diff options
Diffstat (limited to 'src/math/expf.c')
| -rw-r--r-- | src/math/expf.c | 133 |
1 files changed, 65 insertions, 68 deletions
diff --git a/src/math/expf.c b/src/math/expf.c index feee2b0e..f9fbf8e7 100644 --- a/src/math/expf.c +++ b/src/math/expf.c @@ -1,83 +1,80 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */ /* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * Single-precision e^x function. * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== + * Copyright (c) 2017-2018, Arm Limited. + * SPDX-License-Identifier: MIT */ +#include <math.h> +#include <stdint.h> #include "libm.h" +#include "exp2f_data.h" -static const float -half[2] = {0.5,-0.5}, -ln2hi = 6.9314575195e-1f, /* 0x3f317200 */ -ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */ -invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */ /* - * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: - * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 - */ -P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */ -P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */ +EXP2F_TABLE_BITS = 5 +EXP2F_POLY_ORDER = 3 -float expf(float x) +ULP error: 0.502 (nearest rounding.) +Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.) +Wrong count: 170635 (all nearest rounding wrong results with fma.) +Non-nearest ULP error: 1 (rounded ULP error) +*/ + +#define N (1 << EXP2F_TABLE_BITS) +#define InvLn2N __exp2f_data.invln2_scaled +#define T __exp2f_data.tab +#define C __exp2f_data.poly_scaled + +static inline uint32_t top12(float x) { - float_t hi, lo, c, xx, y; - int k, sign; - uint32_t hx; + return asuint(x) >> 20; +} - GET_FLOAT_WORD(hx, x); - sign = hx >> 31; /* sign bit of x */ - hx &= 0x7fffffff; /* high word of |x| */ +float expf(float x) +{ + uint32_t abstop; + uint64_t ki, t; + double_t kd, xd, z, r, r2, y, s; - /* special cases */ - if (hx >= 0x42aeac50) { /* if |x| >= -87.33655f or NaN */ - if (hx > 0x7f800000) /* NaN */ - return x; - if (hx >= 0x42b17218 && !sign) { /* x >= 88.722839f */ - /* overflow */ - x *= 0x1p127f; - return x; - } - if (sign) { - /* underflow */ - FORCE_EVAL(-0x1p-149f/x); - if (hx >= 0x42cff1b5) /* x <= -103.972084f */ - return 0; - } + xd = (double_t)x; + abstop = top12(x) & 0x7ff; + if (predict_false(abstop >= top12(88.0f))) { + /* |x| >= 88 or x is nan. */ + if (asuint(x) == asuint(-INFINITY)) + return 0.0f; + if (abstop >= top12(INFINITY)) + return x + x; + if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ + return __math_oflowf(0); + if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ + return __math_uflowf(0); } - /* argument reduction */ - if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ - if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */ - k = invln2*x + half[sign]; - else - k = 1 - sign - sign; - hi = x - k*ln2hi; /* k*ln2hi is exact here */ - lo = k*ln2lo; - x = hi - lo; - } else if (hx > 0x39000000) { /* |x| > 2**-14 */ - k = 0; - hi = x; - lo = 0; - } else { - /* raise inexact */ - FORCE_EVAL(0x1p127f + x); - return 1 + x; - } + /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */ + z = InvLn2N * xd; + + /* Round and convert z to int, the result is in [-150*N, 128*N] and + ideally ties-to-even rule is used, otherwise the magnitude of r + can be bigger which gives larger approximation error. */ +#if TOINT_INTRINSICS + kd = roundtoint(z); + ki = converttoint(z); +#else +# define SHIFT __exp2f_data.shift + kd = eval_as_double(z + SHIFT); + ki = asuint64(kd); + kd -= SHIFT; +#endif + r = z - kd; - /* x is now in primary range */ - xx = x*x; - c = x - xx*(P1+xx*P2); - y = 1 + (x*c/(2-c) - lo + hi); - if (k == 0) - return y; - return scalbnf(y, k); + /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ + t = T[ki % N]; + t += ki << (52 - EXP2F_TABLE_BITS); + s = asdouble(t); + z = C[0] * r + C[1]; + r2 = r * r; + y = C[2] * r + 1; + y = z * r2 + y; + y = y * s; + return eval_as_float(y); } |