type2 == FpType.QNaN)
  1620. {
  1621. value2 = FPInfinity(true);
  1622. }
  1623. return FPMax(value1, value2, state);
  1624. }
  1625. public static double FPMin(double value1, double value2, CpuThreadState state)
  1626. {
  1627. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMin: state.Fpcr = 0x{state.CFpcr:X8}");
  1628. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1629. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1630. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1631. if (!done)
  1632. {
  1633. if (value1 < value2)
  1634. {
  1635. if (type1 == FpType.Infinity)
  1636. {
  1637. result = FPInfinity(sign1);
  1638. }
  1639. else if (type1 == FpType.Zero)
  1640. {
  1641. result = FPZero(sign1 || sign2);
  1642. }
  1643. else
  1644. {
  1645. result = value1;
  1646. }
  1647. }
  1648. else
  1649. {
  1650. if (type2 == FpType.Infinity)
  1651. {
  1652. result = FPInfinity(sign2);
  1653. }
  1654. else if (type2 == FpType.Zero)
  1655. {
  1656. result = FPZero(sign1 || sign2);
  1657. }
  1658. else
  1659. {
  1660. result = value2;
  1661. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1662. {
  1663. state.SetFpsrFlag(Fpsr.Ufc);
  1664. result = FPZero(result < 0d);
  1665. }
  1666. }
  1667. }
  1668. }
  1669. return result;
  1670. }
  1671. public static double FPMinNum(double value1, double value2, CpuThreadState state)
  1672. {
  1673. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMinNum: state.Fpcr = 0x{state.CFpcr:X8}");
  1674. value1.FPUnpack(out FpType type1, out _, out _, state);
  1675. value2.FPUnpack(out FpType type2, out _, out _, state);
  1676. if (type1 == FpType.QNaN && type2 != FpType.QNaN)
  1677. {
  1678. value1 = FPInfinity(false);
  1679. }
  1680. else if (type1 != FpType.QNaN && type2 == FpType.QNaN)
  1681. {
  1682. value2 = FPInfinity(false);
  1683. }
  1684. return FPMin(value1, value2, state);
  1685. }
  1686. public static double FPMul(double value1, double value2, CpuThreadState state)
  1687. {
  1688. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMul: state.Fpcr = 0x{state.CFpcr:X8}");
  1689. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1690. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1691. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1692. if (!done)
  1693. {
  1694. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1695. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1696. if ((inf1 && zero2) || (zero1 && inf2))
  1697. {
  1698. result = FPDefaultNaN();
  1699. FPProcessException(FpExc.InvalidOp, state);
  1700. }
  1701. else if (inf1 || inf2)
  1702. {
  1703. result = FPInfinity(sign1 ^ sign2);
  1704. }
  1705. else if (zero1 || zero2)
  1706. {
  1707. result = FPZero(sign1 ^ sign2);
  1708. }
  1709. else
  1710. {
  1711. result = value1 * value2;
  1712. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1713. {
  1714. state.SetFpsrFlag(Fpsr.Ufc);
  1715. result = FPZero(result < 0d);
  1716. }
  1717. }
  1718. }
  1719. return result;
  1720. }
  1721. public static double FPMulAdd(
  1722. double valueA,
  1723. double value1,
  1724. double value2,
  1725. CpuThreadState state)
  1726. {
  1727. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMulAdd: state.Fpcr = 0x{state.CFpcr:X8}");
  1728. valueA = valueA.FPUnpack(out FpType typeA, out bool signA, out ulong addend, state);
  1729. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1730. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1731. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1732. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1733. double result = FPProcessNaNs3(typeA, type1, type2, addend, op1, op2, out bool done, state);
  1734. if (typeA == FpType.QNaN && ((inf1 && zero2) || (zero1 && inf2)))
  1735. {
  1736. result = FPDefaultNaN();
  1737. FPProcessException(FpExc.InvalidOp, state);
  1738. }
  1739. if (!done)
  1740. {
  1741. bool infA = typeA == FpType.Infinity; bool zeroA = typeA == FpType.Zero;
  1742. bool signP = sign1 ^ sign2;
  1743. bool infP = inf1 || inf2;
  1744. bool zeroP = zero1 || zero2;
  1745. if ((inf1 && zero2) || (zero1 && inf2) || (infA && infP && signA != signP))
  1746. {
  1747. result = FPDefaultNaN();
  1748. FPProcessException(FpExc.InvalidOp, state);
  1749. }
  1750. else if ((infA && !signA) || (infP && !signP))
  1751. {
  1752. result = FPInfinity(false);
  1753. }
  1754. else if ((infA && signA) || (infP && signP))
  1755. {
  1756. result = FPInfinity(true);
  1757. }
  1758. else if (zeroA && zeroP && signA == signP)
  1759. {
  1760. result = FPZero(signA);
  1761. }
  1762. else
  1763. {
  1764. // TODO: When available, use: T Math.FusedMultiplyAdd(T, T, T);
  1765. // https://github.com/dotnet/corefx/issues/31903
  1766. result = valueA + (value1 * value2);
  1767. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1768. {
  1769. state.SetFpsrFlag(Fpsr.Ufc);
  1770. result = FPZero(result < 0d);
  1771. }
  1772. }
  1773. }
  1774. return result;
  1775. }
  1776. [MethodImpl(MethodImplOptions.AggressiveInlining)]
  1777. public static double FPMulSub(
  1778. double valueA,
  1779. double value1,
  1780. double value2,
  1781. CpuThreadState state)
  1782. {
  1783. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMulSub: state.Fpcr = 0x{state.CFpcr:X8}");
  1784. value1 = value1.FPNeg();
  1785. return FPMulAdd(valueA, value1, value2, state);
  1786. }
  1787. public static double FPMulX(double value1, double value2, CpuThreadState state)
  1788. {
  1789. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPMulX: state.Fpcr = 0x{state.CFpcr:X8}");
  1790. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1791. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1792. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1793. if (!done)
  1794. {
  1795. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1796. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1797. if ((inf1 && zero2) || (zero1 && inf2))
  1798. {
  1799. result = FPTwo(sign1 ^ sign2);
  1800. }
  1801. else if (inf1 || inf2)
  1802. {
  1803. result = FPInfinity(sign1 ^ sign2);
  1804. }
  1805. else if (zero1 || zero2)
  1806. {
  1807. result = FPZero(sign1 ^ sign2);
  1808. }
  1809. else
  1810. {
  1811. result = value1 * value2;
  1812. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1813. {
  1814. state.SetFpsrFlag(Fpsr.Ufc);
  1815. result = FPZero(result < 0d);
  1816. }
  1817. }
  1818. }
  1819. return result;
  1820. }
  1821. public static double FPRecipEstimate(double value, CpuThreadState state)
  1822. {
  1823. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPRecipEstimate: state.Fpcr = 0x{state.CFpcr:X8}");
  1824. value.FPUnpack(out FpType type, out bool sign, out ulong op, state);
  1825. double result;
  1826. if (type == FpType.SNaN || type == FpType.QNaN)
  1827. {
  1828. result = FPProcessNaN(type, op, state);
  1829. }
  1830. else if (type == FpType.Infinity)
  1831. {
  1832. result = FPZero(sign);
  1833. }
  1834. else if (type == FpType.Zero)
  1835. {
  1836. result = FPInfinity(sign);
  1837. FPProcessException(FpExc.DivideByZero, state);
  1838. }
  1839. else if (Math.Abs(value) < Math.Pow(2d, -1024))
  1840. {
  1841. bool overflowToInf;
  1842. switch (state.FPRoundingMode())
  1843. {
  1844. default:
  1845. case RoundMode.ToNearest: overflowToInf = true; break;
  1846. case RoundMode.TowardsPlusInfinity: overflowToInf = !sign; break;
  1847. case RoundMode.TowardsMinusInfinity: overflowToInf = sign; break;
  1848. case RoundMode.TowardsZero: overflowToInf = false; break;
  1849. }
  1850. result = overflowToInf ? FPInfinity(sign) : FPMaxNormal(sign);
  1851. FPProcessException(FpExc.Overflow, state);
  1852. FPProcessException(FpExc.Inexact, state);
  1853. }
  1854. else if (state.GetFpcrFlag(Fpcr.Fz) && (Math.Abs(value) >= Math.Pow(2d, 1022)))
  1855. {
  1856. result = FPZero(sign);
  1857. state.SetFpsrFlag(Fpsr.Ufc);
  1858. }
  1859. else
  1860. {
  1861. ulong fraction = op & 0x000FFFFFFFFFFFFFul;
  1862. uint exp = (uint)((op & 0x7FF0000000000000ul) >> 52);
  1863. if (exp == 0u)
  1864. {
  1865. if ((fraction & 0x0008000000000000ul) == 0ul)
  1866. {
  1867. fraction = (fraction & 0x0003FFFFFFFFFFFFul) << 2;
  1868. exp -= 1u;
  1869. }
  1870. else
  1871. {
  1872. fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1;
  1873. }
  1874. }
  1875. uint scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44);
  1876. uint resultExp = 2045u - exp;
  1877. uint estimate = (uint)SoftFloat.RecipEstimateTable[scaled - 256u] + 256u;
  1878. fraction = (ulong)(estimate & 0xFFu) << 44;
  1879. if (resultExp == 0u)
  1880. {
  1881. fraction = ((fraction & 0x000FFFFFFFFFFFFEul) | 0x0010000000000000ul) >> 1;
  1882. }
  1883. else if (resultExp + 1u == 0u)
  1884. {
  1885. fraction = ((fraction & 0x000FFFFFFFFFFFFCul) | 0x0010000000000000ul) >> 2;
  1886. resultExp = 0u;
  1887. }
  1888. result = BitConverter.Int64BitsToDouble(
  1889. (long)((sign ? 1ul : 0ul) << 63 | (resultExp & 0x7FFul) << 52 | (fraction & 0x000FFFFFFFFFFFFFul)));
  1890. }
  1891. return result;
  1892. }
  1893. public static double FPRecipStepFused(double value1, double value2, CpuThreadState state)
  1894. {
  1895. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPRecipStepFused: state.Fpcr = 0x{state.CFpcr:X8}");
  1896. value1 = value1.FPNeg();
  1897. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  1898. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  1899. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  1900. if (!done)
  1901. {
  1902. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  1903. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  1904. if ((inf1 && zero2) || (zero1 && inf2))
  1905. {
  1906. result = FPTwo(false);
  1907. }
  1908. else if (inf1 || inf2)
  1909. {
  1910. result = FPInfinity(sign1 ^ sign2);
  1911. }
  1912. else
  1913. {
  1914. // TODO: When available, use: T Math.FusedMultiplyAdd(T, T, T);
  1915. // https://github.com/dotnet/corefx/issues/31903
  1916. result = 2d + (value1 * value2);
  1917. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  1918. {
  1919. state.SetFpsrFlag(Fpsr.Ufc);
  1920. result = FPZero(result < 0d);
  1921. }
  1922. }
  1923. }
  1924. return result;
  1925. }
  1926. public static double FPRecpX(double value, CpuThreadState state)
  1927. {
  1928. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPRecpX: state.Fpcr = 0x{state.CFpcr:X8}");
  1929. value.FPUnpack(out FpType type, out bool sign, out ulong op, state);
  1930. double result;
  1931. if (type == FpType.SNaN || type == FpType.QNaN)
  1932. {
  1933. result = FPProcessNaN(type, op, state);
  1934. }
  1935. else
  1936. {
  1937. ulong notExp = (~op >> 52) & 0x7FFul;
  1938. ulong maxExp = 0x7FEul;
  1939. result = BitConverter.Int64BitsToDouble(
  1940. (long)((sign ? 1ul : 0ul) << 63 | (notExp == 0x7FFul ? maxExp : notExp) << 52));
  1941. }
  1942. return result;
  1943. }
  1944. public static double FPRSqrtEstimate(double value, CpuThreadState state)
  1945. {
  1946. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPRSqrtEstimate: state.Fpcr = 0x{state.CFpcr:X8}");
  1947. value.FPUnpack(out FpType type, out bool sign, out ulong op, state);
  1948. double result;
  1949. if (type == FpType.SNaN || type == FpType.QNaN)
  1950. {
  1951. result = FPProcessNaN(type, op, state);
  1952. }
  1953. else if (type == FpType.Zero)
  1954. {
  1955. result = FPInfinity(sign);
  1956. FPProcessException(FpExc.DivideByZero, state);
  1957. }
  1958. else if (sign)
  1959. {
  1960. result = FPDefaultNaN();
  1961. FPProcessException(FpExc.InvalidOp, state);
  1962. }
  1963. else if (type == FpType.Infinity)
  1964. {
  1965. result = FPZero(false);
  1966. }
  1967. else
  1968. {
  1969. ulong fraction = op & 0x000FFFFFFFFFFFFFul;
  1970. uint exp = (uint)((op & 0x7FF0000000000000ul) >> 52);
  1971. if (exp == 0u)
  1972. {
  1973. while ((fraction & 0x0008000000000000ul) == 0ul)
  1974. {
  1975. fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1;
  1976. exp -= 1u;
  1977. }
  1978. fraction = (fraction & 0x0007FFFFFFFFFFFFul) << 1;
  1979. }
  1980. uint scaled;
  1981. if ((exp & 1u) == 0u)
  1982. {
  1983. scaled = (uint)(((fraction & 0x000FF00000000000ul) | 0x0010000000000000ul) >> 44);
  1984. }
  1985. else
  1986. {
  1987. scaled = (uint)(((fraction & 0x000FE00000000000ul) | 0x0010000000000000ul) >> 45);
  1988. }
  1989. uint resultExp = (3068u - exp) >> 1;
  1990. uint estimate = (uint)SoftFloat.RecipSqrtEstimateTable[scaled - 128u] + 256u;
  1991. result = BitConverter.Int64BitsToDouble((long)((resultExp & 0x7FFul) << 52 | (estimate & 0xFFul) << 44));
  1992. }
  1993. return result;
  1994. }
  1995. public static double FPRSqrtStepFused(double value1, double value2, CpuThreadState state)
  1996. {
  1997. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPRSqrtStepFused: state.Fpcr = 0x{state.CFpcr:X8}");
  1998. value1 = value1.FPNeg();
  1999. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  2000. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  2001. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  2002. if (!done)
  2003. {
  2004. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  2005. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  2006. if ((inf1 && zero2) || (zero1 && inf2))
  2007. {
  2008. result = FPOnePointFive(false);
  2009. }
  2010. else if (inf1 || inf2)
  2011. {
  2012. result = FPInfinity(sign1 ^ sign2);
  2013. }
  2014. else
  2015. {
  2016. // TODO: When available, use: T Math.FusedMultiplyAdd(T, T, T);
  2017. // https://github.com/dotnet/corefx/issues/31903
  2018. result = (3d + (value1 * value2)) / 2d;
  2019. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  2020. {
  2021. state.SetFpsrFlag(Fpsr.Ufc);
  2022. result = FPZero(result < 0d);
  2023. }
  2024. }
  2025. }
  2026. return result;
  2027. }
  2028. public static double FPSqrt(double value, CpuThreadState state)
  2029. {
  2030. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPSqrt: state.Fpcr = 0x{state.CFpcr:X8}");
  2031. value = value.FPUnpack(out FpType type, out bool sign, out ulong op, state);
  2032. double result;
  2033. if (type == FpType.SNaN || type == FpType.QNaN)
  2034. {
  2035. result = FPProcessNaN(type, op, state);
  2036. }
  2037. else if (type == FpType.Zero)
  2038. {
  2039. result = FPZero(sign);
  2040. }
  2041. else if (type == FpType.Infinity && !sign)
  2042. {
  2043. result = FPInfinity(sign);
  2044. }
  2045. else if (sign)
  2046. {
  2047. result = FPDefaultNaN();
  2048. FPProcessException(FpExc.InvalidOp, state);
  2049. }
  2050. else
  2051. {
  2052. result = Math.Sqrt(value);
  2053. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  2054. {
  2055. state.SetFpsrFlag(Fpsr.Ufc);
  2056. result = FPZero(result < 0d);
  2057. }
  2058. }
  2059. return result;
  2060. }
  2061. public static double FPSub(double value1, double value2, CpuThreadState state)
  2062. {
  2063. Debug.WriteLineIf(state.CFpcr != 0, $"SoftFloat64.FPSub: state.Fpcr = 0x{state.CFpcr:X8}");
  2064. value1 = value1.FPUnpack(out FpType type1, out bool sign1, out ulong op1, state);
  2065. value2 = value2.FPUnpack(out FpType type2, out bool sign2, out ulong op2, state);
  2066. double result = FPProcessNaNs(type1, type2, op1, op2, out bool done, state);
  2067. if (!done)
  2068. {
  2069. bool inf1 = type1 == FpType.Infinity; bool zero1 = type1 == FpType.Zero;
  2070. bool inf2 = type2 == FpType.Infinity; bool zero2 = type2 == FpType.Zero;
  2071. if (inf1 && inf2 && sign1 == sign2)
  2072. {
  2073. result = FPDefaultNaN();
  2074. FPProcessException(FpExc.InvalidOp, state);
  2075. }
  2076. else if ((inf1 && !sign1) || (inf2 && sign2))
  2077. {
  2078. result = FPInfinity(false);
  2079. }
  2080. else if ((inf1 && sign1) || (inf2 && !sign2))
  2081. {
  2082. result = FPInfinity(true);
  2083. }
  2084. else if (zero1 && zero2 && sign1 == !sign2)
  2085. {
  2086. result = FPZero(sign1);
  2087. }
  2088. else
  2089. {
  2090. result = value1 - value2;
  2091. if (state.GetFpcrFlag(Fpcr.Fz) && double.IsSubnormal(result))
  2092. {
  2093. state.SetFpsrFlag(Fpsr.Ufc);
  2094. result = FPZero(result < 0d);
  2095. }
  2096. }
  2097. }
  2098. return result;
  2099. }
  2100. private static double FPDefaultNaN()
  2101. {
  2102. return -double.NaN;
  2103. }
  2104. private static double FPInfinity(bool sign)
  2105. {
  2106. return sign ? double.NegativeInfinity : double.PositiveInfinity;
  2107. }
  2108. private static double FPZero(bool sign)
  2109. {
  2110. return sign ? -0d : +0d;
  2111. }
  2112. private static double FPMaxNormal(bool sign)
  2113. {
  2114. return sign ? double.MinValue : double.MaxValue;
  2115. }
  2116. private static double FPTwo(bool sign)
  2117. {
  2118. return sign ? -2d : +2d;
  2119. }
  2120. private static double FPOnePointFive(bool sign)
  2121. {
  2122. return sign ? -1.5d : +1.5d;
  2123. }
  2124. private static double FPNeg(this double value)
  2125. {
  2126. return -value;
  2127. }
  2128. private static double ZerosOrOnes(bool ones)
  2129. {
  2130. return BitConverter.Int64BitsToDouble(ones ? -1L : 0L);
  2131. }
  2132. private static double FPUnpack(
  2133. this double value,
  2134. out FpType type,
  2135. out bool sign,
  2136. out ulong valueBits,
  2137. CpuThreadState state)
  2138. {
  2139. valueBits = (ulong)BitConverter.DoubleToInt64Bits(value);
  2140. sign = (~valueBits & 0x8000000000000000ul) == 0ul;
  2141. if ((valueBits & 0x7FF0000000000000ul) == 0ul)
  2142. {
  2143. if ((valueBits & 0x000FFFFFFFFFFFFFul) == 0ul || state.GetFpcrFlag(Fpcr.Fz))
  2144. {
  2145. type = FpType.Zero;
  2146. value = FPZero(sign);
  2147. if ((valueBits & 0x000FFFFFFFFFFFFFul) != 0ul)
  2148. {
  2149. FPProcessException(FpExc.InputDenorm, state);
  2150. }
  2151. }
  2152. else
  2153. {
  2154. type = FpType.Nonzero;
  2155. }
  2156. }
  2157. else if ((~valueBits & 0x7FF0000000000000ul) == 0ul)
  2158. {
  2159. if ((valueBits & 0x000FFFFFFFFFFFFFul) == 0ul)
  2160. {
  2161. type = FpType.Infinity;
  2162. }
  2163. else
  2164. {
  2165. type = (~valueBits & 0x0008000000000000ul) == 0ul ? FpType.QNaN : FpType.SNaN;
  2166. value = FPZero(sign);
  2167. }
  2168. }
  2169. else
  2170. {
  2171. type = FpType.Nonzero;
  2172. }
  2173. return value;
  2174. }
  2175. private static double FPProcessNaNs(
  2176. FpType type1,
  2177. FpType type2,
  2178. ulong op1,
  2179. ulong op2,
  2180. out bool done,
  2181. CpuThreadState state)
  2182. {
  2183. done = true;
  2184. if (type1 == FpType.SNaN)
  2185. {
  2186. return FPProcessNaN(type1, op1, state);
  2187. }
  2188. else if (type2 == FpType.SNaN)
  2189. {
  2190. return FPProcessNaN(type2, op2, state);
  2191. }
  2192. else if (type1 == FpType.QNaN)
  2193. {
  2194. return FPProcessNaN(type1, op1, state);
  2195. }
  2196. else if (type2 == FpType.QNaN)
  2197. {
  2198. return FPProcessNaN(type2, op2, state);
  2199. }
  2200. done = false;
  2201. return FPZero(false);
  2202. }
  2203. private static double FPProcessNaNs3(
  2204. FpType type1,
  2205. FpType type2,
  2206. FpType type3,
  2207. ulong op1,
  2208. ulong op2,
  2209. ulong op3,
  2210. out bool done,
  2211. CpuThreadState state)
  2212. {
  2213. done = true;
  2214. if (type1 == FpType.SNaN)
  2215. {
  2216. return FPProcessNaN(type1, op1, state);
  2217. }
  2218. else if (type2 == FpType.SNaN)
  2219. {
  2220. return FPProcessNaN(type2, op2, state);
  2221. }
  2222. else if (type3 == FpType.SNaN)
  2223. {
  2224. return FPProcessNaN(type3, op3, state);
  2225. }
  2226. else if (type1 == FpType.QNaN)
  2227. {
  2228. return FPProcessNaN(type1, op1, state);
  2229. }
  2230. else if (type2 == FpType.QNaN)
  2231. {
  2232. return FPProcessNaN(type2, op2, state);
  2233. }
  2234. else if (type3 == FpType.QNaN)
  2235. {
  2236. return FPProcessNaN(type3, op3, state);
  2237. }
  2238. done = false;
  2239. return FPZero(false);
  2240. }
  2241. private static double FPProcessNaN(FpType type, ulong op, CpuThreadState state)
  2242. {
  2243. if (type == FpType.SNaN)
  2244. {
  2245. op |= 1ul << 51;
  2246. FPProcessException(FpExc.InvalidOp, state);
  2247. }
  2248. if (state.GetFpcrFlag(Fpcr.Dn))
  2249. {
  2250. return FPDefaultNaN();
  2251. }
  2252. return BitConverter.Int64BitsToDouble((long)op);
  2253. }
  2254. private static void FPProcessException(FpExc exc, CpuThreadState state)
  2255. {
  2256. int enable = (int)exc + 8;
  2257. if ((state.CFpcr & (1 << enable)) != 0)
  2258. {
  2259. throw new NotImplementedException("Floating-point trap handling.");
  2260. }
  2261. else
  2262. {
  2263. state.CFpsr |= 1 << (int)exc;
  2264. }
  2265. }
  2266. }
  2267. }