| ... | @@ -8,6 +8,7 @@ const std = @import("std"); | ... | @@ -8,6 +8,7 @@ const std = @import("std"); |
| 8 | const math = std.math; | 8 | const math = std.math; |
| 9 | const expect = std.testing.expect; | 9 | const expect = std.testing.expect; |
| 10 | const expectEqual = std.testing.expectEqual; | 10 | const expectEqual = std.testing.expectEqual; |
| | 11 | const expectApproxEqRel = std.testing.expectApproxEqRel; |
| 11 | | 12 | |
| 12 | const compiler_rt = @import("../compiler_rt.zig"); | 13 | const compiler_rt = @import("../compiler_rt.zig"); |
| 13 | const symbol = @import("../compiler_rt.zig").symbol; | 14 | const symbol = @import("../compiler_rt.zig").symbol; |
| ... | @@ -436,9 +437,234 @@ pub fn __logx(a: f80) callconv(.c) f80 { | ... | @@ -436,9 +437,234 @@ pub fn __logx(a: f80) callconv(.c) f80 { |
| 436 | return @floatCast(logq(a)); | 437 | return @floatCast(logq(a)); |
| 437 | } | 438 | } |
| 438 | | 439 | |
| 439 | pub fn logq(a: f128) callconv(.c) f128 { | 440 | /// Implementation of "Table-driven implementation of the exponential function in IEEE floating-point arithmetic" |
| 440 | // TODO: more correct implementation | 441 | /// By PTP Tang in ACM Transactions on Mathematical Software (TOMS), 1989 |
| 441 | return log(@floatCast(a)); | 442 | /// |
| | 443 | /// https://dl.acm.org/doi/pdf/10.1145/63522.214389 |
| | 444 | /// |
| | 445 | /// Adapted to work for f128 by Christophe Delage. |
| | 446 | /// |
| | 447 | /// Accuracy on 100 million random numbers in [0, inf) (exponent uniformly random) |
| | 448 | /// <= 0.5 ulp: 99.99%, worst case <= 0.530 ulp |
| | 449 | /// |
| | 450 | /// Accuracy on 10 million random numbers near x = 1 (testing the proc2 case): |
| | 451 | /// <= 0.5 ulp: 99.85%, worst case <= 0.532 ulp |
| | 452 | pub fn logq(x: f128) callconv(.c) f128 { |
| | 453 | const bitsize = 7; |
| | 454 | const size = 1 << bitsize; |
| | 455 | |
| | 456 | if (!math.isFinite(x)) { |
| | 457 | if (math.isNan(x)) { |
| | 458 | if (math.isSignalNan(x)) math.raiseInvalid(); |
| | 459 | return math.nan(f128); |
| | 460 | } |
| | 461 | if (math.isPositiveInf(x)) return x; |
| | 462 | } |
| | 463 | if (x <= 0.0) { |
| | 464 | if (x >= 0.0) { |
| | 465 | math.raiseDivByZero(); |
| | 466 | return -math.inf(f128); |
| | 467 | } |
| | 468 | math.raiseInvalid(); |
| | 469 | return math.nan(f128); |
| | 470 | } |
| | 471 | |
| | 472 | // exp(-1 / 16) rounded down |
| | 473 | const proc2_lo: f128 = 0.939413062813475786119710824622305; |
| | 474 | // exp(1 / 16) rounded up |
| | 475 | const proc2_hi: f128 = 1.0644944589178594295633905946428897; |
| | 476 | if (proc2_lo < x and x < proc2_hi) { |
| | 477 | const f = x - 1.0; |
| | 478 | |
| | 479 | const g = 1 / (2 + f); |
| | 480 | const u = 2 * f * g; |
| | 481 | const v = u * u; |
| | 482 | const uv = u * v; |
| | 483 | |
| | 484 | const v64: f64 = @floatCast(v); |
| | 485 | |
| | 486 | // use f64 for the last few coefficients to improve performance |
| | 487 | const p19 = 2.0165671588771827537210411918018159e-7; |
| | 488 | const p17 = 8.97568550755477160981619052649713e-7 + v64 * p19; |
| | 489 | const p15 = 4.069010449774280288178309893970754e-6 + v64 * p17; |
| | 490 | const p13 = 1.8780048076832339308077858301484127e-5 + v * p15; |
| | 491 | const p11 = 8.87784090909092440759545734146088e-5 + v * p13; |
| | 492 | const p9 = 4.340277777777777776216500817402857e-4 + v * p11; |
| | 493 | const p7 = 2.2321428571428571428572328745789477e-3 + v * p9; |
| | 494 | const p5 = 1.249999999999999999999999997455655e-2 + v * p7; |
| | 495 | |
| | 496 | const q_hi = uv * 8.333333333333333333333333333333581e-2; |
| | 497 | const q_lo = uv * v * p5; |
| | 498 | const q = q_hi + q_lo; |
| | 499 | |
| | 500 | const fa: f128 = @as(f64, @floatCast(f)); |
| | 501 | const ua: f128 = @as(f64, @floatCast(u)); |
| | 502 | |
| | 503 | const fb: f128 = f - fa; |
| | 504 | const ub: f128 = ((2 * (f - ua) - ua * fa) - ua * fb) * g; |
| | 505 | |
| | 506 | return ua + (ub + q); |
| | 507 | } |
| | 508 | |
| | 509 | const ym = frexp2(x); |
| | 510 | const y = ym.significand; |
| | 511 | const m = ym.exponent; |
| | 512 | |
| | 513 | const F0 = @round(math.ldexp(y, bitsize)); |
| | 514 | const j0: usize = @intFromFloat(F0); |
| | 515 | const j = j0 - size; |
| | 516 | const F = math.ldexp(F0, -bitsize); |
| | 517 | const f = y - F; |
| | 518 | |
| | 519 | const u = (f + f) / (y + F); |
| | 520 | const v = u * u; |
| | 521 | |
| | 522 | const v64: f64 = @floatCast(v); |
| | 523 | // use f64 for the last coefficient to improve performance |
| | 524 | const p11 = 8.877925718782769769445565656611838e-5; |
| | 525 | const p9 = 4.340277777635300605611118803507141e-4 + v64 * p11; |
| | 526 | const p7 = 2.2321428571428572515097318595359542e-3 + v * p9; |
| | 527 | const p5 = 1.249999999999999999999963839743372e-2 + v * p7; |
| | 528 | const p3 = 8.333333333333333333333333333372414e-2 + v * p5; |
| | 529 | |
| | 530 | const q = u * v * p3; |
| | 531 | |
| | 532 | const log1p_tab = [size + 1]struct { hi: f128, lo: f128 }{ |
| | 533 | .{ .hi = 0, .lo = 0 }, |
| | 534 | .{ .hi = 0x1.fe02a6b106788fc3769039p-8, .lo = 0x1.dc282d2b3db2c3ef9a073a876702p-100 }, |
| | 535 | .{ .hi = 0x1.fc0a8b0fc03e3cf9eda74d4p-7, .lo = -0x1.0a8552414fc416fc223acca2ebfp-100 }, |
| | 536 | .{ .hi = 0x1.7b91b07d5b11aa927f54c72p-6, .lo = -0x1.287fc46561dfab5bc5cceecb4882p-99 }, |
| | 537 | .{ .hi = 0x1.f829b0e7833004cf8fc13c8p-6, .lo = -0x1.0dd605151051eb3220ca52e20939p-100 }, |
| | 538 | .{ .hi = 0x1.39e87b9febd5fa9015b202bp-5, .lo = -0x1.1bac6e550a3c3dc859cfe2e178a8p-99 }, |
| | 539 | .{ .hi = 0x1.77458f632dcfc4634f2a1eep-5, .lo = 0x1.2960b1e4dfb80d9544ec6583eb3ap-99 }, |
| | 540 | .{ .hi = 0x1.b42dd711971bec28d14c7dap-5, .lo = -0x1.2645ad50c7672fc0eb08d862221dp-102 }, |
| | 541 | .{ .hi = 0x1.f0a30c01162a6617cc9716fp-5, .lo = -0x1.4cd0ece597165991495b4d31cf5cp-101 }, |
| | 542 | .{ .hi = 0x1.16536eea37ae0e8625c173ep-4, .lo = -0x1.66d0dc92deb7d2ccbd2caa9640cap-99 }, |
| | 543 | .{ .hi = 0x1.341d7961bd1d092998376108p-4, .lo = -0x1.976457ef2f89ad243dcc3578cf7ep-99 }, |
| | 544 | .{ .hi = 0x1.51b073f06183f69278e686ap-4, .lo = 0x1.7c8ac25e4e3f04de1f086f5cb4b1p-99 }, |
| | 545 | .{ .hi = 0x1.6f0d28ae56b4b9be499b9edp-4, .lo = 0x1.9b640ce50c1ef65087fdf23812f4p-100 }, |
| | 546 | .{ .hi = 0x1.8c345d6319b20f5acb42a66p-4, .lo = -0x1.254bca8fd9fc1bf283b3b4b8662dp-100 }, |
| | 547 | .{ .hi = 0x1.a926d3a4ad563650bd22a9cp-4, .lo = 0x1.d5263cd4fb3f11769cc680ef5589p-99 }, |
| | 548 | .{ .hi = 0x1.c5e548f5bc74315d617ef818p-4, .lo = -0x1.e4e896269950723c88d353ee9c18p-100 }, |
| | 549 | .{ .hi = 0x1.e27076e2af2e5e9ea87ffe2p-4, .lo = -0x1.61eaa246b143bfe80906a822f768p-104 }, |
| | 550 | .{ .hi = 0x1.fec9131dbeabaaa2e5199f9p-4, .lo = 0x1.9271dff48f15d409017630a93931p-99 }, |
| | 551 | .{ .hi = 0x1.0d77e7cd08e596697717a40cp-3, .lo = 0x1.574712132d3f6340e183be2031c6p-102 }, |
| | 552 | .{ .hi = 0x1.1b72ad52f67a029060468e58p-3, .lo = 0x1.ae73f3bc7ec84ca997609536a037p-99 }, |
| | 553 | .{ .hi = 0x1.29552f81ff5234c05dc7102p-3, .lo = -0x1.20b2ef60436f8f081d60452c9fc1p-100 }, |
| | 554 | .{ .hi = 0x1.371fc201e8f743bcd96c55e4p-3, .lo = -0x1.d80d17e0cd92558ad6fcd608bb1bp-100 }, |
| | 555 | .{ .hi = 0x1.44d2b6ccb7d1e67d3d950f88p-3, .lo = -0x1.e1f3be9a83374584faad83fa4fecp-103 }, |
| | 556 | .{ .hi = 0x1.526e5e3a1b437a2e401d6e3cp-3, .lo = 0x1.6334db798c76a888aa87317b14f8p-100 }, |
| | 557 | .{ .hi = 0x1.5ff3070a793d3c873e20a074p-3, .lo = -0x1.edc45019551c65501060ce71fa98p-99 }, |
| | 558 | .{ .hi = 0x1.6d60fe719d21c8d54765c4ccp-3, .lo = -0x1.790e412e6d3ed18e4a7c22362e49p-101 }, |
| | 559 | .{ .hi = 0x1.7ab890210d9091be36b2d6ap-3, .lo = 0x1.820191ff8525362042cad5d8c597p-101 }, |
| | 560 | .{ .hi = 0x1.87fa06520c910902009017dcp-3, .lo = 0x1.32ef5a55704b6b7eb4ebea28a6cdp-100 }, |
| | 561 | .{ .hi = 0x1.9525a9cf456b47641307538cp-3, .lo = -0x1.da62766be8258611d132d71d84acp-101 }, |
| | 562 | .{ .hi = 0x1.a23bc1fe2b563193711b07a8p-3, .lo = 0x1.98c27e3f1b66d8b32de61c04cf95p-99 }, |
| | 563 | .{ .hi = 0x1.af3c94e80bff2d8ce601937cp-3, .lo = 0x1.9eb976769b8b9a5d50ca14a7622fp-100 }, |
| | 564 | .{ .hi = 0x1.bc286742d8cd629f9ce890ep-3, .lo = 0x1.ea9e1e2c3dca46c83cd6d19e5e9bp-99 }, |
| | 565 | .{ .hi = 0x1.c8ff7c79a9a21ac25d81ef3p-3, .lo = -0x1.1976d471342b17dca47c9d1e1d98p-105 }, |
| | 566 | .{ .hi = 0x1.d5c216b4fbb915b910d65f94p-3, .lo = -0x1.5ff1e1c98c2ed4063968ad2332f8p-100 }, |
| | 567 | .{ .hi = 0x1.e27076e2af2e5e9ea87ffe2p-3, .lo = -0x1.61eaa246b143bfe80906a822f768p-103 }, |
| | 568 | .{ .hi = 0x1.ef0adcbdc59365218de5437p-3, .lo = 0x1.06429f5a5098683a47c3a3ca5835p-100 }, |
| | 569 | .{ .hi = 0x1.fb9186d5e3e2a8d55466c378p-3, .lo = 0x1.4d2ca09202c222ad91640bd8b2fcp-99 }, |
| | 570 | .{ .hi = 0x1.0402594b4d040dae27bd0b6p-2, .lo = -0x1.16a1bbb899f343f105ee37cafa25p-100 }, |
| | 571 | .{ .hi = 0x1.0a324e27390e35f73f7a0188p-2, .lo = -0x1.fe78eb90fe52820fb4690e4910e3p-99 }, |
| | 572 | .{ .hi = 0x1.1058bf9ae4ad5189fa0ab4ccp-2, .lo = -0x1.9c60f598d3a32076376a5960e735p-99 }, |
| | 573 | .{ .hi = 0x1.1675cababa60e039cc7d571p-2, .lo = 0x1.b8b823f067d04a43c19f534c3c8ep-100 }, |
| | 574 | .{ .hi = 0x1.1c898c16999fafbc68e75404p-2, .lo = -0x1.c443cc477d114a1350a26c9b5535p-100 }, |
| | 575 | .{ .hi = 0x1.22941fbcf7965a242853da76p-2, .lo = -0x1.5e685a2caa590b0f13a31703b136p-101 }, |
| | 576 | .{ .hi = 0x1.2895a13de86a35eb49304fc2p-2, .lo = -0x1.f8d3a52b8aa6834f50a903b31253p-99 }, |
| | 577 | .{ .hi = 0x1.2e8e2bae11d309c2cc91a85p-2, .lo = 0x1.03679bdbbd6b7d91378a909a6793p-99 }, |
| | 578 | .{ .hi = 0x1.347dd9a987d54d645674fedcp-2, .lo = 0x1.821ee510a580b3b30ef57f83ca28p-99 }, |
| | 579 | .{ .hi = 0x1.3a64c556945e9c72f35cd74p-2, .lo = 0x1.a11beb7a3cee7e029e46e1334dfep-99 }, |
| | 580 | .{ .hi = 0x1.404308686a7e3bd0c127df4cp-2, .lo = 0x1.92985641827d9d91a2da0d4f2207p-100 }, |
| | 581 | .{ .hi = 0x1.4618bc21c5ec27d0b7b37b34p-2, .lo = -0x1.c65df511a65b67fe9778d8694229p-101 }, |
| | 582 | .{ .hi = 0x1.4be5f957778a0db4c9949f7p-2, .lo = -0x1.3cdc28d5974f3185a1f581529353p-101 }, |
| | 583 | .{ .hi = 0x1.51aad872df82d09c93d60cfap-2, .lo = 0x1.5e311d4f4f357cbfae095f10fcd3p-99 }, |
| | 584 | .{ .hi = 0x1.5767717455a6c549ab6ca0dap-2, .lo = -0x1.f42ff0747cbcce6c0841fd7ceb87p-100 }, |
| | 585 | .{ .hi = 0x1.5d1bdbf5809ca508d8e0f72p-2, .lo = -0x1.eea60c7f4b594bd65b44f6b20634p-104 }, |
| | 586 | .{ .hi = 0x1.62c82f2b9c7952f6f5f22a6p-2, .lo = 0x1.ca2e7226c55dd257f44b5002c8cdp-102 }, |
| | 587 | .{ .hi = 0x1.686c81e9b14aec442be1014ep-2, .lo = 0x1.c34b25bdbda38672b32ca47f535dp-101 }, |
| | 588 | .{ .hi = 0x1.6e08eaa2ba1e38c139318d72p-2, .lo = -0x1.07a1f9d2a3058cd3f047b933d485p-99 }, |
| | 589 | .{ .hi = 0x1.739d7f6bbd0069ce24c53faep-2, .lo = -0x1.8210d2a910f7918ad34542221b6cp-99 }, |
| | 590 | .{ .hi = 0x1.792a55fdd47a27c15da47fa8p-2, .lo = -0x1.297ea603cd10e7c702842a1590aep-100 }, |
| | 591 | .{ .hi = 0x1.7eaf83b82afc364b3a5e7b4ap-2, .lo = 0x1.50437160cbfcbf71ee8d4b3cd067p-100 }, |
| | 592 | .{ .hi = 0x1.842d1da1e8b17493b1465e12p-2, .lo = -0x1.899770fb9eb8e0c7f06a12cd88c3p-100 }, |
| | 593 | .{ .hi = 0x1.89a3386c1425ab5a71881104p-2, .lo = -0x1.f549800739afc97f5d4b9c15fc12p-101 }, |
| | 594 | .{ .hi = 0x1.8f11e873662c77e1769d5698p-2, .lo = 0x1.a29979cbfcbc0e45410ee8ca0d17p-100 }, |
| | 595 | .{ .hi = 0x1.947941c2116faba4cdd147d2p-2, .lo = -0x1.f22a2b6b19ed11af82f2c0e6730ep-99 }, |
| | 596 | .{ .hi = 0x1.99d958117e08acba92eec478p-2, .lo = 0x1.8dfba4bb71c95f44a3225b5d8f8fp-101 }, |
| | 597 | .{ .hi = 0x1.9f323ecbf984bf2b68d766f4p-2, .lo = 0x1.4886067d20ffb34547d7c2b38ad8p-104 }, |
| | 598 | .{ .hi = 0x1.a484090e5bb0a2bfca6b70ecp-2, .lo = -0x1.62da6c6290af3949ca12eb97e6bbp-99 }, |
| | 599 | .{ .hi = 0x1.a9cec9a9a08498d484ff52f2p-2, .lo = 0x1.50d7be11fc8ee26768c44e9f35aap-100 }, |
| | 600 | .{ .hi = 0x1.af1293247786b1133844a15ep-2, .lo = -0x1.ebf9e3b2fb68378f9b7aa0ef6685p-101 }, |
| | 601 | .{ .hi = 0x1.b44f77bcc8f628cbeedaae98p-2, .lo = 0x1.c3c779029d5a684301e7888d5449p-99 }, |
| | 602 | .{ .hi = 0x1.b9858969310fb598fb14f88ep-2, .lo = 0x1.e1cf79039d5a31010282d8264afap-99 }, |
| | 603 | .{ .hi = 0x1.beb4d9da71b7bf7861d37abcp-2, .lo = -0x1.f29b495a7c83dffb9899ad6da116p-101 }, |
| | 604 | .{ .hi = 0x1.c3dd7a7cdad4d73b3c14b7aap-2, .lo = -0x1.649f44ae71a827ebf6601862d429p-100 }, |
| | 605 | .{ .hi = 0x1.c8ff7c79a9a21ac25d81ef3p-2, .lo = -0x1.1976d471342b17dca47c9d1e1d98p-104 }, |
| | 606 | .{ .hi = 0x1.ce1af0b85f3eb7b7d2bcaadp-2, .lo = 0x1.33a4e218c8c00b2f6f2b23998791p-99 }, |
| | 607 | .{ .hi = 0x1.d32fe7e00ebd561dec8cbebep-2, .lo = 0x1.1b7e8c55a6ffaf7eb72c1ff893cdp-99 }, |
| | 608 | .{ .hi = 0x1.d83e7258a2f3e50515ba2ecap-2, .lo = -0x1.7778ad7b599f3edc40a13fe57cp-99 }, |
| | 609 | .{ .hi = 0x1.dd46a04c1c4a0bee626a49d2p-2, .lo = -0x1.23c02c15f2f66328a06054db5e01p-101 }, |
| | 610 | .{ .hi = 0x1.e24881a7c6c261cbd8f45954p-2, .lo = 0x1.48c6c5403df1764e1ed219643a85p-99 }, |
| | 611 | .{ .hi = 0x1.e744261d68787e37da36f3ccp-2, .lo = -0x1.2e44bfb5e71d55a11feaedf56a94p-100 }, |
| | 612 | .{ .hi = 0x1.ec399d2468cc0175cee53f36p-2, .lo = -0x1.8d2027bb4681af8a138d77633327p-99 }, |
| | 613 | .{ .hi = 0x1.f128f5faf06ecb35c83b1132p-2, .lo = -0x1.851461536ddd17ac271709c2b464p-101 }, |
| | 614 | .{ .hi = 0x1.f6123fa7028ac61456c3cb6cp-2, .lo = 0x1.a0a432a2414cc0b049c0fb73b4dep-99 }, |
| | 615 | .{ .hi = 0x1.faf588f78f31ed9afb3e4ea8p-2, .lo = 0x1.afec6d4cde2ef184dc7b6e634ba1p-100 }, |
| | 616 | .{ .hi = 0x1.ffd2e0857f4985597d0364c8p-2, .lo = 0x1.af246e3379d3ea68e29866b3b38bp-100 }, |
| | 617 | .{ .hi = 0x1.02552a5a5d0fec69c695d7eep-1, .lo = 0x1.fff1a3725c5c6261a75dc4f512adp-99 }, |
| | 618 | .{ .hi = 0x1.04bdf9da926d265fcc1008b2p-1, .lo = 0x1.df6a6d08e4470f10c7053f04f1ep-99 }, |
| | 619 | .{ .hi = 0x1.0723e5c1cdf404e579638911p-1, .lo = 0x1.baad95bd2eba9089087bae740509p-99 }, |
| | 620 | .{ .hi = 0x1.0986f4f573520b91fda94ff4p-1, .lo = 0x1.fe038113f135a26389f13c4bde3ap-100 }, |
| | 621 | .{ .hi = 0x1.0be72e4252a82b69897bb33ep-1, .lo = -0x1.9649bc990440ca2c12ee56f6c90bp-108 }, |
| | 622 | .{ .hi = 0x1.0e44985d1cc8bf6eae5de969p-1, .lo = 0x1.8f8d1fbacf70a2da185e84859e36p-99 }, |
| | 623 | .{ .hi = 0x1.109f39e2d4c96fde3ec9b0b8p-1, .lo = -0x1.b9d06df4e0c8337c0da8f63aefc7p-99 }, |
| | 624 | .{ .hi = 0x1.12f719593efbc53012319c7dp-1, .lo = 0x1.a96893b2757f50123379aecd147cp-102 }, |
| | 625 | .{ .hi = 0x1.154c3d2f4d5e9a98f33a3966p-1, .lo = -0x1.d7f56258b99e197c61c0a23b2403p-101 }, |
| | 626 | .{ .hi = 0x1.179eabbd899a0bfc60e6fa08p-1, .lo = -0x1.68f2a71c8279b89eb8392b7a41ep-100 }, |
| | 627 | .{ .hi = 0x1.19ee6b467c96ecc5cbdd7782p-1, .lo = -0x1.0c2a8ef8715f93d3c8e2c9016713p-100 }, |
| | 628 | .{ .hi = 0x1.1c3b81f713c24bc94f8ecdfcp-1, .lo = -0x1.d103880b3dc864d107231c87eaa7p-100 }, |
| | 629 | .{ .hi = 0x1.1e85f5e7040d03dec59a5f3ep-1, .lo = 0x1.e35f2e7ca4f4817696ad39f9a4b2p-100 }, |
| | 630 | .{ .hi = 0x1.20cdcd192ab6d93503d0f75cp-1, .lo = -0x1.3db0bb5bf2b76be256c1a2a08a8p-103 }, |
| | 631 | .{ .hi = 0x1.23130d7bebf4282de368722dp-1, .lo = -0x1.6dfadc7219019f05279c9cfd2b08p-99 }, |
| | 632 | .{ .hi = 0x1.2555bce98f7cb3c043adad1p-1, .lo = 0x1.e71084750a06eb301ae8308feca1p-100 }, |
| | 633 | .{ .hi = 0x1.2795e1289b11aeb783f3db97p-1, .lo = -0x1.e3801fe56c1467b5e622105c5e41p-99 }, |
| | 634 | .{ .hi = 0x1.29d37fec2b08ac85cd6cba5dp-1, .lo = -0x1.824a2f303e0aa6995ef5598cc5b7p-100 }, |
| | 635 | .{ .hi = 0x1.2c0e9ed448e8bb97a9c31ba3p-1, .lo = -0x1.8676adfad5c83dea45d7349693e3p-99 }, |
| | 636 | .{ .hi = 0x1.2e47436e4026840542186922p-1, .lo = 0x1.ab1252cf29452c88ebc5ce2f36f2p-101 }, |
| | 637 | .{ .hi = 0x1.307d7334f10be1fb590a1f56p-1, .lo = 0x1.b66f70c05b80999c08cdd48a021p-99 }, |
| | 638 | .{ .hi = 0x1.32b1339121d71320556b67b2p-1, .lo = 0x1.6b06715ba133462ddf94bde6b3a5p-100 }, |
| | 639 | .{ .hi = 0x1.34e289d9ce1d316eb92d885dp-1, .lo = -0x1.b151b59c44058fa92837dec71351p-101 }, |
| | 640 | .{ .hi = 0x1.37117b54747b5c5dd024844ep-1, .lo = -0x1.037076a726793d7e93c9b2f3eef6p-100 }, |
| | 641 | .{ .hi = 0x1.393e0d3562a19a9c4426036ep-1, .lo = -0x1.cf1c277a3a0d863fefb367ef8616p-102 }, |
| | 642 | .{ .hi = 0x1.3b68449fffc22af8edec1859p-1, .lo = 0x1.b341d6de6d9b9591a54790d29adcp-100 }, |
| | 643 | .{ .hi = 0x1.3d9026a7156faa404263d0adp-1, .lo = 0x1.3cf6b809d96954adf1ff9360bd04p-100 }, |
| | 644 | .{ .hi = 0x1.3fb5b84d16f425b4e9d505cbp-1, .lo = -0x1.110c9bd8986629a5a46a5834774cp-99 }, |
| | 645 | .{ .hi = 0x1.41d8fe84672ae6464bcc2f46p-1, .lo = 0x1.779538890dd44eadeb32e848f817p-105 }, |
| | 646 | .{ .hi = 0x1.43f9fe2f9ce677a727b9b60fp-1, .lo = -0x1.e6927c891167a0306333dca3b8a4p-101 }, |
| | 647 | .{ .hi = 0x1.4618bc21c5ec27d0b7b37b34p-1, .lo = -0x1.c65df511a65b67fe9778d8694229p-100 }, |
| | 648 | .{ .hi = 0x1.48353d1ea88df73d5e8bb302p-1, .lo = -0x1.7b4f3e104187cc8aca358d9263f9p-104 }, |
| | 649 | .{ .hi = 0x1.4a4f85db03ebb0227bf47a6fp-1, .lo = -0x1.e49ce91908e6e2750b818bba40e6p-100 }, |
| | 650 | .{ .hi = 0x1.4c679afccee39b168ecdd318p-1, .lo = 0x1.bf619db0d889bbe38f559618dbd3p-99 }, |
| | 651 | .{ .hi = 0x1.4e7d811b75bb09cb09856458p-1, .lo = 0x1.5770d0c5ebca2047bba2c9ee4f52p-99 }, |
| | 652 | .{ .hi = 0x1.50913cc01686b4bcb3a5b0b5p-1, .lo = 0x1.b0f69791cf6c54c4e5d96f1d584fp-99 }, |
| | 653 | .{ .hi = 0x1.52a2d265bc5aaee77c8af15bp-1, .lo = 0x1.7aea7bed0920f6a4c39b31ea388bp-100 }, |
| | 654 | .{ .hi = 0x1.54b2467999497a915428b43ep-1, .lo = -0x1.f434bb5d154a84758a2a5033748cp-99 }, |
| | 655 | .{ .hi = 0x1.56bf9d5b3f399411c6217364p-1, .lo = -0x1.a6323ea9ce40a3caf6baebad2c64p-104 }, |
| | 656 | .{ .hi = 0x1.58cadb5cd79893092f25d931p-1, .lo = -0x1.d3d5761cff2a6a51ddc9c241881cp-99 }, |
| | 657 | .{ .hi = 0x1.5ad404c359f2cfb29aaa5f02p-1, .lo = 0x1.cd40845839e04578161ccf77753bp-100 }, |
| | 658 | .{ .hi = 0x1.5cdb1dc6c17648cf6e3c5d71p-1, .lo = -0x1.f3a84fed7a8e6b8a7923783c6bf7p-99 }, |
| | 659 | .{ .hi = 0x1.5ee02a924167570d6095fd24p-1, .lo = 0x1.03ef4c629f04ae4e7a29309e6688p-100 }, |
| | 660 | .{ .hi = 0x1.60e32f44788d8ca7c895a0b5p-1, .lo = -0x1.3557995d063914a66aa81ead3fdbp-101 }, |
| | 661 | .{ .hi = 0x1.62e42fefa39ef35793c7673p-1, .lo = 0x1.f97b57a079a193394c5b16c5068cp-103 }, |
| | 662 | }; |
| | 663 | const xm: f128 = @floatFromInt(m); |
| | 664 | const l_hi = xm * log1p_tab[128].hi + log1p_tab[j].hi; |
| | 665 | const l_lo = xm * log1p_tab[128].lo + log1p_tab[j].lo; |
| | 666 | |
| | 667 | return l_hi + (u + (q + l_lo)); |
| 442 | } | 668 | } |
| 443 | | 669 | |
| 444 | pub fn logl(x: c_longdouble) callconv(.c) c_longdouble { | 670 | pub fn logl(x: c_longdouble) callconv(.c) c_longdouble { |
| ... | @@ -450,6 +676,30 @@ pub fn logl(x: c_longdouble) callconv(.c) c_longdouble { | ... | @@ -450,6 +676,30 @@ pub fn logl(x: c_longdouble) callconv(.c) c_longdouble { |
| 450 | } | 676 | } |
| 451 | } | 677 | } |
| 452 | | 678 | |
| | 679 | /// Returns (f, k) such that x = f * 2^k and f in [1,2). |
| | 680 | /// Asserts that x is finite and positive. |
| | 681 | pub fn frexp2(x: f128) math.Frexp(f128) { |
| | 682 | std.debug.assert(math.isFinite(x)); |
| | 683 | std.debug.assert(x > 0.0); |
| | 684 | |
| | 685 | const bits: u128 = @bitCast(x); |
| | 686 | const uexp: i32 = @intCast(bits >> 112); |
| | 687 | |
| | 688 | std.debug.assert(uexp >= 0); |
| | 689 | |
| | 690 | if (uexp == 0) { |
| | 691 | const shift: u7 = @intCast(@clz(bits) - 15); |
| | 692 | |
| | 693 | const exp = -@as(i32, shift) - 0x3ffe; |
| | 694 | const frac: f128 = @bitCast((bits << shift) | (0x3fff << 112)); |
| | 695 | return .{ .significand = frac, .exponent = exp }; |
| | 696 | } |
| | 697 | |
| | 698 | const exp = uexp - 0x3fff; |
| | 699 | const frac: f128 = @bitCast((0x3fff << 112) | ((bits << 16) >> 16)); |
| | 700 | return .{ .significand = frac, .exponent = exp }; |
| | 701 | } |
| | 702 | |
| 453 | test "logf() special" { | 703 | test "logf() special" { |
| 454 | try expectEqual(logf(0.0), -math.inf(f32)); | 704 | try expectEqual(logf(0.0), -math.inf(f32)); |
| 455 | try expectEqual(logf(-0.0), -math.inf(f32)); | 705 | try expectEqual(logf(-0.0), -math.inf(f32)); |
| ... | @@ -519,3 +769,41 @@ test "log() boundary" { | ... | @@ -519,3 +769,41 @@ test "log() boundary" { |
| 519 | try expectEqual(log(0x1p-1022), -0x1.6232bdd7abcd2p+9); // First subnormal | 769 | try expectEqual(log(0x1p-1022), -0x1.6232bdd7abcd2p+9); // First subnormal |
| 520 | try expect(math.isNan(log(-0x1p-1022))); // First negative subnormal | 770 | try expect(math.isNan(log(-0x1p-1022))); // First negative subnormal |
| 521 | } | 771 | } |
| | 772 | |
| | 773 | test "logq() special" { |
| | 774 | try expectEqual(logq(0.0), -math.inf(f128)); |
| | 775 | try expectEqual(logq(-0.0), -math.inf(f128)); |
| | 776 | try expect(math.isPositiveZero(logq(1.0))); |
| | 777 | // Sadly, the rounding gods decided that 0.9999999999999999999999999999999999 |
| | 778 | // is the correctly rounded value of logq(math.e) |
| | 779 | try expectApproxEqRel(logq(math.e), 1.0, math.floatEpsAt(f128, 1.0)); |
| | 780 | try expectEqual(logq(math.inf(f128)), math.inf(f128)); |
| | 781 | try expect(math.isNan(logq(-1.0))); |
| | 782 | try expect(math.isNan(logq(-math.inf(f128)))); |
| | 783 | try expect(math.isNan(logq(math.nan(f128)))); |
| | 784 | try expect(math.isNan(logq(math.snan(f128)))); |
| | 785 | } |
| | 786 | |
| | 787 | test "logq() boundary" { |
| | 788 | try expectEqual(logq(0x1.ffffffffffffffffffffffffffffp16383), 0x1.62e42fefa39ef35793c7673007e6p13); // Max input value |
| | 789 | try expectEqual(logq(0x1p-16494), -0x1.6546282207802c89d24d65e96274p13); // Min positive input value |
| | 790 | try expect(math.isNan(logq(-0x1p-16494))); // Min negative input value |
| | 791 | try expectEqual(logq(0x1.0000000000000000000000000001p0), 0x1.ffffffffffffffffffffffffffffp-113); // Last value before result reaches +0 |
| | 792 | try expectEqual(logq(0x1.ffffffffffffffffffffffffffffp-1), -0x1p-113); // Last value before result reaches -0 |
| | 793 | try expectEqual(logq(0x1p-16382), -0x1.62d918ce2421d65ff90ac8f4ce66p13); // First subnormal |
| | 794 | try expect(math.isNan(logq(-0x1p-16382))); // First negative subnormal |
| | 795 | } |
| | 796 | |
| | 797 | test "logq() sanity" { |
| | 798 | try expectEqual(logq(4.151135979023751199079583784623537e-4), -7.7869583453055243113993340258295346e0); |
| | 799 | try expectEqual(logq(9.614234245933828353176667689130293e-14), -2.9972946567656004014786271559909435e1); |
| | 800 | try expectEqual(logq(1.012889803704721484375e13), 2.9946413646144315985379677542014356e1); |
| | 801 | try expectEqual(logq(2.397741857206453154086912e24), 5.613656963346284538829358703465392e1); |
| | 802 | try expectEqual(logq(3.442377567808290806386655232e27), 6.3405959896920645453203836625419693e1); |
| | 803 | try expectEqual(logq(1.0689155158234028407981544637594257e-8), -1.835403614606774451014272772421113e1); |
| | 804 | try expectEqual(logq(1.4813913545768791536741499811327596e-10), -2.263286917934202003739900705050399e1); |
| | 805 | try expectEqual(logq(4.518948965781299591064453125e10), 2.453413036705097282892685629562292e1); |
| | 806 | try expectEqual(logq(1.200355637363589375e14), 3.2418809179272977400408325788186897e1); |
| | 807 | try expectEqual(logq(6.6145398293682003021240234375e9), 2.261253606737223221601998075023261e1); |
| | 808 | try expectEqual(logq(5.16179116383965741056e20), 4.7692985503915646405875629300054525e1); |
| | 809 | } |
Christophe Delage <christ@ophe.net> 2026-05-28 17:01:16+02:00
lib