Implement missing Math logarithm functions from ES6 (#3617)
Math.log2, Math.log10, Math.log1p, Math.expm1 C implementation ported from fdlibm Part of Issue #3568 JerryScript-DCO-1.0-Signed-off-by: Rafal Walczyna r.walczyna@samsung.com
This commit is contained in:
Rafal Walczyna
@@ -570,38 +570,22 @@ ecma_builtin_math_dispatch_routine (uint16_t builtin_routine_id, /**< built-in w
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}
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case ECMA_MATH_OBJECT_EXPM1:
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{
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#ifdef JERRY_LIBM_MATH_H
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return ecma_raise_type_error (ECMA_ERR_MSG ("UNIMPLEMENTED: Math.expm1"));
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#else /* !JERRY_LIBM_MATH_H */
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x = DOUBLE_TO_ECMA_NUMBER_T (expm1 (x));
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#endif /* JERRY_LIBM_MATH_H */
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break;
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}
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case ECMA_MATH_OBJECT_LOG1P:
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{
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#ifdef JERRY_LIBM_MATH_H
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return ecma_raise_type_error (ECMA_ERR_MSG ("UNIMPLEMENTED: Math.log1p"));
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#else /* !JERRY_LIBM_MATH_H */
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x = DOUBLE_TO_ECMA_NUMBER_T (log1p (x));
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#endif /* JERRY_LIBM_MATH_H */
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break;
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}
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case ECMA_MATH_OBJECT_LOG10:
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{
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#ifdef JERRY_LIBM_MATH_H
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return ecma_raise_type_error (ECMA_ERR_MSG ("UNIMPLEMENTED: Math.log10"));
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#else /* !JERRY_LIBM_MATH_H */
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x = DOUBLE_TO_ECMA_NUMBER_T (log10 (x));
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#endif /* JERRY_LIBM_MATH_H */
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break;
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}
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case ECMA_MATH_OBJECT_LOG2:
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{
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#ifdef JERRY_LIBM_MATH_H
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return ecma_raise_type_error (ECMA_ERR_MSG ("UNIMPLEMENTED: Math.log2"));
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#else /* !JERRY_LIBM_MATH_H */
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x = DOUBLE_TO_ECMA_NUMBER_T (log2 (x));
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#endif /* JERRY_LIBM_MATH_H */
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break;
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}
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case ECMA_MATH_OBJECT_SINH:
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@@ -0,0 +1,305 @@
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/* Copyright JS Foundation and other contributors, http://js.foundation
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* This file is based on work under the following copyright and permission
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* notice:
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*
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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*
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* @(#)s_expm1.c 5.1 93/09/24
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*/
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#include "jerry-libm-internal.h"
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/* expm1(x)
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* Returns exp(x)-1, the exponential of x minus 1.
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*
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* Method
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* 1. Argument reduction:
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* Given x, find r and integer k such that
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*
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* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
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*
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* Here a correction term c will be computed to compensate
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* the error in r when rounded to a floating-point number.
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*
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* 2. Approximating expm1(r) by a special rational function on
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* the interval [0,0.34658]:
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* Since
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* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
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* we define R1(r*r) by
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* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
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* That is,
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* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
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* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
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* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
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* We use a special Reme algorithm on [0,0.347] to generate
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* a polynomial of degree 5 in r*r to approximate R1. The
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* maximum error of this polynomial approximation is bounded
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* by 2**-61. In other words,
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* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
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* where Q1 = -1.6666666666666567384E-2,
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* Q2 = 3.9682539681370365873E-4,
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* Q3 = -9.9206344733435987357E-6,
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* Q4 = 2.5051361420808517002E-7,
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* Q5 = -6.2843505682382617102E-9;
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* z = r*r,
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* with error bounded by
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* | 5 | -61
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* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
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* | |
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*
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* expm1(r) = exp(r)-1 is then computed by the following
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* specific way which minimize the accumulation rounding error:
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* 2 3
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* r r [ 3 - (R1 + R1*r/2) ]
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* expm1(r) = r + --- + --- * [--------------------]
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* 2 2 [ 6 - r*(3 - R1*r/2) ]
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*
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* To compensate the error in the argument reduction, we use
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* expm1(r+c) = expm1(r) + c + expm1(r)*c
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* ~ expm1(r) + c + r*c
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* Thus c+r*c will be added in as the correction terms for
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* expm1(r+c). Now rearrange the term to avoid optimization
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* screw up:
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* ( 2 2 )
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* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
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* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
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* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
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* ( )
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*
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* = r - E
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* 3. Scale back to obtain expm1(x):
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* From step 1, we have
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* expm1(x) = either 2^k*[expm1(r)+1] - 1
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* = or 2^k*[expm1(r) + (1-2^-k)]
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* 4. Implementation notes:
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* (A). To save one multiplication, we scale the coefficient Qi
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* to Qi*2^i, and replace z by (x^2)/2.
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* (B). To achieve maximum accuracy, we compute expm1(x) by
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* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
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* (ii) if k=0, return r-E
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* (iii) if k=-1, return 0.5*(r-E)-0.5
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* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
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* else return 1.0+2.0*(r-E);
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* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
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* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
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* (vii) return 2^k(1-((E+2^-k)-r))
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*
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* Special cases:
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* expm1(INF) is INF, expm1(NaN) is NaN;
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* expm1(-INF) is -1, and
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* for finite argument, only expm1(0)=0 is exact.
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*
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* Accuracy:
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* according to an error analysis, the error is always less than
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* 1 ulp (unit in the last place).
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*
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* Misc. info.
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* For IEEE double
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* if x > 7.09782712893383973096e+02 then expm1(x) overflow
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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#define one 1.0
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#define huge 1.0e+300
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#define tiny 1.0e-300
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#define o_threshold 7.09782712893383973096e+02 /* 0x40862E42, 0xFEFA39EF */
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#define ln2_hi 6.93147180369123816490e-01 /* 0x3fe62e42, 0xfee00000 */
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#define ln2_lo 1.90821492927058770002e-10 /* 0x3dea39ef, 0x35793c76 */
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#define invln2 1.44269504088896338700e+00 /* 0x3ff71547, 0x652b82fe */
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/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
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#define Q1 -3.33333333333331316428e-02 /* BFA11111 111110F4 */
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#define Q2 1.58730158725481460165e-03 /* 3F5A01A0 19FE5585 */
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#define Q3 -7.93650757867487942473e-05 /* BF14CE19 9EAADBB7 */
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#define Q4 4.00821782732936239552e-06 /* 3ED0CFCA 86E65239 */
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#define Q5 -2.01099218183624371326e-07 /* BE8AFDB7 6E09C32D */
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double
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expm1 (double x)
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{
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double y, hi, lo, c, e, hxs, hfx, r1;
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double_accessor t, twopk;
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int k, xsb;
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unsigned int hx;
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hx = __HI (x);
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xsb = hx & 0x80000000; /* sign bit of x */
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hx &= 0x7fffffff; /* high word of |x| */
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/* filter out huge and non-finite argument */
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if (hx >= 0x4043687A)
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{
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/* if |x|>=56*ln2 */
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if (hx >= 0x40862E42)
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{
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/* if |x|>=709.78... */
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if (hx >= 0x7ff00000)
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{
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unsigned int low;
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low = __LO (x);
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if (((hx & 0xfffff) | low) != 0)
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{
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/* NaN */
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return x + x;
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}
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else
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{
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/* exp(+-inf)-1={inf,-1} */
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return (xsb == 0) ? x : -1.0;
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}
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}
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if (x > o_threshold)
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{
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/* overflow */
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return huge * huge;
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}
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}
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if (xsb != 0)
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{
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/* x < -56*ln2, return -1.0 with inexact */
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if (x + tiny < 0.0) /* raise inexact */
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{
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/* return -1 */
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return tiny - one;
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}
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}
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}
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/* argument reduction */
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if (hx > 0x3fd62e42)
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{
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/* if |x| > 0.5 ln2 */
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if (hx < 0x3FF0A2B2)
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{
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/* and |x| < 1.5 ln2 */
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if (xsb == 0)
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{
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hi = x - ln2_hi;
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lo = ln2_lo;
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k = 1;
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}
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else
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{
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hi = x + ln2_hi;
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lo = -ln2_lo;
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k = -1;
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}
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}
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else
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{
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k = (int) (invln2 * x + ((xsb == 0) ? 0.5 : -0.5));
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t.dbl = k;
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hi = x - t.dbl * ln2_hi; /* t*ln2_hi is exact here */
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lo = t.dbl * ln2_lo;
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}
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x = hi - lo;
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c = (hi - x) - lo;
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}
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else if (hx < 0x3c900000)
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{
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/* when |x|<2**-54, return x */
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return x;
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}
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else
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{
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k = 0;
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}
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/* x is now in primary range */
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hfx = 0.5 * x;
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hxs = x * hfx;
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r1 = one + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
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t.dbl = 3.0 - r1 * hfx;
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e = hxs * ((r1 - t.dbl) / (6.0 - x * t.dbl));
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if (k == 0)
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{
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/* c is 0 */
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return x - (x * e - hxs);
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}
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else
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{
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twopk.as_int.hi = 0x3ff00000 + ((unsigned int) k << 20); /* 2^k */
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twopk.as_int.lo = 0;
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e = (x * (e - c) - c);
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e -= hxs;
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if (k == -1)
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{
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return 0.5 * (x - e) - 0.5;
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}
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if (k == 1)
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{
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if (x < -0.25)
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{
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return -2.0 * (e - (x + 0.5));
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}
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else
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{
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return one + 2.0 * (x - e);
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}
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}
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if ((k <= -2) || (k > 56))
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{
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/* suffice to return exp(x)-1 */
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y = one - (e - x);
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if (k == 1024)
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{
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y = y * 2.0 * 0x1p1023;
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}
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else
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{
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y = y * twopk.dbl;
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}
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return y - one;
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}
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t.dbl = one;
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if (k < 20)
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{
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t.as_int.hi = (0x3ff00000 - (0x200000 >> k)); /* t=1-2^-k */
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y = t.dbl - (e - x);
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y = y * twopk.dbl;
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}
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else
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{
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t.as_int.hi = ((0x3ff - k) << 20); /* 2^-k */
|
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y = x - (e + t.dbl);
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y += one;
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y = y * twopk.dbl;
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}
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}
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return y;
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} /* expm1 */
|
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#undef one
|
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#undef huge
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#undef tiny
|
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#undef o_threshold
|
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#undef ln2_hi
|
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#undef ln2_lo
|
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#undef invln2
|
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#undef Q1
|
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#undef Q2
|
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#undef Q3
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#undef Q4
|
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#undef Q5
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@@ -58,7 +58,11 @@ double atan2 (double, double);
|
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|
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/* Exponential and logarithmic functions. */
|
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double exp (double);
|
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double expm1 (double);
|
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double log (double);
|
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double log1p (double);
|
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double log2 (double);
|
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double log10 (double);
|
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|
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/* Power functions. */
|
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double pow (double, double);
|
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|
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@@ -89,7 +89,11 @@ double sin (double x);
|
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double tan (double x);
|
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|
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double exp (double x);
|
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double expm1 (double x);
|
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double log (double x);
|
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double log1p (double x);
|
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double log2 (double x);
|
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double log10 (double);
|
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|
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double pow (double x, double y);
|
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double sqrt (double x);
|
||||
|
||||
@@ -0,0 +1,116 @@
|
||||
/* Copyright JS Foundation and other contributors, http://js.foundation
|
||||
*
|
||||
* 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.
|
||||
*
|
||||
* This file is based on work under the following copyright and permission
|
||||
* notice:
|
||||
*
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
*
|
||||
* @(#)e_log10.c 1.3 95/01/18
|
||||
*/
|
||||
|
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#include "jerry-libm-internal.h"
|
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|
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/* log10(x)
|
||||
* Return the base 10 logarithm of x
|
||||
*
|
||||
* Method :
|
||||
* Let log10_2hi = leading 40 bits of log10(2) and
|
||||
* log10_2lo = log10(2) - log10_2hi,
|
||||
* ivln10 = 1/log(10) rounded.
|
||||
* Then
|
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* n = ilogb(x),
|
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* if(n<0) n = n+1;
|
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* x = scalbn(x,-n);
|
||||
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
|
||||
*
|
||||
* Note 1:
|
||||
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
|
||||
* mode must set to Round-to-Nearest.
|
||||
* Note 2:
|
||||
* [1/log(10)] rounded to 53 bits has error .198 ulps;
|
||||
* log10 is monotonic at all binary break points.
|
||||
*
|
||||
* Special cases:
|
||||
* log10(x) is NaN with signal if x < 0;
|
||||
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
|
||||
* log10(NaN) is that NaN with no signal;
|
||||
* log10(10**N) = N for N=0,1,...,22.
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following constants.
|
||||
* The decimal values may be used, provided that the compiler will convert
|
||||
* from decimal to binary accurately enough to produce the hexadecimal values
|
||||
* shown.
|
||||
*/
|
||||
|
||||
#define zero 0.0
|
||||
#define two54 1.80143985094819840000e+16 /* 0x43500000, 0x00000000 */
|
||||
#define ivln10 4.34294481903251816668e-01 /* 0x3FDBCB7B, 0x1526E50E */
|
||||
#define log10_2hi 3.01029995663611771306e-01 /* 0x3FD34413, 0x509F6000 */
|
||||
#define log10_2lo 3.69423907715893078616e-13 /* 0x3D59FEF3, 0x11F12B36 */
|
||||
|
||||
double
|
||||
log10 (double x)
|
||||
{
|
||||
double y, z;
|
||||
int i, k, hx;
|
||||
unsigned lx;
|
||||
double_accessor temp;
|
||||
|
||||
hx = __HI (x); /* high word of x */
|
||||
lx = __LO (x); /* low word of x */
|
||||
|
||||
k = 0;
|
||||
if (hx < 0x00100000)
|
||||
{
|
||||
/* x < 2**-1022 */
|
||||
if (((hx & 0x7fffffff) | lx) == 0)
|
||||
{
|
||||
/* log(+-0)=-inf */
|
||||
return -two54 / zero;
|
||||
}
|
||||
if (hx < 0)
|
||||
{
|
||||
/* log(-#) = NaN */
|
||||
return (x - x) / zero;
|
||||
}
|
||||
k -= 54;
|
||||
x *= two54; /* subnormal number, scale up x */
|
||||
hx = __HI (x); /* high word of x */
|
||||
}
|
||||
if (hx >= 0x7ff00000)
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
k += (hx >> 20) - 1023;
|
||||
i = ((unsigned) k & 0x80000000) >> 31;
|
||||
hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
|
||||
y = (double) (k + i);
|
||||
temp.dbl = x;
|
||||
temp.as_int.hi = hx;
|
||||
z = y * log10_2lo + ivln10 * log (temp.dbl);
|
||||
return z + y * log10_2hi;
|
||||
} /* log10 */
|
||||
|
||||
#undef zero
|
||||
#undef two54
|
||||
#undef ivln10
|
||||
#undef log10_2hi
|
||||
#undef log10_2lo
|
||||
@@ -0,0 +1,245 @@
|
||||
/* Copyright JS Foundation and other contributors, http://js.foundation
|
||||
*
|
||||
* 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.
|
||||
*
|
||||
* This file is based on work under the following copyright and permission
|
||||
* notice:
|
||||
*
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
*
|
||||
* @(#)s_log1p.c 5.1 93/09/24
|
||||
*/
|
||||
|
||||
#include "jerry-libm-internal.h"
|
||||
|
||||
/* log1p(x)
|
||||
* Method :
|
||||
* 1. Argument Reduction: find k and f such that
|
||||
* 1+x = 2^k * (1+f),
|
||||
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
*
|
||||
* Note. If k=0, then f=x is exact. However, if k!=0, then f
|
||||
* may not be representable exactly. In that case, a correction
|
||||
* term is need. Let u=1+x rounded. Let c = (1+x)-u, then
|
||||
* log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
|
||||
* and add back the correction term c/u.
|
||||
* (Note: when x > 2**53, one can simply return log(x))
|
||||
*
|
||||
* 2. Approximation of log1p(f).
|
||||
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
|
||||
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
|
||||
* = 2s + s*R
|
||||
* We use a special Reme algorithm on [0,0.1716] to generate
|
||||
* a polynomial of degree 14 to approximate R The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-58.45. In
|
||||
* other words,
|
||||
* 2 4 6 8 10 12 14
|
||||
* R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s
|
||||
* (the values of Lp1 to Lp7 are listed in the program)
|
||||
* and
|
||||
* | 2 14 | -58.45
|
||||
* | Lp1*s +...+Lp7*s - R(z) | <= 2
|
||||
* | |
|
||||
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
|
||||
* In order to guarantee error in log below 1ulp, we compute log
|
||||
* by
|
||||
* log1p(f) = f - (hfsq - s*(hfsq+R)).
|
||||
*
|
||||
* 3. Finally, log1p(x) = k*ln2 + log1p(f).
|
||||
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
|
||||
* Here ln2 is split into two floating point number:
|
||||
* ln2_hi + ln2_lo,
|
||||
* where n*ln2_hi is always exact for |n| < 2000.
|
||||
*
|
||||
* Special cases:
|
||||
* log1p(x) is NaN with signal if x < -1 (including -INF) ;
|
||||
* log1p(+INF) is +INF; log1p(-1) is -INF with signal;
|
||||
* log1p(NaN) is that NaN with no signal.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Constants:
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*
|
||||
* Note: Assuming log() return accurate answer, the following
|
||||
* algorithm can be used to compute log1p(x) to within a few ULP:
|
||||
*
|
||||
* u = 1+x;
|
||||
* if(u==1.0) return x ; else
|
||||
* return log(u)*(x/(u-1.0));
|
||||
*
|
||||
* See HP-15C Advanced Functions Handbook, p.193.
|
||||
*/
|
||||
|
||||
#define zero 0.0
|
||||
#define ln2_hi 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
|
||||
#define ln2_lo 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
|
||||
#define two54 1.80143985094819840000e+16 /* 43500000 00000000 */
|
||||
#define Lp1 6.666666666666735130e-01 /* 3FE55555 55555593 */
|
||||
#define Lp2 3.999999999940941908e-01 /* 3FD99999 9997FA04 */
|
||||
#define Lp3 2.857142874366239149e-01 /* 3FD24924 94229359 */
|
||||
#define Lp4 2.222219843214978396e-01 /* 3FCC71C5 1D8E78AF */
|
||||
#define Lp5 1.818357216161805012e-01 /* 3FC74664 96CB03DE */
|
||||
#define Lp6 1.531383769920937332e-01 /* 3FC39A09 D078C69F */
|
||||
#define Lp7 1.479819860511658591e-01 /* 3FC2F112 DF3E5244 */
|
||||
|
||||
double
|
||||
log1p (double x)
|
||||
{
|
||||
double hfsq, f, c, s, z, R;
|
||||
double_accessor u;
|
||||
int k, hx, hu, ax;
|
||||
|
||||
hx = __HI (x);
|
||||
ax = hx & 0x7fffffff;
|
||||
c = 0;
|
||||
k = 1;
|
||||
if (hx < 0x3FDA827A)
|
||||
{
|
||||
/* 1+x < sqrt(2)+ */
|
||||
if (ax >= 0x3ff00000)
|
||||
{
|
||||
/* x <= -1.0 */
|
||||
if (x == -1.0)
|
||||
{
|
||||
/* log1p(-1) = +inf */
|
||||
return -two54 / zero;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* log1p(x<-1) = NaN */
|
||||
return NAN;
|
||||
}
|
||||
}
|
||||
if (ax < 0x3e200000)
|
||||
{ /* |x| < 2**-29 */
|
||||
if ((two54 + x > zero) /* raise inexact */
|
||||
&& (ax < 0x3c900000)) /* |x| < 2**-54 */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
else
|
||||
{
|
||||
return x - x * x * 0.5;
|
||||
}
|
||||
}
|
||||
if ((hx > 0) || hx <= ((int) 0xbfd2bec4))
|
||||
{
|
||||
/* sqrt(2)/2- <= 1+x < sqrt(2)+ */
|
||||
k = 0;
|
||||
f = x;
|
||||
hu = 1;
|
||||
}
|
||||
}
|
||||
if (hx >= 0x7ff00000)
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
if (k != 0)
|
||||
{
|
||||
if (hx < 0x43400000)
|
||||
{
|
||||
u.dbl = 1.0 + x;
|
||||
hu = u.as_int.hi;
|
||||
k = (hu >> 20) - 1023;
|
||||
c = (k > 0) ? 1.0 - (u.dbl - x) : x - (u.dbl - 1.0); /* correction term */
|
||||
c /= u.dbl;
|
||||
}
|
||||
else
|
||||
{
|
||||
u.dbl = x;
|
||||
hu = u.as_int.hi;
|
||||
k = (hu >> 20) - 1023;
|
||||
c = 0;
|
||||
}
|
||||
hu &= 0x000fffff;
|
||||
/*
|
||||
* The approximation to sqrt(2) used in thresholds is not
|
||||
* critical. However, the ones used above must give less
|
||||
* strict bounds than the one here so that the k==0 case is
|
||||
* never reached from here, since here we have committed to
|
||||
* using the correction term but don't use it if k==0.
|
||||
*/
|
||||
if (hu < 0x6a09e)
|
||||
{
|
||||
/* u ~< sqrt(2) */
|
||||
u.as_int.hi = hu | 0x3ff00000; /* normalize u */
|
||||
}
|
||||
else
|
||||
{
|
||||
k += 1;
|
||||
u.as_int.hi = hu | 0x3fe00000; /* normalize u/2 */
|
||||
hu = (0x00100000 - hu) >> 2;
|
||||
}
|
||||
f = u.dbl - 1.0;
|
||||
}
|
||||
hfsq = 0.5 * f * f;
|
||||
if (hu == 0)
|
||||
{
|
||||
/* |f| < 2**-20 */
|
||||
if (f == zero)
|
||||
{
|
||||
if (k == 0)
|
||||
{
|
||||
return zero;
|
||||
}
|
||||
else
|
||||
{
|
||||
c += k * ln2_lo;
|
||||
return k * ln2_hi + c;
|
||||
}
|
||||
}
|
||||
R = hfsq * (1.0 - 0.66666666666666666 * f);
|
||||
if (k == 0)
|
||||
{
|
||||
return f - R;
|
||||
}
|
||||
else
|
||||
{
|
||||
return k * ln2_hi - ((R - (k * ln2_lo + c)) - f);
|
||||
}
|
||||
}
|
||||
s = f / (2.0 + f);
|
||||
z = s * s;
|
||||
R = z * (Lp1 +
|
||||
z * (Lp2 + z * (Lp3 + z * (Lp4 + z * (Lp5 + z * (Lp6 + z * Lp7))))));
|
||||
if (k == 0)
|
||||
{
|
||||
return f - (hfsq - s * (hfsq + R));
|
||||
}
|
||||
else
|
||||
{
|
||||
return k * ln2_hi - ((hfsq - (s * (hfsq + R) + (k * ln2_lo + c))) - f);
|
||||
}
|
||||
} /* log1p */
|
||||
|
||||
#undef zero
|
||||
#undef ln2_hi
|
||||
#undef ln2_lo
|
||||
#undef two54
|
||||
#undef Lp1
|
||||
#undef Lp2
|
||||
#undef Lp3
|
||||
#undef Lp4
|
||||
#undef Lp5
|
||||
#undef Lp6
|
||||
#undef Lp7
|
||||
@@ -0,0 +1,160 @@
|
||||
/* Copyright JS Foundation and other contributors, http://js.foundation
|
||||
*
|
||||
* 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.
|
||||
*
|
||||
* This file is based on work under the following copyright and permission
|
||||
* notice:
|
||||
*
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
*
|
||||
* @(#)e_log2.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-libm-internal.h"
|
||||
|
||||
/* log2(x)
|
||||
* Return the base 2 logarithm of x. See e_log.c and k_log.h for most
|
||||
* comments.
|
||||
*
|
||||
* This reduces x to {k, 1+f} exactly as in e_log.c, then calls the kernel,
|
||||
* then does the combining and scaling steps
|
||||
* log2(x) = (f - 0.5*f*f + k_log1p(f)) / ln2 + k
|
||||
* in not-quite-routine extra precision.
|
||||
*/
|
||||
|
||||
#define zero 0.0
|
||||
#define two54 1.80143985094819840000e+16 /* 0x43500000, 0x00000000 */
|
||||
#define ivln2hi 1.44269504072144627571e+00 /* 0x3FF71547, 0x65200000 */
|
||||
#define ivln2lo 1.67517131648865118353e-10 /* 0x3DE705FC, 0x2EEFA200 */
|
||||
#define Lg1 6.666666666666735130e-01 /* 0x3FE55555, 0x55555593 */
|
||||
#define Lg2 3.999999999940941908e-01 /* 0x3FD99999, 0x9997FA04 */
|
||||
#define Lg3 2.857142874366239149e-01 /* 0x3FD24924, 0x94229359 */
|
||||
#define Lg4 2.222219843214978396e-01 /* 0x3FCC71C5, 0x1D8E78AF */
|
||||
#define Lg5 1.818357216161805012e-01 /* 0x3FC74664, 0x96CB03DE */
|
||||
#define Lg6 1.531383769920937332e-01 /* 0x3FC39A09, 0xD078C69F */
|
||||
#define Lg7 1.479819860511658591e-01 /* 0x3FC2F112, 0xDF3E5244 */
|
||||
|
||||
double
|
||||
log2 (double x)
|
||||
{
|
||||
double f, hfsq, hi, lo, r, val_hi, val_lo, w, y;
|
||||
int i, k, hx;
|
||||
unsigned int lx;
|
||||
double_accessor temp;
|
||||
|
||||
hx = __HI (x); /* high word of x */
|
||||
lx = __LO (x); /* low word of x */
|
||||
|
||||
k = 0;
|
||||
if (hx < 0x00100000)
|
||||
{ /* x < 2**-1022 */
|
||||
if (((hx & 0x7fffffff) | lx) == 0)
|
||||
{
|
||||
return -two54 / zero; /* log(+-0)=-inf */
|
||||
}
|
||||
if (hx < 0)
|
||||
{
|
||||
return (x - x) / zero; /* log(-#) = NaN */
|
||||
}
|
||||
k -= 54;
|
||||
x *= two54; /* subnormal number, scale up x */
|
||||
hx = __HI (x); /* high word of x */
|
||||
}
|
||||
if (hx >= 0x7ff00000)
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
if (hx == 0x3ff00000 && lx == 0)
|
||||
{
|
||||
return zero; /* log(1) = +0 */
|
||||
}
|
||||
k += (hx >> 20) - 1023;
|
||||
hx &= 0x000fffff;
|
||||
i = (hx + 0x95f64) & 0x100000;
|
||||
temp.dbl = x;
|
||||
temp.as_int.hi = hx | (i ^ 0x3ff00000); /* normalize x or x/2 */
|
||||
k += (i >> 20);
|
||||
y = (double) k;
|
||||
f = temp.dbl - 1.0;
|
||||
hfsq = 0.5 * f * f;
|
||||
double s, z, R, t1, t2;
|
||||
|
||||
s = f / (2.0 + f);
|
||||
z = s * s;
|
||||
w = z * z;
|
||||
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
||||
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
||||
R = t2 + t1;
|
||||
r = s * (hfsq + R);
|
||||
/*
|
||||
* f-hfsq must (for args near 1) be evaluated in extra precision
|
||||
* to avoid a large cancellation when x is near sqrt(2) or 1/sqrt(2).
|
||||
* This is fairly efficient since f-hfsq only depends on f, so can
|
||||
* be evaluated in parallel with R. Not combining hfsq with R also
|
||||
* keeps R small (though not as small as a true `lo' term would be),
|
||||
* so that extra precision is not needed for terms involving R.
|
||||
*
|
||||
* Compiler bugs involving extra precision used to break Dekker's
|
||||
* theorem for spitting f-hfsq as hi+lo, unless double_t was used
|
||||
* or the multi-precision calculations were avoided when double_t
|
||||
* has extra precision. These problems are now automatically
|
||||
* avoided as a side effect of the optimization of combining the
|
||||
* Dekker splitting step with the clear-low-bits step.
|
||||
*
|
||||
* y must (for args near sqrt(2) and 1/sqrt(2)) be added in extra
|
||||
* precision to avoid a very large cancellation when x is very near
|
||||
* these values. Unlike the above cancellations, this problem is
|
||||
* specific to base 2. It is strange that adding +-1 is so much
|
||||
* harder than adding +-ln2 or +-log10_2.
|
||||
*
|
||||
* This uses Dekker's theorem to normalize y+val_hi, so the
|
||||
* compiler bugs are back in some configurations, sigh. And I
|
||||
* don't want to used double_t to avoid them, since that gives a
|
||||
* pessimization and the support for avoiding the pessimization
|
||||
* is not yet available.
|
||||
*
|
||||
* The multi-precision calculations for the multiplications are
|
||||
* routine.
|
||||
*/
|
||||
hi = f - hfsq;
|
||||
temp.dbl = hi;
|
||||
temp.as_int.lo = 0;
|
||||
|
||||
lo = (f - hi) - hfsq + r;
|
||||
val_hi = hi * ivln2hi;
|
||||
val_lo = (lo + hi) * ivln2lo + lo * ivln2hi;
|
||||
|
||||
/* spadd(val_hi, val_lo, y), except for not using double_t: */
|
||||
w = y + val_hi;
|
||||
val_lo += (y - w) + val_hi;
|
||||
val_hi = w;
|
||||
|
||||
return val_lo + val_hi;
|
||||
} /* log2 */
|
||||
|
||||
#undef zero
|
||||
#undef two54
|
||||
#undef ivln2hi
|
||||
#undef ivln2lo
|
||||
#undef Lg1
|
||||
#undef Lg2
|
||||
#undef Lg3
|
||||
#undef Lg4
|
||||
#undef Lg5
|
||||
#undef Lg6
|
||||
#undef Lg7
|
||||
@@ -0,0 +1,31 @@
|
||||
// Copyright JS Foundation and other contributors, http://js.foundation
|
||||
//
|
||||
// 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.
|
||||
|
||||
var p_zero = 0.0;
|
||||
var n_zero = -p_zero;
|
||||
|
||||
function isSameZero (x, y)
|
||||
{
|
||||
return x === 0 && (1 / x) === (1 / y);
|
||||
}
|
||||
|
||||
assert(isNaN(Math.expm1(NaN)));
|
||||
assert(isSameZero(Math.expm1(p_zero), p_zero));
|
||||
assert(isSameZero(Math.expm1(n_zero), n_zero));
|
||||
assert(Math.expm1(Number.POSITIVE_INFINITY) === Number.POSITIVE_INFINITY);
|
||||
assert(Math.expm1(Number.NEGATIVE_INFINITY) === -1);
|
||||
assert(1/Math.expm1(-0) === Number.NEGATIVE_INFINITY)
|
||||
assert(1/Math.expm1(0) === Number.POSITIVE_INFINITY)
|
||||
assert(Math.expm1(1) <= 1.00000001 * (Math.E - 1));
|
||||
assert(Math.expm1(1) >= 0.99999999 * (Math.E - 1));
|
||||
@@ -0,0 +1,26 @@
|
||||
// Copyright JS Foundation and other contributors, http://js.foundation
|
||||
//
|
||||
// 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.
|
||||
|
||||
var p_zero = 0.0;
|
||||
var n_zero = -p_zero;
|
||||
|
||||
assert(isNaN(Math.log10(NaN)));
|
||||
assert(isNaN(Math.log10(-42)));
|
||||
assert(isNaN(Math.log10(-3.0)));
|
||||
assert(Math.log10(n_zero) === Number.NEGATIVE_INFINITY);
|
||||
assert(Math.log10(p_zero) === Number.NEGATIVE_INFINITY);
|
||||
assert(Math.log10(1) === p_zero);
|
||||
assert(Math.log10(Number.POSITIVE_INFINITY) === Number.POSITIVE_INFINITY);
|
||||
assert(Math.log10(10.0) === 1);
|
||||
assert(Math.log10(100.0) === 2)
|
||||
@@ -0,0 +1,30 @@
|
||||
// Copyright JS Foundation and other contributors, http://js.foundation
|
||||
//
|
||||
// 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.
|
||||
|
||||
var p_zero = 0.0;
|
||||
var n_zero = -p_zero;
|
||||
|
||||
function isSameZero (x, y)
|
||||
{
|
||||
return x === 0 && (1 / x) === (1 / y);
|
||||
}
|
||||
|
||||
assert(isNaN(Math.log1p(NaN)));
|
||||
assert(isNaN(Math.log1p(-42)));
|
||||
assert(isNaN(Math.log1p(-3.0)));
|
||||
assert(isSameZero(Math.log1p(n_zero), n_zero));
|
||||
assert(isSameZero(Math.log1p(p_zero), p_zero));
|
||||
assert(Math.log1p(-1) === Number.NEGATIVE_INFINITY);
|
||||
assert(Math.log1p(Number.POSITIVE_INFINITY) === Number.POSITIVE_INFINITY);
|
||||
assert(Math.log1p(Math.E - 1) === 1);
|
||||
@@ -0,0 +1,27 @@
|
||||
// Copyright JS Foundation and other contributors, http://js.foundation
|
||||
//
|
||||
// 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.
|
||||
|
||||
var p_zero = 0.0;
|
||||
var n_zero = -p_zero;
|
||||
|
||||
assert(isNaN(Math.log2(NaN)));
|
||||
assert(isNaN(Math.log2(-42)));
|
||||
assert(isNaN(Math.log2(-3.0)));
|
||||
assert(Math.log2(n_zero) === Number.NEGATIVE_INFINITY);
|
||||
assert(Math.log2(p_zero) === Number.NEGATIVE_INFINITY);
|
||||
assert(Math.log2(1) === p_zero);
|
||||
assert(Math.log2(Number.POSITIVE_INFINITY) === Number.POSITIVE_INFINITY);
|
||||
assert(Math.log2(2.0) === 1);
|
||||
assert(Math.log2(4.0) === 2)
|
||||
assert(Math.log2(1024.0) === 10)
|
||||
@@ -205,6 +205,33 @@ check_double ("exp (2.0)", exp (2.0), 7.38905609893065040694E+00);
|
||||
check_double ("exp (3.0)", exp (3.0), 2.00855369231876679237E+01);
|
||||
check_double ("exp (0.7)", exp (0.7), 2.01375270747047663278E+00);
|
||||
check_double ("exp (38.0)", exp (38.0), 3.18559317571137560000E+16);
|
||||
check_double ("expm1 (0.0)", expm1 (0.0), 0.00000000000000000000E+00);
|
||||
check_double ("expm1 (-0.0)", expm1 (-0.0), -0.00000000000000000000E+00);
|
||||
check_double ("expm1 (1.0)", expm1 (1.0), 1.71828182845904531284E+00);
|
||||
check_double ("expm1 (-1.0)", expm1 (-1.0), -6.32120558828557665976E-01);
|
||||
check_double ("expm1 (INFINITY)", expm1 (INFINITY), INF);
|
||||
check_double ("expm1 (-INFINITY)", expm1 (-INFINITY), -1.00000000000000000000E+00);
|
||||
check_double ("expm1 (NAN)", expm1 (NAN), NAN);
|
||||
check_double ("expm1 (7.08e+02)", expm1 (7.08e+02), 3.02338314427605515848E+307);
|
||||
check_double ("expm1 (7.10e+02)", expm1 (7.10e+02), INF);
|
||||
check_double ("expm1 (-7.40e+02)", expm1 (-7.40e+02), -1.00000000000000000000E+00);
|
||||
check_double ("expm1 (-7.50e+02)", expm1 (-7.50e+02), -1.00000000000000000000E+00);
|
||||
check_double ("expm1 (0.34)", expm1 (0.34), 4.04947590563593806667E-01);
|
||||
check_double ("expm1 (-0.34)", expm1 (-0.34), -2.88229677237390291555E-01);
|
||||
check_double ("expm1 (0.35)", expm1 (0.35), 4.19067548593257233058E-01);
|
||||
check_double ("expm1 (-0.35)", expm1 (-0.35), -2.95311910281286560398E-01);
|
||||
check_double ("expm1 (1.03)", expm1 (1.03), 1.80106583469907910455E+00);
|
||||
check_double ("expm1 (-1.03)", expm1 (-1.03), -6.42993039430852619809E-01);
|
||||
check_double ("expm1 (1.04)", expm1 (1.04), 1.82921701435155958926E+00);
|
||||
check_double ("expm1 (-1.04)", expm1 (-1.04), -6.46545318041219840843E-01);
|
||||
check_double ("expm1 (3.72e-09)", expm1 (3.72e-09), 3.72000000691919994955E-09);
|
||||
check_double ("expm1 (-3.72e-09)", expm1 (-3.72e-09), -3.71999999308080000097E-09);
|
||||
check_double ("expm1 (3.73e-09)", expm1 (3.73e-09), 3.73000000695645013275E-09);
|
||||
check_double ("expm1 (-3.73e-09)", expm1 (-3.73e-09), -3.72999999304355016230E-09);
|
||||
check_double ("expm1 (2.0)", expm1 (2.0), 6.38905609893065040694E+00);
|
||||
check_double ("expm1 (3.0)", expm1 (3.0), 1.90855369231876679237E+01);
|
||||
check_double ("expm1 (0.7)", expm1 (0.7), 1.01375270747047641073E+00);
|
||||
check_double ("expm1 (38.0)", expm1 (38.0), 3.18559317571137560000E+16);
|
||||
check_double ("fabs (0.0)", fabs (0.0), 0.00000000000000000000E+00);
|
||||
check_double ("fabs (-0.0)", fabs (-0.0), 0.00000000000000000000E+00);
|
||||
check_double ("fabs (1.0)", fabs (1.0), 1.00000000000000000000E+00);
|
||||
@@ -322,6 +349,63 @@ check_double ("log (0.18)", log (0.18), -1.71479842809192661868E+00);
|
||||
check_double ("log (1999.0)", log (1999.0), 7.60040233450039970364E+00);
|
||||
check_double ("log (2000.0)", log (2000.0), 7.60090245954208221235E+00);
|
||||
check_double ("log (2001.0)", log (2001.0), 7.60140233458373337783E+00);
|
||||
check_double ("log1p (0.0)", log1p (0.0), 0.00000000000000000000E+00);
|
||||
check_double ("log1p (-0.0)", log1p (-0.0), -0.00000000000000000000E+00);
|
||||
check_double ("log1p (1.0)", log1p (1.0), 6.93147180559945286227E-01);
|
||||
check_double ("log1p (-1.0)", log1p (-1.0), -INF);
|
||||
check_double ("log1p (INFINITY)", log1p (INFINITY), INF);
|
||||
check_double ("log1p (-INFINITY)", log1p (-INFINITY), -NAN);
|
||||
check_double ("log1p (NAN)", log1p (NAN), NAN);
|
||||
check_double ("log1p (M_E)", log1p (M_E), 1.31326168751822280889E+00);
|
||||
check_double ("log1p (1.0 / M_E)", log1p (1.0 / M_E), 3.13261687518222864401E-01);
|
||||
check_double ("log1p (2)", log1p (2), 1.09861228866810978211E+00);
|
||||
check_double ("log1p (10)", log1p (10), 2.39789527279837066942E+00);
|
||||
check_double ("log1p (0.7)", log1p (0.7), 5.30628251062170375185E-01);
|
||||
check_double ("log1p (2.22e-308)", log1p (2.22e-308), 2.22000000000000013467E-308);
|
||||
check_double ("log1p (2.23e-308)", log1p (2.23e-308), 2.23000000000000010412E-308);
|
||||
check_double ("log1p (0.17)", log1p (0.17), 1.57003748809664750441E-01);
|
||||
check_double ("log1p (0.18)", log1p (0.18), 1.65514438477573383457E-01);
|
||||
check_double ("log1p (1999.0)", log1p (1999.0), 7.60090245954208221235E+00);
|
||||
check_double ("log1p (2000.0)", log1p (2000.0), 7.60140233458373337783E+00);
|
||||
check_double ("log1p (2001.0)", log1p (2001.0), 7.60190195987516581511E+00);
|
||||
check_double ("log2 (0.0)", log2 (0.0), -INF);
|
||||
check_double ("log2 (-0.0)", log2 (-0.0), -INF);
|
||||
check_double ("log2 (1.0)", log2 (1.0), 0.00000000000000000000E+00);
|
||||
check_double ("log2 (-1.0)", log2 (-1.0), NAN);
|
||||
check_double ("log2 (INFINITY)", log2 (INFINITY), INF);
|
||||
check_double ("log2 (-INFINITY)", log2 (-INFINITY), NAN);
|
||||
check_double ("log2 (NAN)", log2 (NAN), NAN);
|
||||
check_double ("log2 (M_E)", log2 (M_E), 1.44269504088896338700E+00);
|
||||
check_double ("log2 (1.0 / M_E)", log2 (1.0 / M_E), -1.44269504088896338700E+00);
|
||||
check_double ("log2 (2)", log2 (2), 1.00000000000000000000E+00);
|
||||
check_double ("log2 (10)", log2 (10), 3.32192809488736218171E+00);
|
||||
check_double ("log2 (0.7)", log2 (0.7), -5.14573172829758340718E-01);
|
||||
check_double ("log2 (2.22e-308)", log2 (2.22e-308), -1.02200329354873224474E+03);
|
||||
check_double ("log2 (2.23e-308)", log2 (2.23e-308), -1.02199680951516199912E+03);
|
||||
check_double ("log2 (0.17)", log2 (0.17), -2.55639334852438526724E+00);
|
||||
check_double ("log2 (0.18)", log2 (0.18), -2.47393118833241221211E+00);
|
||||
check_double ("log2 (1999.0)", log2 (1999.0), 1.09650627567446274924E+01);
|
||||
check_double ("log2 (2000.0)", log2 (2000.0), 1.09657842846620869892E+01);
|
||||
check_double ("log2 (2001.0)", log2 (2001.0), 1.09665054519057409976E+01);
|
||||
check_double ("log10 (0.0)", log10 (0.0), -INF);
|
||||
check_double ("log10 (-0.0)", log10 (-0.0), -INF);
|
||||
check_double ("log10 (1.0)", log10 (1.0), 0.00000000000000000000E+00);
|
||||
check_double ("log10 (-1.0)", log10 (-1.0), NAN);
|
||||
check_double ("log10 (INFINITY)", log10 (INFINITY), INF);
|
||||
check_double ("log10 (-INFINITY)", log10 (-INFINITY), NAN);
|
||||
check_double ("log10 (NAN)", log10 (NAN), NAN);
|
||||
check_double ("log10 (M_E)", log10 (M_E), 4.34294481903251816668E-01);
|
||||
check_double ("log10 (1.0 / M_E)", log10 (1.0 / M_E), -4.34294481903251816668E-01);
|
||||
check_double ("log10 (2)", log10 (2), 3.01029995663981198017E-01);
|
||||
check_double ("log10 (10)", log10 (10), 1.00000000000000000000E+00);
|
||||
check_double ("log10 (0.7)", log10 (0.7), -1.54901959985743187254E-01);
|
||||
check_double ("log10 (2.22e-308)", log10 (2.22e-308), -3.07653647025549389582E+02);
|
||||
check_double ("log10 (2.23e-308)", log10 (2.23e-308), -3.07651695136951843779E+02);
|
||||
check_double ("log10 (0.17)", log10 (0.17), -7.69551078621726003526E-01);
|
||||
check_double ("log10 (0.18)", log10 (0.18), -7.44727494896693986703E-01);
|
||||
check_double ("log10 (1999.0)", log10 (1999.0), 3.30081279411811712166E+00);
|
||||
check_double ("log10 (2000.0)", log10 (2000.0), 3.30102999566398125353E+00);
|
||||
check_double ("log10 (2001.0)", log10 (2001.0), 3.30124708863621130206E+00);
|
||||
check_double ("pow (0.0, 0.0)", pow (0.0, 0.0), 1.00000000000000000000E+00);
|
||||
check_double ("pow (0.0, -0.0)", pow (0.0, -0.0), 1.00000000000000000000E+00);
|
||||
check_double ("pow (-0.0, 0.0)", pow (-0.0, 0.0), 1.00000000000000000000E+00);
|
||||
|
||||
@@ -309,6 +309,35 @@ main (int argc, char **args)
|
||||
GEN_DBL_TEST (exp (0.7));
|
||||
GEN_DBL_TEST (exp (38.0));
|
||||
|
||||
/* expm1 tests */
|
||||
GEN_DBL_TEST (expm1 (0.0));
|
||||
GEN_DBL_TEST (expm1 (-0.0));
|
||||
GEN_DBL_TEST (expm1 (1.0));
|
||||
GEN_DBL_TEST (expm1 (-1.0));
|
||||
GEN_DBL_TEST (expm1 (INFINITY));
|
||||
GEN_DBL_TEST (expm1 (-INFINITY));
|
||||
GEN_DBL_TEST (expm1 (NAN));
|
||||
GEN_DBL_TEST (expm1 (7.08e+02));
|
||||
GEN_DBL_TEST (expm1 (7.10e+02));
|
||||
GEN_DBL_TEST (expm1 (-7.40e+02));
|
||||
GEN_DBL_TEST (expm1 (-7.50e+02));
|
||||
GEN_DBL_TEST (expm1 (0.34));
|
||||
GEN_DBL_TEST (expm1 (-0.34));
|
||||
GEN_DBL_TEST (expm1 (0.35));
|
||||
GEN_DBL_TEST (expm1 (-0.35));
|
||||
GEN_DBL_TEST (expm1 (1.03));
|
||||
GEN_DBL_TEST (expm1 (-1.03));
|
||||
GEN_DBL_TEST (expm1 (1.04));
|
||||
GEN_DBL_TEST (expm1 (-1.04));
|
||||
GEN_DBL_TEST (expm1 (3.72e-09));
|
||||
GEN_DBL_TEST (expm1 (-3.72e-09));
|
||||
GEN_DBL_TEST (expm1 (3.73e-09));
|
||||
GEN_DBL_TEST (expm1 (-3.73e-09));
|
||||
GEN_DBL_TEST (expm1 (2.0));
|
||||
GEN_DBL_TEST (expm1 (3.0));
|
||||
GEN_DBL_TEST (expm1 (0.7));
|
||||
GEN_DBL_TEST (expm1 (38.0));
|
||||
|
||||
/* fabs tests */
|
||||
GEN_DBL_TEST (fabs (0.0));
|
||||
GEN_DBL_TEST (fabs (-0.0));
|
||||
@@ -455,6 +484,69 @@ main (int argc, char **args)
|
||||
GEN_DBL_TEST (log (2000.0));
|
||||
GEN_DBL_TEST (log (2001.0));
|
||||
|
||||
/* log1p tests */
|
||||
GEN_DBL_TEST (log1p (0.0));
|
||||
GEN_DBL_TEST (log1p (-0.0));
|
||||
GEN_DBL_TEST (log1p (1.0));
|
||||
GEN_DBL_TEST (log1p (-1.0));
|
||||
GEN_DBL_TEST (log1p (INFINITY));
|
||||
GEN_DBL_TEST (log1p (-INFINITY));
|
||||
GEN_DBL_TEST (log1p (NAN));
|
||||
GEN_DBL_TEST (log1p (M_E));
|
||||
GEN_DBL_TEST (log1p (1.0 / M_E));
|
||||
GEN_DBL_TEST (log1p (2));
|
||||
GEN_DBL_TEST (log1p (10));
|
||||
GEN_DBL_TEST (log1p (0.7));
|
||||
GEN_DBL_TEST (log1p (2.22e-308));
|
||||
GEN_DBL_TEST (log1p (2.23e-308));
|
||||
GEN_DBL_TEST (log1p (0.17));
|
||||
GEN_DBL_TEST (log1p (0.18));
|
||||
GEN_DBL_TEST (log1p (1999.0));
|
||||
GEN_DBL_TEST (log1p (2000.0));
|
||||
GEN_DBL_TEST (log1p (2001.0));
|
||||
|
||||
/* log2 tests */
|
||||
GEN_DBL_TEST (log2 (0.0));
|
||||
GEN_DBL_TEST (log2 (-0.0));
|
||||
GEN_DBL_TEST (log2 (1.0));
|
||||
GEN_DBL_TEST (log2 (-1.0));
|
||||
GEN_DBL_TEST (log2 (INFINITY));
|
||||
GEN_DBL_TEST (log2 (-INFINITY));
|
||||
GEN_DBL_TEST (log2 (NAN));
|
||||
GEN_DBL_TEST (log2 (M_E));
|
||||
GEN_DBL_TEST (log2 (1.0 / M_E));
|
||||
GEN_DBL_TEST (log2 (2));
|
||||
GEN_DBL_TEST (log2 (10));
|
||||
GEN_DBL_TEST (log2 (0.7));
|
||||
GEN_DBL_TEST (log2 (2.22e-308));
|
||||
GEN_DBL_TEST (log2 (2.23e-308));
|
||||
GEN_DBL_TEST (log2 (0.17));
|
||||
GEN_DBL_TEST (log2 (0.18));
|
||||
GEN_DBL_TEST (log2 (1999.0));
|
||||
GEN_DBL_TEST (log2 (2000.0));
|
||||
GEN_DBL_TEST (log2 (2001.0));
|
||||
|
||||
/* log10 tests */
|
||||
GEN_DBL_TEST (log10 (0.0));
|
||||
GEN_DBL_TEST (log10 (-0.0));
|
||||
GEN_DBL_TEST (log10 (1.0));
|
||||
GEN_DBL_TEST (log10 (-1.0));
|
||||
GEN_DBL_TEST (log10 (INFINITY));
|
||||
GEN_DBL_TEST (log10 (-INFINITY));
|
||||
GEN_DBL_TEST (log10 (NAN));
|
||||
GEN_DBL_TEST (log10 (M_E));
|
||||
GEN_DBL_TEST (log10 (1.0 / M_E));
|
||||
GEN_DBL_TEST (log10 (2));
|
||||
GEN_DBL_TEST (log10 (10));
|
||||
GEN_DBL_TEST (log10 (0.7));
|
||||
GEN_DBL_TEST (log10 (2.22e-308));
|
||||
GEN_DBL_TEST (log10 (2.23e-308));
|
||||
GEN_DBL_TEST (log10 (0.17));
|
||||
GEN_DBL_TEST (log10 (0.18));
|
||||
GEN_DBL_TEST (log10 (1999.0));
|
||||
GEN_DBL_TEST (log10 (2000.0));
|
||||
GEN_DBL_TEST (log10 (2001.0));
|
||||
|
||||
/* pow tests */
|
||||
GEN_DBL_TEST (pow (0.0, 0.0));
|
||||
GEN_DBL_TEST (pow (0.0, -0.0));
|
||||
|
||||
Reference in New Issue
Block a user