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Diffstat (limited to 'math/powf.c')
| -rw-r--r-- | math/powf.c | 224 |
1 files changed, 224 insertions, 0 deletions
diff --git a/math/powf.c b/math/powf.c new file mode 100644 index 0000000..8ffbe84 --- /dev/null +++ b/math/powf.c @@ -0,0 +1,224 @@ +/* + * Single-precision pow function. + * + * Copyright (c) 2017, Arm Limited. + * SPDX-License-Identifier: Apache-2.0 + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#if WANT_SINGLEPREC +#include "single/e_powf.c" +#else + +#include <math.h> +#include <stdint.h> +#include "math_config.h" + +/* +POWF_LOG2_POLY_ORDER = 5 +EXP2F_TABLE_BITS = 5 + +ULP error: 0.82 (~ 0.5 + relerr*2^24) +relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2) +relerr_log2: 1.83 * 2^-33 (Relative error of logx.) +relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).) +*/ + +#define N (1 << POWF_LOG2_TABLE_BITS) +#define T __powf_log2_data.tab +#define A __powf_log2_data.poly +#define OFF 0x3f330000 + +/* Subnormal input is normalized so ix has negative biased exponent. + Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set. */ +static inline double_t +log2_inline (uint32_t ix) +{ + /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ + double_t z, r, r2, r4, p, q, y, y0, invc, logc; + uint32_t iz, top, tmp; + int k, i; + + /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. + The range is split into N subintervals. + The ith subinterval contains z and c is near its center. */ + tmp = ix - OFF; + i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N; + top = tmp & 0xff800000; + iz = ix - top; + k = (int32_t) top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */ + invc = T[i].invc; + logc = T[i].logc; + z = (double_t) asfloat (iz); + + /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ + r = z * invc - 1; + y0 = logc + (double_t) k; + + /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ + r2 = r * r; + y = A[0] * r + A[1]; + p = A[2] * r + A[3]; + r4 = r2 * r2; + q = A[4] * r + y0; + q = p * r2 + q; + y = y * r4 + q; + return y; +} + +#undef N +#undef T +#define N (1 << EXP2F_TABLE_BITS) +#define T __exp2f_data.tab +#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11)) + +/* The output of log2 and thus the input of exp2 is either scaled by N + (in case of fast toint intrinsics) or not. The unscaled xd must be + in [-1021,1023], sign_bias sets the sign of the result. */ +static inline double_t +exp2_inline (double_t xd, unsigned long sign_bias) +{ + uint64_t ki, ski, t; + /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ + double_t kd, z, r, r2, y, s; + +#if TOINT_INTRINSICS +# define C __exp2f_data.poly_scaled + /* N*x = k + r with r in [-1/2, 1/2] */ + kd = roundtoint (xd); /* k */ + ki = converttoint (xd); +#else +# define C __exp2f_data.poly +# define SHIFT __exp2f_data.shift_scaled + /* x = k/N + r with r in [-1/(2N), 1/(2N)] */ + kd = (double) (xd + SHIFT); /* Rounding to double precision is required. */ + ki = asuint64 (kd); + kd -= SHIFT; /* k/N */ +#endif + r = xd - kd; + + /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ + t = T[ki % N]; + ski = ki + sign_bias; + t += ski << (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 y; +} + +/* Returns 0 if not int, 1 if odd int, 2 if even int. */ +static inline int +checkint (uint32_t iy) +{ + int e = iy >> 23 & 0xff; + if (e < 0x7f) + return 0; + if (e > 0x7f + 23) + return 2; + if (iy & ((1 << (0x7f + 23 - e)) - 1)) + return 0; + if (iy & (1 << (0x7f + 23 - e))) + return 1; + return 2; +} + +static inline int +zeroinfnan (uint32_t ix) +{ + return 2 * ix - 1 >= 2u * 0x7f800000 - 1; +} + +float +ARM__powf (float x, float y) +{ + unsigned long sign_bias = 0; + uint32_t ix, iy; + + ix = asuint (x); + iy = asuint (y); + if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000 + || zeroinfnan (iy), + 0)) + { + /* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */ + if (__builtin_expect (zeroinfnan (iy), 0)) + { + if (2 * iy == 0) + return issignalingf_inline (x) ? x + y : 1.0f; + if (ix == 0x3f800000) + return issignalingf_inline (y) ? x + y : 1.0f; + if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000) + return x + y; + if (2 * ix == 2 * 0x3f800000) + return 1.0f; + if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000)) + return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */ + return y * y; + } + if (__builtin_expect (zeroinfnan (ix), 0)) + { + float_t x2 = x * x; + if (ix & 0x80000000 && checkint (iy) == 1) + { + x2 = -x2; + sign_bias = 1; + } +#if WANT_ERRNO + if (2 * ix == 0 && iy & 0x80000000) + return __math_divzerof (sign_bias); +#endif + return iy & 0x80000000 ? 1 / x2 : x2; + } + /* x and y are non-zero finite. */ + if (ix & 0x80000000) + { + /* Finite x < 0. */ + int yint = checkint (iy); + if (yint == 0) + return __math_invalidf (x); + if (yint == 1) + sign_bias = SIGN_BIAS; + ix &= 0x7fffffff; + } + if (ix < 0x00800000) + { + /* Normalize subnormal x so exponent becomes negative. */ + ix = asuint (x * 0x1p23f); + ix &= 0x7fffffff; + ix -= 23 << 23; + } + } + double_t logx = log2_inline (ix); + double_t ylogx = y * logx; /* Note: cannot overflow, y is single prec. */ + if (__builtin_expect ((asuint64 (ylogx) >> 47 & 0xffff) + >= asuint64 (126.0 * POWF_SCALE) >> 47, + 0)) + { + /* |y*log(x)| >= 126. */ + if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE) + return __math_oflowf (sign_bias); + if (ylogx <= -150.0 * POWF_SCALE) + return __math_uflowf (sign_bias); +#if WANT_ERRNO_UFLOW + if (ylogx < -149.0 * POWF_SCALE) + return __math_may_uflowf (sign_bias); +#endif + } + return (float) exp2_inline (ylogx, sign_bias); +} +#endif |