Rename jerry-libm to jerry-math (#4410)
That "libm" in the name of the library resulted in awkward naming on *nix systems (`libjerry-libm.*`, "lib" occurring twice). And the name of the corresponding header is `math.h` anyway. Note that this is a breaking change in some sense. The commit contains no API change, but the build system does change for users of the math library. JerryScript-DCO-1.0-Signed-off-by: Akos Kiss akiss@inf.u-szeged.hu
This commit is contained in:
Akos Kiss
@@ -0,0 +1,67 @@
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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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cmake_minimum_required (VERSION 2.8.12)
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set(JERRY_MATH_NAME jerry-math)
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project (${JERRY_MATH_NAME} C)
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# Compiler / linker flags
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# TODO: Reduce the below list of warning/error disablings as much as possible
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set(COMPILE_FLAGS_MATH "${COMPILE_FLAGS_MATH} -Wno-error=sign-compare")
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set(COMPILE_FLAGS_MATH "${COMPILE_FLAGS_MATH} -Wno-error=sign-conversion")
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set(COMPILE_FLAGS_MATH "${COMPILE_FLAGS_MATH} -Wno-sign-conversion")
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set(COMPILE_FLAGS_MATH "${COMPILE_FLAGS_MATH} -Wno-sign-compare")
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set(COMPILE_FLAGS_MATH "${COMPILE_FLAGS_MATH} -Wno-strict-aliasing")
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# Include directories
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set(INCLUDE_MATH "${CMAKE_CURRENT_SOURCE_DIR}/include")
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# Source directories
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file(GLOB SOURCE_MATH *.c)
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# "Single" JerryScript libm source/header build.
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# The process will create the following files:
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# * jerryscript-math.c
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# * math.h
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if(ENABLE_ALL_IN_ONE_SOURCE)
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file(GLOB HEADER_MATH *.h)
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set(ALL_IN_FILE "${CMAKE_BINARY_DIR}/src/jerryscript-math.c")
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set(ALL_IN_FILE_H "${CMAKE_BINARY_DIR}/src/math.h")
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add_custom_command(OUTPUT ${ALL_IN_FILE} ${ALL_IN_FILE_H} ${JERRYSCRIPT_CONFIG_H}
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COMMAND python ${CMAKE_SOURCE_DIR}/tools/srcgenerator.py
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--jerry-math
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--output-dir ${CMAKE_BINARY_DIR}/src
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DEPENDS ${SOURCE_MATH}
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${HEADER_MATH}
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${CMAKE_SOURCE_DIR}/tools/srcgenerator.py
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${CMAKE_SOURCE_DIR}/tools/srcmerger.py
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)
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add_custom_target(generate-single-source-math DEPENDS ${ALL_IN_FILE} ${ALL_IN_FILE_H})
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add_dependencies(generate-single-source generate-single-source-math)
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set(SOURCE_MATH ${ALL_IN_FILE} ${ALL_IN_FILE_H})
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endif()
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add_library(${JERRY_MATH_NAME} ${SOURCE_MATH})
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set_property(TARGET ${JERRY_MATH_NAME}
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PROPERTY COMPILE_FLAGS "${COMPILE_FLAGS_MATH}")
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target_include_directories(${JERRY_MATH_NAME} PUBLIC ${INCLUDE_MATH})
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configure_file(libjerry-math.pc.in libjerry-math.pc @ONLY)
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install(TARGETS ${JERRY_MATH_NAME} DESTINATION lib)
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install(FILES ${CMAKE_CURRENT_BINARY_DIR}/libjerry-math.pc DESTINATION lib/pkgconfig)
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install(DIRECTORY ${INCLUDE_MATH}/ DESTINATION include/jerryscript-math)
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@@ -0,0 +1,144 @@
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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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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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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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* @(#)e_acos.c 1.3 95/01/18
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*/
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#include "jerry-math-internal.h"
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/* acos(x)
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*
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* Method:
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* acos(x) = pi/2 - asin(x)
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* acos(-x) = pi/2 + asin(x)
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* For |x|<=0.5
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* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
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* For x>0.5
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* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
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* = 2asin(sqrt((1-x)/2))
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* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
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* = 2f + (2c + 2s*z*R(z))
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* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
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* for f so that f+c ~ sqrt(z).
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* For x<-0.5
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* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
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* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN with invalid signal.
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*
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* Function needed: sqrt
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*/
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#define one 1.00000000000000000000e+00 /* 0x3FF00000, 0x00000000 */
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#define pi 3.14159265358979311600e+00 /* 0x400921FB, 0x54442D18 */
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#define pio2_hi 1.57079632679489655800e+00 /* 0x3FF921FB, 0x54442D18 */
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#define pio2_lo 6.12323399573676603587e-17 /* 0x3C91A626, 0x33145C07 */
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#define pS0 1.66666666666666657415e-01 /* 0x3FC55555, 0x55555555 */
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#define pS1 -3.25565818622400915405e-01 /* 0xBFD4D612, 0x03EB6F7D */
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#define pS2 2.01212532134862925881e-01 /* 0x3FC9C155, 0x0E884455 */
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#define pS3 -4.00555345006794114027e-02 /* 0xBFA48228, 0xB5688F3B */
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#define pS4 7.91534994289814532176e-04 /* 0x3F49EFE0, 0x7501B288 */
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#define pS5 3.47933107596021167570e-05 /* 0x3F023DE1, 0x0DFDF709 */
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#define qS1 -2.40339491173441421878e+00 /* 0xC0033A27, 0x1C8A2D4B */
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#define qS2 2.02094576023350569471e+00 /* 0x40002AE5, 0x9C598AC8 */
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#define qS3 -6.88283971605453293030e-01 /* 0xBFE6066C, 0x1B8D0159 */
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#define qS4 7.70381505559019352791e-02 /* 0x3FB3B8C5, 0xB12E9282 */
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double
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acos (double x)
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{
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double z, p, q, r, w, s, c;
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int hx, ix;
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hx = __HI (x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x3ff00000) /* |x| >= 1 */
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{
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if (((ix - 0x3ff00000) | __LO (x)) == 0) /* |x| == 1 */
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{
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if (hx > 0) /* acos(1) = 0 */
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{
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return 0.0;
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}
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else /* acos(-1) = pi */
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{
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return pi + 2.0 * pio2_lo;
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}
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}
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return NAN; /* acos(|x|>1) is NaN */
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}
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if (ix < 0x3fe00000) /* |x| < 0.5 */
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{
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if (ix <= 0x3c600000) /* if |x| < 2**-57 */
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{
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return pio2_hi + pio2_lo;
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}
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z = x * x;
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p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
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q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
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r = p / q;
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return pio2_hi - (x - (pio2_lo - x * r));
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}
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else if (hx < 0) /* x < -0.5 */
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{
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z = (one + x) * 0.5;
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p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
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q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
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s = sqrt (z);
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r = p / q;
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w = r * s - pio2_lo;
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return pi - 2.0 * (s + w);
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}
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else /* x > 0.5 */
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{
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double_accessor df;
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z = (one - x) * 0.5;
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s = sqrt (z);
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df.dbl = s;
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df.as_int.lo = 0;
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c = (z - df.dbl * df.dbl) / (s + df.dbl);
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p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
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q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
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r = p / q;
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w = r * s + c;
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return 2.0 * (df.dbl + w);
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}
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} /* acos */
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#undef one
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#undef pi
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#undef pio2_hi
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#undef pio2_lo
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#undef pS0
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#undef pS1
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#undef pS2
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#undef pS3
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#undef pS4
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#undef pS5
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#undef qS1
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#undef qS2
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#undef qS3
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#undef qS4
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@@ -0,0 +1,92 @@
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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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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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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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* @(#)e_acosh.c 1.3 95/01/18
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*/
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#include "jerry-math-internal.h"
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/* acosh(x)
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* Method :
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* Based on
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* acosh(x) = log [ x + sqrt(x * x - 1) ]
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* we have
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* acosh(x) := log(x) + ln2, if x is large; else
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* acosh(x) := log(2x - 1 / (sqrt(x * x - 1) + x)), if x > 2; else
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* acosh(x) := log1p(t + sqrt(2.0 * t + t * t)); where t = x - 1.
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*
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* Special cases:
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* acosh(x) is NaN with signal if x < 1.
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* acosh(NaN) is NaN without signal.
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*/
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#define one 1.0
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#define ln2 6.93147180559945286227e-01 /* 0x3FE62E42, 0xFEFA39EF */
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double
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acosh (double x)
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{
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double t;
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int hx;
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hx = __HI (x);
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if (hx < 0x3ff00000)
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{
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/* x < 1 */
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return NAN;
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}
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else if (hx >= 0x41b00000)
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{
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/* x > 2**28 */
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if (hx >= 0x7ff00000)
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{
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/* x is inf of 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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/* acosh(huge) = log(2x) */
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return log (x) + ln2;
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}
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}
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else if (((hx - 0x3ff00000) | __LO (x)) == 0)
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{
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/* acosh(1) = 0 */
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return 0.0;
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}
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else if (hx > 0x40000000)
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{
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/* 2**28 > x > 2 */
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t = x * x;
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return log (2.0 * x - one / (x + sqrt (t - one)));
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}
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else
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{
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/* 1 < x < 2 */
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t = x - one;
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return log1p (t + sqrt (2.0 * t + t * t));
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}
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} /* acosh */
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#undef one
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#undef ln2
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@@ -0,0 +1,154 @@
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/* Copyright JS Foundation and other contributors, http://js.foundation
|
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*
|
||||
* 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_asin.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* asin(x)
|
||||
*
|
||||
* Method:
|
||||
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
|
||||
* we approximate asin(x) on [0,0.5] by
|
||||
* asin(x) = x + x*x^2*R(x^2)
|
||||
* where
|
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* R(x^2) is a rational approximation of (asin(x)-x)/x^3
|
||||
* and its remez error is bounded by
|
||||
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
|
||||
*
|
||||
* For x in [0.5,1]
|
||||
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
|
||||
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
|
||||
* then for x>0.98
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
|
||||
* For x<=0.98, let pio4_hi = pio2_hi/2, then
|
||||
* f = hi part of s;
|
||||
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
|
||||
* and
|
||||
* asin(x) = pi/2 - 2*(s+s*z*R(z))
|
||||
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
|
||||
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
|
||||
*
|
||||
* Special cases:
|
||||
* if x is NaN, return x itself;
|
||||
* if |x|>1, return NaN with invalid signal.
|
||||
*/
|
||||
|
||||
#define one 1.00000000000000000000e+00 /* 0x3FF00000, 0x00000000 */
|
||||
#define huge 1.000e+300
|
||||
#define pio2_hi 1.57079632679489655800e+00 /* 0x3FF921FB, 0x54442D18 */
|
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#define pio2_lo 6.12323399573676603587e-17 /* 0x3C91A626, 0x33145C07 */
|
||||
#define pio4_hi 7.85398163397448278999e-01 /* 0x3FE921FB, 0x54442D18 */
|
||||
/* coefficient for R(x^2) */
|
||||
#define pS0 1.66666666666666657415e-01 /* 0x3FC55555, 0x55555555 */
|
||||
#define pS1 -3.25565818622400915405e-01 /* 0xBFD4D612, 0x03EB6F7D */
|
||||
#define pS2 2.01212532134862925881e-01 /* 0x3FC9C155, 0x0E884455 */
|
||||
#define pS3 -4.00555345006794114027e-02 /* 0xBFA48228, 0xB5688F3B */
|
||||
#define pS4 7.91534994289814532176e-04 /* 0x3F49EFE0, 0x7501B288 */
|
||||
#define pS5 3.47933107596021167570e-05 /* 0x3F023DE1, 0x0DFDF709 */
|
||||
#define qS1 -2.40339491173441421878e+00 /* 0xC0033A27, 0x1C8A2D4B */
|
||||
#define qS2 2.02094576023350569471e+00 /* 0x40002AE5, 0x9C598AC8 */
|
||||
#define qS3 -6.88283971605453293030e-01 /* 0xBFE6066C, 0x1B8D0159 */
|
||||
#define qS4 7.70381505559019352791e-02 /* 0x3FB3B8C5, 0xB12E9282 */
|
||||
|
||||
double
|
||||
asin (double x)
|
||||
{
|
||||
double t, p, q, c, r, s;
|
||||
double_accessor w;
|
||||
int hx, ix;
|
||||
|
||||
hx = __HI (x);
|
||||
ix = hx & 0x7fffffff;
|
||||
if (ix >= 0x3ff00000) /* |x| >= 1 */
|
||||
{
|
||||
if (((ix - 0x3ff00000) | __LO (x)) == 0) /* asin(1) = +-pi/2 with inexact */
|
||||
{
|
||||
return x * pio2_hi + x * pio2_lo;
|
||||
}
|
||||
return NAN; /* asin(|x|>1) is NaN */
|
||||
}
|
||||
else if (ix < 0x3fe00000) /* |x| < 0.5 */
|
||||
{
|
||||
if (ix < 0x3e400000) /* if |x| < 2**-27 */
|
||||
{
|
||||
if (huge + x > one) /* return x with inexact if x != 0 */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
}
|
||||
t = x * x;
|
||||
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
|
||||
q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
|
||||
w.dbl = p / q;
|
||||
return x + x * w.dbl;
|
||||
}
|
||||
/* 1 > |x| >= 0.5 */
|
||||
w.dbl = one - fabs (x);
|
||||
t = w.dbl * 0.5;
|
||||
p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
|
||||
q = one + t * (qS1 + t * (qS2 + t * (qS3 + t * qS4)));
|
||||
s = sqrt (t);
|
||||
if (ix >= 0x3FEF3333) /* if |x| > 0.975 */
|
||||
{
|
||||
w.dbl = p / q;
|
||||
t = pio2_hi - (2.0 * (s + s * w.dbl) - pio2_lo);
|
||||
}
|
||||
else
|
||||
{
|
||||
w.dbl = s;
|
||||
w.as_int.lo = 0;
|
||||
c = (t - w.dbl * w.dbl) / (s + w.dbl);
|
||||
r = p / q;
|
||||
p = 2.0 * s * r - (pio2_lo - 2.0 * c);
|
||||
q = pio4_hi - 2.0 * w.dbl;
|
||||
t = pio4_hi - (p - q);
|
||||
}
|
||||
if (hx > 0)
|
||||
{
|
||||
return t;
|
||||
}
|
||||
else
|
||||
{
|
||||
return -t;
|
||||
}
|
||||
} /* asin */
|
||||
|
||||
#undef one
|
||||
#undef huge
|
||||
#undef pio2_hi
|
||||
#undef pio2_lo
|
||||
#undef pio4_hi
|
||||
#undef pS0
|
||||
#undef pS1
|
||||
#undef pS2
|
||||
#undef pS3
|
||||
#undef pS4
|
||||
#undef pS5
|
||||
#undef qS1
|
||||
#undef qS2
|
||||
#undef qS3
|
||||
#undef qS4
|
||||
@@ -0,0 +1,95 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_asinh.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* asinh(x)
|
||||
* Method :
|
||||
* Based on
|
||||
* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
|
||||
* we have
|
||||
* asinh(x) := x if 1 + x * x = 1,
|
||||
* := sign(x) * (log(x)+ln2)) for large |x|, else
|
||||
* := sign(x) * log(2|x| + 1 / (|x| + sqrt(x * x + 1))) if|x| > 2, else
|
||||
* := sign(x) * log1p(|x| + x^2 / (1 + sqrt(1 + x^2)))
|
||||
*/
|
||||
|
||||
#define one 1.0
|
||||
#define ln2 6.93147180559945286227e-01 /* 0x3FE62E42, 0xFEFA39EF */
|
||||
#define huge 1.0e+300
|
||||
|
||||
double
|
||||
asinh (double x)
|
||||
{
|
||||
double t, w;
|
||||
int hx, ix;
|
||||
hx = __HI (x);
|
||||
ix = hx & 0x7fffffff;
|
||||
if (ix >= 0x7ff00000)
|
||||
{
|
||||
/* x is inf or NaN */
|
||||
return x + x;
|
||||
}
|
||||
if (ix < 0x3e300000)
|
||||
{
|
||||
/* |x| < 2**-28 */
|
||||
if (huge + x > one)
|
||||
{
|
||||
/* return x inexact except 0 */
|
||||
return x;
|
||||
}
|
||||
}
|
||||
if (ix > 0x41b00000)
|
||||
{
|
||||
/* |x| > 2**28 */
|
||||
w = log (fabs (x)) + ln2;
|
||||
}
|
||||
else if (ix > 0x40000000)
|
||||
{
|
||||
/* 2**28 > |x| > 2.0 */
|
||||
t = fabs (x);
|
||||
w = log (2.0 * t + one / (sqrt (x * x + one) + t));
|
||||
}
|
||||
else
|
||||
{
|
||||
/* 2.0 > |x| > 2**-28 */
|
||||
t = x * x;
|
||||
w = log1p (fabs (x) + t / (one + sqrt (one + t)));
|
||||
}
|
||||
if (hx > 0)
|
||||
{
|
||||
return w;
|
||||
}
|
||||
else
|
||||
{
|
||||
return -w;
|
||||
}
|
||||
} /* asinh */
|
||||
|
||||
#undef one
|
||||
#undef ln2
|
||||
#undef huge
|
||||
@@ -0,0 +1,175 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_atan.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* atan(x)
|
||||
*
|
||||
* Method:
|
||||
* 1. Reduce x to positive by atan(x) = -atan(-x).
|
||||
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
|
||||
* is further reduced to one of the following intervals and the
|
||||
* arctangent of t is evaluated by the corresponding formula:
|
||||
*
|
||||
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
|
||||
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
|
||||
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
|
||||
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
|
||||
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
static const double atanhi[] =
|
||||
{
|
||||
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
||||
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
||||
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
||||
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
||||
};
|
||||
|
||||
static const double atanlo[] =
|
||||
{
|
||||
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
||||
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
||||
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
||||
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
||||
};
|
||||
|
||||
#define aT0 3.33333333333329318027e-01 /* 0x3FD55555, 0x5555550D */
|
||||
#define aT1 -1.99999999998764832476e-01 /* 0xBFC99999, 0x9998EBC4 */
|
||||
#define aT2 1.42857142725034663711e-01 /* 0x3FC24924, 0x920083FF */
|
||||
#define aT3 -1.11111104054623557880e-01 /* 0xBFBC71C6, 0xFE231671 */
|
||||
#define aT4 9.09088713343650656196e-02 /* 0x3FB745CD, 0xC54C206E */
|
||||
#define aT5 -7.69187620504482999495e-02 /* 0xBFB3B0F2, 0xAF749A6D */
|
||||
#define aT6 6.66107313738753120669e-02 /* 0x3FB10D66, 0xA0D03D51 */
|
||||
#define aT7 -5.83357013379057348645e-02 /* 0xBFADDE2D, 0x52DEFD9A */
|
||||
#define aT8 4.97687799461593236017e-02 /* 0x3FA97B4B, 0x24760DEB */
|
||||
#define aT9 -3.65315727442169155270e-02 /* 0xBFA2B444, 0x2C6A6C2F */
|
||||
#define aT10 1.62858201153657823623e-02 /* 0x3F90AD3A, 0xE322DA11 */
|
||||
|
||||
#define one 1.0
|
||||
#define huge 1.0e300
|
||||
|
||||
double
|
||||
atan (double x)
|
||||
{
|
||||
double w, s1, s2, z;
|
||||
int ix, hx, id;
|
||||
|
||||
hx = __HI (x);
|
||||
ix = hx & 0x7fffffff;
|
||||
if (ix >= 0x44100000) /* if |x| >= 2^66 */
|
||||
{
|
||||
if (ix > 0x7ff00000 || (ix == 0x7ff00000 && (__LO (x) != 0)))
|
||||
{
|
||||
return x + x; /* NaN */
|
||||
}
|
||||
if (hx > 0)
|
||||
{
|
||||
return atanhi[3] + atanlo[3];
|
||||
}
|
||||
else
|
||||
{
|
||||
return -atanhi[3] - atanlo[3];
|
||||
}
|
||||
}
|
||||
if (ix < 0x3fdc0000) /* |x| < 0.4375 */
|
||||
{
|
||||
if (ix < 0x3e200000) /* |x| < 2^-29 */
|
||||
{
|
||||
if (huge + x > one) /* raise inexact */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
}
|
||||
id = -1;
|
||||
}
|
||||
else
|
||||
{
|
||||
x = fabs (x);
|
||||
if (ix < 0x3ff30000) /* |x| < 1.1875 */
|
||||
{
|
||||
if (ix < 0x3fe60000) /* 7/16 <= |x| < 11/16 */
|
||||
{
|
||||
id = 0;
|
||||
x = (2.0 * x - one) / (2.0 + x);
|
||||
}
|
||||
else /* 11/16 <= |x| < 19/16 */
|
||||
{
|
||||
id = 1;
|
||||
x = (x - one) / (x + one);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
if (ix < 0x40038000) /* |x| < 2.4375 */
|
||||
{
|
||||
id = 2;
|
||||
x = (x - 1.5) / (one + 1.5 * x);
|
||||
}
|
||||
else /* 2.4375 <= |x| < 2^66 */
|
||||
{
|
||||
id = 3;
|
||||
x = -1.0 / x;
|
||||
}
|
||||
}
|
||||
}
|
||||
/* end of argument reduction */
|
||||
z = x * x;
|
||||
w = z * z;
|
||||
/* break sum from i=0 to 10 aT[i] z**(i+1) into odd and even poly */
|
||||
s1 = z * (aT0 + w * (aT2 + w * (aT4 + w * (aT6 + w * (aT8 + w * aT10)))));
|
||||
s2 = w * (aT1 + w * (aT3 + w * (aT5 + w * (aT7 + w * aT9))));
|
||||
if (id < 0)
|
||||
{
|
||||
return x - x * (s1 + s2);
|
||||
}
|
||||
else
|
||||
{
|
||||
z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
|
||||
return (hx < 0) ? -z : z;
|
||||
}
|
||||
} /* atan */
|
||||
|
||||
#undef aT0
|
||||
#undef aT1
|
||||
#undef aT2
|
||||
#undef aT3
|
||||
#undef aT4
|
||||
#undef aT5
|
||||
#undef aT6
|
||||
#undef aT7
|
||||
#undef aT8
|
||||
#undef aT9
|
||||
#undef aT10
|
||||
#undef one
|
||||
#undef huge
|
||||
@@ -0,0 +1,209 @@
|
||||
/* 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_atan2.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* atan2(y,x)
|
||||
*
|
||||
* Method:
|
||||
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
|
||||
* 2. Reduce x to positive by (if x and y are unexceptional):
|
||||
* ARG (x+iy) = arctan(y/x) ... if x > 0,
|
||||
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
|
||||
*
|
||||
* Special cases:
|
||||
* ATAN2((anything), NaN ) is NaN;
|
||||
* ATAN2(NAN , (anything) ) is NaN;
|
||||
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
|
||||
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
|
||||
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
|
||||
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
|
||||
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
|
||||
* ATAN2(+-INF,+INF ) is +-pi/4 ;
|
||||
* ATAN2(+-INF,-INF ) is +-3pi/4;
|
||||
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
|
||||
*
|
||||
* 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 tiny 1.0e-300
|
||||
#define zero 0.0
|
||||
#define pi_o_4 7.8539816339744827900E-01 /* 0x3FE921FB, 0x54442D18 */
|
||||
#define pi_o_2 1.5707963267948965580E+00 /* 0x3FF921FB, 0x54442D18 */
|
||||
#define pi 3.1415926535897931160E+00 /* 0x400921FB, 0x54442D18 */
|
||||
#define pi_lo 1.2246467991473531772E-16 /* 0x3CA1A626, 0x33145C07 */
|
||||
|
||||
double
|
||||
atan2 (double y, double x)
|
||||
{
|
||||
double_accessor z;
|
||||
int k, m, hx, hy, ix, iy;
|
||||
unsigned lx, ly;
|
||||
|
||||
hx = __HI (x);
|
||||
ix = hx & 0x7fffffff;
|
||||
lx = __LO (x);
|
||||
hy = __HI (y);
|
||||
iy = hy & 0x7fffffff;
|
||||
ly = __LO (y);
|
||||
if (((ix | ((lx | -lx) >> 31)) > 0x7ff00000) || ((iy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* x or y is NaN */
|
||||
{
|
||||
return x + y;
|
||||
}
|
||||
if (((hx - 0x3ff00000) | lx) == 0) /* x = 1.0 */
|
||||
{
|
||||
return atan (y);
|
||||
}
|
||||
m = ((hy < 0) ? 1 : 0) + ((hx < 0) ? 2 : 0); /* 2 * sign(x) + sign(y) */
|
||||
|
||||
/* when y = 0 */
|
||||
if ((iy | ly) == 0)
|
||||
{
|
||||
switch (m)
|
||||
{
|
||||
case 0:
|
||||
case 1:
|
||||
{
|
||||
return y; /* atan(+-0,+anything) = +-0 */
|
||||
}
|
||||
case 2:
|
||||
{
|
||||
return pi + tiny; /* atan(+0,-anything) = pi */
|
||||
}
|
||||
case 3:
|
||||
{
|
||||
return -pi - tiny; /* atan(-0,-anything) = -pi */
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when x = 0 */
|
||||
if ((ix | lx) == 0)
|
||||
{
|
||||
return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;
|
||||
}
|
||||
|
||||
/* when x is INF */
|
||||
if (ix == 0x7ff00000)
|
||||
{
|
||||
if (iy == 0x7ff00000)
|
||||
{
|
||||
switch (m)
|
||||
{
|
||||
case 0: /* atan(+INF,+INF) */
|
||||
{
|
||||
return pi_o_4 + tiny;
|
||||
}
|
||||
case 1: /* atan(-INF,+INF) */
|
||||
{
|
||||
return -pi_o_4 - tiny;
|
||||
}
|
||||
case 2: /* atan(+INF,-INF) */
|
||||
{
|
||||
return 3.0 * pi_o_4 + tiny;
|
||||
}
|
||||
case 3: /* atan(-INF,-INF) */
|
||||
{
|
||||
return -3.0 * pi_o_4 - tiny;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
switch (m)
|
||||
{
|
||||
case 0: /* atan(+...,+INF) */
|
||||
{
|
||||
return zero;
|
||||
}
|
||||
case 1: /* atan(-...,+INF) */
|
||||
{
|
||||
return -zero;
|
||||
}
|
||||
case 2: /* atan(+...,-INF) */
|
||||
{
|
||||
return pi + tiny;
|
||||
}
|
||||
case 3: /* atan(-...,-INF) */
|
||||
{
|
||||
return -pi - tiny;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
/* when y is INF */
|
||||
if (iy == 0x7ff00000)
|
||||
{
|
||||
return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;
|
||||
}
|
||||
|
||||
/* compute y / x */
|
||||
k = (iy - ix) >> 20;
|
||||
if (k > 60) /* |y / x| > 2**60 */
|
||||
{
|
||||
z.dbl = pi_o_2 + 0.5 * pi_lo;
|
||||
}
|
||||
else if (hx < 0 && k < -60) /* |y| / x < -2**60 */
|
||||
{
|
||||
z.dbl = 0.0;
|
||||
}
|
||||
else /* safe to do y / x */
|
||||
{
|
||||
z.dbl = atan (fabs (y / x));
|
||||
}
|
||||
switch (m)
|
||||
{
|
||||
case 0: /* atan(+,+) */
|
||||
{
|
||||
return z.dbl;
|
||||
}
|
||||
case 1: /* atan(-,+) */
|
||||
{
|
||||
z.as_int.hi ^= 0x80000000;
|
||||
return z.dbl;
|
||||
}
|
||||
case 2: /* atan(+,-) */
|
||||
{
|
||||
return pi - (z.dbl - pi_lo);
|
||||
}
|
||||
/* case 3: */
|
||||
default: /* atan(-,-) */
|
||||
{
|
||||
return (z.dbl - pi_lo) - pi;
|
||||
}
|
||||
}
|
||||
} /* atan2 */
|
||||
|
||||
#undef tiny
|
||||
#undef zero
|
||||
#undef pi_o_4
|
||||
#undef pi_o_2
|
||||
#undef pi
|
||||
#undef pi_lo
|
||||
@@ -0,0 +1,100 @@
|
||||
/* 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_atanh.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* atanh(x)
|
||||
* Method :
|
||||
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
|
||||
* 2.For x >= 0.5
|
||||
* 1 2x x
|
||||
* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
|
||||
* 2 1 - x 1 - x
|
||||
*
|
||||
* For x < 0.5
|
||||
* atanh(x) = 0.5 * log1p(2x + 2x * x / (1 - x))
|
||||
*
|
||||
* Special cases:
|
||||
* atanh(x) is NaN if |x| > 1 with signal;
|
||||
* atanh(NaN) is that NaN with no signal;
|
||||
* atanh(+-1) is +-INF with signal.
|
||||
*
|
||||
*/
|
||||
|
||||
#define zero 0.0
|
||||
#define one 1.0
|
||||
#define huge 1.0e+300
|
||||
|
||||
double
|
||||
atanh (double x)
|
||||
{
|
||||
double t;
|
||||
int hx, ix;
|
||||
double_accessor temp;
|
||||
temp.dbl = x;
|
||||
hx = temp.as_int.hi;
|
||||
ix = hx & 0x7fffffff;
|
||||
|
||||
/* |x| > 1 */
|
||||
if ((ix | ((unsigned int) (temp.as_int.lo | (-temp.as_int.lo)) >> 31)) > 0x3ff00000)
|
||||
{
|
||||
return NAN;
|
||||
}
|
||||
if (ix == 0x3ff00000)
|
||||
{
|
||||
return x / zero;
|
||||
}
|
||||
if (ix < 0x3e300000 && (huge + x) > zero)
|
||||
{
|
||||
return x; /* x<2**-28 */
|
||||
}
|
||||
|
||||
/* x <- |x| */
|
||||
temp.as_int.hi = ix;
|
||||
if (ix < 0x3fe00000)
|
||||
{
|
||||
/* x < 0.5 */
|
||||
t = temp.dbl + temp.dbl;
|
||||
t = 0.5 * log1p (t + t * temp.dbl / (one - temp.dbl));
|
||||
}
|
||||
else
|
||||
{
|
||||
t = 0.5 * log1p ((temp.dbl + temp.dbl) / (one - temp.dbl));
|
||||
}
|
||||
if (hx >= 0)
|
||||
{
|
||||
return t;
|
||||
}
|
||||
else
|
||||
{
|
||||
return -t;
|
||||
}
|
||||
} /* atanh */
|
||||
|
||||
#undef zero
|
||||
#undef one
|
||||
#undef huge
|
||||
@@ -0,0 +1,103 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_cbrt.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* cbrt(x)
|
||||
* Return cube root of x
|
||||
*/
|
||||
|
||||
#define B1 715094163 /* B1 = (682 - 0.03306235651) * 2**20 */
|
||||
#define B2 696219795 /* B2 = (664 - 0.03306235651) * 2**20 */
|
||||
#define C 5.42857142857142815906e-01 /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
|
||||
#define D -7.05306122448979611050e-01 /* -864/1225 = 0xBFE691DE, 0x2532C834 */
|
||||
#define E 1.41428571428571436819e+00 /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
|
||||
#define F 1.60714285714285720630e+00 /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
|
||||
#define G 3.57142857142857150787e-01 /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
|
||||
|
||||
double
|
||||
cbrt (double x)
|
||||
{
|
||||
double r, s, w;
|
||||
double_accessor t, temp;
|
||||
unsigned int sign;
|
||||
t.dbl = 0.0;
|
||||
temp.dbl = x;
|
||||
|
||||
sign = temp.as_int.hi & 0x80000000; /* sign = sign(x) */
|
||||
temp.as_int.hi ^= sign;
|
||||
|
||||
if (temp.as_int.hi >= 0x7ff00000)
|
||||
{
|
||||
/* cbrt(NaN, INF) is itself */
|
||||
return (x + x);
|
||||
}
|
||||
if ((temp.as_int.hi | temp.as_int.lo) == 0)
|
||||
{
|
||||
/* cbrt(0) is itself */
|
||||
return (x);
|
||||
}
|
||||
/* rough cbrt to 5 bits */
|
||||
if (temp.as_int.hi < 0x00100000) /* subnormal number */
|
||||
{
|
||||
t.as_int.hi = 0x43500000; /* set t= 2**54 */
|
||||
t.dbl *= temp.dbl;
|
||||
t.as_int.hi = t.as_int.hi / 3 + B2;
|
||||
}
|
||||
else
|
||||
{
|
||||
t.as_int.hi = temp.as_int.hi / 3 + B1;
|
||||
}
|
||||
|
||||
/* new cbrt to 23 bits, may be implemented in single precision */
|
||||
r = t.dbl * t.dbl / temp.dbl;
|
||||
s = C + r * t.dbl;
|
||||
t.dbl *= G + F / (s + E + D / s);
|
||||
|
||||
/* chopped to 20 bits and make it larger than cbrt(x) */
|
||||
t.as_int.lo = 0;
|
||||
t.as_int.hi += 0x00000001;
|
||||
|
||||
/* one step newton iteration to 53 bits with error less than 0.667 ulps */
|
||||
s = t.dbl * t.dbl; /* t*t is exact */
|
||||
r = temp.dbl / s;
|
||||
w = t.dbl + t.dbl;
|
||||
r = (r - t.dbl) / (w + r); /* r-s is exact */
|
||||
t.dbl = t.dbl + (t.dbl * r);
|
||||
|
||||
/* retore the sign bit */
|
||||
t.as_int.hi |= sign;
|
||||
return (t.dbl);
|
||||
} /* cbrt */
|
||||
|
||||
#undef B1
|
||||
#undef B2
|
||||
#undef C
|
||||
#undef D
|
||||
#undef E
|
||||
#undef F
|
||||
#undef G
|
||||
@@ -0,0 +1,133 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_ceil.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* ceil(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
*
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
*
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to ceil(x).
|
||||
*/
|
||||
|
||||
#define huge 1.0e300
|
||||
|
||||
double
|
||||
ceil (double x)
|
||||
{
|
||||
int i0, i1, j0;
|
||||
unsigned i, j;
|
||||
|
||||
i0 = __HI (x);
|
||||
i1 = __LO (x);
|
||||
j0 = ((i0 >> 20) & 0x7ff) - 0x3ff;
|
||||
if (j0 < 20)
|
||||
{
|
||||
if (j0 < 0) /* raise inexact if x != 0 */
|
||||
{
|
||||
if (huge + x > 0.0) /* return 0 * sign(x) if |x| < 1 */
|
||||
{
|
||||
if (i0 < 0)
|
||||
{
|
||||
i0 = 0x80000000;
|
||||
i1 = 0;
|
||||
}
|
||||
else if ((i0 | i1) != 0)
|
||||
{
|
||||
i0 = 0x3ff00000;
|
||||
i1 = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
i = (0x000fffff) >> j0;
|
||||
if (((i0 & i) | i1) == 0) /* x is integral */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
if (huge + x > 0.0) /* raise inexact flag */
|
||||
{
|
||||
if (i0 > 0)
|
||||
{
|
||||
i0 += (0x00100000) >> j0;
|
||||
}
|
||||
i0 &= (~i);
|
||||
i1 = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
else if (j0 > 51)
|
||||
{
|
||||
if (j0 == 0x400) /* inf or NaN */
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
else /* x is integral */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
i = ((unsigned) (0xffffffff)) >> (j0 - 20);
|
||||
if ((i1 & i) == 0) /* x is integral */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
if (huge + x > 0.0) /* raise inexact flag */
|
||||
{
|
||||
if (i0 > 0)
|
||||
{
|
||||
if (j0 == 20)
|
||||
{
|
||||
i0 += 1;
|
||||
}
|
||||
else
|
||||
{
|
||||
j = i1 + (1 << (52 - j0));
|
||||
if (j < i1) /* got a carry */
|
||||
{
|
||||
i0 += 1;
|
||||
}
|
||||
i1 = j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
|
||||
double_accessor ret;
|
||||
ret.as_int.hi = i0;
|
||||
ret.as_int.lo = i1;
|
||||
return ret.dbl;
|
||||
} /* ceil */
|
||||
|
||||
#undef huge
|
||||
@@ -0,0 +1,41 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_copysign.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* copysign(x,y) returns a value with the magnitude of x and
|
||||
* with the sign bit of y.
|
||||
*/
|
||||
|
||||
double
|
||||
copysign (double x, double y)
|
||||
{
|
||||
double_accessor ret;
|
||||
ret.dbl = x;
|
||||
ret.as_int.hi = (__HI (x) & 0x7fffffff) | (__HI (y) & 0x80000000);
|
||||
return ret.dbl;
|
||||
} /* copysign */
|
||||
@@ -0,0 +1,113 @@
|
||||
/* 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_cosh.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* cosh(x)
|
||||
* Method:
|
||||
* mathematically cosh(x) if defined to be (exp(x) + exp(-x)) / 2
|
||||
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
|
||||
* 2.
|
||||
* [ exp(x) - 1 ]^2
|
||||
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
|
||||
* 2*exp(x)
|
||||
*
|
||||
* exp(x) + 1/exp(x)
|
||||
* ln2/2 <= x <= 22 : cosh(x) := -------------------
|
||||
* 2
|
||||
*
|
||||
* 22 <= x <= lnovft : cosh(x) := exp(x)/2
|
||||
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
|
||||
* ln2ovft < x : cosh(x) := huge * huge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* cosh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only cosh(0) = 1 is exact for finite x.
|
||||
*/
|
||||
|
||||
#define one 1.0
|
||||
#define half 0.5
|
||||
#define huge 1.0e300
|
||||
|
||||
double
|
||||
cosh (double x)
|
||||
{
|
||||
double t, w;
|
||||
int ix;
|
||||
unsigned lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
ix = __HI (x);
|
||||
ix &= 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if (ix >= 0x7ff00000)
|
||||
{
|
||||
return x * x;
|
||||
}
|
||||
/* |x| in [0, 0.5 * ln2], return 1 + expm1(|x|)^2 / (2 * exp(|x|)) */
|
||||
if (ix < 0x3fd62e43)
|
||||
{
|
||||
t = expm1 (fabs (x));
|
||||
w = one + t;
|
||||
if (ix < 0x3c800000)
|
||||
{
|
||||
/* cosh(tiny) = 1 */
|
||||
return w;
|
||||
}
|
||||
return one + (t * t) / (w + w);
|
||||
}
|
||||
|
||||
/* |x| in [0.5 * ln2, 22], return (exp(|x|) + 1 / exp(|x|) / 2; */
|
||||
if (ix < 0x40360000)
|
||||
{
|
||||
t = exp (fabs (x));
|
||||
return half * t + half / t;
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return half * exp(|x|) */
|
||||
if (ix < 0x40862E42)
|
||||
{
|
||||
return half * exp (fabs (x));
|
||||
}
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
lx = ((1 >> 29) + (unsigned int) x);
|
||||
if ((ix < 0x408633CE) ||
|
||||
((ix == 0x408633ce) && (lx <= (unsigned) 0x8fb9f87d)))
|
||||
{
|
||||
w = exp (half * fabs (x));
|
||||
t = half * w;
|
||||
return t * w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, cosh(x) overflow */
|
||||
return huge * huge;
|
||||
} /* cosh */
|
||||
|
||||
#undef one
|
||||
#undef half
|
||||
#undef huge
|
||||
@@ -0,0 +1,220 @@
|
||||
/* 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) 2004 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.
|
||||
*
|
||||
* @(#)e_exp.c 1.6 04/04/22
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* exp(x)
|
||||
* Returns the exponential of x.
|
||||
*
|
||||
* Method:
|
||||
* 1. Argument reduction:
|
||||
* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2.
|
||||
*
|
||||
* Here r will be represented as r = hi-lo for better
|
||||
* accuracy.
|
||||
*
|
||||
* 2. Approximation of exp(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Write
|
||||
* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
|
||||
* We use a special Remes algorithm on [0,0.34658] to generate
|
||||
* a polynomial of degree 5 to approximate R. The maximum error
|
||||
* of this polynomial approximation is bounded by 2**-59. In
|
||||
* other words,
|
||||
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
|
||||
* (where z=r*r, and the values of P1 to P5 are listed below)
|
||||
* and
|
||||
* | 5 | -59
|
||||
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
|
||||
* | |
|
||||
* The computation of exp(r) thus becomes
|
||||
* 2*r
|
||||
* exp(r) = 1 + -------
|
||||
* R - r
|
||||
* r*R1(r)
|
||||
* = 1 + r + ----------- (for better accuracy)
|
||||
* 2 - R1(r)
|
||||
* where
|
||||
* 2 4 10
|
||||
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
|
||||
*
|
||||
* 3. Scale back to obtain exp(x):
|
||||
* From step 1, we have
|
||||
* exp(x) = 2^k * exp(r)
|
||||
*
|
||||
* Special cases:
|
||||
* exp(INF) is INF, exp(NaN) is NaN;
|
||||
* exp(-INF) is 0, and
|
||||
* for finite argument, only exp(0)=1 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info:
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then exp(x) overflow
|
||||
* if x < -7.45133219101941108420e+02 then exp(x) underflow
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
static const double halF[2] =
|
||||
{
|
||||
0.5,
|
||||
-0.5,
|
||||
};
|
||||
static const double ln2HI[2] =
|
||||
{
|
||||
6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
|
||||
-6.93147180369123816490e-01, /* 0xbfe62e42, 0xfee00000 */
|
||||
};
|
||||
static const double ln2LO[2] =
|
||||
{
|
||||
1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
|
||||
-1.90821492927058770002e-10, /* 0xbdea39ef, 0x35793c76 */
|
||||
};
|
||||
|
||||
#define one 1.0
|
||||
#define huge 1.0e+300
|
||||
#define twom1000 9.33263618503218878990e-302 /* 2**-1000=0x01700000,0 */
|
||||
#define o_threshold 7.09782712893383973096e+02 /* 0x40862E42, 0xFEFA39EF */
|
||||
#define u_threshold -7.45133219101941108420e+02 /* 0xc0874910, 0xD52D3051 */
|
||||
#define invln2 1.44269504088896338700e+00 /* 0x3ff71547, 0x652b82fe */
|
||||
#define P1 1.66666666666666019037e-01 /* 0x3FC55555, 0x5555553E */
|
||||
#define P2 -2.77777777770155933842e-03 /* 0xBF66C16C, 0x16BEBD93 */
|
||||
#define P3 6.61375632143793436117e-05 /* 0x3F11566A, 0xAF25DE2C */
|
||||
#define P4 -1.65339022054652515390e-06 /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
#define P5 4.13813679705723846039e-08 /* 0x3E663769, 0x72BEA4D0 */
|
||||
|
||||
double
|
||||
exp (double x) /* default IEEE double exp */
|
||||
{
|
||||
double hi, lo, c, t;
|
||||
int k = 0, xsb;
|
||||
unsigned hx;
|
||||
|
||||
hx = __HI (x); /* high word of x */
|
||||
xsb = (hx >> 31) & 1; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out non-finite argument */
|
||||
if (hx >= 0x40862E42) /* if |x| >= 709.78... */
|
||||
{
|
||||
if (hx >= 0x7ff00000)
|
||||
{
|
||||
if (((hx & 0xfffff) | __LO (x)) != 0) /* NaN */
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
else /* exp(+-inf) = {inf,0} */
|
||||
{
|
||||
return (xsb == 0) ? x : 0.0;
|
||||
}
|
||||
}
|
||||
if (x > o_threshold) /* overflow */
|
||||
{
|
||||
return huge * huge;
|
||||
}
|
||||
if (x < u_threshold) /* underflow */
|
||||
{
|
||||
return twom1000 * twom1000;
|
||||
}
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if (hx > 0x3fd62e42) /* if |x| > 0.5 ln2 */
|
||||
{
|
||||
if (hx < 0x3FF0A2B2) /* and |x| < 1.5 ln2 */
|
||||
{
|
||||
hi = x - ln2HI[xsb];
|
||||
lo = ln2LO[xsb];
|
||||
k = 1 - xsb - xsb;
|
||||
}
|
||||
else
|
||||
{
|
||||
k = (int) (invln2 * x + halF[xsb]);
|
||||
t = k;
|
||||
hi = x - t * ln2HI[0]; /* t * ln2HI is exact here */
|
||||
lo = t * ln2LO[0];
|
||||
}
|
||||
x = hi - lo;
|
||||
}
|
||||
else if (hx < 0x3e300000) /* when |x| < 2**-28 */
|
||||
{
|
||||
if (huge + x > one) /* trigger inexact */
|
||||
{
|
||||
return one + x;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
k = 0;
|
||||
}
|
||||
|
||||
double_accessor ret;
|
||||
|
||||
/* x is now in primary range */
|
||||
t = x * x;
|
||||
c = x - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
||||
if (k == 0)
|
||||
{
|
||||
return one - ((x * c) / (c - 2.0) - x);
|
||||
}
|
||||
else
|
||||
{
|
||||
ret.dbl = one - ((lo - (x * c) / (2.0 - c)) - hi);
|
||||
}
|
||||
if (k >= -1021)
|
||||
{
|
||||
ret.as_int.hi += (((unsigned int) k) << 20); /* add k to y's exponent */
|
||||
return ret.dbl;
|
||||
}
|
||||
else
|
||||
{
|
||||
ret.as_int.hi += ((k + 1000) << 20); /* add k to y's exponent */
|
||||
return ret.dbl * twom1000;
|
||||
}
|
||||
} /* exp */
|
||||
|
||||
#undef one
|
||||
#undef huge
|
||||
#undef twom1000
|
||||
#undef o_threshold
|
||||
#undef u_threshold
|
||||
#undef invln2
|
||||
#undef P1
|
||||
#undef P2
|
||||
#undef P3
|
||||
#undef P4
|
||||
#undef P5
|
||||
@@ -0,0 +1,305 @@
|
||||
/* 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_expm1.c 5.1 93/09/24
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* expm1(x)
|
||||
* Returns exp(x)-1, the exponential of x minus 1.
|
||||
*
|
||||
* Method
|
||||
* 1. Argument reduction:
|
||||
* Given x, find r and integer k such that
|
||||
*
|
||||
* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
|
||||
*
|
||||
* Here a correction term c will be computed to compensate
|
||||
* the error in r when rounded to a floating-point number.
|
||||
*
|
||||
* 2. Approximating expm1(r) by a special rational function on
|
||||
* the interval [0,0.34658]:
|
||||
* Since
|
||||
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
|
||||
* we define R1(r*r) by
|
||||
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
|
||||
* That is,
|
||||
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
|
||||
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
|
||||
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
|
||||
* We use a special Reme algorithm on [0,0.347] to generate
|
||||
* a polynomial of degree 5 in r*r to approximate R1. The
|
||||
* maximum error of this polynomial approximation is bounded
|
||||
* by 2**-61. In other words,
|
||||
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
|
||||
* where Q1 = -1.6666666666666567384E-2,
|
||||
* Q2 = 3.9682539681370365873E-4,
|
||||
* Q3 = -9.9206344733435987357E-6,
|
||||
* Q4 = 2.5051361420808517002E-7,
|
||||
* Q5 = -6.2843505682382617102E-9;
|
||||
* z = r*r,
|
||||
* with error bounded by
|
||||
* | 5 | -61
|
||||
* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
|
||||
* | |
|
||||
*
|
||||
* expm1(r) = exp(r)-1 is then computed by the following
|
||||
* specific way which minimize the accumulation rounding error:
|
||||
* 2 3
|
||||
* r r [ 3 - (R1 + R1*r/2) ]
|
||||
* expm1(r) = r + --- + --- * [--------------------]
|
||||
* 2 2 [ 6 - r*(3 - R1*r/2) ]
|
||||
*
|
||||
* To compensate the error in the argument reduction, we use
|
||||
* expm1(r+c) = expm1(r) + c + expm1(r)*c
|
||||
* ~ expm1(r) + c + r*c
|
||||
* Thus c+r*c will be added in as the correction terms for
|
||||
* expm1(r+c). Now rearrange the term to avoid optimization
|
||||
* screw up:
|
||||
* ( 2 2 )
|
||||
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
|
||||
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
|
||||
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
|
||||
* ( )
|
||||
*
|
||||
* = r - E
|
||||
* 3. Scale back to obtain expm1(x):
|
||||
* From step 1, we have
|
||||
* expm1(x) = either 2^k*[expm1(r)+1] - 1
|
||||
* = or 2^k*[expm1(r) + (1-2^-k)]
|
||||
* 4. Implementation notes:
|
||||
* (A). To save one multiplication, we scale the coefficient Qi
|
||||
* to Qi*2^i, and replace z by (x^2)/2.
|
||||
* (B). To achieve maximum accuracy, we compute expm1(x) by
|
||||
* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
|
||||
* (ii) if k=0, return r-E
|
||||
* (iii) if k=-1, return 0.5*(r-E)-0.5
|
||||
* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
|
||||
* else return 1.0+2.0*(r-E);
|
||||
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
|
||||
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
|
||||
* (vii) return 2^k(1-((E+2^-k)-r))
|
||||
*
|
||||
* Special cases:
|
||||
* expm1(INF) is INF, expm1(NaN) is NaN;
|
||||
* expm1(-INF) is -1, and
|
||||
* for finite argument, only expm1(0)=0 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
|
||||
*
|
||||
* 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 one 1.0
|
||||
#define huge 1.0e+300
|
||||
#define tiny 1.0e-300
|
||||
#define o_threshold 7.09782712893383973096e+02 /* 0x40862E42, 0xFEFA39EF */
|
||||
#define ln2_hi 6.93147180369123816490e-01 /* 0x3fe62e42, 0xfee00000 */
|
||||
#define ln2_lo 1.90821492927058770002e-10 /* 0x3dea39ef, 0x35793c76 */
|
||||
#define invln2 1.44269504088896338700e+00 /* 0x3ff71547, 0x652b82fe */
|
||||
|
||||
/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */
|
||||
#define Q1 -3.33333333333331316428e-02 /* BFA11111 111110F4 */
|
||||
#define Q2 1.58730158725481460165e-03 /* 3F5A01A0 19FE5585 */
|
||||
#define Q3 -7.93650757867487942473e-05 /* BF14CE19 9EAADBB7 */
|
||||
#define Q4 4.00821782732936239552e-06 /* 3ED0CFCA 86E65239 */
|
||||
#define Q5 -2.01099218183624371326e-07 /* BE8AFDB7 6E09C32D */
|
||||
|
||||
double
|
||||
expm1 (double x)
|
||||
{
|
||||
double y, hi, lo, c, e, hxs, hfx, r1;
|
||||
double_accessor t, twopk;
|
||||
int k, xsb;
|
||||
unsigned int hx;
|
||||
|
||||
hx = __HI (x);
|
||||
xsb = hx & 0x80000000; /* sign bit of x */
|
||||
hx &= 0x7fffffff; /* high word of |x| */
|
||||
|
||||
/* filter out huge and non-finite argument */
|
||||
if (hx >= 0x4043687A)
|
||||
{
|
||||
/* if |x|>=56*ln2 */
|
||||
if (hx >= 0x40862E42)
|
||||
{
|
||||
/* if |x|>=709.78... */
|
||||
if (hx >= 0x7ff00000)
|
||||
{
|
||||
unsigned int low;
|
||||
low = __LO (x);
|
||||
if (((hx & 0xfffff) | low) != 0)
|
||||
{
|
||||
/* NaN */
|
||||
return x + x;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* exp(+-inf)-1={inf,-1} */
|
||||
return (xsb == 0) ? x : -1.0;
|
||||
}
|
||||
}
|
||||
if (x > o_threshold)
|
||||
{
|
||||
/* overflow */
|
||||
return huge * huge;
|
||||
}
|
||||
}
|
||||
if (xsb != 0)
|
||||
{
|
||||
/* x < -56*ln2, return -1.0 with inexact */
|
||||
if (x + tiny < 0.0) /* raise inexact */
|
||||
{
|
||||
/* return -1 */
|
||||
return tiny - one;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* argument reduction */
|
||||
if (hx > 0x3fd62e42)
|
||||
{
|
||||
/* if |x| > 0.5 ln2 */
|
||||
if (hx < 0x3FF0A2B2)
|
||||
{
|
||||
/* and |x| < 1.5 ln2 */
|
||||
if (xsb == 0)
|
||||
{
|
||||
hi = x - ln2_hi;
|
||||
lo = ln2_lo;
|
||||
k = 1;
|
||||
}
|
||||
else
|
||||
{
|
||||
hi = x + ln2_hi;
|
||||
lo = -ln2_lo;
|
||||
k = -1;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
k = (int) (invln2 * x + ((xsb == 0) ? 0.5 : -0.5));
|
||||
t.dbl = k;
|
||||
hi = x - t.dbl * ln2_hi; /* t*ln2_hi is exact here */
|
||||
lo = t.dbl * ln2_lo;
|
||||
}
|
||||
x = hi - lo;
|
||||
c = (hi - x) - lo;
|
||||
}
|
||||
else if (hx < 0x3c900000)
|
||||
{
|
||||
/* when |x|<2**-54, return x */
|
||||
return x;
|
||||
}
|
||||
else
|
||||
{
|
||||
k = 0;
|
||||
}
|
||||
|
||||
/* x is now in primary range */
|
||||
hfx = 0.5 * x;
|
||||
hxs = x * hfx;
|
||||
r1 = one + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));
|
||||
t.dbl = 3.0 - r1 * hfx;
|
||||
e = hxs * ((r1 - t.dbl) / (6.0 - x * t.dbl));
|
||||
if (k == 0)
|
||||
{
|
||||
/* c is 0 */
|
||||
return x - (x * e - hxs);
|
||||
}
|
||||
else
|
||||
{
|
||||
twopk.as_int.hi = 0x3ff00000 + ((unsigned int) k << 20); /* 2^k */
|
||||
twopk.as_int.lo = 0;
|
||||
e = (x * (e - c) - c);
|
||||
e -= hxs;
|
||||
if (k == -1)
|
||||
{
|
||||
return 0.5 * (x - e) - 0.5;
|
||||
}
|
||||
if (k == 1)
|
||||
{
|
||||
if (x < -0.25)
|
||||
{
|
||||
return -2.0 * (e - (x + 0.5));
|
||||
}
|
||||
else
|
||||
{
|
||||
return one + 2.0 * (x - e);
|
||||
}
|
||||
}
|
||||
if ((k <= -2) || (k > 56))
|
||||
{
|
||||
/* suffice to return exp(x)-1 */
|
||||
y = one - (e - x);
|
||||
if (k == 1024)
|
||||
{
|
||||
y = y * 2.0 * 0x1p1023;
|
||||
}
|
||||
else
|
||||
{
|
||||
y = y * twopk.dbl;
|
||||
}
|
||||
return y - one;
|
||||
}
|
||||
t.dbl = one;
|
||||
if (k < 20)
|
||||
{
|
||||
t.as_int.hi = (0x3ff00000 - (0x200000 >> k)); /* t=1-2^-k */
|
||||
y = t.dbl - (e - x);
|
||||
y = y * twopk.dbl;
|
||||
}
|
||||
else
|
||||
{
|
||||
t.as_int.hi = ((0x3ff - k) << 20); /* 2^-k */
|
||||
y = x - (e + t.dbl);
|
||||
y += one;
|
||||
y = y * twopk.dbl;
|
||||
}
|
||||
}
|
||||
return y;
|
||||
} /* expm1 */
|
||||
|
||||
#undef one
|
||||
#undef huge
|
||||
#undef tiny
|
||||
#undef o_threshold
|
||||
#undef ln2_hi
|
||||
#undef ln2_lo
|
||||
#undef invln2
|
||||
#undef Q1
|
||||
#undef Q2
|
||||
#undef Q3
|
||||
#undef Q4
|
||||
#undef Q5
|
||||
@@ -0,0 +1,40 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_fabs.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* fabs(x) returns the absolute value of x.
|
||||
*/
|
||||
|
||||
double
|
||||
fabs (double x)
|
||||
{
|
||||
double_accessor ret;
|
||||
ret.dbl = x;
|
||||
ret.as_int.hi &= 0x7fffffff;
|
||||
return ret.dbl;
|
||||
} /* fabs */
|
||||
@@ -0,0 +1,41 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_finite.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* finite(x) returns 1 is x is finite, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
int
|
||||
finite (double x)
|
||||
{
|
||||
int hx;
|
||||
|
||||
hx = __HI (x);
|
||||
return (unsigned) ((hx & 0x7fffffff) - 0x7ff00000) >> 31;
|
||||
} /* finite */
|
||||
@@ -0,0 +1,132 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_floor.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* floor(x)
|
||||
* Return x rounded toward -inf to integral value
|
||||
*
|
||||
* Method:
|
||||
* Bit twiddling.
|
||||
*
|
||||
* Exception:
|
||||
* Inexact flag raised if x not equal to floor(x).
|
||||
*/
|
||||
|
||||
#define huge 1.0e300
|
||||
|
||||
double
|
||||
floor (double x)
|
||||
{
|
||||
int i0, i1, j0;
|
||||
unsigned i, j;
|
||||
|
||||
i0 = __HI (x);
|
||||
i1 = __LO (x);
|
||||
j0 = ((i0 >> 20) & 0x7ff) - 0x3ff;
|
||||
if (j0 < 20)
|
||||
{
|
||||
if (j0 < 0) /* raise inexact if x != 0 */
|
||||
{
|
||||
if (huge + x > 0.0) /* return 0 * sign(x) if |x| < 1 */
|
||||
{
|
||||
if (i0 >= 0)
|
||||
{
|
||||
i0 = i1 = 0;
|
||||
}
|
||||
else if (((i0 & 0x7fffffff) | i1) != 0)
|
||||
{
|
||||
i0 = 0xbff00000;
|
||||
i1 = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
i = (0x000fffff) >> j0;
|
||||
if (((i0 & i) | i1) == 0) /* x is integral */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
if (huge + x > 0.0) /* raise inexact flag */
|
||||
{
|
||||
if (i0 < 0)
|
||||
{
|
||||
i0 += (0x00100000) >> j0;
|
||||
}
|
||||
i0 &= (~i);
|
||||
i1 = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
else if (j0 > 51)
|
||||
{
|
||||
if (j0 == 0x400) /* inf or NaN */
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
else /* x is integral */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
i = ((unsigned) (0xffffffff)) >> (j0 - 20);
|
||||
if ((i1 & i) == 0) /* x is integral */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
if (huge + x > 0.0) /* raise inexact flag */
|
||||
{
|
||||
if (i0 < 0)
|
||||
{
|
||||
if (j0 == 20)
|
||||
{
|
||||
i0 += 1;
|
||||
}
|
||||
else
|
||||
{
|
||||
j = i1 + (1 << (52 - j0));
|
||||
if (j < i1) /* got a carry */
|
||||
{
|
||||
i0 += 1;
|
||||
}
|
||||
i1 = j;
|
||||
}
|
||||
}
|
||||
i1 &= (~i);
|
||||
}
|
||||
}
|
||||
|
||||
double_accessor ret;
|
||||
ret.as_int.hi = i0;
|
||||
ret.as_int.lo = i1;
|
||||
return ret.dbl;
|
||||
} /* floor */
|
||||
|
||||
#undef huge
|
||||
@@ -0,0 +1,232 @@
|
||||
/* 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_fmod.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* fmod(x,y)
|
||||
* Return x mod y in exact arithmetic
|
||||
*
|
||||
* Method: shift and subtract
|
||||
*/
|
||||
|
||||
static const double Zero[] = { 0.0, -0.0, };
|
||||
|
||||
double
|
||||
fmod (double x, double y)
|
||||
{
|
||||
int n, hx, hy, hz, ix, iy, sx, i;
|
||||
unsigned lx, ly, lz;
|
||||
|
||||
hx = __HI (x); /* high word of x */
|
||||
lx = __LO (x); /* low word of x */
|
||||
hy = __HI (y); /* high word of y */
|
||||
ly = __LO (y); /* low word of y */
|
||||
sx = hx & 0x80000000; /* sign of x */
|
||||
hx ^= sx; /* |x| */
|
||||
hy &= 0x7fffffff; /* |y| */
|
||||
|
||||
/* purge off exception values */
|
||||
if ((hy | ly) == 0 || (hx >= 0x7ff00000) || /* y = 0, or x not finite */
|
||||
((hy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* or y is NaN */
|
||||
{
|
||||
return NAN;
|
||||
}
|
||||
if (hx <= hy)
|
||||
{
|
||||
if ((hx < hy) || (lx < ly)) /* |x| < |y| return x */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
if (lx == ly) /* |x| = |y| return x * 0 */
|
||||
{
|
||||
return Zero[(unsigned) sx >> 31];
|
||||
}
|
||||
}
|
||||
|
||||
/* determine ix = ilogb(x) */
|
||||
if (hx < 0x00100000) /* subnormal x */
|
||||
{
|
||||
if (hx == 0)
|
||||
{
|
||||
for (ix = -1043, i = lx; i > 0; i <<= 1)
|
||||
{
|
||||
ix -= 1;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
for (ix = -1022, i = (hx << 11); i > 0; i <<= 1)
|
||||
{
|
||||
ix -= 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
ix = (hx >> 20) - 1023;
|
||||
}
|
||||
|
||||
/* determine iy = ilogb(y) */
|
||||
if (hy < 0x00100000) /* subnormal y */
|
||||
{
|
||||
if (hy == 0)
|
||||
{
|
||||
for (iy = -1043, i = ly; i > 0; i <<= 1)
|
||||
{
|
||||
iy -= 1;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
for (iy = -1022, i = (hy << 11); i > 0; i <<= 1)
|
||||
{
|
||||
iy -= 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
iy = (hy >> 20) - 1023;
|
||||
}
|
||||
|
||||
/* set up {hx,lx}, {hy,ly} and align y to x */
|
||||
if (ix >= -1022)
|
||||
{
|
||||
hx = 0x00100000 | (0x000fffff & hx);
|
||||
}
|
||||
else /* subnormal x, shift x to normal */
|
||||
{
|
||||
n = -1022 - ix;
|
||||
if (n <= 31)
|
||||
{
|
||||
hx = (((unsigned int) hx) << n) | (lx >> (32 - n));
|
||||
lx <<= n;
|
||||
}
|
||||
else
|
||||
{
|
||||
hx = lx << (n - 32);
|
||||
lx = 0;
|
||||
}
|
||||
}
|
||||
if (iy >= -1022)
|
||||
{
|
||||
hy = 0x00100000 | (0x000fffff & hy);
|
||||
}
|
||||
else /* subnormal y, shift y to normal */
|
||||
{
|
||||
n = -1022 - iy;
|
||||
if (n <= 31)
|
||||
{
|
||||
hy = (((unsigned int) hy) << n) | (ly >> (32 - n));
|
||||
ly <<= n;
|
||||
}
|
||||
else
|
||||
{
|
||||
hy = ly << (n - 32);
|
||||
ly = 0;
|
||||
}
|
||||
}
|
||||
|
||||
/* fix point fmod */
|
||||
n = ix - iy;
|
||||
while (n--)
|
||||
{
|
||||
hz = hx - hy;
|
||||
lz = lx - ly;
|
||||
if (lx < ly)
|
||||
{
|
||||
hz -= 1;
|
||||
}
|
||||
if (hz < 0)
|
||||
{
|
||||
hx = hx + hx + (lx >> 31);
|
||||
lx = lx + lx;
|
||||
}
|
||||
else
|
||||
{
|
||||
if ((hz | lz) == 0) /* return sign(x) * 0 */
|
||||
{
|
||||
return Zero[(unsigned) sx >> 31];
|
||||
}
|
||||
hx = hz + hz + (lz >> 31);
|
||||
lx = lz + lz;
|
||||
}
|
||||
}
|
||||
hz = hx - hy;
|
||||
lz = lx - ly;
|
||||
if (lx < ly)
|
||||
{
|
||||
hz -= 1;
|
||||
}
|
||||
if (hz >= 0)
|
||||
{
|
||||
hx = hz;
|
||||
lx = lz;
|
||||
}
|
||||
|
||||
/* convert back to floating value and restore the sign */
|
||||
if ((hx | lx) == 0) /* return sign(x) * 0 */
|
||||
{
|
||||
return Zero[(unsigned) sx >> 31];
|
||||
}
|
||||
while (hx < 0x00100000) /* normalize x */
|
||||
{
|
||||
hx = hx + hx + (lx >> 31);
|
||||
lx = lx + lx;
|
||||
iy -= 1;
|
||||
}
|
||||
|
||||
double_accessor ret;
|
||||
if (iy >= -1022) /* normalize output */
|
||||
{
|
||||
hx = ((hx - 0x00100000) | ((iy + 1023) << 20));
|
||||
ret.as_int.hi = hx | sx;
|
||||
ret.as_int.lo = lx;
|
||||
}
|
||||
else /* subnormal output */
|
||||
{
|
||||
n = -1022 - iy;
|
||||
if (n <= 20)
|
||||
{
|
||||
lx = (lx >> n) | ((unsigned) hx << (32 - n));
|
||||
hx >>= n;
|
||||
}
|
||||
else if (n <= 31)
|
||||
{
|
||||
lx = (hx << (32 - n)) | (lx >> n);
|
||||
hx = sx;
|
||||
}
|
||||
else
|
||||
{
|
||||
lx = hx >> (n - 32);
|
||||
hx = sx;
|
||||
}
|
||||
ret.as_int.hi = hx | sx;
|
||||
ret.as_int.lo = lx;
|
||||
}
|
||||
return ret.dbl; /* exact output */
|
||||
} /* fmod */
|
||||
@@ -0,0 +1,95 @@
|
||||
/* 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.
|
||||
*/
|
||||
|
||||
#ifndef JERRY_MATH_H
|
||||
#define JERRY_MATH_H
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C"
|
||||
{
|
||||
#endif /* __cplusplus */
|
||||
|
||||
/* General Constants. */
|
||||
#define INFINITY (1.0/0.0)
|
||||
#define NAN (0.0/0.0)
|
||||
#define HUGE_VAL INFINITY
|
||||
|
||||
#define isnan(x) ((x) != (x))
|
||||
#define isinf(x) (((x) == INFINITY) || ((x) == -INFINITY))
|
||||
#define isfinite(x) (!(isinf(x)) && (x != NAN))
|
||||
|
||||
/* Exponential and Logarithmic constants. */
|
||||
#define M_E 2.7182818284590452353602874713526625
|
||||
#define M_SQRT2 1.4142135623730950488016887242096981
|
||||
#define M_SQRT1_2 0.7071067811865475244008443621048490
|
||||
#define M_LOG2E 1.4426950408889634073599246810018921
|
||||
#define M_LOG10E 0.4342944819032518276511289189166051
|
||||
#define M_LN2 0.6931471805599453094172321214581765
|
||||
#define M_LN10 2.3025850929940456840179914546843642
|
||||
|
||||
/* Trigonometric Constants. */
|
||||
#define M_PI 3.1415926535897932384626433832795029
|
||||
#define M_PI_2 1.5707963267948966192313216916397514
|
||||
#define M_PI_4 0.7853981633974483096156608458198757
|
||||
#define M_1_PI 0.3183098861837906715377675267450287
|
||||
#define M_2_PI 0.6366197723675813430755350534900574
|
||||
#define M_2_SQRTPI 1.1283791670955125738961589031215452
|
||||
|
||||
/* Trigonometric functions. */
|
||||
double cos (double);
|
||||
double sin (double);
|
||||
double tan (double);
|
||||
double acos (double);
|
||||
double asin (double);
|
||||
double atan (double);
|
||||
double atan2 (double, double);
|
||||
|
||||
/* Hyperbolic functions. */
|
||||
double cosh (double x);
|
||||
double sinh (double x);
|
||||
double tanh (double x);
|
||||
|
||||
/* Inverse hyperbolic functions */
|
||||
double acosh (double);
|
||||
double asinh (double);
|
||||
double atanh (double);
|
||||
|
||||
/* Exponential and logarithmic functions. */
|
||||
double exp (double);
|
||||
double expm1 (double);
|
||||
double log (double);
|
||||
double log1p (double);
|
||||
double log2 (double);
|
||||
double log10 (double);
|
||||
|
||||
/* Power functions. */
|
||||
double pow (double, double);
|
||||
double sqrt (double);
|
||||
double cbrt (double);
|
||||
|
||||
/* Rounding and remainder functions. */
|
||||
double ceil (double);
|
||||
double floor (double);
|
||||
|
||||
/* Other functions. */
|
||||
double fabs (double);
|
||||
double fmod (double, double);
|
||||
|
||||
double nextafter (double, double);
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif /* __cplusplus */
|
||||
#endif /* !JERRY_MATH_H */
|
||||
@@ -0,0 +1,44 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_isnan.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* isnan(x) returns 1 is x is nan, else 0;
|
||||
* no branching!
|
||||
*/
|
||||
|
||||
int
|
||||
isnan (double x)
|
||||
{
|
||||
int hx, lx;
|
||||
|
||||
hx = (__HI (x) & 0x7fffffff);
|
||||
lx = __LO (x);
|
||||
hx |= (unsigned) (lx | (-lx)) >> 31;
|
||||
hx = 0x7ff00000 - hx;
|
||||
return ((unsigned) (hx)) >> 31;
|
||||
} /* isnan */
|
||||
@@ -0,0 +1,126 @@
|
||||
/* 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) 2004 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.
|
||||
*
|
||||
* @(#)fdlibm.h 1.5 04/04/22
|
||||
*/
|
||||
|
||||
#ifndef JERRY_MATH_INTERNAL_H
|
||||
#define JERRY_MATH_INTERNAL_H
|
||||
|
||||
/* Sometimes it's necessary to define __LITTLE_ENDIAN explicitly
|
||||
but these catch some common cases. */
|
||||
|
||||
#ifndef __LITTLE_ENDIAN
|
||||
/* Check if compiler has byte order macro. Some older versions do not.
|
||||
* If byte order is supported and set to little or target is among common
|
||||
* cases checked define __LITTLE_ENDIAN.
|
||||
*/
|
||||
#if (defined (i386) || defined (__i386) || defined (__i386__) || \
|
||||
defined (i486) || defined (__i486) || defined (__i486__) || \
|
||||
defined (intel) || defined (x86) || defined (i86pc) || \
|
||||
defined (__alpha) || defined (__osf__) || \
|
||||
defined (__x86_64__) || defined (__arm__) || defined (__aarch64__) || \
|
||||
defined (__xtensa__) || defined (__MIPSEL)) || \
|
||||
(defined (__BYTE_ORDER__) && (__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__))
|
||||
#define __LITTLE_ENDIAN
|
||||
#endif
|
||||
#endif /* !__LITTLE_ENDIAN */
|
||||
|
||||
#ifdef __LITTLE_ENDIAN
|
||||
#define __HI(x) *(1 + (const int *) &x)
|
||||
#define __LO(x) *(const int *) &x
|
||||
typedef union
|
||||
{
|
||||
double dbl;
|
||||
struct
|
||||
{
|
||||
int lo;
|
||||
int hi;
|
||||
} as_int;
|
||||
} double_accessor;
|
||||
#else /* !__LITTLE_ENDIAN */
|
||||
#define __HI(x) *(const int *) &x
|
||||
#define __LO(x) *(1 + (const int *) &x)
|
||||
|
||||
typedef union
|
||||
{
|
||||
double dbl;
|
||||
struct
|
||||
{
|
||||
int hi;
|
||||
int lo;
|
||||
} as_int;
|
||||
} double_accessor;
|
||||
#endif /* __LITTLE_ENDIAN */
|
||||
|
||||
#ifndef NAN
|
||||
#define NAN (0.0/0.0)
|
||||
#endif
|
||||
|
||||
/*
|
||||
* ANSI/POSIX
|
||||
*/
|
||||
double acos (double x);
|
||||
double asin (double x);
|
||||
double atan (double x);
|
||||
double atan2 (double y, double x);
|
||||
double cos (double x);
|
||||
double sin (double x);
|
||||
double tan (double x);
|
||||
|
||||
double cosh (double x);
|
||||
double sinh (double x);
|
||||
double tanh (double x);
|
||||
|
||||
double acosh (double x);
|
||||
double asinh (double x);
|
||||
double atanh (double x);
|
||||
|
||||
double exp (double x);
|
||||
double expm1 (double x);
|
||||
double log (double x);
|
||||
double log1p (double x);
|
||||
double log2 (double x);
|
||||
double log10 (double);
|
||||
|
||||
double pow (double x, double y);
|
||||
double sqrt (double x);
|
||||
double cbrt (double);
|
||||
|
||||
double ceil (double x);
|
||||
double fabs (double x);
|
||||
double floor (double x);
|
||||
double fmod (double x, double y);
|
||||
|
||||
int isnan (double x);
|
||||
int finite (double x);
|
||||
|
||||
double nextafter (double x, double y);
|
||||
|
||||
/*
|
||||
* Functions callable from C, intended to support IEEE arithmetic.
|
||||
*/
|
||||
double copysign (double x, double y);
|
||||
double scalbn (double x, int n);
|
||||
|
||||
#endif /* !JERRY_MATH_INTERNAL_H */
|
||||
@@ -0,0 +1,10 @@
|
||||
prefix=@CMAKE_INSTALL_PREFIX@
|
||||
libdir=${prefix}/lib
|
||||
includedir=${prefix}/include/jerry-math
|
||||
|
||||
Name: libjerry-math
|
||||
Description: JerryScript: lightweight JavaScript engine (minimal math library)
|
||||
URL: https://github.com/jerryscript-project/jerryscript
|
||||
Version: @JERRY_VERSION@
|
||||
Libs: -L${libdir} -ljerry-math
|
||||
Cflags: -I${includedir}
|
||||
@@ -0,0 +1,202 @@
|
||||
/* 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_log.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* log(x)
|
||||
* Return the logrithm of x
|
||||
*
|
||||
* Method :
|
||||
* 1. Argument Reduction: find k and f such that
|
||||
* x = 2^k * (1+f),
|
||||
* where sqrt(2)/2 < 1+f < sqrt(2) .
|
||||
*
|
||||
* 2. Approximation of log(1+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) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
|
||||
* (the values of Lg1 to Lg7 are listed in the program)
|
||||
* and
|
||||
* | 2 14 | -58.45
|
||||
* | Lg1*s +...+Lg7*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
|
||||
* log(1+f) = f - s*(f - R) (if f is not too large)
|
||||
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
|
||||
*
|
||||
* 3. Finally, log(x) = k*ln2 + log(1+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:
|
||||
* log(x) is NaN with signal if x < 0 (including -INF) ;
|
||||
* log(+INF) is +INF; log(0) is -INF with signal;
|
||||
* log(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.
|
||||
*/
|
||||
|
||||
#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 Lg1 6.666666666666735130e-01 /* 3FE55555 55555593 */
|
||||
#define Lg2 3.999999999940941908e-01 /* 3FD99999 9997FA04 */
|
||||
#define Lg3 2.857142874366239149e-01 /* 3FD24924 94229359 */
|
||||
#define Lg4 2.222219843214978396e-01 /* 3FCC71C5 1D8E78AF */
|
||||
#define Lg5 1.818357216161805012e-01 /* 3FC74664 96CB03DE */
|
||||
#define Lg6 1.531383769920937332e-01 /* 3FC39A09 D078C69F */
|
||||
#define Lg7 1.479819860511658591e-01 /* 3FC2F112 DF3E5244 */
|
||||
|
||||
double
|
||||
log (double x)
|
||||
{
|
||||
double hfsq, f, s, z, R, w, t1, t2, dk;
|
||||
int k, hx, i, j;
|
||||
unsigned lx;
|
||||
|
||||
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;
|
||||
hx &= 0x000fffff;
|
||||
i = (hx + 0x95f64) & 0x100000;
|
||||
|
||||
double_accessor temp;
|
||||
temp.dbl = x;
|
||||
temp.as_int.hi = hx | (i ^ 0x3ff00000); /* normalize x or x / 2 */
|
||||
k += (i >> 20);
|
||||
f = temp.dbl - 1.0;
|
||||
|
||||
if ((0x000fffff & (2 + hx)) < 3) /* |f| < 2**-20 */
|
||||
{
|
||||
if (f == zero)
|
||||
{
|
||||
if (k == 0)
|
||||
{
|
||||
return zero;
|
||||
}
|
||||
else
|
||||
{
|
||||
dk = (double) k;
|
||||
return dk * ln2_hi + dk * ln2_lo;
|
||||
}
|
||||
}
|
||||
R = f * f * (0.5 - 0.33333333333333333 * f);
|
||||
if (k == 0)
|
||||
{
|
||||
return f - R;
|
||||
}
|
||||
else
|
||||
{
|
||||
dk = (double) k;
|
||||
return dk * ln2_hi - ((R - dk * ln2_lo) - f);
|
||||
}
|
||||
}
|
||||
s = f / (2.0 + f);
|
||||
dk = (double) k;
|
||||
z = s * s;
|
||||
i = hx - 0x6147a;
|
||||
w = z * z;
|
||||
j = 0x6b851 - hx;
|
||||
t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
|
||||
t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
|
||||
i |= j;
|
||||
R = t2 + t1;
|
||||
if (i > 0)
|
||||
{
|
||||
hfsq = 0.5 * f * f;
|
||||
if (k == 0)
|
||||
{
|
||||
return f - (hfsq - s * (hfsq + R));
|
||||
}
|
||||
else
|
||||
{
|
||||
return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - f);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
if (k == 0)
|
||||
{
|
||||
return f - s * (f - R);
|
||||
}
|
||||
else
|
||||
{
|
||||
return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
|
||||
}
|
||||
}
|
||||
} /* log */
|
||||
|
||||
#undef zero
|
||||
#undef ln2_hi
|
||||
#undef ln2_lo
|
||||
#undef two54
|
||||
#undef Lg1
|
||||
#undef Lg2
|
||||
#undef Lg3
|
||||
#undef Lg4
|
||||
#undef Lg5
|
||||
#undef Lg6
|
||||
#undef Lg7
|
||||
@@ -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
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* 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
|
||||
* n = ilogb(x),
|
||||
* if(n<0) n = n+1;
|
||||
* 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-math-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-math-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 +1,135 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_nextafter.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
double
|
||||
nextafter (double x,
|
||||
double y)
|
||||
{
|
||||
int hx, hy, ix, iy;
|
||||
unsigned lx, ly;
|
||||
double_accessor ret;
|
||||
|
||||
hx = __HI (x); /* high word of x */
|
||||
lx = __LO (x); /* low word of x */
|
||||
hy = __HI (y); /* high word of y */
|
||||
ly = __LO (y); /* low word of y */
|
||||
ix = hx & 0x7fffffff; /* |x| */
|
||||
iy = hy & 0x7fffffff; /* |y| */
|
||||
|
||||
if (((ix >= 0x7ff00000) && ((ix - 0x7ff00000) | lx) != 0) /* x is nan */
|
||||
|| ((iy >= 0x7ff00000) && ((iy - 0x7ff00000) | ly) != 0)) /* y is nan */
|
||||
{
|
||||
return x + y;
|
||||
}
|
||||
|
||||
if (x == y)
|
||||
{
|
||||
return x; /* x=y, return x */
|
||||
}
|
||||
|
||||
if ((ix | lx) == 0)
|
||||
{ /* x == 0 */
|
||||
ret.as_int.hi = hy & 0x80000000; /* return +-minsubnormal */
|
||||
ret.as_int.lo = 1;
|
||||
y = ret.dbl * ret.dbl;
|
||||
if (y == ret.dbl)
|
||||
{
|
||||
return y;
|
||||
}
|
||||
else
|
||||
{
|
||||
return ret.dbl; /* raise underflow flag */
|
||||
}
|
||||
}
|
||||
|
||||
if (hx >= 0)
|
||||
{ /* x > 0 */
|
||||
if (hx > hy || ((hx == hy) && (lx > ly)))
|
||||
{ /* x > y, x -= ulp */
|
||||
if (lx == 0)
|
||||
{
|
||||
hx -= 1;
|
||||
}
|
||||
|
||||
lx -= 1;
|
||||
}
|
||||
else
|
||||
{ /* x < y, x += ulp */
|
||||
lx += 1;
|
||||
|
||||
if (lx == 0)
|
||||
{
|
||||
hx += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{ /* x < 0 */
|
||||
if (hy >= 0 || hx > hy || ((hx == hy) && (lx > ly)))
|
||||
{ /* x < y, x -= ulp */
|
||||
if (lx == 0)
|
||||
{
|
||||
hx -= 1;
|
||||
}
|
||||
|
||||
lx -= 1;
|
||||
}
|
||||
else
|
||||
{ /* x > y, x += ulp */
|
||||
lx += 1;
|
||||
|
||||
if (lx == 0)
|
||||
{
|
||||
hx += 1;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
hy = hx & 0x7ff00000;
|
||||
|
||||
if (hy >= 0x7ff00000)
|
||||
{
|
||||
return x + x; /* overflow */
|
||||
}
|
||||
|
||||
if (hy < 0x00100000)
|
||||
{ /* underflow */
|
||||
y = x * x;
|
||||
if (y != x)
|
||||
{ /* raise underflow flag */
|
||||
ret.as_int.hi = hx;
|
||||
ret.as_int.lo = lx;
|
||||
return ret.dbl;
|
||||
}
|
||||
}
|
||||
|
||||
ret.as_int.hi = hx;
|
||||
ret.as_int.lo = lx;
|
||||
return ret.dbl;
|
||||
} /* nextafter */
|
||||
@@ -0,0 +1,476 @@
|
||||
/* 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) 2004 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.
|
||||
*
|
||||
* @(#)e_pow.c 1.5 04/04/22
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* pow(x,y) return x**y
|
||||
*
|
||||
* n
|
||||
* Method: Let x = 2 * (1+f)
|
||||
* 1. Compute and return log2(x) in two pieces:
|
||||
* log2(x) = w1 + w2,
|
||||
* where w1 has 53-24 = 29 bit trailing zeros.
|
||||
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
|
||||
* arithmetic, where |y'|<=0.5.
|
||||
* 3. Return x**y = 2**n*exp(y'*log2)
|
||||
*
|
||||
* Special cases:
|
||||
* 0. +1 ** (anything) is 1
|
||||
* 1. (anything) ** 0 is 1
|
||||
* 2. (anything) ** 1 is itself
|
||||
* 3. (anything) ** NAN is NAN
|
||||
* 4. NAN ** (anything except 0) is NAN
|
||||
* 5. +-(|x| > 1) ** +INF is +INF
|
||||
* 6. +-(|x| > 1) ** -INF is +0
|
||||
* 7. +-(|x| < 1) ** +INF is +0
|
||||
* 8. +-(|x| < 1) ** -INF is +INF
|
||||
* 9. -1 ** +-INF is 1
|
||||
* 10. +0 ** (+anything except 0, NAN) is +0
|
||||
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
|
||||
* 12. +0 ** (-anything except 0, NAN) is +INF
|
||||
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
|
||||
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
||||
* 15. +INF ** (+anything except 0,NAN) is +INF
|
||||
* 16. +INF ** (-anything except 0,NAN) is +0
|
||||
* 17. -INF ** (anything) = -0 ** (-anything)
|
||||
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
||||
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
||||
*
|
||||
* Accuracy:
|
||||
* pow(x,y) returns x**y nearly rounded. In particular
|
||||
* pow(integer,integer)
|
||||
* always returns the correct integer provided it is
|
||||
* representable.
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
|
||||
static const double bp[] =
|
||||
{
|
||||
1.0,
|
||||
1.5,
|
||||
};
|
||||
static const double dp_h[] =
|
||||
{
|
||||
0.0,
|
||||
5.84962487220764160156e-01, /* 0x3FE2B803, 0x40000000 */
|
||||
};
|
||||
static const double dp_l[] =
|
||||
{
|
||||
0.0,
|
||||
1.35003920212974897128e-08, /* 0x3E4CFDEB, 0x43CFD006 */
|
||||
};
|
||||
|
||||
#define zero 0.0
|
||||
#define one 1.0
|
||||
#define two 2.0
|
||||
#define two53 9007199254740992.0 /* 0x43400000, 0x00000000 */
|
||||
#define huge 1.0e300
|
||||
#define tiny 1.0e-300
|
||||
/* poly coefs for (3/2) * (log(x) - 2s - 2/3 * s**3 */
|
||||
#define L1 5.99999999999994648725e-01 /* 0x3FE33333, 0x33333303 */
|
||||
#define L2 4.28571428578550184252e-01 /* 0x3FDB6DB6, 0xDB6FABFF */
|
||||
#define L3 3.33333329818377432918e-01 /* 0x3FD55555, 0x518F264D */
|
||||
#define L4 2.72728123808534006489e-01 /* 0x3FD17460, 0xA91D4101 */
|
||||
#define L5 2.30660745775561754067e-01 /* 0x3FCD864A, 0x93C9DB65 */
|
||||
#define L6 2.06975017800338417784e-01 /* 0x3FCA7E28, 0x4A454EEF */
|
||||
#define P1 1.66666666666666019037e-01 /* 0x3FC55555, 0x5555553E */
|
||||
#define P2 -2.77777777770155933842e-03 /* 0xBF66C16C, 0x16BEBD93 */
|
||||
#define P3 6.61375632143793436117e-05 /* 0x3F11566A, 0xAF25DE2C */
|
||||
#define P4 -1.65339022054652515390e-06 /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
#define P5 4.13813679705723846039e-08 /* 0x3E663769, 0x72BEA4D0 */
|
||||
#define lg2 6.93147180559945286227e-01 /* 0x3FE62E42, 0xFEFA39EF */
|
||||
#define lg2_h 6.93147182464599609375e-01 /* 0x3FE62E43, 0x00000000 */
|
||||
#define lg2_l -1.90465429995776804525e-09 /* 0xBE205C61, 0x0CA86C39 */
|
||||
#define ovt 8.0085662595372944372e-0017 /* -(1024-log2(ovfl+.5ulp)) */
|
||||
#define cp 9.61796693925975554329e-01 /* 0x3FEEC709, 0xDC3A03FD = 2 / (3 ln2) */
|
||||
#define cp_h 9.61796700954437255859e-01 /* 0x3FEEC709, 0xE0000000 = (float) cp */
|
||||
#define cp_l -7.02846165095275826516e-09 /* 0xBE3E2FE0, 0x145B01F5 = tail of cp_h */
|
||||
#define ivln2 1.44269504088896338700e+00 /* 0x3FF71547, 0x652B82FE = 1 / ln2 */
|
||||
#define ivln2_h 1.44269502162933349609e+00 /* 0x3FF71547, 0x60000000 = 24b 1 / ln2 */
|
||||
#define ivln2_l 1.92596299112661746887e-08 /* 0x3E54AE0B, 0xF85DDF44 = 1 / ln2 tail */
|
||||
|
||||
double
|
||||
pow (double x, double y)
|
||||
{
|
||||
double_accessor t1, ax, p_h, y1, t, z;
|
||||
double z_h, z_l, p_l;
|
||||
double t2, r, s, u, v, w;
|
||||
int i, j, k, yisint, n;
|
||||
int hx, hy, ix, iy;
|
||||
unsigned lx, ly;
|
||||
|
||||
hx = __HI (x);
|
||||
lx = __LO (x);
|
||||
hy = __HI (y);
|
||||
ly = __LO (y);
|
||||
ix = hx & 0x7fffffff;
|
||||
iy = hy & 0x7fffffff;
|
||||
|
||||
/* x == one: 1**y = 1 */
|
||||
if (((hx - 0x3ff00000) | lx) == 0)
|
||||
{
|
||||
return one;
|
||||
}
|
||||
|
||||
/* y == zero: x**0 = 1 */
|
||||
if ((iy | ly) == 0)
|
||||
{
|
||||
return one;
|
||||
}
|
||||
|
||||
/* +-NaN return x + y */
|
||||
if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
|
||||
{
|
||||
return x + y;
|
||||
}
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if (hx < 0)
|
||||
{
|
||||
if (iy >= 0x43400000) /* even integer y */
|
||||
{
|
||||
yisint = 2;
|
||||
}
|
||||
else if (iy >= 0x3ff00000)
|
||||
{
|
||||
k = (iy >> 20) - 0x3ff; /* exponent */
|
||||
if (k > 20)
|
||||
{
|
||||
j = ly >> (52 - k);
|
||||
if ((j << (52 - k)) == ly)
|
||||
{
|
||||
yisint = 2 - (j & 1);
|
||||
}
|
||||
}
|
||||
else if (ly == 0)
|
||||
{
|
||||
j = iy >> (20 - k);
|
||||
if ((j << (20 - k)) == iy)
|
||||
{
|
||||
yisint = 2 - (j & 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if (ly == 0)
|
||||
{
|
||||
if (iy == 0x7ff00000) /* y is +-inf */
|
||||
{
|
||||
if (((ix - 0x3ff00000) | lx) == 0) /* +-1**+-inf is 1 */
|
||||
{
|
||||
return one;
|
||||
}
|
||||
else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
|
||||
{
|
||||
return (hy >= 0) ? y : zero;
|
||||
}
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
{
|
||||
return (hy < 0) ? -y : zero;
|
||||
}
|
||||
}
|
||||
if (iy == 0x3ff00000) /* y is +-1 */
|
||||
{
|
||||
if (hy < 0)
|
||||
{
|
||||
return one / x;
|
||||
}
|
||||
else
|
||||
{
|
||||
return x;
|
||||
}
|
||||
}
|
||||
if (hy == 0x40000000) /* y is 2 */
|
||||
{
|
||||
return x * x;
|
||||
}
|
||||
if (hy == 0x3fe00000) /* y is 0.5 */
|
||||
{
|
||||
if (hx >= 0) /* x >= +0 */
|
||||
{
|
||||
return sqrt (x);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
ax.dbl = fabs (x);
|
||||
/* special value of x */
|
||||
if (lx == 0)
|
||||
{
|
||||
if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000)
|
||||
{
|
||||
z.dbl = ax.dbl; /* x is +-0,+-inf,+-1 */
|
||||
if (hy < 0)
|
||||
{
|
||||
z.dbl = one / z.dbl; /* z = (1 / |x|) */
|
||||
}
|
||||
if (hx < 0)
|
||||
{
|
||||
if (((ix - 0x3ff00000) | yisint) == 0)
|
||||
{
|
||||
z.dbl = NAN; /* (-1)**non-int is NaN */
|
||||
}
|
||||
else if (yisint == 1)
|
||||
{
|
||||
z.dbl = -z.dbl; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
}
|
||||
return z.dbl;
|
||||
}
|
||||
}
|
||||
|
||||
n = (hx < 0) ? 0 : 1;
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if ((n | yisint) == 0)
|
||||
{
|
||||
return NAN;
|
||||
}
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if ((n | (yisint - 1)) == 0)
|
||||
{
|
||||
s = -one; /* (-ve)**(odd int) */
|
||||
}
|
||||
|
||||
/* |y| is huge */
|
||||
if (iy > 0x41e00000) /* if |y| > 2**31 */
|
||||
{
|
||||
if (iy > 0x43f00000) /* if |y| > 2**64, must o/uflow */
|
||||
{
|
||||
if (ix <= 0x3fefffff)
|
||||
{
|
||||
return (hy < 0) ? huge * huge : tiny * tiny;
|
||||
}
|
||||
if (ix >= 0x3ff00000)
|
||||
{
|
||||
return (hy > 0) ? huge * huge : tiny * tiny;
|
||||
}
|
||||
}
|
||||
/* over/underflow if x is not close to one */
|
||||
if (ix < 0x3fefffff)
|
||||
{
|
||||
return (hy < 0) ? s * huge * huge : s * tiny * tiny;
|
||||
}
|
||||
if (ix > 0x3ff00000)
|
||||
{
|
||||
return (hy > 0) ? s * huge * huge : s * tiny * tiny;
|
||||
}
|
||||
/* now |1 - x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x - x^2 / 2 + x^3 / 3 - x^4 / 4 */
|
||||
t.dbl = ax.dbl - one; /* t has 20 trailing zeros */
|
||||
w = (t.dbl * t.dbl) * (0.5 - t.dbl * (0.3333333333333333333333 - t.dbl * 0.25));
|
||||
u = ivln2_h * t.dbl; /* ivln2_h has 21 sig. bits */
|
||||
v = t.dbl * ivln2_l - w * ivln2;
|
||||
t1.dbl = u + v;
|
||||
t1.as_int.lo = 0;
|
||||
t2 = v - (t1.dbl - u);
|
||||
}
|
||||
else
|
||||
{
|
||||
double_accessor s_h, t_h;
|
||||
double ss, s2, s_l, t_l;
|
||||
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if (ix < 0x00100000)
|
||||
{
|
||||
ax.dbl *= two53;
|
||||
n -= 53;
|
||||
ix = ax.as_int.hi;
|
||||
}
|
||||
n += ((ix) >> 20) - 0x3ff;
|
||||
j = ix & 0x000fffff;
|
||||
/* determine interval */
|
||||
ix = j | 0x3ff00000; /* normalize ix */
|
||||
if (j <= 0x3988E) /* |x| < sqrt(3/2) */
|
||||
{
|
||||
k = 0;
|
||||
}
|
||||
else if (j < 0xBB67A) /* |x| < sqrt(3) */
|
||||
{
|
||||
k = 1;
|
||||
}
|
||||
else
|
||||
{
|
||||
k = 0;
|
||||
n += 1;
|
||||
ix -= 0x00100000;
|
||||
}
|
||||
ax.as_int.hi = ix;
|
||||
|
||||
/* compute ss = s_h + s_l = (x - 1) / (x + 1) or (x - 1.5) / (x + 1.5) */
|
||||
u = ax.dbl - bp[k]; /* bp[0] = 1.0, bp[1] = 1.5 */
|
||||
v = one / (ax.dbl + bp[k]);
|
||||
ss = u * v;
|
||||
s_h.dbl = ss;
|
||||
s_h.as_int.lo = 0;
|
||||
/* t_h = ax + bp[k] High */
|
||||
t_h.dbl = zero;
|
||||
t_h.as_int.hi = ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18);
|
||||
t_l = ax.dbl - (t_h.dbl - bp[k]);
|
||||
s_l = v * ((u - s_h.dbl * t_h.dbl) - s_h.dbl * t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = ss * ss;
|
||||
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
||||
r += s_l * (s_h.dbl + ss);
|
||||
s2 = s_h.dbl * s_h.dbl;
|
||||
t_h.dbl = 3.0 + s2 + r;
|
||||
t_h.as_int.lo = 0;
|
||||
t_l = r - ((t_h.dbl - 3.0) - s2);
|
||||
/* u + v = ss * (1 + ...) */
|
||||
u = s_h.dbl * t_h.dbl;
|
||||
v = s_l * t_h.dbl + t_l * ss;
|
||||
/* 2 / (3 * log2) * (ss + ...) */
|
||||
p_h.dbl = u + v;
|
||||
p_h.as_int.lo = 0;
|
||||
p_l = v - (p_h.dbl - u);
|
||||
z_h = cp_h * p_h.dbl; /* cp_h + cp_l = 2 / (3 * log2) */
|
||||
z_l = cp_l * p_h.dbl + p_l * cp + dp_l[k];
|
||||
/* log2(ax) = (ss + ...) * 2 / (3 * log2) = n + dp_h + z_h + z_l */
|
||||
t.dbl = (double) n;
|
||||
t1.dbl = (((z_h + z_l) + dp_h[k]) + t.dbl);
|
||||
t1.as_int.lo = 0;
|
||||
t2 = z_l - (((t1.dbl - t.dbl) - dp_h[k]) - z_h);
|
||||
}
|
||||
|
||||
/* split up y into y1 + y2 and compute (y1 + y2) * (t1 + t2) */
|
||||
y1.dbl = y;
|
||||
y1.as_int.lo = 0;
|
||||
p_l = (y - y1.dbl) * t1.dbl + y * t2;
|
||||
p_h.dbl = y1.dbl * t1.dbl;
|
||||
z.dbl = p_l + p_h.dbl;
|
||||
j = z.as_int.hi;
|
||||
i = z.as_int.lo;
|
||||
if (j >= 0x40900000) /* z >= 1024 */
|
||||
{
|
||||
if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
|
||||
{
|
||||
return s * huge * huge; /* overflow */
|
||||
}
|
||||
else
|
||||
{
|
||||
if (p_l + ovt > z.dbl - p_h.dbl)
|
||||
{
|
||||
return s * huge * huge; /* overflow */
|
||||
}
|
||||
}
|
||||
}
|
||||
else if ((j & 0x7fffffff) >= 0x4090cc00) /* z <= -1075 */
|
||||
{
|
||||
if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */
|
||||
{
|
||||
return s * tiny * tiny; /* underflow */
|
||||
}
|
||||
else
|
||||
{
|
||||
if (p_l <= z.dbl - p_h.dbl)
|
||||
{
|
||||
return s * tiny * tiny; /* underflow */
|
||||
}
|
||||
}
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h + p_l)
|
||||
*/
|
||||
i = j & 0x7fffffff;
|
||||
k = (i >> 20) - 0x3ff;
|
||||
n = 0;
|
||||
if (i > 0x3fe00000) /* if |z| > 0.5, set n = [z + 0.5] */
|
||||
{
|
||||
n = j + (0x00100000 >> (k + 1));
|
||||
k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
|
||||
t.dbl = zero;
|
||||
t.as_int.hi = (n & ~(0x000fffff >> k));
|
||||
n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
|
||||
if (j < 0)
|
||||
{
|
||||
n = -n;
|
||||
}
|
||||
p_h.dbl -= t.dbl;
|
||||
}
|
||||
t.dbl = p_l + p_h.dbl;
|
||||
t.as_int.lo = 0;
|
||||
u = t.dbl * lg2_h;
|
||||
v = (p_l - (t.dbl - p_h.dbl)) * lg2 + t.dbl * lg2_l;
|
||||
z.dbl = u + v;
|
||||
w = v - (z.dbl - u);
|
||||
t.dbl = z.dbl * z.dbl;
|
||||
t1.dbl = z.dbl - t.dbl * (P1 + t.dbl * (P2 + t.dbl * (P3 + t.dbl * (P4 + t.dbl * P5))));
|
||||
r = (z.dbl * t1.dbl) / (t1.dbl - two) - (w + z.dbl * w);
|
||||
z.dbl = one - (r - z.dbl);
|
||||
j = z.as_int.hi;
|
||||
j += (n << 20);
|
||||
if ((j >> 20) <= 0) /* subnormal output */
|
||||
{
|
||||
z.dbl = scalbn (z.dbl, n);
|
||||
}
|
||||
else
|
||||
{
|
||||
z.as_int.hi += (n << 20);
|
||||
}
|
||||
return s * z.dbl;
|
||||
} /* pow */
|
||||
|
||||
#undef zero
|
||||
#undef one
|
||||
#undef two
|
||||
#undef two53
|
||||
#undef huge
|
||||
#undef tiny
|
||||
#undef L1
|
||||
#undef L2
|
||||
#undef L3
|
||||
#undef L4
|
||||
#undef L5
|
||||
#undef L6
|
||||
#undef P1
|
||||
#undef P2
|
||||
#undef P3
|
||||
#undef P4
|
||||
#undef P5
|
||||
#undef lg2
|
||||
#undef lg2_h
|
||||
#undef lg2_l
|
||||
#undef ovt
|
||||
#undef cp
|
||||
#undef cp_h
|
||||
#undef cp_l
|
||||
#undef ivln2
|
||||
#undef ivln2_h
|
||||
#undef ivln2_l
|
||||
@@ -0,0 +1,99 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_scalbn.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* scalbn(x,n) returns x* 2**n computed by exponent
|
||||
* manipulation rather than by actually performing an
|
||||
* exponentiation or a multiplication.
|
||||
*/
|
||||
|
||||
#define two54 1.80143985094819840000e+16 /* 0x43500000, 0x00000000 */
|
||||
#define twom54 5.55111512312578270212e-17 /* 0x3C900000, 0x00000000 */
|
||||
#define huge 1.0e+300
|
||||
#define tiny 1.0e-300
|
||||
|
||||
double
|
||||
scalbn (double x, int n)
|
||||
{
|
||||
int k, hx, lx;
|
||||
|
||||
hx = __HI (x);
|
||||
lx = __LO (x);
|
||||
k = (hx & 0x7ff00000) >> 20; /* extract exponent */
|
||||
if (k == 0) /* 0 or subnormal x */
|
||||
{
|
||||
if ((lx | (hx & 0x7fffffff)) == 0) /* +-0 */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
x *= two54;
|
||||
hx = __HI (x);
|
||||
k = ((hx & 0x7ff00000) >> 20) - 54;
|
||||
if (n < -50000) /*underflow */
|
||||
{
|
||||
return tiny * x;
|
||||
}
|
||||
}
|
||||
if (k == 0x7ff) /* NaN or Inf */
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
k = k + n;
|
||||
if (k > 0x7fe) /* overflow */
|
||||
{
|
||||
return huge * copysign (huge, x);
|
||||
}
|
||||
if (k > 0) /* normal result */
|
||||
{
|
||||
double_accessor ret;
|
||||
ret.dbl = x;
|
||||
ret.as_int.hi = (hx & 0x800fffff) | (k << 20);
|
||||
return ret.dbl;
|
||||
}
|
||||
if (k <= -54)
|
||||
{
|
||||
if (n > 50000) /* in case integer overflow in n + k */
|
||||
{
|
||||
return huge * copysign (huge, x); /*overflow */
|
||||
}
|
||||
else
|
||||
{
|
||||
return tiny * copysign (tiny, x); /*underflow */
|
||||
}
|
||||
}
|
||||
k += 54; /* subnormal result */
|
||||
double_accessor ret;
|
||||
ret.dbl = x;
|
||||
ret.as_int.hi = (hx & 0x800fffff) | (k << 20);
|
||||
return ret.dbl * twom54;
|
||||
} /* scalbn */
|
||||
|
||||
#undef two54
|
||||
#undef twom54
|
||||
#undef huge
|
||||
#undef tiny
|
||||
@@ -0,0 +1,115 @@
|
||||
/* 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_sinh.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* __sinh(x)
|
||||
* Method:
|
||||
* mathematically sinh(x) if defined to be (exp(x) - exp(-x)) / 2
|
||||
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
|
||||
* 2.
|
||||
* E + E/(E+1)
|
||||
* 0 <= x <= 22 : sinh(x) := -------------, E = expm1(x)
|
||||
* 2
|
||||
*
|
||||
* 22 <= x <= lnovft : sinh(x) := exp(x) / 2
|
||||
* lnovft <= x <= ln2ovft: sinh(x) := exp(x / 2) / 2 * exp(x / 2)
|
||||
* ln2ovft < x : sinh(x) := x * shuge (overflow)
|
||||
*
|
||||
* Special cases:
|
||||
* sinh(x) is |x| if x is +INF, -INF, or NaN.
|
||||
* only sinh(0) = 0 is exact for finite x.
|
||||
*/
|
||||
|
||||
#define one 1.0
|
||||
#define half 0.5
|
||||
#define shuge 1.0e307
|
||||
|
||||
double
|
||||
sinh (double x)
|
||||
{
|
||||
double t, w, h;
|
||||
int ix, jx;
|
||||
unsigned lx;
|
||||
|
||||
/* High word of |x|. */
|
||||
jx = __HI (x);
|
||||
ix = jx & 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if (ix >= 0x7ff00000)
|
||||
{
|
||||
return x + x;
|
||||
}
|
||||
|
||||
h = 0.5;
|
||||
if (jx < 0)
|
||||
{
|
||||
h = -h;
|
||||
}
|
||||
/* |x| in [0,22], return sign(x) * 0.5 * (E + E / (E + 1))) */
|
||||
if (ix < 0x40360000)
|
||||
{
|
||||
/* |x| < 22 */
|
||||
if (ix < 0x3e300000)
|
||||
{
|
||||
/* |x| < 2**-28 */
|
||||
if (shuge + x > one)
|
||||
{
|
||||
/* sinh(tiny) = tiny with inexact */
|
||||
return x;
|
||||
}
|
||||
}
|
||||
t = expm1 (fabs (x));
|
||||
if (ix < 0x3ff00000)
|
||||
{
|
||||
return h * (2.0 * t - t * t / (t + one));
|
||||
}
|
||||
return h * (t + t / (t + one));
|
||||
}
|
||||
|
||||
/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
|
||||
if (ix < 0x40862E42)
|
||||
{
|
||||
return h * exp (fabs (x));
|
||||
}
|
||||
/* |x| in [log(maxdouble), overflowthresold] */
|
||||
lx = ((1 >> 29) + (unsigned int) x);
|
||||
if (ix < 0x408633CE || ((ix == 0x408633ce) && (lx <= (unsigned) 0x8fb9f87d)))
|
||||
{
|
||||
w = exp (0.5 * fabs (x));
|
||||
t = h * w;
|
||||
return t * w;
|
||||
}
|
||||
|
||||
/* |x| > overflowthresold, sinh(x) overflow */
|
||||
return x * shuge;
|
||||
} /* sinh */
|
||||
|
||||
#undef one
|
||||
#undef half
|
||||
#undef huge
|
||||
@@ -0,0 +1,496 @@
|
||||
/* 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_sqrt.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* sqrt(x)
|
||||
* Return correctly rounded sqrt.
|
||||
*
|
||||
* ------------------------------------------
|
||||
* | Use the hardware sqrt if you have one |
|
||||
* ------------------------------------------
|
||||
*
|
||||
* Method:
|
||||
* Bit by bit method using integer arithmetic. (Slow, but portable)
|
||||
* 1. Normalization
|
||||
* Scale x to y in [1,4) with even powers of 2:
|
||||
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
|
||||
* sqrt(x) = 2^k * sqrt(y)
|
||||
* 2. Bit by bit computation
|
||||
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
|
||||
* i 0
|
||||
* i+1 2
|
||||
* s = 2*q , and y = 2 * ( y - q ). (1)
|
||||
* i i i i
|
||||
*
|
||||
* To compute q from q , one checks whether
|
||||
* i+1 i
|
||||
*
|
||||
* -(i+1) 2
|
||||
* (q + 2 ) <= y. (2)
|
||||
* i
|
||||
* -(i+1)
|
||||
* If (2) is false, then q = q ; otherwise q = q + 2 .
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* With some algebric manipulation, it is not difficult to see
|
||||
* that (2) is equivalent to
|
||||
* -(i+1)
|
||||
* s + 2 <= y (3)
|
||||
* i i
|
||||
*
|
||||
* The advantage of (3) is that s and y can be computed by
|
||||
* i i
|
||||
* the following recurrence formula:
|
||||
* if (3) is false
|
||||
*
|
||||
* s = s , y = y ; (4)
|
||||
* i+1 i i+1 i
|
||||
*
|
||||
* otherwise,
|
||||
* -i -(i+1)
|
||||
* s = s + 2 , y = y - s - 2 (5)
|
||||
* i+1 i i+1 i i
|
||||
*
|
||||
* One may easily use induction to prove (4) and (5).
|
||||
* Note. Since the left hand side of (3) contain only i+2 bits,
|
||||
* it does not necessary to do a full (53-bit) comparison
|
||||
* in (3).
|
||||
* 3. Final rounding
|
||||
* After generating the 53 bits result, we compute one more bit.
|
||||
* Together with the remainder, we can decide whether the
|
||||
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
|
||||
* (it will never equal to 1/2ulp).
|
||||
* The rounding mode can be detected by checking whether
|
||||
* huge + tiny is equal to huge, and whether huge - tiny is
|
||||
* equal to huge for some floating point number "huge" and "tiny".
|
||||
*
|
||||
* Special cases:
|
||||
* sqrt(+-0) = +-0 ... exact
|
||||
* sqrt(inf) = inf
|
||||
* sqrt(-ve) = NaN ... with invalid signal
|
||||
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
|
||||
*
|
||||
* Other methods: see the appended file at the end of the program below.
|
||||
*/
|
||||
|
||||
#define one 1.0
|
||||
#define tiny 1.0e-300
|
||||
|
||||
double
|
||||
sqrt (double x)
|
||||
{
|
||||
int sign = (int) 0x80000000;
|
||||
unsigned r, t1, s1, ix1, q1;
|
||||
int ix0, s0, q, m, t, i;
|
||||
|
||||
ix0 = __HI (x); /* high word of x */
|
||||
ix1 = __LO (x); /* low word of x */
|
||||
|
||||
/* take care of Inf and NaN */
|
||||
if ((ix0 & 0x7ff00000) == 0x7ff00000)
|
||||
{
|
||||
return x * x + x; /* sqrt(NaN) = NaN, sqrt(+inf) = +inf, sqrt(-inf) = sNaN */
|
||||
}
|
||||
/* take care of zero */
|
||||
if (ix0 <= 0)
|
||||
{
|
||||
if (((ix0 & (~sign)) | ix1) == 0) /* sqrt(+-0) = +-0 */
|
||||
{
|
||||
return x;
|
||||
}
|
||||
else if (ix0 < 0) /* sqrt(-ve) = sNaN */
|
||||
{
|
||||
return NAN;
|
||||
}
|
||||
}
|
||||
/* normalize x */
|
||||
m = (ix0 >> 20);
|
||||
if (m == 0) /* subnormal x */
|
||||
{
|
||||
while (ix0 == 0)
|
||||
{
|
||||
m -= 21;
|
||||
ix0 |= (ix1 >> 11);
|
||||
ix1 <<= 21;
|
||||
}
|
||||
for (i = 0; (ix0 & 0x00100000) == 0; i++)
|
||||
{
|
||||
ix0 <<= 1;
|
||||
}
|
||||
m -= i - 1;
|
||||
ix0 |= (ix1 >> (32 - i));
|
||||
ix1 <<= i;
|
||||
}
|
||||
m -= 1023; /* unbias exponent */
|
||||
ix0 = (ix0 & 0x000fffff) | 0x00100000;
|
||||
if (m & 1) /* odd m, double x to make it even */
|
||||
{
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
}
|
||||
m >>= 1; /* m = [m / 2] */
|
||||
|
||||
/* generate sqrt(x) bit by bit */
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
|
||||
r = 0x00200000; /* r = moving bit from right to left */
|
||||
|
||||
while (r != 0)
|
||||
{
|
||||
t = s0 + r;
|
||||
if (t <= ix0)
|
||||
{
|
||||
s0 = t + r;
|
||||
ix0 -= t;
|
||||
q += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
r >>= 1;
|
||||
}
|
||||
|
||||
r = sign;
|
||||
while (r != 0)
|
||||
{
|
||||
t1 = s1 + r;
|
||||
t = s0;
|
||||
if ((t < ix0) || ((t == ix0) && (t1 <= ix1)))
|
||||
{
|
||||
s1 = t1 + r;
|
||||
if (((t1 & sign) == sign) && (s1 & sign) == 0)
|
||||
{
|
||||
s0 += 1;
|
||||
}
|
||||
ix0 -= t;
|
||||
if (ix1 < t1)
|
||||
{
|
||||
ix0 -= 1;
|
||||
}
|
||||
ix1 -= t1;
|
||||
q1 += r;
|
||||
}
|
||||
ix0 += ix0 + ((ix1 & sign) >> 31);
|
||||
ix1 += ix1;
|
||||
r >>= 1;
|
||||
}
|
||||
|
||||
double_accessor ret;
|
||||
|
||||
/* use floating add to find out rounding direction */
|
||||
if ((ix0 | ix1) != 0)
|
||||
{
|
||||
ret.dbl = one - tiny; /* trigger inexact flag */
|
||||
if (ret.dbl >= one)
|
||||
{
|
||||
ret.dbl = one + tiny;
|
||||
if (q1 == (unsigned) 0xffffffff)
|
||||
{
|
||||
q1 = 0;
|
||||
q += 1;
|
||||
}
|
||||
else if (ret.dbl > one)
|
||||
{
|
||||
if (q1 == (unsigned) 0xfffffffe)
|
||||
{
|
||||
q += 1;
|
||||
}
|
||||
q1 += 2;
|
||||
}
|
||||
else
|
||||
{
|
||||
q1 += (q1 & 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
ix0 = (q >> 1) + 0x3fe00000;
|
||||
ix1 = q1 >> 1;
|
||||
if ((q & 1) == 1)
|
||||
{
|
||||
ix1 |= sign;
|
||||
}
|
||||
ix0 += (m << 20);
|
||||
ret.as_int.hi = ix0;
|
||||
ret.as_int.lo = ix1;
|
||||
return ret.dbl;
|
||||
} /* sqrt */
|
||||
|
||||
#undef one
|
||||
#undef tiny
|
||||
|
||||
/*
|
||||
Other methods (use floating-point arithmetic)
|
||||
-------------
|
||||
(This is a copy of a drafted paper by Prof W. Kahan
|
||||
and K.C. Ng, written in May, 1986)
|
||||
|
||||
Two algorithms are given here to implement sqrt(x)
|
||||
(IEEE double precision arithmetic) in software.
|
||||
Both supply sqrt(x) correctly rounded. The first algorithm (in
|
||||
Section A) uses newton iterations and involves four divisions.
|
||||
The second one uses reciproot iterations to avoid division, but
|
||||
requires more multiplications. Both algorithms need the ability
|
||||
to chop results of arithmetic operations instead of round them,
|
||||
and the INEXACT flag to indicate when an arithmetic operation
|
||||
is executed exactly with no roundoff error, all part of the
|
||||
standard (IEEE 754-1985). The ability to perform shift, add,
|
||||
subtract and logical AND operations upon 32-bit words is needed
|
||||
too, though not part of the standard.
|
||||
|
||||
A. sqrt(x) by Newton Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
|
||||
1 11 52 ...widths
|
||||
------------------------------------------------------
|
||||
x: |s| e | f |
|
||||
------------------------------------------------------
|
||||
msb lsb msb lsb ...order
|
||||
|
||||
------------------------ ------------------------
|
||||
x0: |s| e | f1 | x1: | f2 |
|
||||
------------------------ ------------------------
|
||||
|
||||
By performing shifts and subtracts on x0 and x1 (both regarded
|
||||
as integers), we obtain an 8-bit approximation of sqrt(x) as
|
||||
follows.
|
||||
|
||||
k := (x0>>1) + 0x1ff80000;
|
||||
y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
|
||||
Here k is a 32-bit integer and T1[] is an integer array containing
|
||||
correction terms. Now magically the floating value of y (y's
|
||||
leading 32-bit word is y0, the value of its trailing word is 0)
|
||||
approximates sqrt(x) to almost 8-bit.
|
||||
|
||||
Value of T1:
|
||||
static int T1[32]= {
|
||||
0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
|
||||
29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
|
||||
83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
|
||||
16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Heron's rule three times to y, we have y approximates
|
||||
sqrt(x) to within 1 ulp (Unit in the Last Place):
|
||||
|
||||
y := (y+x/y)/2 ... almost 17 sig. bits
|
||||
y := (y+x/y)/2 ... almost 35 sig. bits
|
||||
y := y-(y-x/y)/2 ... within 1 ulp
|
||||
|
||||
Remark 1.
|
||||
Another way to improve y to within 1 ulp is:
|
||||
|
||||
y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
|
||||
y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
|
||||
|
||||
2
|
||||
(x-y )*y
|
||||
y := y + 2* ---------- ...within 1 ulp
|
||||
2
|
||||
3y + x
|
||||
|
||||
This formula has one division fewer than the one above; however,
|
||||
it requires more multiplications and additions. Also x must be
|
||||
scaled in advance to avoid spurious overflow in evaluating the
|
||||
expression 3y*y+x. Hence it is not recommended uless division
|
||||
is slow. If division is very slow, then one should use the
|
||||
reciproot algorithm given in section B.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
I := FALSE; ... reset INEXACT flag I
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
z := x/y; ... chopped quotient, possibly inexact
|
||||
If(not I) then { ... if the quotient is exact
|
||||
if(z=y) {
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
} else {
|
||||
z := z - ulp; ... special rounding
|
||||
}
|
||||
}
|
||||
i := TRUE; ... sqrt(x) is inexact
|
||||
If (r=RN) then z=z+ulp ... rounded-to-nearest
|
||||
If (r=RP) then { ... round-toward-+inf
|
||||
y = y+ulp; z=z+ulp;
|
||||
}
|
||||
y := y+z; ... chopped sum
|
||||
y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
|
||||
I := i; ... restore inexact flag
|
||||
R := r; ... restore rounded mode
|
||||
return sqrt(x):=y.
|
||||
|
||||
(4) Special cases
|
||||
|
||||
Square root of +inf, +-0, or NaN is itself;
|
||||
Square root of a negative number is NaN with invalid signal.
|
||||
|
||||
B. sqrt(x) by Reciproot Iteration
|
||||
|
||||
(1) Initial approximation
|
||||
|
||||
Let x0 and x1 be the leading and the trailing 32-bit words of
|
||||
a floating point number x (in IEEE double format) respectively
|
||||
(see section A). By performing shifs and subtracts on x0 and y0,
|
||||
we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
|
||||
|
||||
k := 0x5fe80000 - (x0>>1);
|
||||
y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
|
||||
|
||||
Here k is a 32-bit integer and T2[] is an integer array
|
||||
containing correction terms. Now magically the floating
|
||||
value of y (y's leading 32-bit word is y0, the value of
|
||||
its trailing word y1 is set to zero) approximates 1/sqrt(x)
|
||||
to almost 7.8-bit.
|
||||
|
||||
Value of T2:
|
||||
static int T2[64]= {
|
||||
0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
|
||||
0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
|
||||
0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
|
||||
0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
|
||||
0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
|
||||
0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
|
||||
0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
|
||||
0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
|
||||
|
||||
(2) Iterative refinement
|
||||
|
||||
Apply Reciproot iteration three times to y and multiply the
|
||||
result by x to get an approximation z that matches sqrt(x)
|
||||
to about 1 ulp. To be exact, we will have
|
||||
-1ulp < sqrt(x)-z<1.0625ulp.
|
||||
|
||||
... set rounding mode to Round-to-nearest
|
||||
y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
|
||||
y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
|
||||
... special arrangement for better accuracy
|
||||
z := x*y ... 29 bits to sqrt(x), with z*y<1
|
||||
z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
|
||||
|
||||
Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
|
||||
(a) the term z*y in the final iteration is always less than 1;
|
||||
(b) the error in the final result is biased upward so that
|
||||
-1 ulp < sqrt(x) - z < 1.0625 ulp
|
||||
instead of |sqrt(x)-z|<1.03125ulp.
|
||||
|
||||
(3) Final adjustment
|
||||
|
||||
By twiddling y's last bit it is possible to force y to be
|
||||
correctly rounded according to the prevailing rounding mode
|
||||
as follows. Let r and i be copies of the rounding mode and
|
||||
inexact flag before entering the square root program. Also we
|
||||
use the expression y+-ulp for the next representable floating
|
||||
numbers (up and down) of y. Note that y+-ulp = either fixed
|
||||
point y+-1, or multiply y by nextafter(1,+-inf) in chopped
|
||||
mode.
|
||||
|
||||
R := RZ; ... set rounding mode to round-toward-zero
|
||||
switch(r) {
|
||||
case RN: ... round-to-nearest
|
||||
if(x<= z*(z-ulp)...chopped) z = z - ulp; else
|
||||
if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
|
||||
break;
|
||||
case RZ:case RM: ... round-to-zero or round-to--inf
|
||||
R:=RP; ... reset rounding mod to round-to-+inf
|
||||
if(x<z*z ... rounded up) z = z - ulp; else
|
||||
if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
|
||||
break;
|
||||
case RP: ... round-to-+inf
|
||||
if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
|
||||
if(x>z*z ...chopped) z = z+ulp;
|
||||
break;
|
||||
}
|
||||
|
||||
Remark 3. The above comparisons can be done in fixed point. For
|
||||
example, to compare x and w=z*z chopped, it suffices to compare
|
||||
x1 and w1 (the trailing parts of x and w), regarding them as
|
||||
two's complement integers.
|
||||
|
||||
...Is z an exact square root?
|
||||
To determine whether z is an exact square root of x, let z1 be the
|
||||
trailing part of z, and also let x0 and x1 be the leading and
|
||||
trailing parts of x.
|
||||
|
||||
If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
|
||||
I := 1; ... Raise Inexact flag: z is not exact
|
||||
else {
|
||||
j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
|
||||
k := z1 >> 26; ... get z's 25-th and 26-th
|
||||
fraction bits
|
||||
I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
|
||||
}
|
||||
R:= r ... restore rounded mode
|
||||
return sqrt(x):=z.
|
||||
|
||||
If multiplication is cheaper then the foregoing red tape, the
|
||||
Inexact flag can be evaluated by
|
||||
|
||||
I := i;
|
||||
I := (z*z!=x) or I.
|
||||
|
||||
Note that z*z can overwrite I; this value must be sensed if it is
|
||||
True.
|
||||
|
||||
Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
|
||||
zero.
|
||||
|
||||
--------------------
|
||||
z1: | f2 |
|
||||
--------------------
|
||||
bit 31 bit 0
|
||||
|
||||
Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
|
||||
or even of logb(x) have the following relations:
|
||||
|
||||
-------------------------------------------------
|
||||
bit 27,26 of z1 bit 1,0 of x1 logb(x)
|
||||
-------------------------------------------------
|
||||
00 00 odd and even
|
||||
01 01 even
|
||||
10 10 odd
|
||||
10 00 even
|
||||
11 01 even
|
||||
-------------------------------------------------
|
||||
|
||||
(4) Special cases (see (4) of Section A).
|
||||
*/
|
||||
@@ -0,0 +1,117 @@
|
||||
/* 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.
|
||||
*
|
||||
* @(#)s_tanh.c 1.3 95/01/18
|
||||
*/
|
||||
|
||||
#include "jerry-math-internal.h"
|
||||
|
||||
/* tanh(x)
|
||||
* Return the Hyperbolic Tangent of x
|
||||
*
|
||||
* Method:
|
||||
* x -x
|
||||
* e - e
|
||||
* 0. tanh(x) is defined to be -----------
|
||||
* x -x
|
||||
* e + e
|
||||
*
|
||||
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
||||
* 2. 0 <= x <= 2**-55 : tanh(x) := x * (one + x)
|
||||
*
|
||||
* -t
|
||||
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
||||
* t + 2
|
||||
*
|
||||
* 2
|
||||
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t = expm1(2x)
|
||||
* t + 2
|
||||
*
|
||||
* 22.0 < x <= INF : tanh(x) := 1.
|
||||
*
|
||||
* Special cases:
|
||||
* tanh(NaN) is NaN;
|
||||
* only tanh(0) = 0 is exact for finite x.
|
||||
*/
|
||||
#define one 1.0
|
||||
#define two 2.0
|
||||
#define tiny 1.0e-300
|
||||
|
||||
double
|
||||
tanh (double x)
|
||||
{
|
||||
double t, z;
|
||||
int jx, ix;
|
||||
|
||||
/* High word of |x|. */
|
||||
jx = __HI (x);
|
||||
ix = jx & 0x7fffffff;
|
||||
|
||||
/* x is INF or NaN */
|
||||
if (ix >= 0x7ff00000)
|
||||
{
|
||||
if (jx >= 0)
|
||||
{
|
||||
/* tanh(+-inf) = +-1 */
|
||||
return one / x + one;
|
||||
}
|
||||
else
|
||||
{
|
||||
/* tanh(NaN) = NaN */
|
||||
return one / x - one;
|
||||
}
|
||||
}
|
||||
|
||||
/* |x| < 22 */
|
||||
if (ix < 0x40360000)
|
||||
{
|
||||
/* |x| < 2**-55 */
|
||||
if (ix < 0x3c800000)
|
||||
{
|
||||
/* tanh(small) = small */
|
||||
return x * (one + x);
|
||||
}
|
||||
if (ix >= 0x3ff00000)
|
||||
{
|
||||
/* |x| >= 1 */
|
||||
t = expm1 (two * fabs (x));
|
||||
z = one - two / (t + two);
|
||||
}
|
||||
else
|
||||
{
|
||||
t = expm1 (-two * fabs (x));
|
||||
z = -t / (t + two);
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
/* |x| > 22, return +-1 */
|
||||
z = one - tiny; /* raised inexact flag */
|
||||
}
|
||||
return (jx >= 0) ? z : -z;
|
||||
} /* tanh */
|
||||
|
||||
#undef one
|
||||
#undef two
|
||||
#undef tiny
|
||||
+1101
File diff suppressed because it is too large
Load Diff
Reference in New Issue
Block a user