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math: Add powf()
Signed-off-by: Asahi Lina <lina@asahilina.net>
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Asahi Lina
parent
f7639885ce
commit
af85202b58
6 changed files with 260 additions and 1 deletions
2
Makefile
2
Makefile
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@ -134,6 +134,8 @@ FP_OBJECTS := \
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kboot_gpu.o \
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math/expf.o \
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math/exp2f_data.o \
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math/powf.o \
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math/powf_data.o
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BUILD_OBJS := $(patsubst %,build/%,$(OBJECTS))
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BUILD_FP_OBJS := $(patsubst %,build/%,$(FP_OBJECTS))
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@ -63,6 +63,9 @@ union ldshape {
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/* Support signaling NaNs. */
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#define WANT_SNAN 0
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#define WANT_ERRNO 0
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#define WANT_ERRNO_UFLOW 0
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#if WANT_SNAN
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#error SNaN is unsupported
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#else
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@ -263,7 +266,7 @@ static inline float __math_oflowf(uint32_t sign)
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return __math_xflowf(sign, 0x1p97f);
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}
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float __math_uflowf(uint32_t sign)
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static inline float __math_uflowf(uint32_t sign)
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{
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return __math_xflowf(sign, 0x1p-95f);
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}
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191
src/math/powf.c
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191
src/math/powf.c
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@ -0,0 +1,191 @@
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/*
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* Copyright (c) 2017-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#include <math.h>
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#include <stdint.h>
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#include "exp2f_data.h"
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#include "libm.h"
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#include "powf_data.h"
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#define double_t double
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#define float_t float
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/*
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POWF_LOG2_POLY_ORDER = 5
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EXP2F_TABLE_BITS = 5
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ULP error: 0.82 (~ 0.5 + relerr*2^24)
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relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
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relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
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relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
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*/
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#define N (1 << POWF_LOG2_TABLE_BITS)
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#define T __powf_log2_data.tab
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#define A __powf_log2_data.poly
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#define OFF 0x3f330000
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float __math_invalidf(float x)
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{
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return (x - x) / (x - x);
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}
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/* Subnormal input is normalized so ix has negative biased exponent.
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Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set. */
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static inline double_t log2_inline(uint32_t ix)
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{
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double_t z, r, r2, r4, p, q, y, y0, invc, logc;
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uint32_t iz, top, tmp;
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int k, i;
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/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
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The range is split into N subintervals.
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The ith subinterval contains z and c is near its center. */
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tmp = ix - OFF;
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i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N;
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top = tmp & 0xff800000;
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iz = ix - top;
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k = (int32_t)top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
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invc = T[i].invc;
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logc = T[i].logc;
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z = (double_t)asfloat(iz);
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/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
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r = z * invc - 1;
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y0 = logc + (double_t)k;
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/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
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r2 = r * r;
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y = A[0] * r + A[1];
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p = A[2] * r + A[3];
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r4 = r2 * r2;
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q = A[4] * r + y0;
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q = p * r2 + q;
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y = y * r4 + q;
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return y;
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}
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#undef N
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#undef T
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#define N (1 << EXP2F_TABLE_BITS)
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#define T __exp2f_data.tab
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#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
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/* The output of log2 and thus the input of exp2 is either scaled by N
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(in case of fast toint intrinsics) or not. The unscaled xd must be
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in [-1021,1023], sign_bias sets the sign of the result. */
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static inline float exp2_inline(double_t xd, uint32_t sign_bias)
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{
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uint64_t ki, ski, t;
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double_t kd, z, r, r2, y, s;
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#if TOINT_INTRINSICS
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#define C __exp2f_data.poly_scaled
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/* N*x = k + r with r in [-1/2, 1/2] */
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kd = roundtoint(xd); /* k */
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ki = converttoint(xd);
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#else
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#define C __exp2f_data.poly
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#define SHIFT __exp2f_data.shift_scaled
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/* x = k/N + r with r in [-1/(2N), 1/(2N)] */
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kd = eval_as_double(xd + SHIFT);
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ki = asuint64(kd);
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kd -= SHIFT; /* k/N */
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#endif
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r = xd - kd;
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/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
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t = T[ki % N];
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ski = ki + sign_bias;
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t += ski << (52 - EXP2F_TABLE_BITS);
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s = asdouble(t);
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z = C[0] * r + C[1];
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r2 = r * r;
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y = C[2] * r + 1;
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y = z * r2 + y;
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y = y * s;
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return eval_as_float(y);
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}
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/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
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the bit representation of a non-zero finite floating-point value. */
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static inline int checkint(uint32_t iy)
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{
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int e = iy >> 23 & 0xff;
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if (e < 0x7f)
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return 0;
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if (e > 0x7f + 23)
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return 2;
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if (iy & ((1 << (0x7f + 23 - e)) - 1))
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return 0;
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if (iy & (1 << (0x7f + 23 - e)))
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return 1;
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return 2;
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}
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static inline int zeroinfnan(uint32_t ix)
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{
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return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
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}
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float powf(float x, float y)
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{
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uint32_t sign_bias = 0;
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uint32_t ix, iy;
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ix = asuint(x);
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iy = asuint(y);
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if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000 || zeroinfnan(iy))) {
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/* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */
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if (predict_false(zeroinfnan(iy))) {
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if (2 * iy == 0)
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return issignalingf_inline(x) ? x + y : 1.0f;
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if (ix == 0x3f800000)
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return issignalingf_inline(y) ? x + y : 1.0f;
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if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000)
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return x + y;
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if (2 * ix == 2 * 0x3f800000)
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return 1.0f;
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if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
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return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
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return y * y;
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}
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if (predict_false(zeroinfnan(ix))) {
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float_t x2 = x * x;
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if (ix & 0x80000000 && checkint(iy) == 1)
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x2 = -x2;
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/* Without the barrier some versions of clang hoist the 1/x2 and
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thus division by zero exception can be signaled spuriously. */
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return iy & 0x80000000 ? fp_barrierf(1 / x2) : x2;
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}
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/* x and y are non-zero finite. */
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if (ix & 0x80000000) {
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/* Finite x < 0. */
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int yint = checkint(iy);
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if (yint == 0)
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return __math_invalidf(x);
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if (yint == 1)
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sign_bias = SIGN_BIAS;
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ix &= 0x7fffffff;
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}
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if (ix < 0x00800000) {
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/* Normalize subnormal x so exponent becomes negative. */
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ix = asuint(x * 0x1p23f);
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ix &= 0x7fffffff;
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ix -= 23 << 23;
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}
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}
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double_t logx = log2_inline(ix);
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double_t ylogx = y * logx; /* cannot overflow, y is single prec. */
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if (predict_false((asuint64(ylogx) >> 47 & 0xffff) >= asuint64(126.0 * POWF_SCALE) >> 47)) {
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/* |y*log(x)| >= 126. */
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if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
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return __math_oflowf(sign_bias);
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if (ylogx <= -150.0 * POWF_SCALE)
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return __math_uflowf(sign_bias);
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}
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return exp2_inline(ylogx, sign_bias);
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}
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36
src/math/powf_data.c
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36
src/math/powf_data.c
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@ -0,0 +1,36 @@
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/*
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* Data definition for powf.
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*
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* Copyright (c) 2017-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#include "powf_data.h"
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const struct powf_log2_data __powf_log2_data = {
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.tab =
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{
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{0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE},
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{0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE},
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{0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE},
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{0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE},
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{0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE},
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{0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE},
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{0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE},
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{0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE},
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{0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE},
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{0x1p+0, 0x0p+0 * POWF_SCALE},
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{0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE},
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{0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE},
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{0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE},
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{0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE},
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{0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE},
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{0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE},
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},
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.poly = {
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0x1.27616c9496e0bp-2 * POWF_SCALE,
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-0x1.71969a075c67ap-2 * POWF_SCALE,
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0x1.ec70a6ca7baddp-2 * POWF_SCALE,
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-0x1.7154748bef6c8p-1 * POWF_SCALE,
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0x1.71547652ab82bp0 * POWF_SCALE,
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}};
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26
src/math/powf_data.h
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26
src/math/powf_data.h
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@ -0,0 +1,26 @@
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/*
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* Copyright (c) 2017-2018, Arm Limited.
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* SPDX-License-Identifier: MIT
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*/
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#ifndef _POWF_DATA_H
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#define _POWF_DATA_H
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#include "exp2f_data.h"
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#include "libm.h"
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#define POWF_LOG2_TABLE_BITS 4
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#define POWF_LOG2_POLY_ORDER 5
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#if TOINT_INTRINSICS
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#define POWF_SCALE_BITS EXP2F_TABLE_BITS
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#else
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#define POWF_SCALE_BITS 0
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#endif
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#define POWF_SCALE ((double)(1 << POWF_SCALE_BITS))
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extern const struct powf_log2_data {
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struct {
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double invc, logc;
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} tab[1 << POWF_LOG2_TABLE_BITS];
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double poly[POWF_LOG2_POLY_ORDER];
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} __powf_log2_data;
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#endif
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@ -12,5 +12,6 @@
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#endif
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float expf(float);
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float powf(float, float);
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#endif
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