lib/libm: Add acosh, asinh, atanh, tan; get working with stmhal.
acoshf, asinhf, atanhf were added from musl. mathsincos.c was split up into its original, separate files (from newlibe-nano-2). tan was added. All of the important missing float functions are now implemented, and pyboard now passes tests/float/math_fun.py (finally!).
This commit is contained in:
Damien George
parent
6936f4626c
commit
f04329e93b
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/*****************************************************************************/
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/*****************************************************************************/
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// acoshf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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#include "libm.h"
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#if FLT_EVAL_METHOD==2
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#undef sqrtf
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#define sqrtf sqrtl
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#elif FLT_EVAL_METHOD==1
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#undef sqrtf
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#define sqrtf sqrt
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#endif
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/* acosh(x) = log(x + sqrt(x*x-1)) */
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float acoshf(float x)
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{
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union {float f; uint32_t i;} u = {x};
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uint32_t a = u.i & 0x7fffffff;
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if (a < 0x3f800000+(1<<23))
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/* |x| < 2, invalid if x < 1 or nan */
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/* up to 2ulp error in [1,1.125] */
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return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
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if (a < 0x3f800000+(12<<23))
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/* |x| < 0x1p12 */
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return logf(2*x - 1/(x+sqrtf(x*x-1)));
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/* x >= 0x1p12 */
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return logf(x) + 0.693147180559945309417232121458176568f;
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// asinhf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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#include "libm.h"
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/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
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float asinhf(float x)
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{
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union {float f; uint32_t i;} u = {.f = x};
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uint32_t i = u.i & 0x7fffffff;
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unsigned s = u.i >> 31;
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/* |x| */
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u.i = i;
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x = u.f;
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if (i >= 0x3f800000 + (12<<23)) {
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/* |x| >= 0x1p12 or inf or nan */
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x = logf(x) + 0.693147180559945309417232121458176568f;
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} else if (i >= 0x3f800000 + (1<<23)) {
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/* |x| >= 2 */
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x = logf(2*x + 1/(sqrtf(x*x+1)+x));
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} else if (i >= 0x3f800000 - (12<<23)) {
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/* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */
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x = log1pf(x + x*x/(sqrtf(x*x+1)+1));
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} else {
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/* |x| < 0x1p-12, raise inexact if x!=0 */
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FORCE_EVAL(x + 0x1p120f);
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}
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return s ? -x : x;
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// atanhf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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#include "libm.h"
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/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
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float atanhf(float x)
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{
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union {float f; uint32_t i;} u = {.f = x};
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unsigned s = u.i >> 31;
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float_t y;
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/* |x| */
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u.i &= 0x7fffffff;
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y = u.f;
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if (u.i < 0x3f800000 - (1<<23)) {
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if (u.i < 0x3f800000 - (32<<23)) {
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/* handle underflow */
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if (u.i < (1<<23))
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FORCE_EVAL((float)(y*y));
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} else {
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/* |x| < 0.5, up to 1.7ulp error */
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y = 0.5f*log1pf(2*y + 2*y*y/(1-y));
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}
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} else {
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/* avoid overflow */
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y = 0.5f*log1pf(2*(y/(1-y)));
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}
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return s ? -y : y;
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}
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/*
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* This file is part of the Micro Python project, http://micropython.org/
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*
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* These math functions are taken from newlib-nano-2, the newlib/libm/math
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* directory, available from https://github.com/32bitmicro/newlib-nano-2.
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*
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* Appropriate copyright headers are reproduced below.
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*/
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/* ef_rem_pio2.c -- float version of e_rem_pio2.c
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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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 SunPro, 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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*
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*/
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/* __ieee754_rem_pio2f(x,y)
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*
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* return the remainder of x rem pi/2 in y[0]+y[1]
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* use __kernel_rem_pio2f()
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*/
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#include "fdlibm.h"
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/*
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* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
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*/
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#ifdef __STDC__
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static const __int32_t two_over_pi[] = {
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#else
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static __int32_t two_over_pi[] = {
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#endif
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0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
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0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
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0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
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0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
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0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
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0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
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0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
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0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
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0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
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0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
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0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
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0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
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0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
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0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
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0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
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0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
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0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
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0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
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0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
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0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
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0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
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0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
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};
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/* This array is like the one in e_rem_pio2.c, but the numbers are
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single precision and the last 8 bits are forced to 0. */
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#ifdef __STDC__
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static const __int32_t npio2_hw[] = {
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#else
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static __int32_t npio2_hw[] = {
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#endif
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0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
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0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
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0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
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0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
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0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
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0x4242c700, 0x42490f00
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};
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/*
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* invpio2: 24 bits of 2/pi
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* pio2_1: first 17 bit of pi/2
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* pio2_1t: pi/2 - pio2_1
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* pio2_2: second 17 bit of pi/2
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* pio2_2t: pi/2 - (pio2_1+pio2_2)
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* pio2_3: third 17 bit of pi/2
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* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
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*/
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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zero = 0.0000000000e+00, /* 0x00000000 */
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half = 5.0000000000e-01, /* 0x3f000000 */
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two8 = 2.5600000000e+02, /* 0x43800000 */
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invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
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pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
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pio2_1t = 1.0804334124e-05, /* 0x37354443 */
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pio2_2 = 1.0804273188e-05, /* 0x37354400 */
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pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
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pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
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pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
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#ifdef __STDC__
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__int32_t __ieee754_rem_pio2f(float x, float *y)
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#else
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__int32_t __ieee754_rem_pio2f(x,y)
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float x,y[];
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#endif
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{
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float z,w,t,r,fn;
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float tx[3];
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__int32_t i,j,n,ix,hx;
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int e0,nx;
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GET_FLOAT_WORD(hx,x);
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ix = hx&0x7fffffff;
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if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
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{y[0] = x; y[1] = 0; return 0;}
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if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
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if(hx>0) {
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z = x - pio2_1;
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if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
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y[0] = z - pio2_1t;
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y[1] = (z-y[0])-pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z -= pio2_2;
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y[0] = z - pio2_2t;
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y[1] = (z-y[0])-pio2_2t;
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}
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return 1;
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} else { /* negative x */
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z = x + pio2_1;
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if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
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y[0] = z + pio2_1t;
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y[1] = (z-y[0])+pio2_1t;
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} else { /* near pi/2, use 24+24+24 bit pi */
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z += pio2_2;
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y[0] = z + pio2_2t;
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y[1] = (z-y[0])+pio2_2t;
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}
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return -1;
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}
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}
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if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
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t = fabsf(x);
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n = (__int32_t) (t*invpio2+half);
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fn = (float)n;
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r = t-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 40 bit */
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if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
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y[0] = r-w; /* quick check no cancellation */
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} else {
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__uint32_t high;
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j = ix>>23;
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y[0] = r-w;
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GET_FLOAT_WORD(high,y[0]);
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i = j-((high>>23)&0xff);
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if(i>8) { /* 2nd iteration needed, good to 57 */
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t = r;
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w = fn*pio2_2;
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r = t-w;
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w = fn*pio2_2t-((t-r)-w);
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y[0] = r-w;
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GET_FLOAT_WORD(high,y[0]);
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i = j-((high>>23)&0xff);
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if(i>25) { /* 3rd iteration need, 74 bits acc */
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t = r; /* will cover all possible cases */
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w = fn*pio2_3;
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r = t-w;
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w = fn*pio2_3t-((t-r)-w);
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y[0] = r-w;
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}
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}
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}
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y[1] = (r-y[0])-w;
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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else return n;
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}
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/*
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* all other (large) arguments
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*/
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if(!FLT_UWORD_IS_FINITE(ix)) {
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y[0]=y[1]=x-x; return 0;
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}
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/* set z = scalbn(|x|,ilogb(x)-7) */
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e0 = (int)((ix>>23)-134); /* e0 = ilogb(z)-7; */
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SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23));
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for(i=0;i<2;i++) {
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tx[i] = (float)((__int32_t)(z));
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z = (z-tx[i])*two8;
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}
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tx[2] = z;
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nx = 3;
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while(tx[nx-1]==zero) nx--; /* skip zero term */
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n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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return n;
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}
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@ -0,0 +1,227 @@
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/*
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* This file is part of the Micro Python project, http://micropython.org/
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*
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* This file is adapted from from newlib-nano-2, the newlib/libm/common/fdlib.h,
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||||||
|
* available from https://github.com/32bitmicro/newlib-nano-2. The main change
|
||||||
|
* is removal of anything to do with double precision.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* @(#)fdlibm.h 5.1 93/09/24 */
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include <math.h>
|
||||||
|
|
||||||
|
/* Default to XOPEN_MODE. */
|
||||||
|
#define _XOPEN_MODE
|
||||||
|
|
||||||
|
/* Most routines need to check whether a float is finite, infinite, or not a
|
||||||
|
number, and many need to know whether the result of an operation will
|
||||||
|
overflow. These conditions depend on whether the largest exponent is
|
||||||
|
used for NaNs & infinities, or whether it's used for finite numbers. The
|
||||||
|
macros below wrap up that kind of information:
|
||||||
|
|
||||||
|
FLT_UWORD_IS_FINITE(X)
|
||||||
|
True if a positive float with bitmask X is finite.
|
||||||
|
|
||||||
|
FLT_UWORD_IS_NAN(X)
|
||||||
|
True if a positive float with bitmask X is not a number.
|
||||||
|
|
||||||
|
FLT_UWORD_IS_INFINITE(X)
|
||||||
|
True if a positive float with bitmask X is +infinity.
|
||||||
|
|
||||||
|
FLT_UWORD_MAX
|
||||||
|
The bitmask of FLT_MAX.
|
||||||
|
|
||||||
|
FLT_UWORD_HALF_MAX
|
||||||
|
The bitmask of FLT_MAX/2.
|
||||||
|
|
||||||
|
FLT_UWORD_EXP_MAX
|
||||||
|
The bitmask of the largest finite exponent (129 if the largest
|
||||||
|
exponent is used for finite numbers, 128 otherwise).
|
||||||
|
|
||||||
|
FLT_UWORD_LOG_MAX
|
||||||
|
The bitmask of log(FLT_MAX), rounded down. This value is the largest
|
||||||
|
input that can be passed to exp() without producing overflow.
|
||||||
|
|
||||||
|
FLT_UWORD_LOG_2MAX
|
||||||
|
The bitmask of log(2*FLT_MAX), rounded down. This value is the
|
||||||
|
largest input than can be passed to cosh() without producing
|
||||||
|
overflow.
|
||||||
|
|
||||||
|
FLT_LARGEST_EXP
|
||||||
|
The largest biased exponent that can be used for finite numbers
|
||||||
|
(255 if the largest exponent is used for finite numbers, 254
|
||||||
|
otherwise) */
|
||||||
|
|
||||||
|
#ifdef _FLT_LARGEST_EXPONENT_IS_NORMAL
|
||||||
|
#define FLT_UWORD_IS_FINITE(x) 1
|
||||||
|
#define FLT_UWORD_IS_NAN(x) 0
|
||||||
|
#define FLT_UWORD_IS_INFINITE(x) 0
|
||||||
|
#define FLT_UWORD_MAX 0x7fffffff
|
||||||
|
#define FLT_UWORD_EXP_MAX 0x43010000
|
||||||
|
#define FLT_UWORD_LOG_MAX 0x42b2d4fc
|
||||||
|
#define FLT_UWORD_LOG_2MAX 0x42b437e0
|
||||||
|
#define HUGE ((float)0X1.FFFFFEP128)
|
||||||
|
#else
|
||||||
|
#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L)
|
||||||
|
#define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L)
|
||||||
|
#define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L)
|
||||||
|
#define FLT_UWORD_MAX 0x7f7fffffL
|
||||||
|
#define FLT_UWORD_EXP_MAX 0x43000000
|
||||||
|
#define FLT_UWORD_LOG_MAX 0x42b17217
|
||||||
|
#define FLT_UWORD_LOG_2MAX 0x42b2d4fc
|
||||||
|
#define HUGE ((float)3.40282346638528860e+38)
|
||||||
|
#endif
|
||||||
|
#define FLT_UWORD_HALF_MAX (FLT_UWORD_MAX-(1L<<23))
|
||||||
|
#define FLT_LARGEST_EXP (FLT_UWORD_MAX>>23)
|
||||||
|
|
||||||
|
/* Many routines check for zero and subnormal numbers. Such things depend
|
||||||
|
on whether the target supports denormals or not:
|
||||||
|
|
||||||
|
FLT_UWORD_IS_ZERO(X)
|
||||||
|
True if a positive float with bitmask X is +0. Without denormals,
|
||||||
|
any float with a zero exponent is a +0 representation. With
|
||||||
|
denormals, the only +0 representation is a 0 bitmask.
|
||||||
|
|
||||||
|
FLT_UWORD_IS_SUBNORMAL(X)
|
||||||
|
True if a non-zero positive float with bitmask X is subnormal.
|
||||||
|
(Routines should check for zeros first.)
|
||||||
|
|
||||||
|
FLT_UWORD_MIN
|
||||||
|
The bitmask of the smallest float above +0. Call this number
|
||||||
|
REAL_FLT_MIN...
|
||||||
|
|
||||||
|
FLT_UWORD_EXP_MIN
|
||||||
|
The bitmask of the float representation of REAL_FLT_MIN's exponent.
|
||||||
|
|
||||||
|
FLT_UWORD_LOG_MIN
|
||||||
|
The bitmask of |log(REAL_FLT_MIN)|, rounding down.
|
||||||
|
|
||||||
|
FLT_SMALLEST_EXP
|
||||||
|
REAL_FLT_MIN's exponent - EXP_BIAS (1 if denormals are not supported,
|
||||||
|
-22 if they are).
|
||||||
|
*/
|
||||||
|
|
||||||
|
#ifdef _FLT_NO_DENORMALS
|
||||||
|
#define FLT_UWORD_IS_ZERO(x) ((x)<0x00800000L)
|
||||||
|
#define FLT_UWORD_IS_SUBNORMAL(x) 0
|
||||||
|
#define FLT_UWORD_MIN 0x00800000
|
||||||
|
#define FLT_UWORD_EXP_MIN 0x42fc0000
|
||||||
|
#define FLT_UWORD_LOG_MIN 0x42aeac50
|
||||||
|
#define FLT_SMALLEST_EXP 1
|
||||||
|
#else
|
||||||
|
#define FLT_UWORD_IS_ZERO(x) ((x)==0)
|
||||||
|
#define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L)
|
||||||
|
#define FLT_UWORD_MIN 0x00000001
|
||||||
|
#define FLT_UWORD_EXP_MIN 0x43160000
|
||||||
|
#define FLT_UWORD_LOG_MIN 0x42cff1b5
|
||||||
|
#define FLT_SMALLEST_EXP -22
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
#undef __P
|
||||||
|
#define __P(p) p
|
||||||
|
#else
|
||||||
|
#define __P(p) ()
|
||||||
|
#endif
|
||||||
|
|
||||||
|
/*
|
||||||
|
* set X_TLOSS = pi*2**52, which is possibly defined in <values.h>
|
||||||
|
* (one may replace the following line by "#include <values.h>")
|
||||||
|
*/
|
||||||
|
|
||||||
|
#define X_TLOSS 1.41484755040568800000e+16
|
||||||
|
|
||||||
|
/* Functions that are not documented, and are not in <math.h>. */
|
||||||
|
|
||||||
|
/* Undocumented float functions. */
|
||||||
|
#ifdef _SCALB_INT
|
||||||
|
extern float scalbf __P((float, int));
|
||||||
|
#else
|
||||||
|
extern float scalbf __P((float, float));
|
||||||
|
#endif
|
||||||
|
extern float significandf __P((float));
|
||||||
|
|
||||||
|
/* ieee style elementary float functions */
|
||||||
|
extern float __ieee754_sqrtf __P((float));
|
||||||
|
extern float __ieee754_acosf __P((float));
|
||||||
|
extern float __ieee754_acoshf __P((float));
|
||||||
|
extern float __ieee754_logf __P((float));
|
||||||
|
extern float __ieee754_atanhf __P((float));
|
||||||
|
extern float __ieee754_asinf __P((float));
|
||||||
|
extern float __ieee754_atan2f __P((float,float));
|
||||||
|
extern float __ieee754_expf __P((float));
|
||||||
|
extern float __ieee754_coshf __P((float));
|
||||||
|
extern float __ieee754_fmodf __P((float,float));
|
||||||
|
extern float __ieee754_powf __P((float,float));
|
||||||
|
extern float __ieee754_lgammaf_r __P((float,int *));
|
||||||
|
extern float __ieee754_gammaf_r __P((float,int *));
|
||||||
|
extern float __ieee754_log10f __P((float));
|
||||||
|
extern float __ieee754_sinhf __P((float));
|
||||||
|
extern float __ieee754_hypotf __P((float,float));
|
||||||
|
extern float __ieee754_j0f __P((float));
|
||||||
|
extern float __ieee754_j1f __P((float));
|
||||||
|
extern float __ieee754_y0f __P((float));
|
||||||
|
extern float __ieee754_y1f __P((float));
|
||||||
|
extern float __ieee754_jnf __P((int,float));
|
||||||
|
extern float __ieee754_ynf __P((int,float));
|
||||||
|
extern float __ieee754_remainderf __P((float,float));
|
||||||
|
extern __int32_t __ieee754_rem_pio2f __P((float,float*));
|
||||||
|
#ifdef _SCALB_INT
|
||||||
|
extern float __ieee754_scalbf __P((float,int));
|
||||||
|
#else
|
||||||
|
extern float __ieee754_scalbf __P((float,float));
|
||||||
|
#endif
|
||||||
|
|
||||||
|
/* float versions of fdlibm kernel functions */
|
||||||
|
extern float __kernel_sinf __P((float,float,int));
|
||||||
|
extern float __kernel_cosf __P((float,float));
|
||||||
|
extern float __kernel_tanf __P((float,float,int));
|
||||||
|
extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const __int32_t*));
|
||||||
|
|
||||||
|
/* A union which permits us to convert between a float and a 32 bit
|
||||||
|
int. */
|
||||||
|
|
||||||
|
typedef union
|
||||||
|
{
|
||||||
|
float value;
|
||||||
|
__uint32_t word;
|
||||||
|
} ieee_float_shape_type;
|
||||||
|
|
||||||
|
/* Get a 32 bit int from a float. */
|
||||||
|
|
||||||
|
#define GET_FLOAT_WORD(i,d) \
|
||||||
|
do { \
|
||||||
|
ieee_float_shape_type gf_u; \
|
||||||
|
gf_u.value = (d); \
|
||||||
|
(i) = gf_u.word; \
|
||||||
|
} while (0)
|
||||||
|
|
||||||
|
/* Set a float from a 32 bit int. */
|
||||||
|
|
||||||
|
#define SET_FLOAT_WORD(d,i) \
|
||||||
|
do { \
|
||||||
|
ieee_float_shape_type sf_u; \
|
||||||
|
sf_u.word = (i); \
|
||||||
|
(d) = sf_u.value; \
|
||||||
|
} while (0)
|
||||||
|
|
||||||
|
/* Macros to avoid undefined behaviour that can arise if the amount
|
||||||
|
of a shift is exactly equal to the size of the shifted operand. */
|
||||||
|
|
||||||
|
#define SAFE_LEFT_SHIFT(op,amt) \
|
||||||
|
(((amt) < 8 * sizeof(op)) ? ((op) << (amt)) : 0)
|
||||||
|
|
||||||
|
#define SAFE_RIGHT_SHIFT(op,amt) \
|
||||||
|
(((amt) < 8 * sizeof(op)) ? ((op) >> (amt)) : 0)
|
||||||
|
|
@ -0,0 +1,68 @@
|
||||||
|
/*
|
||||||
|
* This file is part of the Micro Python project, http://micropython.org/
|
||||||
|
*
|
||||||
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||||
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* kf_cos.c -- float version of k_cos.c
|
||||||
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "fdlibm.h"
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
static const float
|
||||||
|
#else
|
||||||
|
static float
|
||||||
|
#endif
|
||||||
|
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||||
|
C1 = 4.1666667908e-02, /* 0x3d2aaaab */
|
||||||
|
C2 = -1.3888889225e-03, /* 0xbab60b61 */
|
||||||
|
C3 = 2.4801587642e-05, /* 0x37d00d01 */
|
||||||
|
C4 = -2.7557314297e-07, /* 0xb493f27c */
|
||||||
|
C5 = 2.0875723372e-09, /* 0x310f74f6 */
|
||||||
|
C6 = -1.1359647598e-11; /* 0xad47d74e */
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
float __kernel_cosf(float x, float y)
|
||||||
|
#else
|
||||||
|
float __kernel_cosf(x, y)
|
||||||
|
float x,y;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
float a,hz,z,r,qx;
|
||||||
|
__int32_t ix;
|
||||||
|
GET_FLOAT_WORD(ix,x);
|
||||||
|
ix &= 0x7fffffff; /* ix = |x|'s high word*/
|
||||||
|
if(ix<0x32000000) { /* if x < 2**27 */
|
||||||
|
if(((int)x)==0) return one; /* generate inexact */
|
||||||
|
}
|
||||||
|
z = x*x;
|
||||||
|
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
||||||
|
if(ix < 0x3e99999a) /* if |x| < 0.3 */
|
||||||
|
return one - ((float)0.5*z - (z*r - x*y));
|
||||||
|
else {
|
||||||
|
if(ix > 0x3f480000) { /* x > 0.78125 */
|
||||||
|
qx = (float)0.28125;
|
||||||
|
} else {
|
||||||
|
SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
|
||||||
|
}
|
||||||
|
hz = (float)0.5*z-qx;
|
||||||
|
a = one-qx;
|
||||||
|
return a - (hz - (z*r-x*y));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,217 @@
|
||||||
|
/*
|
||||||
|
* This file is part of the Micro Python project, http://micropython.org/
|
||||||
|
*
|
||||||
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||||
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* kf_rem_pio2.c -- float version of k_rem_pio2.c
|
||||||
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "fdlibm.h"
|
||||||
|
|
||||||
|
/* In the float version, the input parameter x contains 8 bit
|
||||||
|
integers, not 24 bit integers. 113 bit precision is not supported. */
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
static const int init_jk[] = {4,7,9}; /* initial value for jk */
|
||||||
|
#else
|
||||||
|
static int init_jk[] = {4,7,9};
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
static const float PIo2[] = {
|
||||||
|
#else
|
||||||
|
static float PIo2[] = {
|
||||||
|
#endif
|
||||||
|
1.5703125000e+00, /* 0x3fc90000 */
|
||||||
|
4.5776367188e-04, /* 0x39f00000 */
|
||||||
|
2.5987625122e-05, /* 0x37da0000 */
|
||||||
|
7.5437128544e-08, /* 0x33a20000 */
|
||||||
|
6.0026650317e-11, /* 0x2e840000 */
|
||||||
|
7.3896444519e-13, /* 0x2b500000 */
|
||||||
|
5.3845816694e-15, /* 0x27c20000 */
|
||||||
|
5.6378512969e-18, /* 0x22d00000 */
|
||||||
|
8.3009228831e-20, /* 0x1fc40000 */
|
||||||
|
3.2756352257e-22, /* 0x1bc60000 */
|
||||||
|
6.3331015649e-25, /* 0x17440000 */
|
||||||
|
};
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
static const float
|
||||||
|
#else
|
||||||
|
static float
|
||||||
|
#endif
|
||||||
|
zero = 0.0,
|
||||||
|
one = 1.0,
|
||||||
|
two8 = 2.5600000000e+02, /* 0x43800000 */
|
||||||
|
twon8 = 3.9062500000e-03; /* 0x3b800000 */
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2)
|
||||||
|
#else
|
||||||
|
int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2)
|
||||||
|
float x[], y[]; int e0,nx,prec; __int32_t ipio2[];
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
__int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
||||||
|
float z,fw,f[20],fq[20],q[20];
|
||||||
|
|
||||||
|
/* initialize jk*/
|
||||||
|
jk = init_jk[prec];
|
||||||
|
jp = jk;
|
||||||
|
|
||||||
|
/* determine jx,jv,q0, note that 3>q0 */
|
||||||
|
jx = nx-1;
|
||||||
|
jv = (e0-3)/8; if(jv<0) jv=0;
|
||||||
|
q0 = e0-8*(jv+1);
|
||||||
|
|
||||||
|
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
||||||
|
j = jv-jx; m = jx+jk;
|
||||||
|
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
|
||||||
|
|
||||||
|
/* compute q[0],q[1],...q[jk] */
|
||||||
|
for (i=0;i<=jk;i++) {
|
||||||
|
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
||||||
|
}
|
||||||
|
|
||||||
|
jz = jk;
|
||||||
|
recompute:
|
||||||
|
/* distill q[] into iq[] reversingly */
|
||||||
|
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
||||||
|
fw = (float)((__int32_t)(twon8* z));
|
||||||
|
iq[i] = (__int32_t)(z-two8*fw);
|
||||||
|
z = q[j-1]+fw;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* compute n */
|
||||||
|
z = scalbnf(z,(int)q0); /* actual value of z */
|
||||||
|
z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
|
||||||
|
n = (__int32_t) z;
|
||||||
|
z -= (float)n;
|
||||||
|
ih = 0;
|
||||||
|
if(q0>0) { /* need iq[jz-1] to determine n */
|
||||||
|
i = (iq[jz-1]>>(8-q0)); n += i;
|
||||||
|
iq[jz-1] -= i<<(8-q0);
|
||||||
|
ih = iq[jz-1]>>(7-q0);
|
||||||
|
}
|
||||||
|
else if(q0==0) ih = iq[jz-1]>>8;
|
||||||
|
else if(z>=(float)0.5) ih=2;
|
||||||
|
|
||||||
|
if(ih>0) { /* q > 0.5 */
|
||||||
|
n += 1; carry = 0;
|
||||||
|
for(i=0;i<jz ;i++) { /* compute 1-q */
|
||||||
|
j = iq[i];
|
||||||
|
if(carry==0) {
|
||||||
|
if(j!=0) {
|
||||||
|
carry = 1; iq[i] = 0x100- j;
|
||||||
|
}
|
||||||
|
} else iq[i] = 0xff - j;
|
||||||
|
}
|
||||||
|
if(q0>0) { /* rare case: chance is 1 in 12 */
|
||||||
|
switch(q0) {
|
||||||
|
case 1:
|
||||||
|
iq[jz-1] &= 0x7f; break;
|
||||||
|
case 2:
|
||||||
|
iq[jz-1] &= 0x3f; break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if(ih==2) {
|
||||||
|
z = one - z;
|
||||||
|
if(carry!=0) z -= scalbnf(one,(int)q0);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/* check if recomputation is needed */
|
||||||
|
if(z==zero) {
|
||||||
|
j = 0;
|
||||||
|
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
||||||
|
if(j==0) { /* need recomputation */
|
||||||
|
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
||||||
|
|
||||||
|
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
||||||
|
f[jx+i] = (float) ipio2[jv+i];
|
||||||
|
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
||||||
|
q[i] = fw;
|
||||||
|
}
|
||||||
|
jz += k;
|
||||||
|
goto recompute;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/* chop off zero terms */
|
||||||
|
if(z==(float)0.0) {
|
||||||
|
jz -= 1; q0 -= 8;
|
||||||
|
while(iq[jz]==0) { jz--; q0-=8;}
|
||||||
|
} else { /* break z into 8-bit if necessary */
|
||||||
|
z = scalbnf(z,-(int)q0);
|
||||||
|
if(z>=two8) {
|
||||||
|
fw = (float)((__int32_t)(twon8*z));
|
||||||
|
iq[jz] = (__int32_t)(z-two8*fw);
|
||||||
|
jz += 1; q0 += 8;
|
||||||
|
iq[jz] = (__int32_t) fw;
|
||||||
|
} else iq[jz] = (__int32_t) z ;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* convert integer "bit" chunk to floating-point value */
|
||||||
|
fw = scalbnf(one,(int)q0);
|
||||||
|
for(i=jz;i>=0;i--) {
|
||||||
|
q[i] = fw*(float)iq[i]; fw*=twon8;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
||||||
|
for(i=jz;i>=0;i--) {
|
||||||
|
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
||||||
|
fq[jz-i] = fw;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* compress fq[] into y[] */
|
||||||
|
switch(prec) {
|
||||||
|
case 0:
|
||||||
|
fw = 0.0;
|
||||||
|
for (i=jz;i>=0;i--) fw += fq[i];
|
||||||
|
y[0] = (ih==0)? fw: -fw;
|
||||||
|
break;
|
||||||
|
case 1:
|
||||||
|
case 2:
|
||||||
|
fw = 0.0;
|
||||||
|
for (i=jz;i>=0;i--) fw += fq[i];
|
||||||
|
y[0] = (ih==0)? fw: -fw;
|
||||||
|
fw = fq[0]-fw;
|
||||||
|
for (i=1;i<=jz;i++) fw += fq[i];
|
||||||
|
y[1] = (ih==0)? fw: -fw;
|
||||||
|
break;
|
||||||
|
case 3: /* painful */
|
||||||
|
for (i=jz;i>0;i--) {
|
||||||
|
fw = fq[i-1]+fq[i];
|
||||||
|
fq[i] += fq[i-1]-fw;
|
||||||
|
fq[i-1] = fw;
|
||||||
|
}
|
||||||
|
for (i=jz;i>1;i--) {
|
||||||
|
fw = fq[i-1]+fq[i];
|
||||||
|
fq[i] += fq[i-1]-fw;
|
||||||
|
fq[i-1] = fw;
|
||||||
|
}
|
||||||
|
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
||||||
|
if(ih==0) {
|
||||||
|
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
||||||
|
} else {
|
||||||
|
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
return n&7;
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,58 @@
|
||||||
|
/*
|
||||||
|
* This file is part of the Micro Python project, http://micropython.org/
|
||||||
|
*
|
||||||
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||||
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* kf_sin.c -- float version of k_sin.c
|
||||||
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "fdlibm.h"
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
static const float
|
||||||
|
#else
|
||||||
|
static float
|
||||||
|
#endif
|
||||||
|
half = 5.0000000000e-01,/* 0x3f000000 */
|
||||||
|
S1 = -1.6666667163e-01, /* 0xbe2aaaab */
|
||||||
|
S2 = 8.3333337680e-03, /* 0x3c088889 */
|
||||||
|
S3 = -1.9841270114e-04, /* 0xb9500d01 */
|
||||||
|
S4 = 2.7557314297e-06, /* 0x3638ef1b */
|
||||||
|
S5 = -2.5050759689e-08, /* 0xb2d72f34 */
|
||||||
|
S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
float __kernel_sinf(float x, float y, int iy)
|
||||||
|
#else
|
||||||
|
float __kernel_sinf(x, y, iy)
|
||||||
|
float x,y; int iy; /* iy=0 if y is zero */
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
float z,r,v;
|
||||||
|
__int32_t ix;
|
||||||
|
GET_FLOAT_WORD(ix,x);
|
||||||
|
ix &= 0x7fffffff; /* high word of x */
|
||||||
|
if(ix<0x32000000) /* |x| < 2**-27 */
|
||||||
|
{if((int)x==0) return x;} /* generate inexact */
|
||||||
|
z = x*x;
|
||||||
|
v = z*x;
|
||||||
|
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
||||||
|
if(iy==0) return x+v*(S1+z*r);
|
||||||
|
else return x-((z*(half*y-v*r)-y)-v*S1);
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,105 @@
|
||||||
|
/*
|
||||||
|
* This file is part of the Micro Python project, http://micropython.org/
|
||||||
|
*
|
||||||
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||||
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* kf_tan.c -- float version of k_tan.c
|
||||||
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "libm.h"
|
||||||
|
#ifdef __STDC__
|
||||||
|
static const float
|
||||||
|
#else
|
||||||
|
static float
|
||||||
|
#endif
|
||||||
|
one = 1.0000000000e+00, /* 0x3f800000 */
|
||||||
|
pio4 = 7.8539812565e-01, /* 0x3f490fda */
|
||||||
|
pio4lo= 3.7748947079e-08, /* 0x33222168 */
|
||||||
|
T[] = {
|
||||||
|
3.3333334327e-01, /* 0x3eaaaaab */
|
||||||
|
1.3333334029e-01, /* 0x3e088889 */
|
||||||
|
5.3968254477e-02, /* 0x3d5d0dd1 */
|
||||||
|
2.1869488060e-02, /* 0x3cb327a4 */
|
||||||
|
8.8632395491e-03, /* 0x3c11371f */
|
||||||
|
3.5920790397e-03, /* 0x3b6b6916 */
|
||||||
|
1.4562094584e-03, /* 0x3abede48 */
|
||||||
|
5.8804126456e-04, /* 0x3a1a26c8 */
|
||||||
|
2.4646313977e-04, /* 0x398137b9 */
|
||||||
|
7.8179444245e-05, /* 0x38a3f445 */
|
||||||
|
7.1407252108e-05, /* 0x3895c07a */
|
||||||
|
-1.8558637748e-05, /* 0xb79bae5f */
|
||||||
|
2.5907305826e-05, /* 0x37d95384 */
|
||||||
|
};
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
float __kernel_tanf(float x, float y, int iy)
|
||||||
|
#else
|
||||||
|
float __kernel_tanf(x, y, iy)
|
||||||
|
float x,y; int iy;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
float z,r,v,w,s;
|
||||||
|
__int32_t ix,hx;
|
||||||
|
GET_FLOAT_WORD(hx,x);
|
||||||
|
ix = hx&0x7fffffff; /* high word of |x| */
|
||||||
|
if(ix<0x31800000) /* x < 2**-28 */
|
||||||
|
{if((int)x==0) { /* generate inexact */
|
||||||
|
if((ix|(iy+1))==0) return one/fabsf(x);
|
||||||
|
else return (iy==1)? x: -one/x;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
|
||||||
|
if(hx<0) {x = -x; y = -y;}
|
||||||
|
z = pio4-x;
|
||||||
|
w = pio4lo-y;
|
||||||
|
x = z+w; y = 0.0;
|
||||||
|
}
|
||||||
|
z = x*x;
|
||||||
|
w = z*z;
|
||||||
|
/* Break x^5*(T[1]+x^2*T[2]+...) into
|
||||||
|
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
||||||
|
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
||||||
|
*/
|
||||||
|
r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
|
||||||
|
v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
|
||||||
|
s = z*x;
|
||||||
|
r = y + z*(s*(r+v)+y);
|
||||||
|
r += T[0]*s;
|
||||||
|
w = x+r;
|
||||||
|
if(ix>=0x3f2ca140) {
|
||||||
|
v = (float)iy;
|
||||||
|
return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
|
||||||
|
}
|
||||||
|
if(iy==1) return w;
|
||||||
|
else { /* if allow error up to 2 ulp,
|
||||||
|
simply return -1.0/(x+r) here */
|
||||||
|
/* compute -1.0/(x+r) accurately */
|
||||||
|
float a,t;
|
||||||
|
__int32_t i;
|
||||||
|
z = w;
|
||||||
|
GET_FLOAT_WORD(i,z);
|
||||||
|
SET_FLOAT_WORD(z,i&0xfffff000);
|
||||||
|
v = r-(z - x); /* z+v = r+x */
|
||||||
|
t = a = -(float)1.0/w; /* a = -1.0/w */
|
||||||
|
GET_FLOAT_WORD(i,t);
|
||||||
|
SET_FLOAT_WORD(t,i&0xfffff000);
|
||||||
|
s = (float)1.0+t*z;
|
||||||
|
return t+a*(s+t*v);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
@ -19,6 +19,8 @@
|
||||||
#include <stdint.h>
|
#include <stdint.h>
|
||||||
#include <math.h>
|
#include <math.h>
|
||||||
|
|
||||||
|
#define FLT_EVAL_METHOD 0
|
||||||
|
|
||||||
#define FORCE_EVAL(x) do { \
|
#define FORCE_EVAL(x) do { \
|
||||||
if (sizeof(x) == sizeof(float)) { \
|
if (sizeof(x) == sizeof(float)) { \
|
||||||
volatile float __x; \
|
volatile float __x; \
|
||||||
|
|
|
||||||
|
|
@ -0,0 +1,83 @@
|
||||||
|
/*****************************************************************************/
|
||||||
|
/*****************************************************************************/
|
||||||
|
// log1pf from musl-0.9.15
|
||||||
|
/*****************************************************************************/
|
||||||
|
/*****************************************************************************/
|
||||||
|
|
||||||
|
/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "libm.h"
|
||||||
|
|
||||||
|
static const float
|
||||||
|
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
|
||||||
|
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
|
||||||
|
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
|
||||||
|
Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
|
||||||
|
Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
|
||||||
|
Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
|
||||||
|
Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
|
||||||
|
|
||||||
|
float log1pf(float x)
|
||||||
|
{
|
||||||
|
union {float f; uint32_t i;} u = {x};
|
||||||
|
float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
|
||||||
|
uint32_t ix,iu;
|
||||||
|
int k;
|
||||||
|
|
||||||
|
ix = u.i;
|
||||||
|
k = 1;
|
||||||
|
if (ix < 0x3ed413d0 || ix>>31) { /* 1+x < sqrt(2)+ */
|
||||||
|
if (ix >= 0xbf800000) { /* x <= -1.0 */
|
||||||
|
if (x == -1)
|
||||||
|
return x/0.0f; /* log1p(-1)=+inf */
|
||||||
|
return (x-x)/0.0f; /* log1p(x<-1)=NaN */
|
||||||
|
}
|
||||||
|
if (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */
|
||||||
|
/* underflow if subnormal */
|
||||||
|
if ((ix&0x7f800000) == 0)
|
||||||
|
FORCE_EVAL(x*x);
|
||||||
|
return x;
|
||||||
|
}
|
||||||
|
if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
|
||||||
|
k = 0;
|
||||||
|
c = 0;
|
||||||
|
f = x;
|
||||||
|
}
|
||||||
|
} else if (ix >= 0x7f800000)
|
||||||
|
return x;
|
||||||
|
if (k) {
|
||||||
|
u.f = 1 + x;
|
||||||
|
iu = u.i;
|
||||||
|
iu += 0x3f800000 - 0x3f3504f3;
|
||||||
|
k = (int)(iu>>23) - 0x7f;
|
||||||
|
/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
|
||||||
|
if (k < 25) {
|
||||||
|
c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
|
||||||
|
c /= u.f;
|
||||||
|
} else
|
||||||
|
c = 0;
|
||||||
|
/* reduce u into [sqrt(2)/2, sqrt(2)] */
|
||||||
|
iu = (iu&0x007fffff) + 0x3f3504f3;
|
||||||
|
u.i = iu;
|
||||||
|
f = u.f - 1;
|
||||||
|
}
|
||||||
|
s = f/(2.0f + f);
|
||||||
|
z = s*s;
|
||||||
|
w = z*z;
|
||||||
|
t1= w*(Lg2+w*Lg4);
|
||||||
|
t2= z*(Lg1+w*Lg3);
|
||||||
|
R = t2 + t1;
|
||||||
|
hfsq = 0.5f*f*f;
|
||||||
|
dk = k;
|
||||||
|
return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
|
||||||
|
}
|
||||||
|
|
@ -113,10 +113,6 @@ float log10f(float x) { return logf(x) / (float)_M_LN10; }
|
||||||
float tanhf(float x) { return sinhf(x) / coshf(x); }
|
float tanhf(float x) { return sinhf(x) / coshf(x); }
|
||||||
|
|
||||||
// TODO we need import these functions from some library (eg musl or newlib)
|
// TODO we need import these functions from some library (eg musl or newlib)
|
||||||
float acoshf(float x) { return 0.0; }
|
|
||||||
float asinhf(float x) { return 0.0; }
|
|
||||||
float atanhf(float x) { return 0.0; }
|
|
||||||
float tanf(float x) { return 0.0; }
|
|
||||||
float tgammaf(float x) { return 0.0; }
|
float tgammaf(float x) { return 0.0; }
|
||||||
float lgammaf(float x) { return 0.0; }
|
float lgammaf(float x) { return 0.0; }
|
||||||
float erff(float x) { return 0.0; }
|
float erff(float x) { return 0.0; }
|
||||||
|
|
|
||||||
|
|
@ -1,627 +0,0 @@
|
||||||
/*
|
|
||||||
* This file is part of the Micro Python project, http://micropython.org/
|
|
||||||
*
|
|
||||||
* These math functions are taken from newlib 2.1.0, the newlib/libm directory.
|
|
||||||
* Appropriate copyright headers are reproduced below.
|
|
||||||
*
|
|
||||||
* The MIT License (MIT)
|
|
||||||
*
|
|
||||||
* Copyright (c) 2013, 2014 Damien P. George
|
|
||||||
*
|
|
||||||
* Permission is hereby granted, free of charge, to any person obtaining a copy
|
|
||||||
* of this software and associated documentation files (the "Software"), to deal
|
|
||||||
* in the Software without restriction, including without limitation the rights
|
|
||||||
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
|
||||||
* copies of the Software, and to permit persons to whom the Software is
|
|
||||||
* furnished to do so, subject to the following conditions:
|
|
||||||
*
|
|
||||||
* The above copyright notice and this permission notice shall be included in
|
|
||||||
* all copies or substantial portions of the Software.
|
|
||||||
*
|
|
||||||
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
|
||||||
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
|
||||||
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
|
||||||
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
|
||||||
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
|
||||||
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
|
|
||||||
* THE SOFTWARE.
|
|
||||||
*/
|
|
||||||
|
|
||||||
#include <stdint.h>
|
|
||||||
#include <math.h>
|
|
||||||
|
|
||||||
/* @(#)fdlibm.h 5.1 93/09/24 */
|
|
||||||
/*
|
|
||||||
* ====================================================
|
|
||||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
||||||
*
|
|
||||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
||||||
* Permission to use, copy, modify, and distribute this
|
|
||||||
* software is freely granted, provided that this notice
|
|
||||||
* is preserved.
|
|
||||||
* ====================================================
|
|
||||||
*/
|
|
||||||
|
|
||||||
#define FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L)
|
|
||||||
|
|
||||||
/* A union which permits us to convert between a float and a 32 bit
|
|
||||||
int. */
|
|
||||||
|
|
||||||
typedef union
|
|
||||||
{
|
|
||||||
float value;
|
|
||||||
__uint32_t word;
|
|
||||||
} ieee_float_shape_type;
|
|
||||||
|
|
||||||
|
|
||||||
/* Get a 32 bit int from a float. */
|
|
||||||
|
|
||||||
#define GET_FLOAT_WORD(i,d) \
|
|
||||||
do { \
|
|
||||||
ieee_float_shape_type gf_u; \
|
|
||||||
gf_u.value = (d); \
|
|
||||||
(i) = gf_u.word; \
|
|
||||||
} while (0)
|
|
||||||
|
|
||||||
/* Set a float from a 32 bit int. */
|
|
||||||
|
|
||||||
#define SET_FLOAT_WORD(d,i) \
|
|
||||||
do { \
|
|
||||||
ieee_float_shape_type sf_u; \
|
|
||||||
sf_u.word = (i); \
|
|
||||||
(d) = sf_u.value; \
|
|
||||||
} while (0)
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
/* kf_rem_pio2.c -- float version of k_rem_pio2.c
|
|
||||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
||||||
*/
|
|
||||||
|
|
||||||
/*
|
|
||||||
* ====================================================
|
|
||||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
||||||
*
|
|
||||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
||||||
* Permission to use, copy, modify, and distribute this
|
|
||||||
* software is freely granted, provided that this notice
|
|
||||||
* is preserved.
|
|
||||||
* ====================================================
|
|
||||||
*/
|
|
||||||
|
|
||||||
/* In the float version, the input parameter x contains 8 bit
|
|
||||||
integers, not 24 bit integers. 113 bit precision is not supported. */
|
|
||||||
|
|
||||||
#ifdef __STDC__
|
|
||||||
static const int init_jk[] = {4,7,9}; /* initial value for jk */
|
|
||||||
#else
|
|
||||||
static int init_jk[] = {4,7,9};
|
|
||||||
#endif
|
|
||||||
|
|
||||||
#ifdef __STDC__
|
|
||||||
static const float PIo2[] = {
|
|
||||||
#else
|
|
||||||
static float PIo2[] = {
|
|
||||||
#endif
|
|
||||||
1.5703125000e+00, /* 0x3fc90000 */
|
|
||||||
4.5776367188e-04, /* 0x39f00000 */
|
|
||||||
2.5987625122e-05, /* 0x37da0000 */
|
|
||||||
7.5437128544e-08, /* 0x33a20000 */
|
|
||||||
6.0026650317e-11, /* 0x2e840000 */
|
|
||||||
7.3896444519e-13, /* 0x2b500000 */
|
|
||||||
5.3845816694e-15, /* 0x27c20000 */
|
|
||||||
5.6378512969e-18, /* 0x22d00000 */
|
|
||||||
8.3009228831e-20, /* 0x1fc40000 */
|
|
||||||
3.2756352257e-22, /* 0x1bc60000 */
|
|
||||||
6.3331015649e-25, /* 0x17440000 */
|
|
||||||
};
|
|
||||||
|
|
||||||
static const float
|
|
||||||
zero = 0.0000000000e+00, /* 0x00000000 */
|
|
||||||
one = 1.0000000000e+00, /* 0x3f800000 */
|
|
||||||
two8 = 2.5600000000e+02, /* 0x43800000 */
|
|
||||||
twon8 = 3.9062500000e-03; /* 0x3b800000 */
|
|
||||||
|
|
||||||
int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2)
|
|
||||||
{
|
|
||||||
__int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
|
||||||
float z,fw,f[20],fq[20],q[20];
|
|
||||||
|
|
||||||
/* initialize jk*/
|
|
||||||
jk = init_jk[prec];
|
|
||||||
jp = jk;
|
|
||||||
|
|
||||||
/* determine jx,jv,q0, note that 3>q0 */
|
|
||||||
jx = nx-1;
|
|
||||||
jv = (e0-3)/8; if(jv<0) jv=0;
|
|
||||||
q0 = e0-8*(jv+1);
|
|
||||||
|
|
||||||
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
|
||||||
j = jv-jx; m = jx+jk;
|
|
||||||
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
|
|
||||||
|
|
||||||
/* compute q[0],q[1],...q[jk] */
|
|
||||||
for (i=0;i<=jk;i++) {
|
|
||||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
|
||||||
}
|
|
||||||
|
|
||||||
jz = jk;
|
|
||||||
recompute:
|
|
||||||
/* distill q[] into iq[] reversingly */
|
|
||||||
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
|
||||||
fw = (float)((__int32_t)(twon8* z));
|
|
||||||
iq[i] = (__int32_t)(z-two8*fw);
|
|
||||||
z = q[j-1]+fw;
|
|
||||||
}
|
|
||||||
|
|
||||||
/* compute n */
|
|
||||||
z = scalbnf(z,(int)q0); /* actual value of z */
|
|
||||||
z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
|
|
||||||
n = (__int32_t) z;
|
|
||||||
z -= (float)n;
|
|
||||||
ih = 0;
|
|
||||||
if(q0>0) { /* need iq[jz-1] to determine n */
|
|
||||||
i = (iq[jz-1]>>(8-q0)); n += i;
|
|
||||||
iq[jz-1] -= i<<(8-q0);
|
|
||||||
ih = iq[jz-1]>>(7-q0);
|
|
||||||
}
|
|
||||||
else if(q0==0) ih = iq[jz-1]>>8;
|
|
||||||
else if(z>=(float)0.5) ih=2;
|
|
||||||
|
|
||||||
if(ih>0) { /* q > 0.5 */
|
|
||||||
n += 1; carry = 0;
|
|
||||||
for(i=0;i<jz ;i++) { /* compute 1-q */
|
|
||||||
j = iq[i];
|
|
||||||
if(carry==0) {
|
|
||||||
if(j!=0) {
|
|
||||||
carry = 1; iq[i] = 0x100- j;
|
|
||||||
}
|
|
||||||
} else iq[i] = 0xff - j;
|
|
||||||
}
|
|
||||||
if(q0>0) { /* rare case: chance is 1 in 12 */
|
|
||||||
switch(q0) {
|
|
||||||
case 1:
|
|
||||||
iq[jz-1] &= 0x7f; break;
|
|
||||||
case 2:
|
|
||||||
iq[jz-1] &= 0x3f; break;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
if(ih==2) {
|
|
||||||
z = one - z;
|
|
||||||
if(carry!=0) z -= scalbnf(one,(int)q0);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
/* check if recomputation is needed */
|
|
||||||
if(z==zero) {
|
|
||||||
j = 0;
|
|
||||||
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
|
||||||
if(j==0) { /* need recomputation */
|
|
||||||
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
|
||||||
|
|
||||||
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
|
||||||
f[jx+i] = (float) ipio2[jv+i];
|
|
||||||
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
|
||||||
q[i] = fw;
|
|
||||||
}
|
|
||||||
jz += k;
|
|
||||||
goto recompute;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
/* chop off zero terms */
|
|
||||||
if(z==(float)0.0) {
|
|
||||||
jz -= 1; q0 -= 8;
|
|
||||||
while(iq[jz]==0) { jz--; q0-=8;}
|
|
||||||
} else { /* break z into 8-bit if necessary */
|
|
||||||
z = scalbnf(z,-(int)q0);
|
|
||||||
if(z>=two8) {
|
|
||||||
fw = (float)((__int32_t)(twon8*z));
|
|
||||||
iq[jz] = (__int32_t)(z-two8*fw);
|
|
||||||
jz += 1; q0 += 8;
|
|
||||||
iq[jz] = (__int32_t) fw;
|
|
||||||
} else iq[jz] = (__int32_t) z ;
|
|
||||||
}
|
|
||||||
|
|
||||||
/* convert integer "bit" chunk to floating-point value */
|
|
||||||
fw = scalbnf(one,(int)q0);
|
|
||||||
for(i=jz;i>=0;i--) {
|
|
||||||
q[i] = fw*(float)iq[i]; fw*=twon8;
|
|
||||||
}
|
|
||||||
|
|
||||||
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
|
||||||
for(i=jz;i>=0;i--) {
|
|
||||||
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
|
||||||
fq[jz-i] = fw;
|
|
||||||
}
|
|
||||||
|
|
||||||
/* compress fq[] into y[] */
|
|
||||||
switch(prec) {
|
|
||||||
case 0:
|
|
||||||
fw = 0.0;
|
|
||||||
for (i=jz;i>=0;i--) fw += fq[i];
|
|
||||||
y[0] = (ih==0)? fw: -fw;
|
|
||||||
break;
|
|
||||||
case 1:
|
|
||||||
case 2:
|
|
||||||
fw = 0.0;
|
|
||||||
for (i=jz;i>=0;i--) fw += fq[i];
|
|
||||||
y[0] = (ih==0)? fw: -fw;
|
|
||||||
fw = fq[0]-fw;
|
|
||||||
for (i=1;i<=jz;i++) fw += fq[i];
|
|
||||||
y[1] = (ih==0)? fw: -fw;
|
|
||||||
break;
|
|
||||||
case 3: /* painful */
|
|
||||||
for (i=jz;i>0;i--) {
|
|
||||||
fw = fq[i-1]+fq[i];
|
|
||||||
fq[i] += fq[i-1]-fw;
|
|
||||||
fq[i-1] = fw;
|
|
||||||
}
|
|
||||||
for (i=jz;i>1;i--) {
|
|
||||||
fw = fq[i-1]+fq[i];
|
|
||||||
fq[i] += fq[i-1]-fw;
|
|
||||||
fq[i-1] = fw;
|
|
||||||
}
|
|
||||||
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
|
||||||
if(ih==0) {
|
|
||||||
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
|
||||||
} else {
|
|
||||||
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
return n&7;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
/* ef_rem_pio2.c -- float version of e_rem_pio2.c
|
|
||||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
||||||
*/
|
|
||||||
|
|
||||||
/*
|
|
||||||
* ====================================================
|
|
||||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
||||||
*
|
|
||||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
||||||
* Permission to use, copy, modify, and distribute this
|
|
||||||
* software is freely granted, provided that this notice
|
|
||||||
* is preserved.
|
|
||||||
* ====================================================
|
|
||||||
*
|
|
||||||
*/
|
|
||||||
|
|
||||||
/* __ieee754_rem_pio2f(x,y)
|
|
||||||
*
|
|
||||||
* return the remainder of x rem pi/2 in y[0]+y[1]
|
|
||||||
* use __kernel_rem_pio2f()
|
|
||||||
*/
|
|
||||||
|
|
||||||
|
|
||||||
/*
|
|
||||||
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
|
||||||
*/
|
|
||||||
static const __int32_t two_over_pi[] = {
|
|
||||||
0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
|
|
||||||
0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
|
|
||||||
0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
|
|
||||||
0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
|
|
||||||
0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
|
|
||||||
0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
|
|
||||||
0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
|
|
||||||
0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
|
|
||||||
0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
|
|
||||||
0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
|
|
||||||
0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
|
|
||||||
0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
|
|
||||||
0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
|
|
||||||
0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
|
|
||||||
0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
|
|
||||||
0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
|
|
||||||
0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
|
|
||||||
0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
|
|
||||||
0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
|
|
||||||
0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
|
|
||||||
0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
|
|
||||||
0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
|
|
||||||
};
|
|
||||||
|
|
||||||
/* This array is like the one in e_rem_pio2.c, but the numbers are
|
|
||||||
single precision and the last 8 bits are forced to 0. */
|
|
||||||
static const __int32_t npio2_hw[] = {
|
|
||||||
0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
|
|
||||||
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
|
|
||||||
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
|
|
||||||
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
|
|
||||||
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
|
|
||||||
0x4242c700, 0x42490f00
|
|
||||||
};
|
|
||||||
|
|
||||||
/*
|
|
||||||
* invpio2: 24 bits of 2/pi
|
|
||||||
* pio2_1: first 17 bit of pi/2
|
|
||||||
* pio2_1t: pi/2 - pio2_1
|
|
||||||
* pio2_2: second 17 bit of pi/2
|
|
||||||
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
|
||||||
* pio2_3: third 17 bit of pi/2
|
|
||||||
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
|
||||||
*/
|
|
||||||
|
|
||||||
static const float
|
|
||||||
half = 5.0000000000e-01, /* 0x3f000000 */
|
|
||||||
invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
|
|
||||||
pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
|
|
||||||
pio2_1t = 1.0804334124e-05, /* 0x37354443 */
|
|
||||||
pio2_2 = 1.0804273188e-05, /* 0x37354400 */
|
|
||||||
pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
|
|
||||||
pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
|
|
||||||
pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
|
|
||||||
|
|
||||||
__int32_t __ieee754_rem_pio2f(float x, float *y)
|
|
||||||
{
|
|
||||||
float z,w,t,r,fn;
|
|
||||||
float tx[3];
|
|
||||||
__int32_t i,j,n,ix,hx;
|
|
||||||
int e0,nx;
|
|
||||||
|
|
||||||
GET_FLOAT_WORD(hx,x);
|
|
||||||
ix = hx&0x7fffffff;
|
|
||||||
if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
|
|
||||||
{y[0] = x; y[1] = 0; return 0;}
|
|
||||||
if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
|
|
||||||
if(hx>0) {
|
|
||||||
z = x - pio2_1;
|
|
||||||
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
|
|
||||||
y[0] = z - pio2_1t;
|
|
||||||
y[1] = (z-y[0])-pio2_1t;
|
|
||||||
} else { /* near pi/2, use 24+24+24 bit pi */
|
|
||||||
z -= pio2_2;
|
|
||||||
y[0] = z - pio2_2t;
|
|
||||||
y[1] = (z-y[0])-pio2_2t;
|
|
||||||
}
|
|
||||||
return 1;
|
|
||||||
} else { /* negative x */
|
|
||||||
z = x + pio2_1;
|
|
||||||
if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
|
|
||||||
y[0] = z + pio2_1t;
|
|
||||||
y[1] = (z-y[0])+pio2_1t;
|
|
||||||
} else { /* near pi/2, use 24+24+24 bit pi */
|
|
||||||
z += pio2_2;
|
|
||||||
y[0] = z + pio2_2t;
|
|
||||||
y[1] = (z-y[0])+pio2_2t;
|
|
||||||
}
|
|
||||||
return -1;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
|
|
||||||
t = fabsf(x);
|
|
||||||
n = (__int32_t) (t*invpio2+half);
|
|
||||||
fn = (float)n;
|
|
||||||
r = t-fn*pio2_1;
|
|
||||||
w = fn*pio2_1t; /* 1st round good to 40 bit */
|
|
||||||
if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
|
|
||||||
y[0] = r-w; /* quick check no cancellation */
|
|
||||||
} else {
|
|
||||||
__uint32_t high;
|
|
||||||
j = ix>>23;
|
|
||||||
y[0] = r-w;
|
|
||||||
GET_FLOAT_WORD(high,y[0]);
|
|
||||||
i = j-((high>>23)&0xff);
|
|
||||||
if(i>8) { /* 2nd iteration needed, good to 57 */
|
|
||||||
t = r;
|
|
||||||
w = fn*pio2_2;
|
|
||||||
r = t-w;
|
|
||||||
w = fn*pio2_2t-((t-r)-w);
|
|
||||||
y[0] = r-w;
|
|
||||||
GET_FLOAT_WORD(high,y[0]);
|
|
||||||
i = j-((high>>23)&0xff);
|
|
||||||
if(i>25) { /* 3rd iteration need, 74 bits acc */
|
|
||||||
t = r; /* will cover all possible cases */
|
|
||||||
w = fn*pio2_3;
|
|
||||||
r = t-w;
|
|
||||||
w = fn*pio2_3t-((t-r)-w);
|
|
||||||
y[0] = r-w;
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
y[1] = (r-y[0])-w;
|
|
||||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
|
||||||
else return n;
|
|
||||||
}
|
|
||||||
/*
|
|
||||||
* all other (large) arguments
|
|
||||||
*/
|
|
||||||
if(!FLT_UWORD_IS_FINITE(ix)) {
|
|
||||||
y[0]=y[1]=x-x; return 0;
|
|
||||||
}
|
|
||||||
/* set z = scalbn(|x|,ilogb(x)-7) */
|
|
||||||
e0 = (int)((ix>>23)-134); /* e0 = ilogb(z)-7; */
|
|
||||||
SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23));
|
|
||||||
for(i=0;i<2;i++) {
|
|
||||||
tx[i] = (float)((__int32_t)(z));
|
|
||||||
z = (z-tx[i])*two8;
|
|
||||||
}
|
|
||||||
tx[2] = z;
|
|
||||||
nx = 3;
|
|
||||||
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
|
||||||
n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
|
|
||||||
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
|
||||||
return n;
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
/* kf_sin.c -- float version of k_sin.c
|
|
||||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
||||||
*/
|
|
||||||
|
|
||||||
/*
|
|
||||||
* ====================================================
|
|
||||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
||||||
*
|
|
||||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
||||||
* Permission to use, copy, modify, and distribute this
|
|
||||||
* software is freely granted, provided that this notice
|
|
||||||
* is preserved.
|
|
||||||
* ====================================================
|
|
||||||
*/
|
|
||||||
|
|
||||||
|
|
||||||
static const float
|
|
||||||
S1 = -1.6666667163e-01, /* 0xbe2aaaab */
|
|
||||||
S2 = 8.3333337680e-03, /* 0x3c088889 */
|
|
||||||
S3 = -1.9841270114e-04, /* 0xb9500d01 */
|
|
||||||
S4 = 2.7557314297e-06, /* 0x3638ef1b */
|
|
||||||
S5 = -2.5050759689e-08, /* 0xb2d72f34 */
|
|
||||||
S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */
|
|
||||||
|
|
||||||
float __kernel_sinf(float x, float y, int iy) /* iy=0 if y is zero */
|
|
||||||
{
|
|
||||||
float z,r,v;
|
|
||||||
__int32_t ix;
|
|
||||||
GET_FLOAT_WORD(ix,x);
|
|
||||||
ix &= 0x7fffffff; /* high word of x */
|
|
||||||
if(ix<0x32000000) /* |x| < 2**-27 */
|
|
||||||
{if((int)x==0) return x;} /* generate inexact */
|
|
||||||
z = x*x;
|
|
||||||
v = z*x;
|
|
||||||
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
|
||||||
if(iy==0) return x+v*(S1+z*r);
|
|
||||||
else return x-((z*(half*y-v*r)-y)-v*S1);
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
/* kf_cos.c -- float version of k_cos.c
|
|
||||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
||||||
*/
|
|
||||||
|
|
||||||
/*
|
|
||||||
* ====================================================
|
|
||||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
||||||
*
|
|
||||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
||||||
* Permission to use, copy, modify, and distribute this
|
|
||||||
* software is freely granted, provided that this notice
|
|
||||||
* is preserved.
|
|
||||||
* ====================================================
|
|
||||||
*/
|
|
||||||
|
|
||||||
|
|
||||||
static const float
|
|
||||||
C1 = 4.1666667908e-02, /* 0x3d2aaaab */
|
|
||||||
C2 = -1.3888889225e-03, /* 0xbab60b61 */
|
|
||||||
C3 = 2.4801587642e-05, /* 0x37d00d01 */
|
|
||||||
C4 = -2.7557314297e-07, /* 0xb493f27c */
|
|
||||||
C5 = 2.0875723372e-09, /* 0x310f74f6 */
|
|
||||||
C6 = -1.1359647598e-11; /* 0xad47d74e */
|
|
||||||
|
|
||||||
float __kernel_cosf(float x, float y)
|
|
||||||
{
|
|
||||||
float a,hz,z,r,qx;
|
|
||||||
__int32_t ix;
|
|
||||||
GET_FLOAT_WORD(ix,x);
|
|
||||||
ix &= 0x7fffffff; /* ix = |x|'s high word*/
|
|
||||||
if(ix<0x32000000) { /* if x < 2**27 */
|
|
||||||
if(((int)x)==0) return one; /* generate inexact */
|
|
||||||
}
|
|
||||||
z = x*x;
|
|
||||||
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
|
|
||||||
if(ix < 0x3e99999a) /* if |x| < 0.3 */
|
|
||||||
return one - ((float)0.5*z - (z*r - x*y));
|
|
||||||
else {
|
|
||||||
if(ix > 0x3f480000) { /* x > 0.78125 */
|
|
||||||
qx = (float)0.28125;
|
|
||||||
} else {
|
|
||||||
SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
|
|
||||||
}
|
|
||||||
hz = (float)0.5*z-qx;
|
|
||||||
a = one-qx;
|
|
||||||
return a - (hz - (z*r-x*y));
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
/* sf_sin.c -- float version of s_sin.c.
|
|
||||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
||||||
*/
|
|
||||||
|
|
||||||
/*
|
|
||||||
* ====================================================
|
|
||||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
||||||
*
|
|
||||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
||||||
* Permission to use, copy, modify, and distribute this
|
|
||||||
* software is freely granted, provided that this notice
|
|
||||||
* is preserved.
|
|
||||||
* ====================================================
|
|
||||||
*/
|
|
||||||
|
|
||||||
|
|
||||||
float sinf(float x)
|
|
||||||
{
|
|
||||||
float y[2],z=0.0;
|
|
||||||
__int32_t n,ix;
|
|
||||||
|
|
||||||
GET_FLOAT_WORD(ix,x);
|
|
||||||
|
|
||||||
/* |x| ~< pi/4 */
|
|
||||||
ix &= 0x7fffffff;
|
|
||||||
if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);
|
|
||||||
|
|
||||||
/* sin(Inf or NaN) is NaN */
|
|
||||||
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
|
|
||||||
|
|
||||||
/* argument reduction needed */
|
|
||||||
else {
|
|
||||||
n = __ieee754_rem_pio2f(x,y);
|
|
||||||
switch(n&3) {
|
|
||||||
case 0: return __kernel_sinf(y[0],y[1],1);
|
|
||||||
case 1: return __kernel_cosf(y[0],y[1]);
|
|
||||||
case 2: return -__kernel_sinf(y[0],y[1],1);
|
|
||||||
default:
|
|
||||||
return -__kernel_cosf(y[0],y[1]);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
|
|
||||||
/* sf_cos.c -- float version of s_cos.c.
|
|
||||||
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
||||||
*/
|
|
||||||
|
|
||||||
/*
|
|
||||||
* ====================================================
|
|
||||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
||||||
*
|
|
||||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
||||||
* Permission to use, copy, modify, and distribute this
|
|
||||||
* software is freely granted, provided that this notice
|
|
||||||
* is preserved.
|
|
||||||
* ====================================================
|
|
||||||
*/
|
|
||||||
|
|
||||||
|
|
||||||
float cosf(float x)
|
|
||||||
{
|
|
||||||
float y[2],z=0.0;
|
|
||||||
__int32_t n,ix;
|
|
||||||
|
|
||||||
GET_FLOAT_WORD(ix,x);
|
|
||||||
|
|
||||||
/* |x| ~< pi/4 */
|
|
||||||
ix &= 0x7fffffff;
|
|
||||||
if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
|
|
||||||
|
|
||||||
/* cos(Inf or NaN) is NaN */
|
|
||||||
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
|
|
||||||
|
|
||||||
/* argument reduction needed */
|
|
||||||
else {
|
|
||||||
n = __ieee754_rem_pio2f(x,y);
|
|
||||||
switch(n&3) {
|
|
||||||
case 0: return __kernel_cosf(y[0],y[1]);
|
|
||||||
case 1: return -__kernel_sinf(y[0],y[1],1);
|
|
||||||
case 2: return -__kernel_cosf(y[0],y[1]);
|
|
||||||
default:
|
|
||||||
return __kernel_sinf(y[0],y[1],1);
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
@ -0,0 +1,77 @@
|
||||||
|
/*
|
||||||
|
* This file is part of the Micro Python project, http://micropython.org/
|
||||||
|
*
|
||||||
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||||
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* sf_cos.c -- float version of s_cos.c.
|
||||||
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "fdlibm.h"
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
static const float one=1.0;
|
||||||
|
#else
|
||||||
|
static float one=1.0;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
float cosf(float x)
|
||||||
|
#else
|
||||||
|
float cosf(x)
|
||||||
|
float x;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
float y[2],z=0.0;
|
||||||
|
__int32_t n,ix;
|
||||||
|
|
||||||
|
GET_FLOAT_WORD(ix,x);
|
||||||
|
|
||||||
|
/* |x| ~< pi/4 */
|
||||||
|
ix &= 0x7fffffff;
|
||||||
|
if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
|
||||||
|
|
||||||
|
/* cos(Inf or NaN) is NaN */
|
||||||
|
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
|
||||||
|
|
||||||
|
/* argument reduction needed */
|
||||||
|
else {
|
||||||
|
n = __ieee754_rem_pio2f(x,y);
|
||||||
|
switch(n&3) {
|
||||||
|
case 0: return __kernel_cosf(y[0],y[1]);
|
||||||
|
case 1: return -__kernel_sinf(y[0],y[1],1);
|
||||||
|
case 2: return -__kernel_cosf(y[0],y[1]);
|
||||||
|
default:
|
||||||
|
return __kernel_sinf(y[0],y[1],1);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef _DOUBLE_IS_32BITS
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
double cos(double x)
|
||||||
|
#else
|
||||||
|
double cos(x)
|
||||||
|
double x;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
return (double) cosf((float) x);
|
||||||
|
}
|
||||||
|
|
||||||
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||||
|
|
@ -0,0 +1,71 @@
|
||||||
|
/*
|
||||||
|
* This file is part of the Micro Python project, http://micropython.org/
|
||||||
|
*
|
||||||
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||||
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* sf_sin.c -- float version of s_sin.c.
|
||||||
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "fdlibm.h"
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
float sinf(float x)
|
||||||
|
#else
|
||||||
|
float sinf(x)
|
||||||
|
float x;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
float y[2],z=0.0;
|
||||||
|
__int32_t n,ix;
|
||||||
|
|
||||||
|
GET_FLOAT_WORD(ix,x);
|
||||||
|
|
||||||
|
/* |x| ~< pi/4 */
|
||||||
|
ix &= 0x7fffffff;
|
||||||
|
if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);
|
||||||
|
|
||||||
|
/* sin(Inf or NaN) is NaN */
|
||||||
|
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
|
||||||
|
|
||||||
|
/* argument reduction needed */
|
||||||
|
else {
|
||||||
|
n = __ieee754_rem_pio2f(x,y);
|
||||||
|
switch(n&3) {
|
||||||
|
case 0: return __kernel_sinf(y[0],y[1],1);
|
||||||
|
case 1: return __kernel_cosf(y[0],y[1]);
|
||||||
|
case 2: return -__kernel_sinf(y[0],y[1],1);
|
||||||
|
default:
|
||||||
|
return -__kernel_cosf(y[0],y[1]);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef _DOUBLE_IS_32BITS
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
double sin(double x)
|
||||||
|
#else
|
||||||
|
double sin(x)
|
||||||
|
double x;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
return (double) sinf((float) x);
|
||||||
|
}
|
||||||
|
|
||||||
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||||
|
|
@ -0,0 +1,66 @@
|
||||||
|
/*
|
||||||
|
* This file is part of the Micro Python project, http://micropython.org/
|
||||||
|
*
|
||||||
|
* These math functions are taken from newlib-nano-2, the newlib/libm/math
|
||||||
|
* directory, available from https://github.com/32bitmicro/newlib-nano-2.
|
||||||
|
*
|
||||||
|
* Appropriate copyright headers are reproduced below.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* sf_tan.c -- float version of s_tan.c.
|
||||||
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* ====================================================
|
||||||
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||||
|
*
|
||||||
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||||
|
* Permission to use, copy, modify, and distribute this
|
||||||
|
* software is freely granted, provided that this notice
|
||||||
|
* is preserved.
|
||||||
|
* ====================================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include "fdlibm.h"
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
float tanf(float x)
|
||||||
|
#else
|
||||||
|
float tanf(x)
|
||||||
|
float x;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
float y[2],z=0.0;
|
||||||
|
__int32_t n,ix;
|
||||||
|
|
||||||
|
GET_FLOAT_WORD(ix,x);
|
||||||
|
|
||||||
|
/* |x| ~< pi/4 */
|
||||||
|
ix &= 0x7fffffff;
|
||||||
|
if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1);
|
||||||
|
|
||||||
|
/* tan(Inf or NaN) is NaN */
|
||||||
|
else if (!FLT_UWORD_IS_FINITE(ix)) return x-x; /* NaN */
|
||||||
|
|
||||||
|
/* argument reduction needed */
|
||||||
|
else {
|
||||||
|
n = __ieee754_rem_pio2f(x,y);
|
||||||
|
return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
|
||||||
|
-1 -- n odd */
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef _DOUBLE_IS_32BITS
|
||||||
|
|
||||||
|
#ifdef __STDC__
|
||||||
|
double tan(double x)
|
||||||
|
#else
|
||||||
|
double tan(x)
|
||||||
|
double x;
|
||||||
|
#endif
|
||||||
|
{
|
||||||
|
return (double) tanf((float) x);
|
||||||
|
}
|
||||||
|
|
||||||
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
||||||
|
|
@ -63,12 +63,23 @@ endif
|
||||||
|
|
||||||
SRC_LIB = $(addprefix lib/,\
|
SRC_LIB = $(addprefix lib/,\
|
||||||
libm/math.c \
|
libm/math.c \
|
||||||
libm/mathsincos.c \
|
|
||||||
libm/asinfacosf.c \
|
libm/asinfacosf.c \
|
||||||
libm/atanf.c \
|
libm/atanf.c \
|
||||||
libm/atan2f.c \
|
libm/atan2f.c \
|
||||||
libm/fmodf.c \
|
libm/fmodf.c \
|
||||||
libm/roundf.c \
|
libm/roundf.c \
|
||||||
|
libm/log1pf.c \
|
||||||
|
libm/acoshf.c \
|
||||||
|
libm/asinhf.c \
|
||||||
|
libm/atanhf.c \
|
||||||
|
libm/kf_rem_pio2.c \
|
||||||
|
libm/kf_sin.c \
|
||||||
|
libm/kf_cos.c \
|
||||||
|
libm/kf_tan.c \
|
||||||
|
libm/ef_rem_pio2.c \
|
||||||
|
libm/sf_sin.c \
|
||||||
|
libm/sf_cos.c \
|
||||||
|
libm/sf_tan.c \
|
||||||
)
|
)
|
||||||
|
|
||||||
SRC_C = \
|
SRC_C = \
|
||||||
|
|
|
||||||
|
|
@ -8,18 +8,19 @@ except ImportError:
|
||||||
sys.exit()
|
sys.exit()
|
||||||
|
|
||||||
test_values = [-100., -1.23456, -1, -0.5, 0.0, 0.5, 1.23456, 100.]
|
test_values = [-100., -1.23456, -1, -0.5, 0.0, 0.5, 1.23456, 100.]
|
||||||
|
test_values_small = [-10., -1.23456, -1, -0.5, 0.0, 0.5, 1.23456, 10.] # so we don't overflow 32-bit precision
|
||||||
p_test_values = [0.1, 0.5, 1.23456]
|
p_test_values = [0.1, 0.5, 1.23456]
|
||||||
unit_range_test_values = [-1., -0.75, -0.5, -0.25, 0., 0.25, 0.5, 0.75, 1.]
|
unit_range_test_values = [-1., -0.75, -0.5, -0.25, 0., 0.25, 0.5, 0.75, 1.]
|
||||||
|
|
||||||
functions = [('sqrt', sqrt, p_test_values),
|
functions = [('sqrt', sqrt, p_test_values),
|
||||||
('exp', exp, test_values),
|
('exp', exp, test_values_small),
|
||||||
('expm1', expm1, test_values),
|
('expm1', expm1, test_values_small),
|
||||||
('log', log, p_test_values),
|
('log', log, p_test_values),
|
||||||
('log2', log2, p_test_values),
|
('log2', log2, p_test_values),
|
||||||
('log10', log10, p_test_values),
|
('log10', log10, p_test_values),
|
||||||
('cosh', cosh, test_values),
|
('cosh', cosh, test_values_small),
|
||||||
('sinh', sinh, test_values),
|
('sinh', sinh, test_values_small),
|
||||||
('tanh', tanh, test_values),
|
('tanh', tanh, test_values_small),
|
||||||
('acosh', acosh, [1.0, 5.0, 1.0]),
|
('acosh', acosh, [1.0, 5.0, 1.0]),
|
||||||
('asinh', asinh, test_values),
|
('asinh', asinh, test_values),
|
||||||
('atanh', atanh, [-0.99, -0.5, 0.0, 0.5, 0.99]),
|
('atanh', atanh, [-0.99, -0.5, 0.0, 0.5, 0.99]),
|
||||||
|
|
@ -39,7 +40,7 @@ functions = [('sqrt', sqrt, p_test_values),
|
||||||
for function_name, function, test_vals in functions:
|
for function_name, function, test_vals in functions:
|
||||||
print(function_name)
|
print(function_name)
|
||||||
for value in test_vals:
|
for value in test_vals:
|
||||||
print("{:.7g}".format(function(value)))
|
print("{:.5g}".format(function(value)))
|
||||||
|
|
||||||
binary_functions = [('copysign', copysign, [(23., 42.), (-23., 42.), (23., -42.),
|
binary_functions = [('copysign', copysign, [(23., 42.), (-23., 42.), (23., -42.),
|
||||||
(-23., -42.), (1., 0.0), (1., -0.0)])
|
(-23., -42.), (1., 0.0), (1., -0.0)])
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue