| /** |
| * This file has no copyright assigned and is placed in the Public Domain. |
| * This file is part of the w64 mingw-runtime package. |
| * No warranty is given; refer to the file DISCLAIMER.PD within this package. |
| */ |
| #include "cephes_mconf.h" |
| #ifndef _SET_ERRNO |
| #define _SET_ERRNO(x) |
| #endif |
| |
| |
| /* Table size */ |
| #define NXT 32 |
| /* log2(Table size) */ |
| #define LNXT 5 |
| |
| #ifdef UNK |
| /* log(1+x) = x - .5x^2 + x^3 * P(z)/Q(z) |
| * on the domain 2^(-1/32) - 1 <= x <= 2^(1/32) - 1 |
| */ |
| static uLD P[4] = { |
| { { 8.3319510773868690346226E-4L } }, |
| { { 4.9000050881978028599627E-1L } }, |
| { { 1.7500123722550302671919E0L } }, |
| { { 1.4000100839971580279335E0L } } |
| }; |
| static uLD Q[3] = { |
| { { 5.2500282295834889175431E0L } }, |
| { { 8.4000598057587009834666E0L } }, |
| { { 4.2000302519914740834728E0L } } |
| }; |
| /* A[i] = 2^(-i/32), rounded to IEEE long double precision. |
| * If i is even, A[i] + B[i/2] gives additional accuracy. |
| */ |
| static uLD A[33] = { |
| { { 1.0000000000000000000000E0L } }, |
| { { 9.7857206208770013448287E-1L } }, |
| { { 9.5760328069857364691013E-1L } }, |
| { { 9.3708381705514995065011E-1L } }, |
| { { 9.1700404320467123175367E-1L } }, |
| { { 8.9735453750155359320742E-1L } }, |
| { { 8.7812608018664974155474E-1L } }, |
| { { 8.5930964906123895780165E-1L } }, |
| { { 8.4089641525371454301892E-1L } }, |
| { { 8.2287773907698242225554E-1L } }, |
| { { 8.0524516597462715409607E-1L } }, |
| { { 7.8799042255394324325455E-1L } }, |
| { { 7.7110541270397041179298E-1L } }, |
| { { 7.5458221379671136985669E-1L } }, |
| { { 7.3841307296974965571198E-1L } }, |
| { { 7.2259040348852331001267E-1L } }, |
| { { 7.0710678118654752438189E-1L } }, |
| { { 6.9195494098191597746178E-1L } }, |
| { { 6.7712777346844636413344E-1L } }, |
| { { 6.6261832157987064729696E-1L } }, |
| { { 6.4841977732550483296079E-1L } }, |
| { { 6.3452547859586661129850E-1L } }, |
| { { 6.2092890603674202431705E-1L } }, |
| { { 6.0762367999023443907803E-1L } }, |
| { { 5.9460355750136053334378E-1L } }, |
| { { 5.8186242938878875689693E-1L } }, |
| { { 5.6939431737834582684856E-1L } }, |
| { { 5.5719337129794626814472E-1L } }, |
| { { 5.4525386633262882960438E-1L } }, |
| { { 5.3357020033841180906486E-1L } }, |
| { { 5.2213689121370692017331E-1L } }, |
| { { 5.1094857432705833910408E-1L } }, |
| { { 5.0000000000000000000000E-1L } } |
| }; |
| static uLD B[17] = { |
| { { 0.0000000000000000000000E0L } }, |
| { { 2.6176170809902549338711E-20L } }, |
| { { -1.0126791927256478897086E-20L } }, |
| { { 1.3438228172316276937655E-21L } }, |
| { { 1.2207982955417546912101E-20L } }, |
| { { -6.3084814358060867200133E-21L } }, |
| { { 1.3164426894366316434230E-20L } }, |
| { { -1.8527916071632873716786E-20L } }, |
| { { 1.8950325588932570796551E-20L } }, |
| { { 1.5564775779538780478155E-20L } }, |
| { { 6.0859793637556860974380E-21L } }, |
| { { -2.0208749253662532228949E-20L } }, |
| { { 1.4966292219224761844552E-20L } }, |
| { { 3.3540909728056476875639E-21L } }, |
| { { -8.6987564101742849540743E-22L } }, |
| { { -1.2327176863327626135542E-20L } }, |
| { { 0.0000000000000000000000E0L } } |
| }; |
| |
| /* 2^x = 1 + x P(x), |
| * on the interval -1/32 <= x <= 0 |
| */ |
| static uLD R[] = { |
| { { 1.5089970579127659901157E-5L } }, |
| { { 1.5402715328927013076125E-4L } }, |
| { { 1.3333556028915671091390E-3L } }, |
| { { 9.6181291046036762031786E-3L } }, |
| { { 5.5504108664798463044015E-2L } }, |
| { { 2.4022650695910062854352E-1L } }, |
| { { 6.9314718055994530931447E-1L } } |
| }; |
| |
| #define douba(k) A[k].d |
| #define doubb(k) B[k].d |
| #define MEXP (NXT*16384.0L) |
| /* The following if denormal numbers are supported, else -MEXP: */ |
| #ifdef DENORMAL |
| #define MNEXP (-NXT*(16384.0L+64.0L)) |
| #else |
| #define MNEXP (-NXT*16384.0L) |
| #endif |
| /* log2(e) - 1 */ |
| #define LOG2EA 0.44269504088896340735992L |
| #endif |
| |
| |
| #ifdef IBMPC |
| static const uLD P[] = { |
| { { 0xb804,0xa8b7,0xc6f4,0xda6a,0x3ff4, 0, 0, 0 } }, |
| { { 0x7de9,0xcf02,0x58c0,0xfae1,0x3ffd, 0, 0, 0 } }, |
| { { 0x405a,0x3722,0x67c9,0xe000,0x3fff, 0, 0, 0 } }, |
| { { 0xcd99,0x6b43,0x87ca,0xb333,0x3fff, 0, 0, 0 } } |
| }; |
| static const uLD Q[] = { |
| { { 0x6307,0xa469,0x3b33,0xa800,0x4001, 0, 0, 0 } }, |
| { { 0xfec2,0x62d7,0xa51c,0x8666,0x4002, 0, 0, 0 } }, |
| { { 0xda32,0xd072,0xa5d7,0x8666,0x4001, 0, 0, 0 } } |
| }; |
| static const uLD A[] = { |
| { { 0x0000,0x0000,0x0000,0x8000,0x3fff, 0, 0, 0 } }, |
| { { 0x033a,0x722a,0xb2db,0xfa83,0x3ffe, 0, 0, 0 } }, |
| { { 0xcc2c,0x2486,0x7d15,0xf525,0x3ffe, 0, 0, 0 } }, |
| { { 0xf5cb,0xdcda,0xb99b,0xefe4,0x3ffe, 0, 0, 0 } }, |
| { { 0x392f,0xdd24,0xc6e7,0xeac0,0x3ffe, 0, 0, 0 } }, |
| { { 0x48a8,0x7c83,0x06e7,0xe5b9,0x3ffe, 0, 0, 0 } }, |
| { { 0xe111,0x2a94,0xdeec,0xe0cc,0x3ffe, 0, 0, 0 } }, |
| { { 0x3755,0xdaf2,0xb797,0xdbfb,0x3ffe, 0, 0, 0 } }, |
| { { 0x6af4,0xd69d,0xfcca,0xd744,0x3ffe, 0, 0, 0 } }, |
| { { 0xe45a,0xf12a,0x1d91,0xd2a8,0x3ffe, 0, 0, 0 } }, |
| { { 0x80e4,0x1f84,0x8c15,0xce24,0x3ffe, 0, 0, 0 } }, |
| { { 0x27a3,0x6e2f,0xbd86,0xc9b9,0x3ffe, 0, 0, 0 } }, |
| { { 0xdadd,0x5506,0x2a11,0xc567,0x3ffe, 0, 0, 0 } }, |
| { { 0x9456,0x6670,0x4cca,0xc12c,0x3ffe, 0, 0, 0 } }, |
| { { 0x36bf,0x580c,0xa39f,0xbd08,0x3ffe, 0, 0, 0 } }, |
| { { 0x9ee9,0x62fb,0xaf47,0xb8fb,0x3ffe, 0, 0, 0 } }, |
| { { 0x6484,0xf9de,0xf333,0xb504,0x3ffe, 0, 0, 0 } }, |
| { { 0x2590,0xd2ac,0xf581,0xb123,0x3ffe, 0, 0, 0 } }, |
| { { 0x4ac6,0x42a1,0x3eea,0xad58,0x3ffe, 0, 0, 0 } }, |
| { { 0x0ef8,0xea7c,0x5ab4,0xa9a1,0x3ffe, 0, 0, 0 } }, |
| { { 0x38ea,0xb151,0xd6a9,0xa5fe,0x3ffe, 0, 0, 0 } }, |
| { { 0x6819,0x0c49,0x4303,0xa270,0x3ffe, 0, 0, 0 } }, |
| { { 0x11ae,0x91a1,0x3260,0x9ef5,0x3ffe, 0, 0, 0 } }, |
| { { 0x5539,0xd54e,0x39b9,0x9b8d,0x3ffe, 0, 0, 0 } }, |
| { { 0xa96f,0x8db8,0xf051,0x9837,0x3ffe, 0, 0, 0 } }, |
| { { 0x0961,0xfef7,0xefa8,0x94f4,0x3ffe, 0, 0, 0 } }, |
| { { 0xc336,0xab11,0xd373,0x91c3,0x3ffe, 0, 0, 0 } }, |
| { { 0x53c0,0x45cd,0x398b,0x8ea4,0x3ffe, 0, 0, 0 } }, |
| { { 0xd6e7,0xea8b,0xc1e3,0x8b95,0x3ffe, 0, 0, 0 } }, |
| { { 0x8527,0x92da,0x0e80,0x8898,0x3ffe, 0, 0, 0 } }, |
| { { 0x7b15,0xcc48,0xc367,0x85aa,0x3ffe, 0, 0, 0 } }, |
| { { 0xa1d7,0xac2b,0x8698,0x82cd,0x3ffe, 0, 0, 0 } }, |
| { { 0x0000,0x0000,0x0000,0x8000,0x3ffe, 0, 0, 0 } } |
| }; |
| static const uLD B[] = { |
| { { 0x0000,0x0000,0x0000,0x0000,0x0000, 0, 0, 0 } }, |
| { { 0x1f87,0xdb30,0x18f5,0xf73a,0x3fbd, 0, 0, 0 } }, |
| { { 0xac15,0x3e46,0x2932,0xbf4a,0xbfbc, 0, 0, 0 } }, |
| { { 0x7944,0xba66,0xa091,0xcb12,0x3fb9, 0, 0, 0 } }, |
| { { 0xff78,0x40b4,0x2ee6,0xe69a,0x3fbc, 0, 0, 0 } }, |
| { { 0xc895,0x5069,0xe383,0xee53,0xbfbb, 0, 0, 0 } }, |
| { { 0x7cde,0x9376,0x4325,0xf8ab,0x3fbc, 0, 0, 0 } }, |
| { { 0xa10c,0x25e0,0xc093,0xaefd,0xbfbd, 0, 0, 0 } }, |
| { { 0x7d3e,0xea95,0x1366,0xb2fb,0x3fbd, 0, 0, 0 } }, |
| { { 0x5d89,0xeb34,0x5191,0x9301,0x3fbd, 0, 0, 0 } }, |
| { { 0x80d9,0xb883,0xfb10,0xe5eb,0x3fbb, 0, 0, 0 } }, |
| { { 0x045d,0x288c,0xc1ec,0xbedd,0xbfbd, 0, 0, 0 } }, |
| { { 0xeded,0x5c85,0x4630,0x8d5a,0x3fbd, 0, 0, 0 } }, |
| { { 0x9d82,0xe5ac,0x8e0a,0xfd6d,0x3fba, 0, 0, 0 } }, |
| { { 0x6dfd,0xeb58,0xaf14,0x8373,0xbfb9, 0, 0, 0 } }, |
| { { 0xf938,0x7aac,0x91cf,0xe8da,0xbfbc, 0, 0, 0 } }, |
| { { 0x0000,0x0000,0x0000,0x0000,0x0000, 0, 0, 0 } } |
| }; |
| static const uLD R[] = { |
| { { 0xa69b,0x530e,0xee1d,0xfd2a,0x3fee, 0, 0, 0 } }, |
| { { 0xc746,0x8e7e,0x5960,0xa182,0x3ff2, 0, 0, 0 } }, |
| { { 0x63b6,0xadda,0xfd6a,0xaec3,0x3ff5, 0, 0, 0 } }, |
| { { 0xc104,0xfd99,0x5b7c,0x9d95,0x3ff8, 0, 0, 0 } }, |
| { { 0xe05e,0x249d,0x46b8,0xe358,0x3ffa, 0, 0, 0 } }, |
| { { 0x5d1d,0x162c,0xeffc,0xf5fd,0x3ffc, 0, 0, 0 } }, |
| { { 0x79aa,0xd1cf,0x17f7,0xb172,0x3ffe, 0, 0, 0 } } |
| }; |
| |
| /* 10 byte sizes versus 12 byte */ |
| #define douba(k) (A[(k)].ld) |
| #define doubb(k) (B[(k)].ld) |
| #define MEXP (NXT*16384.0L) |
| #ifdef DENORMAL |
| #define MNEXP (-NXT*(16384.0L+64.0L)) |
| #else |
| #define MNEXP (-NXT*16384.0L) |
| #endif |
| static const |
| union |
| { |
| unsigned short L[8]; |
| long double ld; |
| } log2ea = {{0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, 0, 0, 0}}; |
| |
| #define LOG2EA (log2ea.ld) |
| /* |
| #define LOG2EA 0.44269504088896340735992L |
| */ |
| #endif |
| |
| #ifdef MIEEE |
| static uLD P[] = { |
| { { 0x3ff40000,0xda6ac6f4,0xa8b7b804, 0 } }, |
| { { 0x3ffd0000,0xfae158c0,0xcf027de9, 0 } }, |
| { { 0x3fff0000,0xe00067c9,0x3722405a, 0 } }, |
| { { 0x3fff0000,0xb33387ca,0x6b43cd99, 0 } } |
| }; |
| static uLD Q[] = { |
| { { 0x40010000,0xa8003b33,0xa4696307, 0 } }, |
| { { 0x40020000,0x8666a51c,0x62d7fec2, 0 } }, |
| { { 0x40010000,0x8666a5d7,0xd072da32, 0 } } |
| }; |
| static uLD A[] = { |
| { { 0x3fff0000,0x80000000,0x00000000, 0 } }, |
| { { 0x3ffe0000,0xfa83b2db,0x722a033a, 0 } }, |
| { { 0x3ffe0000,0xf5257d15,0x2486cc2c, 0 } }, |
| { { 0x3ffe0000,0xefe4b99b,0xdcdaf5cb, 0 } }, |
| { { 0x3ffe0000,0xeac0c6e7,0xdd24392f, 0 } }, |
| { { 0x3ffe0000,0xe5b906e7,0x7c8348a8, 0 } }, |
| { { 0x3ffe0000,0xe0ccdeec,0x2a94e111, 0 } }, |
| { { 0x3ffe0000,0xdbfbb797,0xdaf23755, 0 } }, |
| { { 0x3ffe0000,0xd744fcca,0xd69d6af4, 0 } }, |
| { { 0x3ffe0000,0xd2a81d91,0xf12ae45a, 0 } }, |
| { { 0x3ffe0000,0xce248c15,0x1f8480e4, 0 } }, |
| { { 0x3ffe0000,0xc9b9bd86,0x6e2f27a3, 0 } }, |
| { { 0x3ffe0000,0xc5672a11,0x5506dadd, 0 } }, |
| { { 0x3ffe0000,0xc12c4cca,0x66709456, 0 } }, |
| { { 0x3ffe0000,0xbd08a39f,0x580c36bf, 0 } }, |
| { { 0x3ffe0000,0xb8fbaf47,0x62fb9ee9, 0 } }, |
| { { 0x3ffe0000,0xb504f333,0xf9de6484, 0 } }, |
| { { 0x3ffe0000,0xb123f581,0xd2ac2590, 0 } }, |
| { { 0x3ffe0000,0xad583eea,0x42a14ac6, 0 } }, |
| { { 0x3ffe0000,0xa9a15ab4,0xea7c0ef8, 0 } }, |
| { { 0x3ffe0000,0xa5fed6a9,0xb15138ea, 0 } }, |
| { { 0x3ffe0000,0xa2704303,0x0c496819, 0 } }, |
| { { 0x3ffe0000,0x9ef53260,0x91a111ae, 0 } }, |
| { { 0x3ffe0000,0x9b8d39b9,0xd54e5539, 0 } }, |
| { { 0x3ffe0000,0x9837f051,0x8db8a96f, 0 } }, |
| { { 0x3ffe0000,0x94f4efa8,0xfef70961, 0 } }, |
| { { 0x3ffe0000,0x91c3d373,0xab11c336, 0 } }, |
| { { 0x3ffe0000,0x8ea4398b,0x45cd53c0, 0 } }, |
| { { 0x3ffe0000,0x8b95c1e3,0xea8bd6e7, 0 } }, |
| { { 0x3ffe0000,0x88980e80,0x92da8527, 0 } }, |
| { { 0x3ffe0000,0x85aac367,0xcc487b15, 0 } }, |
| { { 0x3ffe0000,0x82cd8698,0xac2ba1d7, 0 } }, |
| { { 0x3ffe0000,0x80000000,0x00000000, 0 } } |
| }; |
| static uLD B[] = { |
| { { 0x00000000,0x00000000,0x00000000, 0 } }, |
| { { 0x3fbd0000,0xf73a18f5,0xdb301f87, 0 } }, |
| { { 0xbfbc0000,0xbf4a2932,0x3e46ac15, 0 } }, |
| { { 0x3fb90000,0xcb12a091,0xba667944, 0 } }, |
| { { 0x3fbc0000,0xe69a2ee6,0x40b4ff78, 0 } }, |
| { { 0xbfbb0000,0xee53e383,0x5069c895, 0 } }, |
| { { 0x3fbc0000,0xf8ab4325,0x93767cde, 0 } }, |
| { { 0xbfbd0000,0xaefdc093,0x25e0a10c, 0 } }, |
| { { 0x3fbd0000,0xb2fb1366,0xea957d3e, 0 } }, |
| { { 0x3fbd0000,0x93015191,0xeb345d89, 0 } }, |
| { { 0x3fbb0000,0xe5ebfb10,0xb88380d9, 0 } }, |
| { { 0xbfbd0000,0xbeddc1ec,0x288c045d, 0 } }, |
| { { 0x3fbd0000,0x8d5a4630,0x5c85eded, 0 } }, |
| { { 0x3fba0000,0xfd6d8e0a,0xe5ac9d82, 0 } }, |
| { { 0xbfb90000,0x8373af14,0xeb586dfd, 0 } }, |
| { { 0xbfbc0000,0xe8da91cf,0x7aacf938, 0 } }, |
| { { 0x00000000,0x00000000,0x00000000, 0 } } |
| }; |
| static uLD R[] = { |
| { { 0x3fee0000,0xfd2aee1d,0x530ea69b, 0 } }, |
| { { 0x3ff20000,0xa1825960,0x8e7ec746, 0 } }, |
| { { 0x3ff50000,0xaec3fd6a,0xadda63b6, 0 } }, |
| { { 0x3ff80000,0x9d955b7c,0xfd99c104, 0 } }, |
| { { 0x3ffa0000,0xe35846b8,0x249de05e, 0 } }, |
| { { 0x3ffc0000,0xf5fdeffc,0x162c5d1d, 0 } }, |
| { { 0x3ffe0000,0xb17217f7,0xd1cf79aa, 0 } } |
| }; |
| |
| #define douba(k) (A[(k)].ld) |
| #define doubb(k) (B[(k)].ld) |
| #define MEXP (NXT*16384.0L) |
| #ifdef DENORMAL |
| #define MNEXP (-NXT*(16384.0L+64.0L)) |
| #else |
| #define MNEXP (-NXT*16382.0L) |
| #endif |
| static uLD L[1] = [ {0x3ffd0000,0xe2a8eca5,0x705fc2ef, 0} }; |
| #define LOG2EA (L[0].ld) |
| #endif |
| |
| |
| #define F W |
| #define Fa Wa |
| #define Fb Wb |
| #define G W |
| #define Ga Wa |
| #define Gb u |
| #define H W |
| #define Ha Wb |
| #define Hb Wb |
| |
| static VOLATILE long double z; |
| static long double w, W, Wa, Wb, ya, yb, u; |
| |
| static __inline__ long double reducl(long double); |
| extern long double __powil(long double, int); |
| extern long double powl(long double, long double); |
| |
| /* No error checking. We handle Infs and zeros ourselves. */ |
| static __inline__ long double |
| __fast_ldexpl (long double x, int expn) |
| { |
| long double res = 0.0L; |
| __asm__ __volatile__ ("fscale" |
| : "=t" (res) |
| : "0" (x), "u" ((long double) expn)); |
| return res; |
| } |
| |
| #define ldexpl __fast_ldexpl |
| |
| long double powl(long double x, long double y) |
| { |
| /* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */ |
| int i, nflg, iyflg, yoddint; |
| long e; |
| |
| if (y == 0.0L) |
| return (1.0L); |
| |
| #ifdef NANS |
| if (isnanl(x)) |
| { |
| _SET_ERRNO (EDOM); |
| return (x); |
| } |
| if (isnanl(y)) |
| { |
| _SET_ERRNO (EDOM); |
| return (y); |
| } |
| #endif |
| |
| if (y == 1.0L) |
| return (x); |
| |
| if (isinfl(y) && (x == -1.0L || x == 1.0L)) |
| return (y); |
| |
| if (x == 1.0L) |
| return (1.0L); |
| |
| if (y >= MAXNUML) |
| { |
| _SET_ERRNO (ERANGE); |
| #ifdef INFINITIES |
| if (x > 1.0L) |
| return (INFINITYL); |
| #else |
| if (x > 1.0L) |
| return (MAXNUML); |
| #endif |
| if (x > 0.0L && x < 1.0L) |
| return (0.0L); |
| #ifdef INFINITIES |
| if (x < -1.0L) |
| return (INFINITYL); |
| #else |
| if (x < -1.0L) |
| return (MAXNUML); |
| #endif |
| if (x > -1.0L && x < 0.0L) |
| return (0.0L); |
| } |
| if (y <= -MAXNUML) |
| { |
| _SET_ERRNO (ERANGE); |
| if (x > 1.0L) |
| return (0.0L); |
| #ifdef INFINITIES |
| if (x > 0.0L && x < 1.0L) |
| return (INFINITYL); |
| #else |
| if (x > 0.0L && x < 1.0L) |
| return (MAXNUML); |
| #endif |
| if (x < -1.0L) |
| return (0.0L); |
| #ifdef INFINITIES |
| if (x > -1.0L && x < 0.0L) |
| return (INFINITYL); |
| #else |
| if (x > -1.0L && x < 0.0L) |
| return (MAXNUML); |
| #endif |
| } |
| if (x >= MAXNUML) |
| { |
| #if INFINITIES |
| if (y > 0.0L) |
| return (INFINITYL); |
| #else |
| if (y > 0.0L) |
| return (MAXNUML); |
| #endif |
| return (0.0L); |
| } |
| |
| w = floorl(y); |
| /* Set iyflg to 1 if y is an integer. */ |
| iyflg = 0; |
| if (w == y) |
| iyflg = 1; |
| |
| /* Test for odd integer y. */ |
| yoddint = 0; |
| if (iyflg) |
| { |
| ya = fabsl(y); |
| ya = floorl(0.5L * ya); |
| yb = 0.5L * fabsl(w); |
| if (ya != yb) |
| yoddint = 1; |
| } |
| |
| if (x <= -MAXNUML) |
| { |
| if (y > 0.0L) |
| { |
| #ifdef INFINITIES |
| if (yoddint) |
| return (-INFINITYL); |
| return (INFINITYL); |
| #else |
| if (yoddint) |
| return (-MAXNUML); |
| return (MAXNUML); |
| #endif |
| } |
| if (y < 0.0L) |
| { |
| #ifdef MINUSZERO |
| if (yoddint) |
| return (NEGZEROL); |
| #endif |
| return (0.0); |
| } |
| } |
| |
| |
| nflg = 0; /* flag = 1 if x<0 raised to integer power */ |
| if (x <= 0.0L) |
| { |
| if (x == 0.0L) |
| { |
| if (y < 0.0) |
| { |
| #ifdef MINUSZERO |
| if (signbitl(x) && yoddint) |
| return (-INFINITYL); |
| #endif |
| #ifdef INFINITIES |
| return (INFINITYL); |
| #else |
| return (MAXNUML); |
| #endif |
| } |
| if (y > 0.0) |
| { |
| #ifdef MINUSZERO |
| if (signbitl(x) && yoddint) |
| return (NEGZEROL); |
| #endif |
| return (0.0); |
| } |
| if (y == 0.0L) |
| return (1.0L); /* 0**0 */ |
| else |
| return (0.0L); /* 0**y */ |
| } |
| else |
| { |
| if (iyflg == 0) |
| { /* noninteger power of negative number */ |
| mtherr(fname, DOMAIN); |
| _SET_ERRNO (EDOM); |
| #ifdef NANS |
| return (NANL); |
| #else |
| return (0.0L); |
| #endif |
| } |
| nflg = 1; |
| } |
| } |
| |
| /* Integer power of an integer. */ |
| |
| if (iyflg) |
| { |
| i = w; |
| w = floorl(x); |
| if ((w == x) && (fabsl(y) < 32768.0)) |
| { |
| w = __powil(x, (int) y); |
| return (w); |
| } |
| } |
| |
| if (nflg) |
| x = fabsl(x); |
| |
| /* separate significand from exponent */ |
| x = frexpl( x, &i ); |
| e = i; |
| |
| /* find significand in antilog table A[] */ |
| i = 1; |
| if (x <= douba(17)) |
| i = 17; |
| if (x <= douba(i + 8)) |
| i += 8; |
| if (x <= douba(i + 4)) |
| i += 4; |
| if (x <= douba(i + 2)) |
| i += 2; |
| if (x >= douba(1)) |
| i = -1; |
| i += 1; |
| |
| /* Find (x - A[i])/A[i] |
| * in order to compute log(x/A[i]): |
| * |
| * log(x) = log( a x/a ) = log(a) + log(x/a) |
| * |
| * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a |
| */ |
| x -= douba(i); |
| x -= doubb(i/2); |
| x /= douba(i); |
| |
| |
| /* rational approximation for log(1+v): |
| * |
| * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v) |
| */ |
| z = x*x; |
| w = x * ( z * polevll(x, P, 3) / p1evll(x, Q, 3) ); |
| w = w - ldexpl(z, -1); /* w - 0.5 * z */ |
| |
| /* Convert to base 2 logarithm: |
| * multiply by log2(e) = 1 + LOG2EA |
| */ |
| z = LOG2EA * w; |
| z += w; |
| z += LOG2EA * x; |
| z += x; |
| |
| /* Compute exponent term of the base 2 logarithm. */ |
| w = -i; |
| w = ldexpl(w, -LNXT); /* divide by NXT */ |
| w += e; |
| /* Now base 2 log of x is w + z. */ |
| |
| /* Multiply base 2 log by y, in extended precision. */ |
| |
| /* separate y into large part ya |
| * and small part yb less than 1/NXT |
| */ |
| ya = reducl(y); |
| yb = y - ya; |
| |
| /* (w+z)(ya+yb) |
| * = w*ya + w*yb + z*y |
| */ |
| F = z * y + w * yb; |
| Fa = reducl(F); |
| Fb = F - Fa; |
| |
| G = Fa + w * ya; |
| Ga = reducl(G); |
| Gb = G - Ga; |
| |
| H = Fb + Gb; |
| Ha = reducl(H); |
| w = ldexpl(Ga + Ha, LNXT); |
| |
| /* Test the power of 2 for overflow */ |
| if (w > MEXP) |
| { |
| _SET_ERRNO (ERANGE); |
| mtherr(fname, OVERFLOW); |
| return (MAXNUML); |
| } |
| |
| if (w < MNEXP) |
| { |
| _SET_ERRNO (ERANGE); |
| mtherr(fname, UNDERFLOW); |
| return (0.0L); |
| } |
| |
| e = w; |
| Hb = H - Ha; |
| |
| if (Hb > 0.0L) |
| { |
| e += 1; |
| Hb -= (1.0L/NXT); /*0.0625L;*/ |
| } |
| |
| /* Now the product y * log2(x) = Hb + e/NXT. |
| * |
| * Compute base 2 exponential of Hb, |
| * where -0.0625 <= Hb <= 0. |
| */ |
| z = Hb * polevll(Hb, R, 6); /* z = 2**Hb - 1 */ |
| |
| /* Express e/NXT as an integer plus a negative number of (1/NXT)ths. |
| * Find lookup table entry for the fractional power of 2. |
| */ |
| if (e < 0) |
| i = 0; |
| else |
| i = 1; |
| i = e/NXT + i; |
| e = NXT*i - e; |
| w = douba(e); |
| z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */ |
| z = z + w; |
| z = ldexpl(z, i); /* multiply by integer power of 2 */ |
| |
| if (nflg) |
| { |
| /* For negative x, |
| * find out if the integer exponent |
| * is odd or even. |
| */ |
| w = ldexpl(y, -1); |
| w = floorl(w); |
| w = ldexpl(w, 1); |
| if (w != y) |
| z = -z; /* odd exponent */ |
| } |
| |
| return (z); |
| } |
| |
| static __inline__ long double |
| __convert_inf_to_maxnum(long double x) |
| { |
| if (isinf(x)) |
| return (x > 0.0L ? MAXNUML : -MAXNUML); |
| else |
| return x; |
| } |
| |
| /* Find a multiple of 1/NXT that is within 1/NXT of x. */ |
| static long double reducl(long double x) |
| { |
| long double t; |
| |
| /* If the call to ldexpl overflows, set it to MAXNUML. |
| This avoids Inf - Inf = Nan result when calculating the 'small' |
| part of a reduction. Instead, the small part becomes Inf, |
| causing under/overflow when adding it to the 'large' part. |
| There must be a cleaner way of doing this. */ |
| t = __convert_inf_to_maxnum (ldexpl( x, LNXT )); |
| t = floorl(t); |
| t = ldexpl(t, -LNXT); |
| return (t); |
| } |
| |