/* * sinhf.s * * by Stephen Canon * * Copyright (c) 2007, Apple Inc. All Rights Reserved. * * This file implements the C99 sinhf function for the MacOS X __i386__ and __x86_64__ abis. */ #include <machine/asm.h> #include "abi.h" // Basic approach // // First, we take the absolute value of x, compute on that, and then patch the sign back in at the // end of the computation. // // Arguments to sinhf can be separated into two ranges - the "uninteresting range" from 11 to // the overflow boundary, on which sinh(x) = e/2 * exp(x - 1), and the "interesting range" on which // exp(-x) and exp(x) are close enough in value that something more careful must be done. // // Particular care is required for values between 0 and 1, where massive cancellation can result in // a rather drastic loss of accuracy. Fortunately, a simple taylor series approximation // // sinh x = x + x^3 / 6 + x^5/120 // // suffices to handle all values smaller than 2^-4. To extend this to all values between 0 and 11, // we do an argument reduction via the sinh addition formula: // // sinh x + y = sinh x cosh y + cosh x sinh y // // Specifically, we separate x into high + low, 0 <= low < 2^-4. We use the value of high to perform // a table lookup for the values of Sh = sinh(high) and Ch = cosh(high). Then let // // Sl = low + 1/6 low^3 + 1/120 low^5 // Cl = 1 + 1/2 low^2 + 0.0416715 low^4 // // *Note that Cl is "almost" the taylor series for cosh(low), but the highest order // term has been fudged to get a smaller absolute error on the approximation interval. // (This allows us to keep our error below .51 ulps globally - actually below .5002 ulps on [-11,11]). // // We now compute // // result = Sl * Ch + Cl * Sh // // For the "uninteresting range", the code is taken directly from expf. Read the // comments in that file for more information. .const .align 4 .quad 0x3f811111111110fe, 0x3fa555f78359bc34 // c5, c4 = 0.0083333..., 0.0416715 .quad 0x4034000000000018, 0x4027ff4991a5ebc5 // c3/c5 = 0.1666666.../c5, c2/c4 = 0.5/c4 .quad 0x0000000000000000, 0x3ff0000000000000 // 0, 1 sinhf_table: .quad 0x3ff0000000000001, 0x0000000000000000 // cosh(0/16) + eps, sinh(0/16) .quad 0x3ff00800aab05b20, 0x3fb002aacccd9cdd // cosh(1/16), sinh(1/16) .quad 0x3ff0200aac16db6f, 0x3fc00aaccd00d2f1 // cosh(2/16), sinh(2/16) .quad 0x3ff048361035cdfa, 0x3fc8241036ac51dd // cosh(3/16), sinh(3/16) .quad 0x3ff080ab05ca6146, 0x3fd02accd9d08102 // cosh(4/16), sinh(4/16) .quad 0x3ff0c9a2067ebbda, 0x3fd453bdbe16906c // cosh(5/16), sinh(5/16) .quad 0x3ff123640f685b59, 0x3fd8910411ce5046 // cosh(6/16), sinh(6/16) .quad 0x3ff18e4aea0b3f4a, 0x3fdce6dd75bf0317 // cosh(7/16), sinh(7/16) .quad 0x3ff20ac1862ae8d0, 0x3fe0acd00fe63b97 // cosh(8/16), sinh(8/16) .quad 0x3ff2994464c307c6, 0x3fe2f6df98c4b901 // cosh(9/16), sinh(9/16) .quad 0x3ff33a621492d6da, 0x3fe553e795dc19cd // cosh(10/16), sinh(10/16) .quad 0x3ff3eebbc0b7bc6c, 0x3fe7c645419678b8 // cosh(11/16), sinh(11/16) .quad 0x3ff4b705d1e5d6a8, 0x3fea506b2dd3c690 // cosh(12/16), sinh(12/16) .quad 0x3ff59408a2dfb8da, 0x3fecf4e3b6afe2ad // cosh(13/16), sinh(13/16) .quad 0x3ff686a148e1e0d1, 0x3fefb6538d14eafc // cosh(14/16), sinh(14/16) .quad 0x3ff78fc270ca6067, 0x3ff14bbe2dd24609 // cosh(15/16), sinh(15/16) .quad 0x3ff8b07551d9f550, 0x3ff2cd9fc44eb982 // cosh(16/16), sinh(16/16) .quad 0x3ff9e9dab7016488, 0x3ff462508bbf80a9 // cosh(17/16), sinh(17/16) .quad 0x3ffb3d2c1fc47ccc, 0x3ff60b6556a69204 // cosh(18/16), sinh(18/16) .quad 0x3ffcabbcf9d3bb3f, 0x3ff7ca875d3c6932 // cosh(19/16), sinh(19/16) .quad 0x3ffe36fbf49645fa, 0x3ff9a175e6cbafe6 // cosh(20/16), sinh(20/16) .quad 0x3fffe0746ff7e2d8, 0x3ffb9208091dcfc6 // cosh(21/16), sinh(21/16) .quad 0x4000d4e803f4eb7f, 0x3ffd9e2e7fb7fef3 // cosh(22/16), sinh(22/16) .quad 0x4001ca6c1f11287b, 0x3fffc7f59cc02b95 // cosh(23/16), sinh(23/16) .quad 0x4002d1bc21e22022, 0x400108c3aabd6a60 // cosh(24/16), sinh(24/16) .quad 0x4003ebdf725cb441, 0x40023e96b6373d25 // cosh(25/16), sinh(25/16) .quad 0x400519f04b551971, 0x400386a9ddab7a8a // cosh(26/16), sinh(26/16) .quad 0x40065d1cd6d130fb, 0x4004e2454f996e13 // cosh(27/16), sinh(27/16) .quad 0x4007b6a85c4bbdc2, 0x400652c4c46b9bbb // cosh(28/16), sinh(28/16) .quad 0x400927ec8416d084, 0x4007d998da4d257b // cosh(29/16), sinh(29/16) .quad 0x400ab25ab120e8ea, 0x4009784885e6af4c // cosh(30/16), sinh(30/16) .quad 0x400c577d7276ad4e, 0x400b307299739d43 // cosh(31/16), sinh(31/16) .quad 0x400e18fa0df2d9bc, 0x400d03cf63b6e19f // cosh(32/16), sinh(32/16) .quad 0x400ff89225a736fd, 0x400ef432686e7235 // cosh(33/16), sinh(33/16) .quad 0x4010fc12bcd212e7, 0x401081c619fefea9 // cosh(34/16), sinh(34/16) .quad 0x40120cd9e3f055a1, 0x401199f6261257ea // cosh(35/16), sinh(35/16) .quad 0x40132faf66118731, 0x4012c3c19fd775d1 // cosh(36/16), sinh(36/16) .quad 0x401465b630f50d1d, 0x401400526b99e613 // cosh(37/16), sinh(37/16) .quad 0x4015b024653c8da5, 0x401550e53487b291 // cosh(38/16), sinh(38/16) .quad 0x401710448ca66a4d, 0x4016b6caa976f3de // cosh(39/16), sinh(39/16) .quad 0x40188776e4b30aa3, 0x40183368cdb0b6d3 // cosh(40/16), sinh(40/16) .quad 0x401a1732beffb81f, 0x4019c83c5f121c3c // cosh(41/16), sinh(41/16) .quad 0x401bc107f8b78338, 0x401b76da52e9f182 // cosh(42/16), sinh(42/16) .quad 0x401d86a08a91c20b, 0x401d40f16b0fbfb3 // cosh(43/16), sinh(43/16) .quad 0x401f69c232ee483d, 0x401f284be4c989bd // cosh(44/16), sinh(44/16) .quad 0x4020b6281ddccbf9, 0x40209768a197a1bd // cosh(45/16), sinh(45/16) .quad 0x4021c826aeef8ae6, 0x4021ab441b6b45a1 // cosh(46/16), sinh(46/16) .quad 0x4022ebeee2166d42, 0x4022d0cc52573d2d // cosh(47/16), sinh(47/16) .quad 0x402422a497d6185e, 0x40240926e70949ae // cosh(48/16), sinh(48/16) .quad 0x40256d7e9fc9a2ac, 0x4025558c4e1e87b4 // cosh(49/16), sinh(49/16) .quad 0x4026cdc7ef8c1654, 0x4026b74908b216cf // cosh(50/16), sinh(50/16) .quad 0x402844e0edc9a1a2, 0x40282fbef0f9eaff // cosh(51/16), sinh(51/16) .quad 0x4029d440d2c3a213, 0x4029c0669c3e8083 // cosh(52/16), sinh(52/16) .quad 0x402b7d771fa82b6c, 0x402b6ad0d38f8723 // cosh(53/16), sinh(53/16) .quad 0x402d422d2e3481ad, 0x402d30a824ae5918 // cosh(54/16), sinh(54/16) .quad 0x402f2427da3249ad, 0x402f13b28cbf4962 // cosh(55/16), sinh(55/16) .quad 0x403092a4a33c887b, 0x40308ae99f364f3b // cosh(56/16), sinh(56/16) .quad 0x4031a3c95f9caa21, 0x40319c8642a0c10e // cosh(57/16), sinh(57/16) .quad 0x4032c6935db9bbdc, 0x4032bfc0e41034cd // cosh(58/16), sinh(58/16) .quad 0x4033fc257fce2961, 0x4033f5bcd66bcbd3 // cosh(59/16), sinh(59/16) .quad 0x403545b571c910c9, 0x40353fb02f7bbd05 // cosh(60/16), sinh(60/16) .quad 0x4036a48cdf1400d7, 0x40369ee4fe18f513 // cosh(61/16), sinh(61/16) .quad 0x40381a0abc59dc70, 0x403814ba94577184 // cosh(62/16), sinh(62/16) .quad 0x4039a7a4a698c57c, 0x4039a2a6e6f59c8a // cosh(63/16), sinh(63/16) .quad 0x403b4ee858de3e80, 0x403b4a3803703631 // cosh(64/16), sinh(64/16) .quad 0x403d117d3a235e29, 0x403d0d159e30fdff // cosh(65/16), sinh(65/16) .quad 0x403ef12604d71220, 0x403eed02ba666cf1 // cosh(66/16), sinh(66/16) .quad 0x404077e144df0f63, 0x404075efb6963d64 // cosh(67/16), sinh(67/16) .quad 0x404187a8c7f5f0ae, 0x404185d55ee4de8c // cosh(68/16), sinh(68/16) .quad 0x4042a8f969d9fab0, 0x4042a7425270a2a2 // cosh(69/16), sinh(69/16) .quad 0x4043dcf49349ecb2, 0x4043db58164c4cde // cosh(70/16), sinh(70/16) .quad 0x404524ce591a551f, 0x4045234ad9e90f00 // cosh(71/16), sinh(71/16) .quad 0x404681ceb0641358, 0x40468062ab5fa9fc // cosh(72/16), sinh(72/16) .quad 0x4047f552b694c5ea, 0x4047f3fcbf99de24 // cosh(73/16), sinh(73/16) .quad 0x404980ce0ea950eb, 0x40497f8ccfa46fa0 // cosh(74/16), sinh(74/16) .quad 0x404b25cc54efd428, 0x404b249e8c872e52 // cosh(75/16), sinh(75/16) .quad 0x404ce5f2aac4f20f, 0x404ce4d72b16f828 // cosh(76/16), sinh(76/16) .quad 0x404ec3015bd8459a, 0x404ec1f7094da8e6 // cosh(77/16), sinh(77/16) .quad 0x40505f6acf4eb766, 0x40505eedb766b932 // cosh(78/16), sinh(78/16) .quad 0x40516db5b8d52617, 0x40516d403528230b // cosh(79/16), sinh(79/16) .quad 0x40528d6fcbeff3aa, 0x40528d0166f07374 // cosh(80/16), sinh(80/16) .quad 0x4053bfb8daad33cb, 0x4053bf5125ed0389 // cosh(81/16), sinh(81/16) .quad 0x405505c347a2941d, 0x40550561db644eef // cosh(82/16), sinh(82/16) .quad 0x405660d538697af3, 0x40566079b338c3f3 // cosh(83/16), sinh(83/16) .quad 0x4057d249dbdfcf6b, 0x4057d1f3e22fd533 // cosh(84/16), sinh(84/16) .quad 0x40595b92c573c6e2, 0x40595b420143af17 // cosh(85/16), sinh(85/16) .quad 0x405afe395ed62077, 0x405afded7f5affc4 // cosh(86/16), sinh(86/16) .quad 0x405cbbe071849fb1, 0x405cbb992ad8a81e // cosh(87/16), sinh(87/16) .quad 0x405e9645c9b6718b, 0x405e9602d48d0661 // cosh(88/16), sinh(88/16) .quad 0x406047a1fa26c59e, 0x4060478286d5f738 // cosh(89/16), sinh(89/16) .quad 0x4061546a0cc58c9a, 0x4061544c8142b58e // cosh(90/16), sinh(90/16) .quad 0x40627287fb30ed34, 0x4062726c39ee144b // cosh(91/16), sinh(91/16) .quad 0x4063a319fb2ff225, 0x4063a2ffe8698457 // cosh(92/16), sinh(92/16) .quad 0x4064e750b824f30a, 0x4064e73839c5fd9c // cosh(93/16), sinh(93/16) .quad 0x4066407083d25b35, 0x40664059815a7498 // cosh(94/16), sinh(94/16) .quad 0x4067afd29ac773cd, 0x4067afbcfd32392a // cosh(95/16), sinh(95/16) .quad 0x406936e67db9b919, 0x406936d22f67c805 // cosh(96/16), sinh(96/16) .quad 0x406ad73361243111, 0x406ad7204dc5865b // cosh(97/16), sinh(97/16) .quad 0x406c9259b49c812f, 0x406c9247c91c272c // cosh(98/16), sinh(98/16) .quad 0x406e6a14c3653934, 0x406e6a03edd63132 // cosh(99/16), sinh(99/16) .quad 0x4070301e37ef03f1, 0x407030164fb4add6 // cosh(100/16), sinh(100/16) .quad 0x40713b6385c6b76d, 0x40713b5c1830ac2d // cosh(101/16), sinh(101/16) .quad 0x407257e5a6ce1350, 0x407257deac6e1e63 // cosh(102/16), sinh(102/16) .quad 0x407386c134dc6c0c, 0x407386baa6b7989b // cosh(103/16), sinh(103/16) .quad 0x4074c92524bd9ddc, 0x4074c91efc453b37 // cosh(104/16), sinh(104/16) .quad 0x40762053f540188a, 0x4076204e2c4b2aea // cosh(105/16), sinh(105/16) .quad 0x40778da4f1ce8eab, 0x40778d9f8293a5b4 // cosh(106/16), sinh(106/16) .quad 0x4079128589d7fce2, 0x407912806ee769b9 // cosh(107/16), sinh(107/16) .quad 0x407ab07abe5d8dd7, 0x407ab075f29bf2fb // cosh(108/16), sinh(108/16) .quad 0x407c6922a7140735, 0x407c691e25b53cb7 // cosh(109/16), sinh(109/16) .quad 0x407e3e36109e018f, 0x407e3e31d5204885 // cosh(110/16), sinh(110/16) .quad 0x408018c51abea3f7, 0x408018c31dd26428 // cosh(111/16), sinh(111/16) .quad 0x4081228949ba3a8c, 0x408122876ba380c9 // cosh(112/16), sinh(112/16) .quad 0x40823d716f972bb3, 0x40823d6fae77b96b // cosh(113/16), sinh(113/16) .quad 0x40836a988c0f760c, 0x40836a96e626065d // cosh(114/16), sinh(114/16) .quad 0x4084ab2bdf58ffc1, 0x4084ab2a52ff8611 // cosh(115/16), sinh(115/16) .quad 0x4086006c177ee7f2, 0x4086006aa328e9c0 // cosh(116/16), sinh(116/16) .quad 0x40876bae912a4be4, 0x40876bad33635429 // cosh(117/16), sinh(117/16) .quad 0x4088ee5ead1b6375, 0x4088ee5d64858e12 // cosh(118/16), sinh(118/16) .quad 0x408a89ff3ba88a65, 0x408a89fe06fb2623 // cosh(119/16), sinh(119/16) .quad 0x408c402bffaed3ce, 0x408c402addb5198d // cosh(120/16), sinh(120/16) .quad 0x408e129b4a773895, 0x408e129a3a0f1671 // cosh(121/16), sinh(121/16) .quad 0x4090018fd9163433, 0x4090018f5922afc4 // cosh(122/16), sinh(122/16) .quad 0x409109d4f24bebc3, 0x409109d47a18f5c9 // cosh(123/16), sinh(123/16) .quad 0x409223254bfc76bb, 0x40922324db11d23c // cosh(124/16), sinh(124/16) .quad 0x40934e9a4df3aa86, 0x40934e99e3e06372 // cosh(125/16), sinh(125/16) .quad 0x40948d5f8628be20, 0x40948d5f2282b85b // cosh(126/16), sinh(126/16) .quad 0x4095e0b3d46538ab, 0x4095e0b376c8c5e0 // cosh(127/16), sinh(127/16) .quad 0x409749eaa93f4e76, 0x409749ea514eca66 // cosh(128/16), sinh(128/16) .quad 0x4098ca6d59a6c18c, 0x4098ca6d070a345e // cosh(129/16), sinh(129/16) .quad 0x409a63bc8857eedb, 0x409a63bc3abcb51f // cosh(130/16), sinh(130/16) .quad 0x409c1771a69e9936, 0x409c17715db7113a // cosh(131/16), sinh(131/16) .quad 0x409de7408de954fc, 0x409de740496c9126 // cosh(132/16), sinh(132/16) .quad 0x409fd4f933c74a08, 0x409fd4f8f370c7de // cosh(133/16), sinh(133/16) .quad 0x40a0f144bd0236f5, 0x40a0f1449ec9e8c6 // cosh(134/16), sinh(134/16) .quad 0x40a208ff8e5a3cb1, 0x40a208ff71f6a696 // cosh(135/16), sinh(135/16) .quad 0x40a332c4e00d669f, 0x40a332c4c56222a3 // cosh(136/16), sinh(136/16) .quad 0x40a46fbe903ead25, 0x40a46fbe77310dcc // cosh(137/16), sinh(137/16) .quad 0x40a5c129b30946fa, 0x40a5c1299b803c8e // cosh(138/16), sinh(138/16) .quad 0x40a72857cfaf3193, 0x40a72857b9933114 // cosh(139/16), sinh(139/16) .quad 0x40a8a6b0323c94ae, 0x40a8a6b01d778043 // cosh(140/16), sinh(140/16) .quad 0x40aa3db152f1c077, 0x40aa3db13f6ed151 // cosh(141/16), sinh(141/16) .quad 0x40abeef254db4e46, 0x40abeef24286ffd5 // cosh(142/16), sinh(142/16) .quad 0x40adbc249d171bee, 0x40adbc248bdf185d // cosh(143/16), sinh(143/16) .quad 0x40afa715845d8894, 0x40afa7157430966f // cosh(144/16), sinh(144/16) .quad 0x40b0d8d812405031, 0x40b0d8d80aa748b0 // cosh(145/16), sinh(145/16) .quad 0x40b1eeffa1d76e64, 0x40b1eeff9ab43ec9 // cosh(146/16), sinh(146/16) .quad 0x40b31717afb27271, 0x40b31717a8fdf6f5 // cosh(147/16), sinh(147/16) .quad 0x40b452486c8cb5c2, 0x40b452486640395b // cosh(148/16), sinh(148/16) .quad 0x40b5a1cd2368027d, 0x40b5a1cd1d7d3828 // cosh(149/16), sinh(149/16) .quad 0x40b706f574f1dc72, 0x40b706f56f62d8e6 // cosh(150/16), sinh(150/16) .quad 0x40b88326a740279b, 0x40b88326a2075b5e // cosh(151/16), sinh(151/16) .quad 0x40ba17dd0b3504d5, 0x40ba17dd064d36ac // cosh(152/16), sinh(152/16) .quad 0x40bbc6ad78ef6678, 0x40bbc6ad7453ae2b // cosh(153/16), sinh(153/16) .quad 0x40bd9146e4c4ed16, 0x40bd9146e070ae8b // cosh(154/16), sinh(154/16) .quad 0x40bf79740e5a27ff, 0x40bf79740a490e9c // cosh(155/16), sinh(155/16) .quad 0x40c0c08ea5c43ade, 0x40c0c08ea3db3808 // cosh(156/16), sinh(156/16) .quad 0x40c1d525386e484e, 0x40c1d52536a2e627 // cosh(157/16), sinh(157/16) .quad 0x40c2fb926ccb3747, 0x40c2fb926b1baa48 // cosh(158/16), sinh(158/16) .quad 0x40c434fcc8994fcd, 0x40c434fcc703e844 // cosh(159/16), sinh(159/16) .quad 0x40c5829dd053712d, 0x40c5829dced69992 // cosh(160/16), sinh(160/16) .quad 0x40c6e5c340cfae1d, 0x40c6e5c33f69e977 // cosh(161/16), sinh(161/16) .quad 0x40c85fd05d17f374, 0x40c85fd05bc7dbe2 // cosh(162/16), sinh(162/16) .quad 0x40c9f23f51caae03, 0x40c9f23f508ef350 // cosh(163/16), sinh(163/16) .quad 0x40cb9ea2af66edc5, 0x40cb9ea2ae3e541e // cosh(164/16), sinh(164/16) .quad 0x40cd66a6fcfe721a, 0x40cd66a6fbe7d0cb // cosh(165/16), sinh(165/16) .quad 0x40cf4c1464e0729e, 0x40cf4c1463dab2ef // cosh(166/16), sinh(166/16) .quad 0x40d0a8683e74f99a, 0x40d0a8683dfa07a7 // cosh(167/16), sinh(167/16) .quad 0x40d1bb7016220cc0, 0x40d1bb7015ae8db6 // cosh(168/16), sinh(168/16) .quad 0x40d2e034d83b3566, 0x40d2e034d7ceb5bc // cosh(169/16), sinh(169/16) .quad 0x40d417db61e917bf, 0x40d417db61832aee // cosh(170/16), sinh(170/16) .quad 0x40d5639b73aecacb, 0x40d5639b734f0adb // cosh(171/16), sinh(171/16) .quad 0x40d6c4c0e94456f9, 0x40d6c4c0e8ea6424 // cosh(172/16), sinh(172/16) .quad 0x40d83cad058e16c7, 0x40d83cad05399712 // cosh(173/16), sinh(173/16) .quad 0x40d9ccd7d3fd0c53, 0x40d9ccd7d3adab38 // cosh(174/16), sinh(174/16) .quad 0x40db76d1a0b9a9b1, 0x40db76d1a06f17c7 // cosh(175/16), sinh(175/16) // Shamelessly stolen from Ians expf code. (sinhf is expf/2 for |x| > 11) expf_c: .quad 0x40bc03f30399c376, 0x3ff000000001ea2a // c4/c8, c0 .quad 0x408f10e7f73e6d8f, 0x3fe62e42fd0933ee // c5/c8, c1 .quad 0x405cb616a9384e69, 0x3fcebfbdfd0f0afa // c6/c8, c2 .quad 0x4027173ebd288ba1, 0x3fac6b0a74f15403 // c7/c8, c3 .quad 0x3eb67fe1dc3105ba // c8 .literal8 e_over_2: .quad 0x3ff5bf0a8b145769 // 0x1.5bf0a8b145769p+0 one_over_ln2: .quad 0x3ff71547652b82fe // 0x1.71547652b82fep+0 lookup_mask: .quad 0x7ffff00000000000 // exponent and 8 bits of mantissa sixteen: .quad 0x4030000000000000 // 16 .text #if defined( __x86_64__ ) #define RELATIVE_ADDR(_a) (_a)( %rip ) #define RELATIVE_ADDR_B(_a) (_a)( %rip ) #else #define RELATIVE_ADDR(_a) (_a)-sinhf_body( %ecx ) #define RELATIVE_ADDR_B(_a) (_a)-sinhf_body_eleven( %ecx ) .align 4 sinhf_pic: movl (%esp), %ecx // Copy address of this instruction to %ecx ret #endif ENTRY(sinhf) #if defined(__i386__) movl FRAME_SIZE(STACKP), %eax movss FRAME_SIZE(STACKP), %xmm0 #else movd %xmm0, %eax #endif andl $0x7fffffff, %eax // |x| movd %eax, %xmm1 cmpl $0x41300000, %eax // Ours goes up to 11 jge 2f // Jump if |x| >= 11f #if defined( __i386__ ) calll sinhf_pic sinhf_body: #endif // |x| < 11, table-based reduction xorpd %xmm6, %xmm6 // zero out xmm6 cvtss2sd %xmm1, %xmm6 // xmm6 <-- (double)|x| andnps %xmm0, %xmm1 // xmm1 <-- signbit(x) movapd %xmm6, %xmm0 // xmm0 <-- |x| movsd RELATIVE_ADDR(sixteen), %xmm3 // xmm3 <-- 16 addsd %xmm3, %xmm6 // xmm6 <-- 16 + |x| (this puts our two 4-bit lookup values in the first two movsd RELATIVE_ADDR(lookup_mask), %xmm4 // mantissa bits of xmm6) andpd %xmm4, %xmm6 // xmm6 <-- 16 + h subsd %xmm6, %xmm3 // xmm3 <-- -h addsd %xmm3, %xmm0 // xmm0 <-- l (|x| = h + l) lea RELATIVE_ADDR(sinhf_table), DX_P movapd -48(DX_P), %xmm3 // xmm3 <-- { c5, c4 } #if defined( __SSE3__ ) movddup %xmm0, %xmm2 // xmm2 <-- { l , l } #else movapd %xmm0, %xmm2 unpcklpd %xmm2, %xmm2 // xmm2 <-- { l , l } #endif addpd -16(DX_P), %xmm0 // xmm0 <-- { l , 1 } mulpd %xmm0, %xmm3 // xmm3 <-- { c5l, c4 } mulpd %xmm2, %xmm2 // xmm2 <-- { l2 , l2 } psrlq $40, %xmm6 // shift the bits of h into position for a lookup movd %xmm6, %eax andl $0x00000ff0, %eax // mask the bits of h movapd (DX_P,AX_P,1), %xmm5 // xmm5 <-- { sinh h, cosh h } mulpd %xmm2, %xmm3 // xmm3 <-- { c5l3, c4l2 } addpd -32(DX_P), %xmm2 // xmm2 <-- { c3/c5 + l2, c2/c4 + l2 } mulpd %xmm3, %xmm2 // xmm2 <-- { c3l3 + c5l5, c2l2 + c4l2 } addpd %xmm2, %xmm0 // xmm0 <-- { l + c3l3 + c5l5, 1 + c2l2 + c4l2 } = { sinh l, cosh l } mulpd %xmm5, %xmm0 // xmm0 <-- { cosh h sinh l, sinh h cosh l } #if defined(__SSE3__) haddpd %xmm0, %xmm0 #else movhlps %xmm0, %xmm2 addsd %xmm2, %xmm0 #endif cvtsd2ss %xmm0, %xmm0 orps %xmm1, %xmm0 // use the stored signbit. #if defined(__i386__) movss %xmm0, FRAME_SIZE( STACKP ) flds FRAME_SIZE( STACKP ) #endif ret 2: // |x| >= 11, cmpl $0x42b2d4fc, %eax // Compare to overflow threshold ja 4f // Jump if |x| > overflow threshold || isnan(x) #if defined( __i386__ ) calll sinhf_pic sinhf_body_eleven: #endif cvtss2sd %xmm1, %xmm2 // xmm2 <-- (double)|x| andnps %xmm0, %xmm1 // xmm1 <-- signbit(x) // xmm1 holds sign(x), xmm2 holds (double)|x| mulsd RELATIVE_ADDR_B(one_over_ln2), %xmm2 subsd RELATIVE_ADDR_B(one_over_ln2), %xmm2 // xmm2 <-- (|x| - 1) / ln(2) movl $1023, %edx // double precision bias // extract fractional part cvttsd2si %xmm2, %eax addl %eax, %edx // edx <-- biased exponent of result cvtsi2sd %eax, %xmm0 movd %edx, %xmm7 psllq $52, %xmm7 // xmm7 <-- exponent of result subsd %xmm0, %xmm2 // fractional part of scaled |x| - 1 lea RELATIVE_ADDR_B(expf_c), DX_P mulsd RELATIVE_ADDR_B(e_over_2), %xmm7 // c0 + c1x1 + c2x2 + c3x3 + c4x4 + c5x5 + c6x6 + c7x7 + c8x8 #if defined( __SSE3__ ) movddup %xmm2, %xmm0 // { x, x } #else movapd %xmm2, %xmm0 // x unpcklpd %xmm0, %xmm0 // { x, x } #endif mulsd %xmm2, %xmm2 // x*x movapd %xmm0, %xmm3 mulpd 48(DX_P), %xmm0 // { c3x, (c7/c8)x } mulpd 16(DX_P), %xmm3 // { c1x, (c5/c8)x } #if defined( __SSE3__ ) movddup %xmm2, %xmm4 // { xx, xx } #else movapd %xmm2, %xmm4 // xx unpcklpd %xmm4, %xmm4 // { xx, xx } #endif mulsd %xmm2, %xmm2 // xx*xx addpd 32(DX_P), %xmm0 // { c2 + c3x, (c6/c8) + (c7/c8)x } addpd (DX_P), %xmm3 // { c0 + c1x, (c4/c8) + (c5/c8)x } mulpd %xmm4, %xmm0 // { c2xx + c3xxx, (c6/c8)xx + (c7/c8)xxx } addsd %xmm2, %xmm3 // { c0 + c1x, (c4/c8) + (c5/c8)x + xxxx } mulsd 64(DX_P), %xmm2 // c8 * xxxx addpd %xmm0, %xmm3 // { c0 + c1x + c2xx + c3xxx, (c4/c8) + (c5/c8)x + (c6/c8)xx + (c7/c8)xxx + xxxx } movhlps %xmm3, %xmm6 // { ?, c0 + c1x + c2xx + c3xxx } mulsd %xmm2, %xmm3 // { ..., c8xxxx* ((c4/c8) + (c5/c8)x + (c6/c8)xx + (c7/c8)xxx + xxxx) } addsd %xmm6, %xmm3 // c0 + c1x + c2xx + c3xxx + c4xxxx + c5xxxxx + c6xxxxxx + c7xxxxxxx + c8xxxxxxxxx mulsd %xmm7, %xmm3 // 2**i * {c0 + c1x + c2xx + c3xxx + c4xxxx + c5xxxxx + c6xxxxxx + c7xxxxxxx + c8xxxxxxxxx} cvtsd2ss %xmm3, %xmm0 orps %xmm1, %xmm0 // restore sign bit #if defined(__i386__) movss %xmm0, FRAME_SIZE( STACKP ) flds FRAME_SIZE( STACKP ) #endif ret 4: // |x| > overflow threshold || isnan(x) cmpl $0x7f800000, %eax jge 5f // overflow case movl $0x7f7fffff, %ecx movd %ecx, %xmm1 mulss %xmm1, %xmm0 // xmm0 <-- x * hugevalf #if defined(__i386__) movss %xmm0, FRAME_SIZE( STACKP ) flds FRAME_SIZE( STACKP ) #endif ret 5: // x = inf, nan addss %xmm0, %xmm0 #if defined(__i386__) movss %xmm0, FRAME_SIZE( STACKP ) flds FRAME_SIZE( STACKP ) #endif ret