diff options
author | Ian Moffett <ian@osmora.org> | 2024-03-07 17:28:52 -0500 |
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committer | Ian Moffett <ian@osmora.org> | 2024-03-07 18:24:51 -0500 |
commit | f5e48e94a2f4d4bbd6e5628c7f2afafc6dbcc459 (patch) | |
tree | 93b156621dc0303816b37f60ba88051b702d92f6 /lib/mlibc/options/ansi/musl-generic-math/powl.c | |
parent | bd5969fc876a10b18613302db7087ef3c40f18e1 (diff) |
build: Build mlibc + add distclean target
Signed-off-by: Ian Moffett <ian@osmora.org>
Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/powl.c')
-rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/powl.c | 522 |
1 files changed, 0 insertions, 522 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/powl.c b/lib/mlibc/options/ansi/musl-generic-math/powl.c deleted file mode 100644 index 5b6da07..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/powl.c +++ /dev/null @@ -1,522 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_powl.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* powl.c - * - * Power function, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, z, powl(); - * - * z = powl( x, y ); - * - * - * DESCRIPTION: - * - * Computes x raised to the yth power. Analytically, - * - * x**y = exp( y log(x) ). - * - * Following Cody and Waite, this program uses a lookup table - * of 2**-i/32 and pseudo extended precision arithmetic to - * obtain several extra bits of accuracy in both the logarithm - * and the exponential. - * - * - * ACCURACY: - * - * The relative error of pow(x,y) can be estimated - * by y dl ln(2), where dl is the absolute error of - * the internally computed base 2 logarithm. At the ends - * of the approximation interval the logarithm equal 1/32 - * and its relative error is about 1 lsb = 1.1e-19. Hence - * the predicted relative error in the result is 2.3e-21 y . - * - * Relative error: - * arithmetic domain # trials peak rms - * - * IEEE +-1000 40000 2.8e-18 3.7e-19 - * .001 < x < 1000, with log(x) uniformly distributed. - * -1000 < y < 1000, y uniformly distributed. - * - * IEEE 0,8700 60000 6.5e-18 1.0e-18 - * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed. - * - * - * ERROR MESSAGES: - * - * message condition value returned - * pow overflow x**y > MAXNUM INFINITY - * pow underflow x**y < 1/MAXNUM 0.0 - * pow domain x<0 and y noninteger 0.0 - * - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double powl(long double x, long double y) -{ - return pow(x, y); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 - -/* Table size */ -#define NXT 32 - -/* 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 const long double P[] = { - 8.3319510773868690346226E-4L, - 4.9000050881978028599627E-1L, - 1.7500123722550302671919E0L, - 1.4000100839971580279335E0L, -}; -static const long double Q[] = { -/* 1.0000000000000000000000E0L,*/ - 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 const long double 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 const long double 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 const long double R[] = { - 1.5089970579127659901157E-5L, - 1.5402715328927013076125E-4L, - 1.3333556028915671091390E-3L, - 9.6181291046036762031786E-3L, - 5.5504108664798463044015E-2L, - 2.4022650695910062854352E-1L, - 6.9314718055994530931447E-1L, -}; - -#define MEXP (NXT*16384.0L) -/* The following if denormal numbers are supported, else -MEXP: */ -#define MNEXP (-NXT*(16384.0L+64.0L)) -/* log2(e) - 1 */ -#define LOG2EA 0.44269504088896340735992L - -#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 const long double MAXLOGL = 1.1356523406294143949492E4L; -static const long double MINLOGL = -1.13994985314888605586758E4L; -static const long double LOGE2L = 6.9314718055994530941723E-1L; -static const long double huge = 0x1p10000L; -/* XXX Prevent gcc from erroneously constant folding this. */ -static const volatile long double twom10000 = 0x1p-10000L; - -static long double reducl(long double); -static long double powil(long double, int); - -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; - volatile long double z=0; - long double w=0, W=0, Wa=0, Wb=0, ya=0, yb=0, u=0; - - /* make sure no invalid exception is raised by nan comparision */ - if (isnan(x)) { - if (!isnan(y) && y == 0.0) - return 1.0; - return x; - } - if (isnan(y)) { - if (x == 1.0) - return 1.0; - return y; - } - if (x == 1.0) - return 1.0; /* 1**y = 1, even if y is nan */ - if (x == -1.0 && !isfinite(y)) - return 1.0; /* -1**inf = 1 */ - if (y == 0.0) - return 1.0; /* x**0 = 1, even if x is nan */ - if (y == 1.0) - return x; - if (y >= LDBL_MAX) { - if (x > 1.0 || x < -1.0) - return INFINITY; - if (x != 0.0) - return 0.0; - } - if (y <= -LDBL_MAX) { - if (x > 1.0 || x < -1.0) - return 0.0; - if (x != 0.0 || y == -INFINITY) - return INFINITY; - } - if (x >= LDBL_MAX) { - if (y > 0.0) - return INFINITY; - return 0.0; - } - - 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(0.5 * ya); - yb = 0.5 * fabsl(w); - if( ya != yb ) - yoddint = 1; - } - - if (x <= -LDBL_MAX) { - if (y > 0.0) { - if (yoddint) - return -INFINITY; - return INFINITY; - } - if (y < 0.0) { - if (yoddint) - return -0.0; - return 0.0; - } - } - nflg = 0; /* (x<0)**(odd int) */ - if (x <= 0.0) { - if (x == 0.0) { - if (y < 0.0) { - if (signbit(x) && yoddint) - /* (-0.0)**(-odd int) = -inf, divbyzero */ - return -1.0/0.0; - /* (+-0.0)**(negative) = inf, divbyzero */ - return 1.0/0.0; - } - if (signbit(x) && yoddint) - return -0.0; - return 0.0; - } - if (iyflg == 0) - return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */ - /* (x<0)**(integer) */ - if (yoddint) - nflg = 1; /* negate result */ - x = -x; - } - /* (+integer)**(integer) */ - if (iyflg && floorl(x) == x && fabsl(y) < 32768.0) { - w = powil(x, (int)y); - return nflg ? -w : w; - } - - /* separate significand from exponent */ - x = frexpl(x, &i); - e = i; - - /* find significand in antilog table A[] */ - i = 1; - if (x <= A[17]) - i = 17; - if (x <= A[i+8]) - i += 8; - if (x <= A[i+4]) - i += 4; - if (x <= A[i+2]) - i += 2; - if (x >= A[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 -= A[i]; - x -= B[i/2]; - x /= A[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 - 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 /= 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 = (Ga + Ha) * NXT; - - /* Test the power of 2 for overflow */ - if (w > MEXP) - return huge * huge; /* overflow */ - if (w < MNEXP) - return twom10000 * twom10000; /* underflow */ - - e = w; - Hb = H - Ha; - - if (Hb > 0.0) { - e += 1; - Hb -= 1.0/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 = A[e]; - z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */ - z = z + w; - z = scalbnl(z, i); /* multiply by integer power of 2 */ - - if (nflg) - z = -z; - return z; -} - - -/* Find a multiple of 1/NXT that is within 1/NXT of x. */ -static long double reducl(long double x) -{ - long double t; - - t = x * NXT; - t = floorl(t); - t = t / NXT; - return t; -} - -/* - * Positive real raised to integer power, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, powil(); - * int n; - * - * y = powil( x, n ); - * - * - * DESCRIPTION: - * - * Returns argument x>0 raised to the nth power. - * The routine efficiently decomposes n as a sum of powers of - * two. The desired power is a product of two-to-the-kth - * powers of x. Thus to compute the 32767 power of x requires - * 28 multiplications instead of 32767 multiplications. - * - * - * ACCURACY: - * - * Relative error: - * arithmetic x domain n domain # trials peak rms - * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18 - * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18 - * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17 - * - * Returns MAXNUM on overflow, zero on underflow. - */ - -static long double powil(long double x, int nn) -{ - long double ww, y; - long double s; - int n, e, sign, lx; - - if (nn == 0) - return 1.0; - - if (nn < 0) { - sign = -1; - n = -nn; - } else { - sign = 1; - n = nn; - } - - /* Overflow detection */ - - /* Calculate approximate logarithm of answer */ - s = x; - s = frexpl( s, &lx); - e = (lx - 1)*n; - if ((e == 0) || (e > 64) || (e < -64)) { - s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L); - s = (2.9142135623730950L * s - 0.5 + lx) * nn * LOGE2L; - } else { - s = LOGE2L * e; - } - - if (s > MAXLOGL) - return huge * huge; /* overflow */ - - if (s < MINLOGL) - return twom10000 * twom10000; /* underflow */ - /* Handle tiny denormal answer, but with less accuracy - * since roundoff error in 1.0/x will be amplified. - * The precise demarcation should be the gradual underflow threshold. - */ - if (s < -MAXLOGL+2.0) { - x = 1.0/x; - sign = -sign; - } - - /* First bit of the power */ - if (n & 1) - y = x; - else - y = 1.0; - - ww = x; - n >>= 1; - while (n) { - ww = ww * ww; /* arg to the 2-to-the-kth power */ - if (n & 1) /* if that bit is set, then include in product */ - y *= ww; - n >>= 1; - } - - if (sign < 0) - y = 1.0/y; - return y; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double powl(long double x, long double y) -{ - return pow(x, y); -} -#endif |